JP2006058175A - Electromagnetic flowmeter - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To correct zero-point errors, without exactly correcting the span and making the flow of objective fluid zero. <P>SOLUTION: The electromagnetic flowmeter comprises the pairs of excitation coils 3 for impressing magnetic field on the fluid; a pair of electrodes 2a, 2b for extracting the first δA/δt component (δ: partial differentiation symbol) and the first correction objective electromotive force and the second δA/δt component of the second frequency and the second correction objective electromotive force; the span correcting part 51 for span correcting the first correction object electromotive force for correction, on the basis of the first δA/δt component and for span correcting the second correction object electromotive force, on the basis of the second δA/δt component; the zero-point correction part 52 for extracting the v×B component, by eliminating the third δA/δt component from either of two correction object electromotive force by extracting the third δA/δt component, on the basis of the corrected first correction object electromotive force and the second correction object electromotive force; and the flow rate output part 6 for computing the flow rate of the fluid from the v×B component. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an electromagnetic flow meter, and more particularly to span correction for automatically correcting a coefficient relating to a flow velocity of a component caused by a flow rate of a fluid to be measured among electromotive forces detected between electrodes, and variations in a magnetic field. The present invention relates to a zero correction technique that automatically corrects the resulting zero point shift.

The theoretical premise part common to both prior art and in order to understand this invention is demonstrated. First, the basic mathematical knowledge that is generally known will be explained.
The cosine wave P · cos (ω · t) and the sine wave Q · sin (ω · t) having the same frequency and different amplitudes are combined into the following cosine wave. P and Q are amplitudes, and ω is an angular frequency.
P · cos (ω · t) + Q · sin (ω · t) = (P ² + Q ² ) ^1/2 · cos (ω · t−ε)
However, ε = tan ⁻¹ (Q / P) (1)

In order to analyze the synthesis of equation (1), the complex is such that the amplitude P of the cosine wave P · cos (ω · t) is the real axis and the amplitude Q of the sine wave Q · sin (ω · t) is the imaginary axis. It is convenient to map to the coordinate plane. That is, on the complex coordinate plane, the distance (P ² + Q ² ) ^1/2 from the origin gives the amplitude of the composite wave, and the angle ε = tan ⁻¹ (Q / P) with the real axis is the composite wave and ω · A phase difference from t is given.

Further, the following relational expression is established on the complex coordinate plane.
L · exp (j · ε) = L · cos (ε) + j · L · sin (ε) (2)
Expression (2) is a notation for a complex vector, and j is an imaginary unit. L gives the length of the complex vector and ε gives the direction of the complex vector. Therefore, in order to analyze the geometric relationship on the complex coordinate plane, it is convenient to use conversion to a complex vector.
In the following explanation, in order to explain how the electromotive force between the electrodes shows and how the prior art uses this behavior, the mapping to the complex coordinate plane and the complex vector as described above are used. Employ geometric analysis by

Next, a complex vector arrangement in the case of one set of coils and one pair of electrodes in an electromagnetic flow meter proposed by the inventor (see Patent Document 1) will be described.
FIG. 29 is a block diagram for explaining the principle of the electromagnetic flowmeter of Patent Document 1. In FIG. This electromagnetic flow meter is connected to the measuring tube 1 through which the fluid to be measured flows, the magnetic field applied to the fluid to be measured and the axis PAX of the measuring tube 1 and perpendicular to both the fluid to be measured. A plane PLN including a pair of electrodes 2a and 2b that are arranged to face each other and detect an electromotive force generated by the magnetic field and the flow of the fluid to be measured and the electrodes 2a and 2b perpendicular to the direction of the measurement tube axis PAX The excitation coil 3 applies a time-varying magnetic field that is asymmetrical before and after the measurement tube 1 with the plane PLN as a boundary.

Here, of the magnetic field generated from the exciting coil 3, the magnetic field component (magnetic flux density) B1 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX connecting the electrodes 2a and 2b is as follows. Shall be given to
B1 = b1 · cos (ω0 · t−θ1) (3)
In equation (3), b1 is the amplitude, ω0 is the angular frequency, and θ1 is the phase difference (phase delay) from ω0 · t. Hereinafter, the magnetic flux density B1 is referred to as a magnetic field B1.

First, the inter-electrode electromotive force that is caused by the change of the magnetic field and is unrelated to the flow velocity of the fluid to be measured will be described. Since the electromotive force resulting from the change of the magnetic field is based on the time derivative dB / dt of the magnetic field, the magnetic field B1 generated from the exciting coil 3 is differentiated as the following equation.
dB1 / dt = −ω0 · b1 · sin (ω0 · t−θ1) (4)
When the flow velocity of the fluid to be measured is 0, the generated eddy current is only a component due to the change in the magnetic field, and the eddy current I due to the change in the magnetic field Ba is oriented as shown in FIG. Therefore, in the plane including the electrode axis EAX and the measurement tube axis PAX, the inter-electrode electromotive force E which is generated by the change of the magnetic field Ba and has no relation to the flow velocity is oriented as shown in FIG. This direction is the minus direction.

At this time, the inter-electrode electromotive force E is obtained by multiplying the time derivative −dB1 / dt of the magnetic field whose direction is considered as shown in the following expression by the proportional coefficient rk and replacing the phase θ1 with θ1 + θ00 (rk and θ00 are , Relating to the structure of the measuring tube 1 including the conductivity and dielectric constant of the fluid to be measured and the arrangement of the electrodes 2a, 2b).
E = rk · ω0 · b1 · sin (ω0 · t−θ1−θ00) (5)
Then, when equation (5) is modified, the following equation is obtained.
E = rk · ω0 · b1 · {sin (−θ1−θ00)} · cos (ω0 · t)
+ Rk · ω0 · b1 · {cos (−θ1−θ00)} · sin (ω0 · t)
= Rk · ω0 · b1 · {−sin (θ1 + θ00)} · cos (ω0 · t)
+ Rk · ω0 · b1 · {cos (θ1 + θ00)} · sin (ω0 · t)
... (6)

Here, when Expression (6) is mapped to the complex coordinate plane with ω0 · t as a reference, the real axis component Ex and the imaginary axis component Ey are expressed by the following expressions.
Ex = rk · ω0 · b1 · {−sin (θ1 + θ00)}
= Rk · ω0 · b1 · {cos (π / 2 + θ1 + θ00)} (7)
Ey = rk · ω0 · b1 · {cos (θ1 + θ00)}
= Rk · ω0 · b1 · {sin (π / 2 + θ1 + θ00)} (8)

Further, Ex and Ey shown in the equations (7) and (8) are converted into a complex vector Ec shown in the following equation.
Ec = Ex + j · Ey
= Rk · ω0 · b1 · {cos (π / 2 + θ1 + θ00)}
+ J · rk · ω0 · b1 · {sin (π / 2 + θ1 + θ00)}
= Rk ・ ω0 ・ b1
{Cos (π / 2 + θ1 + θ00) + j · sin (π / 2 + θ1 + θ00)} = rk · ω0 · b1 · exp {j · (π / 2 + θ1 + θ00)} (9)

The inter-electrode electromotive force Ec of the equation (9) converted into the complex coordinates is caused only by the time change of the magnetic field, and becomes an inter-electrode electromotive force unrelated to the flow velocity. In equation (9), rk · ω0 · b1 · exp {j · (π / 2 + θ1 + θ00)} is a complex vector having a length of rk · ω0 · b1 and an angle from the real axis of π / 2 + θ1 + θ00.
Further, the proportional coefficient rk and the angle θ00 described above can be expressed by the following complex vector kc.
kc = rk · cos (θ00) + j · rk · sin (θ00)
= Rk · exp (j · θ00) (10)
In equation (10), rk is the magnitude of the vector kc, and θ00 is the angle of the vector kc with respect to the real axis.

  Next, the inter-electrode electromotive force resulting from the flow velocity of the fluid to be measured will be described. When the magnitude of the flow velocity of the fluid to be measured is V (V ≠ 0), the generated eddy current includes, in addition to the eddy current I when the flow velocity is 0, a component v × due to the flow velocity vector v of the fluid to be measured. Since Ba is generated, the eddy current Iv caused by the flow velocity vector v and the magnetic field Ba is oriented as shown in FIG. Accordingly, the inter-electrode electromotive force Ev generated by the flow velocity vector v and the magnetic field Ba is opposite to the inter-electrode electromotive force E generated by the time change, and the direction of Ev is the plus direction.

At this time, the inter-electrode electromotive force Ev caused by the flow velocity is obtained by multiplying the magnetic field B1 by the proportional coefficient rkv and replacing the phase θ1 by θ1 + θ01 as shown in the following equation (rkv and θ01 are the magnitudes of the flow velocity). V, the conductivity and dielectric constant of the fluid to be measured, and the structure of the measuring tube 1 including the arrangement of the electrodes 2a and 2b).
Ev = rkv · {b1 · cos (ω0 · t−θ1−θ01)} (11)
When formula (11) is transformed, the following formula is obtained.
Ev = rkv · b1 · cos (ω0 · t) · cos (−θ1−θ01)
−rkv · b1 · sin (ω0 · t) · sin (−θ1−θ01)
= Rkv · b1 · {cos (θ1 + θ01)} · cos (ω0 · t)
+ Rkv · b1 · {sin (θ1 + θ01)} · sin (ω0 · t)
(12)

Here, when Expression (12) is mapped onto the complex coordinate plane with ω0 · t as a reference, the real axis component Evx and the imaginary axis component Evy are expressed by the following expressions.
Evx = rkv · b1 · {cos (θ1 + θ01)} (13)
Evy = rkv · b1 · {sin (θ1 + θ01)} (14)
Further, Evx and Evy shown in Expression (13) and Expression (14) are converted into a complex vector Evc shown in the following expression.
Evc = Evx + j · Evy
= Rkv · b1 · {cos (θ1 + θ01)}
+ J · rkv · b1 · {sin (θ1 + θ01)}
= Rkv · b1 · {cos (θ1 + θ01) + j · sin (θ1 + θ01)}
= Rkv · b1 · exp {j · (θ1 + θ01)} (15)

The interelectrode electromotive force Evc of the equation (15) converted into the complex coordinates becomes the interelectrode electromotive force due to the flow velocity of the fluid to be measured. In equation (15), rkv · b1 · exp {j · (θ1 + θ01)} is a complex vector having a length of rkv · b1 and an angle from the real axis of θ1 + θ01.
The proportional coefficient rkv and the angle θ01 described above can be expressed by the following complex vector kvc.
kvc = rkv · cos (θ01) + j · rkv · sin (θ01)
= Rkv · exp (j · θ01) (16)
In Equation (16), rkv is the magnitude of the vector kvc, and θ01 is the angle of the vector kvc with respect to the real axis. Here, rkv corresponds to a value obtained by multiplying the proportional coefficient rk (see equation (10)) by the magnitude V of the flow velocity and the proportional coefficient γ. That is, the following equation is established.
rkv = γ · rk · V (17)

The total inter-electrode electromotive force Eac obtained by combining the inter-electrode electromotive force Ec caused by the time change of the magnetic field and the inter-electrode electromotive force Evc caused by the fluid flow velocity is an equation obtained by substituting the equation (17) into the equation (15). And the following expression (9).
Eac = rk · ω0 · b1 · exp {j · (π / 2 + θ1 + θ00)}
+ Γ · rk · V · b1 · exp {j · (θ1 + θ01)} (18)

As can be seen from the equation (18), the electromotive force Eac between rk · ω0 · b1 · exp {j · (π / 2 + θ1 + θ00)} and γ · rk · V · b1 · exp {j · (θ1 + θ01)}. It is described by two complex vectors. The complex vector rk · ω0 · b1 · exp {j · (π / 2 + θ1 + θ00)} is a later-described ∂A / 後 述 t component, and the complex vector γ · rk · V · b1 · exp {j · (θ1 + θ01)} is later described. V × B component. The length of the combined vector obtained by combining the two complex vectors represents the amplitude of the output (interelectrode electromotive force Eac), and the angle φ of the combined vector is the interelectrode electromotive force with respect to the phase (excitation current) phase ω0 · t. It represents the phase difference (phase delay) of Eac.
Since the flow rate is obtained by multiplying the flow velocity by the cross-sectional area of the measuring tube, the flow rate and the flow rate are usually in a one-to-one relationship in the calibration in the initial state, and the flow rate and the flow rate can be treated equally. Therefore, the description will be given below as a method for obtaining the flow velocity (in order to obtain the flow rate).

The electromagnetic flow meter of Patent Document 1 extracts a parameter (asymmetric excitation parameter) that is not affected by the span shift, and outputs a flow rate based on this parameter, thereby solving the problem of the span shift. It has been solved.
Here, the span shift will be described with reference to FIG. If the magnitude V of the flow velocity measured by the electromagnetic flowmeter has changed even though the flow velocity of the fluid to be measured has not changed, a span shift can be considered as a factor of this output fluctuation.

  For example, calibration was performed so that the output of the electromagnetic flowmeter is 0 (v) when the flow velocity of the fluid to be measured is 0 in the initial state, and the output is 1 (v) when the flow velocity is 1 (m / sec). And Here, the output of the electromagnetic flow meter is a voltage representing the magnitude V of the flow velocity. As a result of such calibration, if the flow rate of the fluid to be measured is 1 (m / sec), the output of the electromagnetic flowmeter should naturally be 1 (v). However, when a certain time t1 elapses, the output of the electromagnetic flow meter may become 1.2 (v) even though the flow velocity of the fluid to be measured is also 1 (m / sec). A possible cause of this output fluctuation is a span shift. The phenomenon of span shift occurs due to, for example, the fact that the exciting current value flowing through the exciting coil cannot maintain a constant value due to a change in the ambient temperature of the electromagnetic flowmeter.

The electromagnetic flow meter of Patent Document 1 realizes accurate flow measurement by correcting a span shift. However, as another factor affecting the accuracy of flow measurement, there is a shift of 0 point of output. . Here, the shift of the output 0 point will be described with reference to FIG. Assuming that the magnitude V of the flow velocity measured by the electromagnetic flow meter has changed even though the flow velocity of the fluid to be measured has not changed, a shift of 0 point can be considered as a factor of this output fluctuation.
For example, calibration was performed so that the output of the electromagnetic flowmeter is 0 (v) when the flow rate of the fluid to be measured is 0 in the initial state and the output is 1 (v) when the flow velocity is 1 (m / sec). And Here, the output of the electromagnetic flowmeter is a voltage representing the magnitude V of the flow velocity. As a result of such calibration, if the flow rate of the fluid to be measured is 1 (m / sec), the output of the electromagnetic flowmeter should naturally be 1 (v). However, when a certain time t1 has passed, the output of the electromagnetic flowmeter becomes 1.5 (v) even though the flow velocity of the fluid to be measured is also 1 (m / sec), and the flow velocity is further reduced to 0. Even if it returns, 0.5 (v) may be output and may not become 0. A possible cause of this output fluctuation is a zero point shift. The phenomenon of the zero point shift occurs because the voltage generated by the change in the magnetic field fluctuates due to, for example, a change in the ambient temperature of the electromagnetic flow meter and cannot be canceled.

  The sine wave excitation type electromagnetic flow meter that uses a sine wave as the excitation current supplied to the excitation coil has the disadvantage of being easily affected by commercial frequency noise, but this disadvantage is a high frequency excitation method with a higher excitation current frequency. (For example, refer nonpatent literature 1). In addition, the high frequency excitation method has an advantage of being resistant to 1 / f noise such as electrochemical noise and spike noise, and can further improve responsiveness (characteristic for quickly following a flow rate signal against a flow rate change). There are advantages. In a sinusoidal excitation type electromagnetic flow meter, the magnetic field is constantly changing, and in order to eliminate the influence of the inter-electrode electromotive force component generated by the change of the magnetic field, the magnetic field before and after the measurement tube with the electrode axis as the boundary. Are distributed symmetrically. However, in actuality, it is affected by a component generated by a time change of the magnetic field due to a positional shift of the electrode or the extraction line, a shift of the symmetry of the magnetic field generated from the coil, or the like. Therefore, in the electromagnetic flow meter of the sine wave excitation method, the influence of the component generated by the time change of the magnetic field is removed as an offset at the time of calibration. However, the electromagnetic flow meter is affected by the shift of the magnetic field or the change of the magnetic field distribution. It is inevitable that the zero point of the output will shift. In addition, the sinusoidal excitation type electromagnetic flowmeter cancels the component due to the change of the magnetic field by phase detection. However, since this phase detection is not stable, there is a disadvantage that the stability of the output zero point is poor. It was.

  On the other hand, in the case of a rectangular wave excitation type electromagnetic flowmeter that uses a rectangular wave as the excitation current supplied to the excitation coil, the method of detecting the electromotive force between the electrodes is taken when the change in the magnetic field is eliminated. The zero point stability is superior to the sine wave excitation method (see Non-Patent Document 1, for example). However, in the electromagnetic flowmeter of the rectangular wave excitation method, when the excitation current becomes high frequency, the influence of the excitation coil impedance, the excitation current response, the magnetic field response, the overcurrent loss in the excitation coil core and measurement tube, etc. Cannot be ignored, and it becomes difficult to maintain the rectangular wave excitation (that is, to detect the electromotive force between the electrodes when there is no change in the magnetic field), and the stability of the output zero point cannot be ensured. As a result, in the case of a rectangular wave excitation type electromagnetic flow meter, there has been a problem that high-frequency excitation is difficult and improvement in response to flow rate changes and removal of 1 / f noise cannot be realized.

  In addition, in both the sine wave excitation method and the rectangular wave excitation method, it is impossible to confirm whether the zero point has shifted while the fluid to be measured is flowing, so the fluid to be measured is stopped and the flow rate is reduced to zero. In the above, it is necessary to check whether or not the output zero point has been shifted, and to correct the set zero offset.

The applicant has not yet found prior art documents related to the present invention by the time of filing other than the prior art documents specified by the prior art document information described in this specification.
WO 03/027614 Edited by the Japan Measuring Instruments Manufacturers Association, “Flow Measurement AtoZ for Instrumentation Engineers”, Kogyo Kogyosha, 1995, p. 143-160

First, the physical phenomenon necessary for explaining the problem of the span correction of the electromagnetic flow meter will be described. When an object moves in a changing magnetic field, two types of electric fields are generated by electromagnetic induction: (a) an electric field E generated by time-dependent changes in the magnetic field ⁽ⁱ⁾ = ∂A / ∂t, (b) an object moves in the magnetic field As a result, an electric field E ^(v) = v × B is generated. v × B represents an outer product of v and B, and ∂A / ∂t represents a partial differentiation of A with respect to time. v, B, and A respectively correspond to the following, and are vectors having directions in three dimensions (x, y, z) (v: flow velocity, B: magnetic flux density, A: vector potential (the magnetic flux density is B = RotA))). However, the three-dimensional vector here has a different meaning from the vector on the complex plane. By these two types of electric fields, a potential distribution is generated in the fluid, and this potential can be detected by the electrodes.
In the electromagnetic flow meter of Patent Document 1, the angle θ00 of the vector kc with respect to the real axis and the angle θ01 of the vector kvc with respect to the real axis are considered in the basic theoretical development, but the electromagnetic flow rate that can solve the problem of span shift. As a total constraint, θ00 = θ01 = 0 is assumed. That is, the restriction condition is to prepare the conditions of the electromagnetic flowmeter so that the above assumption is satisfied. Note that θ1 is an initial phase, which is a phase portion common to the excitation current and the inter-electrode electromotive force. Therefore, when considering only the phase difference between the excitation current and the inter-electrode electromotive force as in the prior art and the present invention, θ1 = 0 is set to facilitate understanding.

  The influence of the constraint condition on the flow rate measurement will be described using the concept of complex vectors with reference to FIG. In FIG. 34, Re is a real axis and Im is an imaginary axis. First, the inter-electrode electromotive force Ec that depends only on the time change of the magnetic field and does not depend on the flow velocity of the fluid to be measured is referred to as ∂A / ∂t component. The interelectrode electromotive force Evc depending on the flow velocity of the fluid is called a v × B component, and this v × B component is represented by a vector Vb. The above-mentioned span is a coefficient applied to the magnitude V of the flow velocity of the v × B component depending on the flow velocity of the fluid to be measured. In other words, in other words, the definition of θ00 and θ01 is θ00 is the angle of the vector Va with respect to the imaginary axis, and θ01 is the angle of the vector Vb with respect to the real axis.

  In the configuration of the electromagnetic flow meter shown in FIG. 29, θ00 = θ01 = 0 means that the vector Va exists on the imaginary axis Im and the vector Vb exists on the real axis Re. That is, the vectors Va and Vb are in a positional relationship orthogonal to each other. As described above, the electromagnetic flow meter of Patent Document 1 is based on the assumption that the vector Va of the ∂A / ∂t component and the vector Vb of the v × B component are orthogonal.

  However, in an actual electromagnetic flow meter, the above assumption is not always true. Microscopically, the orthogonality of the vector Va of the ∂A / ∂t component and the vector Vb of the v × B component is ensured microscopically, but when viewed macroscopically, the magnetic field applied to the fluid to be measured is ideal. This is because the macro-like ∂A / ∂t component vector Va and the v × B component vector Vb detected by the electrodes must be considered to contain a slight distortion. Therefore, the vectors Va and Vb are not orthogonal, and must be considered as θ00 ≠ 0, θ01 ≠ 0, and θ00 ≠ θ01.

As is clear from the above description, when directing high-precision flow rate measurement, the orthogonality between the vectors Va and Vb must be accurately considered. Since the orthogonality of Vb is assumed, if there is an error in the orthogonality, there is a possibility that accurate span correction and flow rate measurement cannot be performed.
In addition, depending on the material and structure of the electromagnetic flowmeter, the amplitude of the magnetic field generated from the exciting coil may change depending on the frequency due to the loss of the magnetic field. Therefore, in order to perform accurate span correction and flow rate measurement in the electromagnetic flow meter of Patent Document 1, there is a possibility that a procedure for adjusting the amplitude of the magnetic field generated from the exciting coil so as not to fluctuate with frequency may be required. It was.

Next, the problem of the zero correction of the electromagnetic flow meter will be described. The electromagnetic flow meter of Patent Document 1 does not consider the shift of the zero point of the output and cannot correct the zero point error. was there. The flow measurement error caused by the zero point shift in the electromagnetic flow meter of Patent Document 1 is that if the ∂A / ∂t component fluctuates in Equation (18), even if the flow velocity magnitude V is 0, it is between the electrodes. It is clear from the fact that the electromotive force Eac does not become zero.
On the other hand, the electromagnetic flow meter described in Non-Patent Document 1 can correct the zero point error during calibration. However, the sine wave excitation type electromagnetic flowmeter has a problem that the zero point may shift after calibration, and the stability of the zero point cannot be ensured. Also, the rectangular wave excitation type electromagnetic flowmeter has a problem that the stability of 0 point cannot be ensured in high frequency excitation.
Furthermore, in any of the electromagnetic flowmeters described in Patent Document 1 and Non-Patent Document 1, there is a problem that the error of the output 0 point cannot be corrected in a state where the fluid to be measured is kept flowing. .

  The present invention has been made to solve the above-described problems, and can automatically perform accurate span correction even when there is an influence due to magnetic field loss, and can stabilize the zero point of output even in high-frequency excitation. It is an object of the present invention to provide an electromagnetic flow meter that can ensure the performance and can correct an error at zero point without setting the flow rate of the fluid to be measured to zero.

  An electromagnetic flowmeter according to the present invention includes a measurement tube through which a fluid to be measured flows, an electrode that is disposed in the measurement tube and detects an electromotive force generated by a magnetic field applied to the fluid and the flow of the fluid, An excitation unit that applies an asymmetrical and time-varying magnetic field to the fluid, including an electrode, on a first plane perpendicular to the axial direction of the measuring tube, and is independent of the fluid velocity detected by the electrode From the combined electromotive force of the electromotive force of the ∂A / ∂t component and the v × B component caused by the flow velocity of the fluid, the first ∂A / ∂t component and the first The correction target electromotive force is extracted, the second ∂A / ∂t component and the second correction target electromotive force at the second frequency are extracted, and the extracted first ∂A / ∂t component is extracted. Based on the coefficient of the flow velocity magnitude V of the v × B component in the first correction target electromotive force Is a coefficient applied to the magnitude V of the flow velocity of the v × B component in the second correction target electromotive force based on the extracted second ∂A / ∂t component. A span correction unit that performs span correction to remove the variation factor of the span, and the first correction target electromotive force that has been subjected to the span correction and the second correction target electromotive force that has been subjected to the span correction. A third ∂A / ∂t component that is independent of the flow velocity and caused by the time change of the magnetic field is extracted, and the extraction is performed from either one of the two correction target electromotive forces that have been subjected to span correction. A zero point correction unit that extracts the v × B component by removing the third ∂A / ∂t component, and a flow rate output unit that calculates the flow rate of the fluid from the extracted v × B component It is.

Further, in one configuration example of the electromagnetic flowmeter of the present invention, the excitation unit is arranged at a position apart from the first plane perpendicular to the axial direction of the measurement tube including the electrode by providing a first offset. The first exciting coil provided is disposed at a position spaced apart from the first plane by providing a second offset so as to face the first exciting coil with the first plane interposed therebetween. The first excitation coil and the second excitation coil are switched while switching the phase difference and excitation angular frequency between the second excitation coil and the excitation current supplied to the first excitation coil and the excitation current supplied to the second excitation coil. And a power supply unit for supplying an exciting current to the exciting coil.
In one configuration example (first embodiment) of the electromagnetic flowmeter of the present invention, the span correction unit is generated by the first magnetic field generated by the first excitation coil and the second excitation coil. The phase difference between the first magnetic field and the second magnetic field with respect to the first excitation state is Δθ3 and the excitation angular frequency is ω0. The second excitation state changed to Δθ3 + π, the third excitation state in which the excitation angular frequency is changed to ω2 with respect to the first excitation state, and the excitation angular frequency to ω2 with respect to the second excitation state. The amplitude and phase of the composite electromotive force detected by the electrode in each of the four excitation states of the changed fourth excitation state are obtained, and the composite electromotive force of the second excitation state is obtained based on these amplitudes and phases. Extracting the first ∂A / ∂t component and the fourth ∂ The synthesized electromotive force in the excited state is extracted as the second ∂A / ∂t component, the synthesized electromotive force in the first excited state is used as the first correction target electromotive force, and the extracted first ∂A / Based on the ∂t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the combined electromotive force in the third excitation state is changed to the second correction target electromotive force. Based on the extracted second ∂A / ∂t component as the power, span correction is performed to remove the span variation factor included in the v × B component in the second correction target electromotive force, and the 0 The point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, and this span The one extracted from any one of the two corrected electromotive forces to be corrected The v × B component is extracted by removing the third ∂A / ∂t component.

Further, in one configuration example of the electromagnetic flowmeter of the present invention, the excitation unit is arranged at a position apart from the first plane perpendicular to the axial direction of the measurement tube including the electrode by providing a first offset. The first exciting coil provided is disposed at a position spaced apart from the first plane by providing a second offset so as to face the first exciting coil with the first plane interposed therebetween. The excitation current that simultaneously gives a plurality of excitation angular frequencies while switching the phase difference between the excitation current supplied to the second excitation coil and the excitation current supplied to the first excitation coil and the excitation current supplied to the second excitation coil. It consists of a power supply unit that supplies one excitation coil and a second excitation coil.
Further, in one configuration example (second embodiment) of the electromagnetic flowmeter of the present invention, the power supply unit supplies an excitation current that simultaneously provides two excitation angular frequencies having different angular frequencies ω0 and ω2 to the first excitation. The span correction unit supplies a phase difference between the first magnetic field generated by the first excitation coil and the second magnetic field generated by the second excitation coil by Δθ7. Thus, the first excitation state with excitation angular frequencies ω0 and ω2, and the second excitation state in which the phase difference between the first magnetic field and the second magnetic field is changed to Δθ7 + π with respect to the first excitation state. The amplitude and phase of the composite electromotive force detected by the electrode in each of the two excitation states are determined, and the component of the angular frequency ω0 of the composite electromotive force in the second excitation state is calculated based on these amplitudes and phases. While extracting as the first ∂A / ∂t component The component of the angular frequency ω2 of the synthetic electromotive force in the second excitation state is extracted as the second ∂A / ∂t component, and the component of the angular frequency ω0 of the synthetic electromotive force in the first excitation state is extracted as the first component. As a correction target electromotive force, a span variation factor included in a v × B component in the first correction target electromotive force is removed based on the extracted first ∂A / ∂t component, and Based on the extracted second ∂A / ∂t component, the component of the angular frequency ω2 of the composite electromotive force in the first excitation state is the second correction target electromotive force. The span correction for removing the variation factor of the span included in the v × B component is performed, and the zero point correction unit performs the first correction target electromotive force subjected to the span correction and the second correction target subjected to the span correction. The difference from the electromotive force is extracted as the third ∂A / ∂t component, and this span is extracted. Tadashisa from the one of the two corrected electromotive force was, it extracts a the v × B component by removing the third ∂A / ∂t component the extracted.

Further, in one configuration example of the electromagnetic flowmeter of the present invention, the excitation unit is arranged at a position apart from the first plane perpendicular to the axial direction of the measurement tube including the electrode by providing a first offset. The first exciting coil provided is disposed at a position spaced apart from the first plane by providing a second offset so as to face the first exciting coil with the first plane interposed therebetween. The first excitation coil and the second excitation coil are switched while switching the phase difference and excitation angular frequency between the second excitation coil and the excitation current supplied to the first excitation coil and the excitation current supplied to the second excitation coil. And a power supply unit that supplies an excitation current that simultaneously applies a plurality of excitation angular frequencies to the excitation coil.
Further, in one configuration example (third embodiment) of the electromagnetic flowmeter of the present invention, the power supply unit supplies an excitation current that simultaneously gives two excitation angular frequencies having different angular frequencies ω0 ± Δω to the first excitation. An excitation state to be supplied to the coil and the second excitation coil, and an excitation state to supply an excitation current that simultaneously gives two excitation angular frequencies having different angular frequencies ω2 ± Δω to the first excitation coil and the second excitation coil, An excitation current is supplied to the excitation coil while switching the phase, and the span correction unit causes a phase difference between a first magnetic field generated by the first excitation coil and a second magnetic field generated by the second excitation coil. Is a first excitation state having an excitation angular frequency of ω0 ± Δω and a phase difference between the first magnetic field and the second magnetic field with respect to the first excitation state is changed to Δθ9 + π. Excitation state and the first excitation state And a third excitation state in which the excitation angular frequency is changed to ω2 ± Δω, and a fourth excitation state in which the phase difference between the first magnetic field and the second magnetic field is changed to Δθ9 + π with respect to the third excitation state. The amplitude and phase of the combined electromotive force detected by the electrode in each of the four excitation states are determined, and the angular frequency ω0 + Δω of the combined electromotive force in the second excitation state is determined based on these amplitudes and phases. The sum of the electromotive force of the component and the component of the angular frequency ω0−Δω is extracted as the first ∂A / ∂t component, and the component of the angular frequency ω2 + Δω and the angular frequency ω2 of the synthetic electromotive force in the fourth excitation state are extracted. The sum of the electromotive force with the component of -Δω is extracted as the second ∂A / ∂t component, and the component of the angular frequency ω0 + Δω and the component of the angular frequency ω0-Δω of the composite electromotive force in the first excitation state are extracted. The first electromotive force as the first correction target electromotive force is extracted as the first electromotive force. Based on ∂A / ∂t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the angular frequency ω2 + Δω of the composite electromotive force in the third excitation state is removed. Of the second correction target electromotive force based on the extracted second ∂A / ∂t component, with the sum of the electromotive force of the component and the component of the angular frequency ω2−Δω as the second correction target electromotive force. The span correction for removing the variation factor of the span included in the v × B component is performed, and the zero point correction unit performs the first correction target electromotive force subjected to the span correction and the second correction target subjected to the span correction. The difference from the electromotive force is extracted as the third ∂A / ∂t component, and the extracted third ∂A / ∂ is extracted from any one of the two correction target electromotive forces subjected to the span correction. The v × B component is extracted by removing the t component.

Further, in one configuration example of the electromagnetic flowmeter of the present invention, the excitation unit is arranged at a position apart from the first plane perpendicular to the axial direction of the measurement tube including the electrode by providing a first offset. The first exciting coil provided is disposed at a position spaced apart from the first plane by providing a second offset so as to face the first exciting coil with the first plane interposed therebetween. The second excitation coil and a power supply unit that supplies an excitation current that simultaneously or alternately provides a plurality of excitation angular frequencies to the first excitation coil and the second excitation coil.
Further, in one configuration example of the electromagnetic flowmeter of the present invention, the power supply unit supplies an excitation current that simultaneously or alternately applies a plurality of components obtained by modulating a carrier wave having a plurality of frequencies with a modulated wave having a frequency different from the carrier wave. The first and second exciting coils are supplied.

  Further, in one configuration example (fourth embodiment) of the electromagnetic flowmeter of the present invention, the power supply unit generates a first excitation current obtained by amplitude-modulating a carrier wave having an angular frequency ω0 with a modulated wave having an angular frequency ω1. Simultaneously with supplying the first exciting coil, the second exciting current obtained by amplitude-modulating the carrier wave having the angular frequency ω0 with the modulated wave having the same angular frequency and the opposite phase with respect to the modulated wave of the first exciting current. The first excitation state supplied to the second excitation coil and the third excitation current obtained by amplitude-modulating the carrier wave of the angular frequency ω2 with the modulated wave of the angular frequency ω1 are simultaneously supplied to the first excitation coil. a second excitation state in which a fourth excitation current obtained by amplitude-modulating a carrier wave of ω2 with a modulated wave of the same angular frequency and opposite phase with respect to the modulated wave of the third excitation current is supplied to the second excitation coil; Switch The excitation current is supplied to the first excitation coil and the second excitation coil, and the span correction unit detects the combined electromotive force detected by the electrodes in each of the first excitation state and the second excitation state. And the sum of the electromotive force of the component of the angular frequency ω0 + ω1 and the component of the angular frequency ω0−ω1 of the composite electromotive force in the first excitation state is calculated based on the amplitude and phase of the first excitation power. A sum of the electromotive force of the component of the angular frequency ω2 + ω1 and the component of the angular frequency ω2-ω1 of the combined electromotive force in the second excitation state is extracted as the A / ∂t component and the second ∂A / ∂t component The first correction is made based on the extracted first ∂A / ∂t component with the component of the angular frequency ω0 of the composite electromotive force in the first excitation state as the first correction target electromotive force. The variation factor of the span included in the v × B component in the target electromotive force The second correction is performed based on the extracted second ∂A / ∂t component with the component of the angular frequency ω2 of the combined electromotive force in the second excitation state as the second correction target electromotive force. Span correction is performed to remove the span variation factor included in the v × B component in the target electromotive force, and the zero point correction unit performs the span correction on the first correction target electromotive force and the span correction. The difference from the second correction target electromotive force is extracted as the third ∂A / ∂t component, and the extracted third electromotive force is selected from one of the two correction target electromotive forces subjected to the span correction. The v × B component is extracted by removing the ∂A / ∂t component.

  Further, in one configuration example (fifth embodiment) of the electromagnetic flowmeter of the present invention, the power supply unit generates a first excitation current obtained by amplitude-modulating a carrier wave having an angular frequency ω0 with a modulated wave having an angular frequency ω1. Simultaneously with supplying the first exciting coil, the second exciting current obtained by amplitude-modulating the carrier wave having the angular frequency ω0 with the modulated wave having the same angular frequency and the opposite phase with respect to the modulated wave of the first exciting current. The first excitation state supplied to the second excitation coil and the third excitation current obtained by amplitude-modulating the carrier wave of the angular frequency ω2 with the modulation wave of the angular frequency ω1 are simultaneously supplied to the first excitation coil. a second excitation state in which a fourth excitation current obtained by amplitude-modulating a carrier wave of ω2 with a modulated wave of the same angular frequency and opposite phase with respect to the modulated wave of the third excitation current is supplied to the second excitation coil; Switch The excitation current is supplied to the first excitation coil and the second excitation coil, and the span correction unit detects the combined electromotive force detected by the electrodes in each of the first excitation state and the second excitation state. And the component of the angular frequency ω0 of the synthetic electromotive force in the first excitation state is extracted as the first ∂A / ∂t component based on these amplitude and phase, and the second The component of the angular frequency ω2 of the synthetic electromotive force in the excited state is extracted as the second ∂A / ∂t component, and the component of the angular frequency ω0 + ω1 and the angular frequency ω0−ω1 of the synthetic electromotive force in the first excited state are extracted. As the first correction target electromotive force is included in the v × B component of the first correction target electromotive force based on the extracted first ∂A / ∂t component. While removing the variation factor of the span, the composition of the second excitation state The second correction based on the extracted second ∂A / ∂t component, with the sum of electromotive forces of the component of the angular frequency ω2 + ω1 and the component of the angular frequency ω2-ω1 as the second correction target electromotive force. Span correction is performed to remove the span variation factor included in the v × B component in the target electromotive force, and the zero point correction unit performs the span correction on the first correction target electromotive force and the span correction. The difference from the second correction target electromotive force is extracted as the third ∂A / ∂t component, and the extracted third electromotive force is selected from one of the two correction target electromotive forces subjected to the span correction. The v × B component is extracted by removing the ∂A / ∂t component.

  In the configuration example 1 (sixth embodiment) of the electromagnetic flowmeter of the present invention, the power supply unit performs the first excitation in which the carrier wave having the angular frequency ω0 is phase-modulated or frequency-modulated by the modulation wave having the angular frequency ω1. Secondly, the current is supplied to the first exciting coil, and at the same time, the carrier wave having the angular frequency ω0 is phase-modulated or frequency-modulated by the modulated wave having the same angular frequency and the opposite phase with respect to the modulated wave of the first exciting current. And a third excitation current obtained by phase-modulating or frequency-modulating a carrier wave having an angular frequency ω2 with a modulated wave having an angular frequency ω1. At the same time as supplying to the coil, the fourth excitation current obtained by phase-modulating or frequency-modulating the carrier wave having the angular frequency ω2 with the modulation wave having the same angular frequency and the opposite phase with respect to the modulation wave of the third excitation current. While switching the second excitation state to be supplied to the second excitation coil, an excitation current is supplied to the first excitation coil and the second excitation coil, and the span correction unit is connected to the first excitation state and the second excitation state. The amplitude and phase of the composite electromotive force detected by the electrode in each of the two excitation states are obtained, and the angular frequency ω0 + ζ1 · ω1 (ζ1 of ζ1) of the composite electromotive force in the first excitation state is obtained based on these amplitude and phase A sum of electromotive forces of a positive integer component and an angular frequency ω0−ζ1 · ω1 component is extracted as the first ∂A / ∂t component, and the angular frequency of the composite electromotive force in the second excitation state is extracted. The sum of electromotive forces of the component of ω2 + ζ2 · ω1 (ζ2 is a positive integer) and the component of the angular frequency ω2-ζ2 · ω1 is extracted as the second ∂A / ∂t component, and the first excitation state is synthesized. The component of the electromotive force at the angular frequency ω0 is the first correction target electromotive force. And removing the variation factor of the span included in the v × B component in the first correction target electromotive force based on the extracted first ∂A / ∂t component, and the second excitation state. The component of the angular frequency ω2 of the combined electromotive force is set as the second correction target electromotive force, and the v × B component in the second correction target electromotive force is calculated based on the extracted second ∂A / ∂t component. The span correction is performed to remove the included variation factor of the span, and the zero point correction unit calculates the difference between the first corrected electromotive force corrected for the span and the second corrected electromotive force corrected for the span. By extracting the third ∂A / ∂t component as the third ∂A / ∂t component and removing the extracted third ∂A / ∂t component from any one of the two correction target electromotive forces subjected to the span correction The v × B component is extracted.

  Further, in one configuration example (seventh embodiment) of the electromagnetic flowmeter of the present invention, the power source section performs first excitation in which a carrier wave having an angular frequency ω0 is phase-modulated or frequency-modulated by a modulated wave having an angular frequency ω1. Secondly, the current is supplied to the first exciting coil, and at the same time, the carrier wave having the angular frequency ω0 is phase-modulated or frequency-modulated by the modulated wave having the same angular frequency and the opposite phase with respect to the modulated wave of the first exciting current. And a third excitation current obtained by phase-modulating or frequency-modulating a carrier wave having an angular frequency ω2 with a modulated wave having an angular frequency ω1. At the same time as supplying to the coil, the fourth excitation current obtained by phase-modulating or frequency-modulating the carrier wave having the angular frequency ω2 with the modulation wave having the same angular frequency and the opposite phase with respect to the modulation wave of the third excitation current. While switching the second excitation state to be supplied to the second excitation coil, an excitation current is supplied to the first excitation coil and the second excitation coil, and the span correction unit is connected to the first excitation state and the second excitation state. The amplitude and phase of the composite electromotive force detected by the electrode in each of the two excitation states are obtained, and the component of the angular frequency ω0 of the composite electromotive force in the first excitation state is determined based on these amplitudes and phases. In addition to extracting the first ∂A / 抽出 t component, the component of the angular frequency ω2 of the combined electromotive force in the second excitation state is extracted as the second ∂A / ∂t component, and the first excitation state The sum of electromotive forces of the component of angular frequency ω0 + ζ1 · ω1 (ζ1 is a positive integer) and the component of angular frequency ω0−ζ1 · ω1 of the combined electromotive force of The first correction target electromotive force based on ∂A / ∂t component And a component of the angular frequency ω2 + ζ2 · ω1 (ζ2 is a positive integer) and an angular frequency ω2−ζ2 · The sum of electromotive forces with the component of ω1 is included in the v × B component in the second correction target electromotive force based on the extracted second ∂A / ∂t component as the second correction target electromotive force. The zero correction unit removes the difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction. By extracting the third ∂A / ∂t component extracted as the third ∂A / ∂t component and removing the extracted third ∂A / ∂t component from any one of the two correction target electromotive forces subjected to span correction. XB component is extracted.

Further, in one configuration example of the electromagnetic flowmeter of the present invention, the excitation unit includes an excitation coil that applies a magnetic field to the fluid, and a power supply unit that supplies an excitation current to the excitation coil while switching an excitation angular frequency. The first electrode disposed at a position apart from the second plane perpendicular to the axial direction of the measurement tube, including the axis of the excitation coil, with a first offset, and the first electrode The second electrode is disposed at a position away from the two planes by providing a second offset so as to face the first electrode with the second plane interposed therebetween.
Further, in one configuration example (eighth embodiment) of the electromagnetic flowmeter of the present invention, the power supply section includes a first excitation state in which an excitation current having an angular frequency ω0 is supplied to the excitation coil, and an angular frequency ω2. The excitation current is supplied to the excitation coil while switching between the second excitation state for supplying the excitation current to the excitation coil, and the span correction unit is configured to change the excitation current in each of the first excitation state and the second excitation state. The amplitude and phase of the first synthetic electromotive force detected by the first electrode and the second synthetic electromotive force detected by the second electrode are obtained, and the first and second electromotive forces are detected based on the amplitude and phase. A sum of electromotive forces in the same excitation state and a difference in electromotive force in the same excitation state of the composite electromotive force and the second composite electromotive force are obtained for each of the first excitation state and the second excitation state, and the first excitation state is obtained. The state electromotive force difference is the first ∂A / ∂t component And extracting the electromotive force difference in the second excitation state as the second ∂A / ∂t component, and using the electromotive force sum in the first excitation state as the first correction target electromotive force, Based on the extracted first ∂A / ∂t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the occurrence of the second excitation state is performed. Using the power sum as the second correction target electromotive force, the variation factor of the span included in the v × B component in the second correction target electromotive force is calculated based on the extracted second ∂A / ∂t component. Span correction to be removed is performed, and the zero point correction unit calculates a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction to the third ∂A / Any one of the two correction target electromotive forces extracted as the ∂t component and subjected to the span correction The v × B component is extracted by removing the extracted third ∂A / ∂t component.

Further, in one configuration example of the electromagnetic flowmeter of the present invention, the excitation unit includes an excitation coil that applies a magnetic field to the fluid, and a power supply unit that supplies an excitation current that simultaneously provides a plurality of excitation angular frequencies to the excitation coil. The first electrode disposed at a position spaced apart from the second plane perpendicular to the axial direction of the measurement tube, including the axis of the excitation coil, by providing a first offset; A second electrode disposed at a position spaced apart from the second plane by providing a second offset so as to face the first electrode across the second plane. .
In one configuration example (9th embodiment) of the electromagnetic flowmeter of the present invention, the power supply unit supplies an excitation current that simultaneously gives two excitation angular frequencies having different angular frequencies ω0 and ω2 to the excitation coil. The span correction unit obtains the amplitude and phase of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitude and Based on the phase, the sum of the electromotive forces of the same frequency components and the electromotive force difference of the same frequency components of the first composite electromotive force and the second composite electromotive force are obtained for each of the angular frequencies ω0 and ω2, and the angular frequency ω0 The electromotive force difference is extracted as the first ∂A / ∂t component, the electromotive force difference at the angular frequency ω2 is extracted as the second ∂A / ∂t component, and the electromotive force sum of the angular frequency ω0 is extracted. As the first correction target electromotive force, the extracted first Based on ∂A / ∂t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the electromotive force sum of the angular frequency ω2 is set as the second correction target. As the electromotive force, based on the extracted second ∂A / ∂t component, span correction is performed to remove a span variation factor included in the v × B component in the second correction target electromotive force, and The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, The v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two correction target electromotive forces subjected to span correction.

In one configuration example of the electromagnetic flowmeter of the present invention, the power supply unit supplies an excitation current that simultaneously gives two different excitation angular frequencies to the excitation coil.
In one configuration example (tenth embodiment) of the electromagnetic flowmeter of the present invention, the power supply unit supplies an excitation current that simultaneously gives two excitation angular frequencies having different angular frequencies ω0 ± Δω to the excitation coil. The excitation current is supplied to the excitation coil while switching between the first excitation state to be performed and the second excitation state to supply the excitation coil with an excitation current that simultaneously gives two excitation angular frequencies having different angular frequencies ω2 ± Δω. The span correction unit includes a first synthetic electromotive force detected by the first electrode and a second detected by the second electrode in each of the first excitation state and the second excitation state. Obtaining the amplitude and phase of the combined electromotive force, and based on these amplitudes and phases, the electromotive force sum of the same frequency component and the electromotive force difference of the same frequency component of the first combined electromotive force and the second combined electromotive force, Angular circumference of the first excitation state The wave number ω0 ± Δω and the angular frequency ω2 ± Δω of the second excitation state are obtained for each, and the sum of the electromotive force difference of the angular frequency ω0 + Δω of the first excitation state and the electromotive force difference of the angular frequency ω0−Δω is calculated. The sum of the electromotive force difference of the angular frequency ω2 + Δω and the electromotive force difference of the angular frequency ω2-Δω in the second excitation state is extracted as the first ∂A / ∂t component and the second ∂A / ∂t component is extracted, and the sum of the electromotive force sum of the angular frequencies ω0 + Δω and the sum of the electromotive forces of the angular frequencies ω0-Δω in the first excitation state is used as the first correction target electromotive force. Based on ∂A / ∂t component, the variation factor of the span included in the v × B component of the first correction target electromotive force is removed, and the electromotive force sum of the angular frequency ω2 + Δω in the second excitation state And the sum of the electromotive forces of the angular frequencies ω2−Δω as the second correction target electromotive force, Based on the output second 補正 A / ∂t component, span correction is performed to remove a span variation factor included in the v × B component of the second correction target electromotive force. The difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction is extracted as the third ∂A / ∂t component, and this span corrected 2 The v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two correction target electromotive forces.

In one configuration example of the electromagnetic flowmeter of the present invention, the excitation unit supplies an excitation coil that applies a magnetic field to the fluid and an excitation current that simultaneously or alternately provides a plurality of excitation angular frequencies to the excitation coil. A first power supply unit, and the electrode is disposed at a position spaced apart from a second plane perpendicular to the axial direction of the measurement tube, including the axis of the excitation coil, by providing a first offset. An electrode and a second electrode disposed at a position spaced apart from the second plane by providing a second offset so as to face the first electrode across the second plane Is.
Further, in one configuration example of the electromagnetic flowmeter of the present invention, the power supply unit excites an excitation current that simultaneously or alternately gives a plurality of components obtained by modulating a carrier wave having a plurality of frequencies with a modulated wave having a frequency different from the carrier wave. It supplies to the coil.

  According to the present invention, from the combined electromotive force detected by the electrode, the electromotive force of the ∂A / ∂t component independent of the fluid flow velocity and the electromotive force of the v × B component caused by the fluid flow velocity, The first ∂A / ∂t component and the first correction target electromotive force at the first frequency are extracted, and the second ∂A / ∂t component and the second correction target electromotive force at the second frequency are extracted. And the variation factor of the span, which is a coefficient related to the magnitude V of the flow velocity of the v × B component in the first correction target electromotive force, is removed based on the extracted first ∂A / ∂t component. At the same time, based on the extracted second ∂A / ∂t component, span correction for removing a span variation factor which is a coefficient related to the flow velocity magnitude V of the v × B component in the second correction target electromotive force Based on the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction. A third ∂A / ∂t component that is unrelated to the flow velocity of the fluid is extracted, and the third ∂A / ∂t component is removed from any one of the two correction target electromotive forces subjected to the span correction. Since the v × B component is extracted by the above and the flow rate of the fluid is calculated from the extracted v × B component, accurate span correction can be automatically performed and the flow rate of the fluid to be measured is set to zero. Therefore, the zero point of the output of the electromagnetic flow meter can be corrected, and the stability of the zero point can be ensured even in the high frequency excitation. In the present invention, the first correction target electromotive force at the first frequency is subjected to span correction using the first ∂A / ∂t component at the same first frequency, and the second correction at the second frequency is performed. The correction target electromotive force is subjected to span correction using the second ∂A / ∂t component at the same second frequency, and zero correction is performed based on the two correction target electromotive forces that have been subjected to span correction. Even if there is an influence due to the loss of the error, accurate span correction and zero correction can be performed. As a result, in the present invention, highly accurate flow rate measurement can be performed.

[Basic principle]
In the present invention, when a combined vector Va + Vb of a vector Va of ∂A / ∂t component and a vector Vb of v × B component is obtained from an electromotive force detected by an electrode of an electromagnetic flow meter, the vector Va is a magnetic field. The vector Vb is a vector that changes only in proportion to the magnitude V of the flow velocity of the fluid to be measured, and the vector Vb changes in proportion to the magnitude V of the flow velocity of the fluid to be measured. Pay attention.

  In the present invention, a first ∂A / ∂t component that can eliminate the span variation factor included in the v × B component is extracted from the combined vector Va + Vb, and the first ∂A / ∂t is extracted. By normalizing the combined vector Va + Vb using the components, the span variation factor included in the v × B component in the combined vector Va + Vb is eliminated. By extracting the first ∂A / ∂t component, regardless of whether the first ∂A / と t component and the v × B component are orthogonal, the first 第 A / ∂t component and It is important to be able to treat the v × B component as separate vectors.

  Next, in the present invention, a second ∂A / ∂t component that causes a 0-point variation is extracted from the normalized composite vector Va + Vb, and the second ∂A / Vb is extracted from the normalized composite vector Va + Vb. By subtracting the ∂t component, only the v × B component is extracted. As a result, in the present invention, an output in which both the span variation factor and the zero point variation factor are eliminated can be obtained, and the flow rate of the fluid to be measured can be calculated from the v × B component. Without setting the v × B component to 0 (without setting the flow rate to 0) and without setting the ∂A / ∂t component to 0 (without setting the excitation frequency to 0), only the v × B component is set. It is important to be able to take it out. In the present invention, in consideration of the difference in magnetic field loss depending on the frequency, the synthesized vectors are normalized in the components of the excitation angular frequencies ω0 and ω2, and the difference between the normalized ∂A / ∂t components is calculated. By performing zero correction based on this, it is possible to perform zero correction with little influence of magnetic field loss.

Hereinafter, the basic principle of the present invention for actually correcting the zero point and the span will be described.
First, the principle of an electromagnetic flowmeter having two excitation coils and a pair of electrodes among the electromagnetic flowmeters based on the basic principle of the present invention will be described with reference to FIG. The electromagnetic flow meter of FIG. 1 has the plane PLN when the plane PLN including the electrodes 2a and 2b, which is orthogonal to the direction of the measurement tube 1, the electrodes 2a and 2b, and the measurement tube axis PAX, is the boundary of the measurement tube 1. And a first exciting coil 3a and a second exciting coil 3b for applying a time-varying magnetic field that is asymmetric before and after the measuring tube 1 at the boundary to the fluid to be measured. The first excitation coil 3a is disposed at a position separated from the plane PLN by, for example, an offset distance d1 on the downstream side. The second excitation coil 3b is disposed at a position separated from the plane PLN, for example, by an offset distance d2 on the upstream side so as to face the first excitation coil 3a across the plane PLN.

  When the second excitation coil 3b is disposed so as to face the first excitation coil 3a across the plane PLN, out of the inter-electrode electromotive force detected by the electrodes 2a and 2b, the first excitation coil 3a The v × B component caused by the generated magnetic field and the fluid flow velocity is in the same direction as the v × B component caused by the magnetic field and the fluid flow velocity generated from the second exciting coil 3b. On the other hand, of the electromotive force between the electrodes, ∂A / ∂t component caused by the change of the magnetic field generated from the first excitation coil 3a and ∂A / caused by the change of the magnetic field generated by the second excitation coil 3b. The direction is opposite to the ∂t component. Therefore, the ∂A / ∂t component resulting from the change in the magnetic field generated from the first excitation coil 3a, the v × B component resulting from the magnetic field generated from the first excitation coil 3a and the fluid flow velocity, and the second All the combined vectors of the ∂A / ∂t component resulting from the change in the magnetic field generated from the exciting coil 3b and the v × B component resulting from the magnetic field generated from the second exciting coil 3b and the fluid flow velocity It is necessary to perform correction in consideration of the fact that the variation factor of the v × B component and the variation factor of the ∂A / ∂t component are not equal.

Here, of the magnetic field Bb generated from the first exciting coil 3a, the magnetic field component (magnetic flux density) B2 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX connecting the electrodes 2a and 2b, Of the magnetic field Bc generated from the second exciting coil 3b, the magnetic field component (magnetic flux density) B3 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX is given as follows: To do.
B2 = b2 · cos (ω0 · t−θ2) (19)
B3 = b3 · cos (ω0 · t−θ3) (20)
In equations (19) and (20), b2 and b3 are the amplitudes of the magnetic flux densities B2 and B3, ω0 is the angular frequency, θ2 is the phase difference (phase lag) between the magnetic flux density B2 and ω0 · t, and θ3 is the magnetic flux. The phase difference between the density B3 and ω0 · t. Hereinafter, the magnetic flux density B2 is defined as the magnetic field B2, and the magnetic flux density B3 is defined as the magnetic field B3.

  When the flow velocity of the fluid to be measured is 0, the generated eddy current is only a component due to the change in the magnetic field, and the eddy current I1 due to the change in the magnetic field Bb and the eddy current I2 due to the change in the magnetic field Bc are as shown in FIG. It becomes the direction. Therefore, in the plane including the electrode axis EAX and the measurement tube axis PAX, the inter-electrode electromotive force E1 which is generated by the change of the magnetic field Bb and which is irrelevant to the flow velocity, and the electrode which is generated by the change of the magnetic field Bc and which is irrelevant to the flow velocity. The electromotive forces E2 are opposite to each other as shown in FIG.

  When the flow velocity of the fluid to be measured is V (V ≠ 0), the generated eddy current includes the component v × Bb due to the flow velocity vector v of the fluid to be measured, in addition to the eddy currents I1 and I2 at the flow velocity of 0. , V × Bc are generated, the eddy current Iv1 due to the flow velocity vector v and the magnetic field Bb, and the eddy current Iv2 due to the flow velocity vector v and the magnetic field Bc are oriented as shown in FIG. Therefore, the interelectrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bb and the interelectrode electromotive force Ev2 generated by the flow velocity vector v and the magnetic field Bc are in the same direction.

Considering the direction of the interelectrode electromotive force described in FIG. 2 and FIG. 3, the entire inter-electrode total including the interelectrode electromotive force caused by the time change of the magnetic field and the interelectrode electromotive force caused by the flow velocity of the fluid to be measured. The electromotive force Eac2 representing the electromotive force as a complex vector is expressed by the following equation corresponding to the equation (18) using the equations (10), (16), and (17).
Eac2 = rk · ω0 · b2 · exp {j · (π / 2 + θ2 + θ00)}
+ Γ · rk · V · b2 · exp {j · (θ2 + θ01)}
+ Rk · ω0 · b3 · exp {j · (−π / 2 + θ3 + θ00)}
+ Γ · rk · V · b3 · exp {j · (θ3 + θ01)} (21)

Here, the relationship between the phase delay θ2 of the magnetic field B2 with respect to ω0 · t and the phase delay θ3 of the magnetic field B3 with respect to ω0 · t is θ3 = θ2 + Δθ3, and the angle θ00 of the ∂A / ∂t component with respect to the imaginary axis and v with respect to the real axis When the relationship between the xB component and the angle θ01 is θ01 = θ00 + Δθ01 is defined as the first excitation state, and the interelectrode electromotive force Eac2 in this first excitation state is Eac20, the interelectrode electromotive force Eac20 is It becomes like this.
Eac20 = rk · exp {j · (θ2 + θ00)}
Exp (j · π / 2) · {b2-b3 · exp (j · Δθ3)} · ω0
+ Rk · exp {j · (θ2 + θ00)}
Γ · exp (j · Δθ01) · {b2 + b3 · exp (j · Δθ3)} V (22)

In addition, a state in which the phase difference between the magnetic field B2 and the magnetic field B3 changes by a constant value π from the first excitation state (θ3 = π + θ2 + Δθ3) and θ01 = θ00 + Δθ01 is defined as the second excitation state. When the interelectrode electromotive force Eac2 in the state is Eac2R, the interelectrode electromotive force Eac2R is expressed by the following equation from the equation (22).
Eac2R = rk · exp {j · (θ2 + θ00)}
Exp (j · π / 2) · {b2 + b3 · exp (j · Δθ3)} · ω0
+ Rk · exp {j · (θ2 + θ00)}
Γ · exp (j · Δθ01) · {b2-b3 · exp (j · Δθ3)} V (23)

  The first term on the right side of Equation (21) is the ∂A / ∂t component resulting from the change in the magnetic field generated from the first excitation coil 3a, and the second term on the right side is the relationship between the magnetic field and fluid generated from the first excitation coil 3a. The v × B component resulting from the flow velocity, the third term on the right side is the ∂A / ∂t component resulting from the change in the magnetic field generated from the second excitation coil 3b, and the fourth term on the right side is generated from the second excitation coil 3b. It becomes a v × B component resulting from the magnetic field and the flow velocity of the fluid.

  The combination of the first term on the right side of Equation (22) and the first term on the right side of Equation (23) is the ∂A / ∂t component resulting from the change in the magnetic field generated from the first excitation coil 3a. All ∂A / ∂t components combined with ∂A / ∂t components resulting from changes in the magnetic field generated from the second excitation coil 3b, the second term on the right side of equation (22) and the right side of equation (23) The combination of the second term is the v × B component resulting from the magnetic field and fluid flow velocity generated from the first excitation coil 3a and v resulting from the magnetic field and fluid flow velocity generated from the second excitation coil 3b. All v × B components are combined with the × B component.

  In the equation (22), the coefficient variation factors related to the flow velocity magnitude V of all v × B components do not match the coefficient variation factors related to the angular frequency ω0 of all ∂A / 成分 t components. As can be seen, in the configuration of the electromagnetic flow meter of FIG. 1, zero correction and span correction cannot be performed using one ∂A / ∂t component extracted from the combined vector. Therefore, assuming that the phase difference between the coils is the phase difference in the first excitation state plus π, the coefficient variation factors related to the magnitude V of the flow velocity of all v × B components in equation (22) and equation (23) The variation factors of the coefficients related to the angular frequency ω0 of all the ∂A / ∂t components in are equal, and correction can be performed by extracting the 励磁 A / ∂t components in the second excitation state. The principle applicable in this case will be described below.

When an excitation current having an angular frequency ω0 is supplied only to the first excitation coil 3a, the inter-electrode electromotive force detected by the electrodes 2a and 2b is expressed by the following vectors Va10 and v × B components of 成分 A / ∂t components: This corresponds to the combined vector Va10 + Vb10 of the vector Vb10.
Va10 = ra · exp (j · θa) · B1c [ω0] · C · ω0 (24)
Vb10 = rb · exp (j · θb) · B1c [ω0] · C · V (25)
FIG. 4 shows a vector Va10, a vector Vb10, and a combined vector Va10 + Vb10.

  Here, the vector Va10 of the ∂A / ∂t component is an electromotive force generated by a change in the magnetic field, and thus has a magnitude proportional to the excitation angular frequency ω0. When the known proportionality constant part of the magnitude of the vector Va10 is represented by ra, the known direction of the vector Va10 is represented by θa, and the term related to the magnetic field when the excitation angular frequency is ω0 is represented by B1c [ω0] in a functional form. C (complex vector) is given as an element that changes due to factors other than the fluctuation of the magnetic field. Further, the vector Vb10 of the v × B component is an electromotive force generated by the movement of the fluid in the measurement tube, and therefore has a magnitude proportional to the magnitude V of the flow velocity. When a known proportional constant part of the magnitude of the vector Vb10 is rb, a known direction of the vector Vb10 is θb, and a term related to the magnetic field when the excitation frequency is ω0 is expressed in a functional form as B1c [ω0], C (Complex vector) is given as an element that changes due to factors other than the fluctuation of the magnetic field. Therefore, C in the vector Va10 of ∂A / ∂t component and C in the vector Vb10 of v × B component are the same element.

On the other hand, when an excitation current having an angular frequency ω 0 is supplied only to the second excitation coil 3 b, the inter-electrode electromotive force detected by the electrodes 2 a and 2 b is the following vector Va20 and v × B of ∂A / ∂t components: This corresponds to a composite vector Va20 + Vb20 of the component vector Vb20.
Va20 = −ra · exp (j · θa) · B2c [ω0] · C · ω0 (26)
Vb20 = rb · exp (j · θb) · B2c [ω0] · C · V (27)
FIG. 5 shows a vector Va20, a vector Vb20, and a combined vector Va20 + Vb20.

  Here, a known proportionality constant portion of the magnitude of the vector Va20 of the ∂A / ∂t component is ra, a known direction of the vector Va20 is θa, and a term related to the magnetic field when the excitation angular frequency is ω0 is B2c [ When expressed in a functional form as ω0], C (complex vector) is given as an element that changes due to a factor other than the fluctuation of the magnetic field. Further, the function of the vector Vb20 of the v × B component with the known proportionality constant portion being rb, the known direction of the vector Vb20 being θb, and the term related to the magnetic field when the excitation frequency is ω0 is B2c [ω0]. When expressed in a form, C (complex vector) is given as an element that changes due to factors other than the fluctuation of the magnetic field. Therefore, C in the vector Va20 of the ∂A / ∂t component and C in the vector Vb20 of the v × B component are the same element.

∂A / ∂t component (FIG. 4) resulting from a change in the magnetic field generated from the first excitation coil 3a (FIG. 4) and ∂A / ∂t component resulting from a change in the magnetic field generated from the second excitation coil 3b (FIG. 5) If the excitation current of the angular frequency ω0 is supplied to both the exciting coils 3a and 3b, the inter-electrode electromotive force is the following vector of ∂A / ∂t components: It can be seen that this corresponds to the combined vector Vas0 + Vbs0 of Vas0 and the vector Vbs0 of the v × B component.
Vas0 = Va10 + Va20
= Ra · exp (j · θa) · (B1c [ω0] −B2c [ω0]) · C · ω0
... (28)
Vbs0 = Vb10 + Vb20
= Rb · exp (j · θb) · (B1c [ω0] + B2c [ω0]) · C · V
... (29)

  FIG. 6 shows a vector Vas0, a vector Vbs0, and a combined vector Vas0 + Vbs0. Among the coefficients related to the magnitude V of the flow velocity of the vector Vbs0 shown in Expression (29), (B1c [ω0] + B2c [ω0]) · C is given as a span variation factor. Further, when the magnitude V of the flow velocity is 0, the magnitude of the combined vector fluctuates due to the fluctuation of the vector Vas0 (that is, the zero point fluctuates).

Span fluctuation factor (B1c [ω0] −B2c [ω0]) · C and v × B component vector Vbs0 in the vector Vas0 of ∂A / ∂t component in the combined vector Vas0 + Vbs0 subject to zero correction and span correction Variation factors (B1c [ω0] + B2c [ω0]) · C have different values. Therefore, even if the vector Vbs0 of the v × B component is normalized by the vector Vas0 of the ∂A / ∂t component in the combined vector Vas0 + Vbs0, the variation factor of the span (B1c [ω0] −B2c [ω0] ) / (B1c [ω0] + B2c [ω0]) remains, and the span variation factor cannot be removed.
Vbs0 / Vas0 = (rb / ra) · exp {j · (θb−θa)}
・ {(B1c [ω0] −B2c [ω0])
/ (B1c [ω0] + B2c [ω0])} (V / ω) (30)

Therefore, it is necessary to extract the first ∂A / ∂t component including the same span variation factor (B1c [ω0] + B2c [ω0]) · C as the variation factor of the v × B component. In order to extract such a first ∂A / ∂t component, the first phase difference between the magnetic field generated from the first excitation coil 3a and the magnetic field generated from the second excitation coil 3b is Δθ3. When the excitation state is changed to the second excitation state where the phase difference is Δθ3 + π, the fact that B2c [ω0] · C is inverted is used. That is, when only the second excitation coil 3b is excited at the angular frequency ω0 under the phase condition of the second excitation state in which the phase difference is changed by + π with respect to the first excitation state, it is detected by the electrodes 2a and 2b. The combined vector is inverted with respect to the combined vector (FIG. 5) detected in the first excitation state, and corresponds to the combined vector Va20R + Vb20R of the following vector A20 / Vt component Va20R and v × B component vector Vb20R. .
Va20R = ra · exp (j · θa) · B2c [ω0] · C · ω0 (31)
Vb20R = −rb · exp (j · θb) · B2c [ω0] · C · V (32)
FIG. 7 shows a vector Va20R, a vector Vb20R, and a combined vector Va20R + Vb20R.

A first excitation current having an angular frequency ω0 is supplied to the first excitation coil 3a, and a second excitation current having a phase difference from the first excitation current of Δθ3 + π and an angular frequency of ω0 is supplied to the second excitation coil 3b. The inter-electrode electromotive force when supplied corresponds to a combined vector Vas0R + Vbs0R of a vector Vas0R of the following ∂A / ∂t component and a vector Vbs0R of the v × B component.
Vas0R = Va10 + Va20R
= Ra · exp (j · θa) · (B1c [ω0] + B2c [ω0]) · C · ω0
... (33)
Vbs0R = Vb10 + Vb20R
= Rb · exp (j · θb) · (B1c [ω0] −B2c [ω0]) · C · V
... (34)
FIG. 8 shows a vector Vas0R, a vector Vbs0R, and a combined vector Vas0R + Vbs0R.

  The span variation factor in the vector Vas0R of ∂A / ∂t component is equal to the span variation factor (B1c [ω0] + B2c [ω0]) · C of the vector Vbs0 of the v × B component. Therefore, if Vas0R is extracted as the first ∂A / ∂t component, the vector Vbs0 can be normalized. There are the following two methods for extracting the first ∂A / ∂t component vector Vas0R. The first extraction method is a method of approximately extracting the first ０A / ∂t component vector Vas0R as Vbs0R≈0 when it can be approximated as Vas0R >> Vbs0R. The second extraction method is a method of approximately extracting the vector Vas0R of the ∂A / ∂t component from the combined vector when excited at the angular frequency (ω0 ± Δω).

  The composite vector Vas0 + Vbs0 is normalized by the vector Vas0R of the first ∂A / ∂t component. There are the following two methods for detecting the composite vector Vas0 + Vbs0 to be normalized. The first detection method is a method for directly obtaining the composite vector Vas0 + Vbs0 by exciting at the angular frequency ω0. The second detection method is a method of approximately obtaining a composite vector Vas0 + Vbs0 from a composite vector when excitation is performed at an angular frequency (ω0 ± Δω), similarly to the case where the first ∂A / ∂t component is extracted. is there.

As an example of using the second detection method, a case of taking the excitation angular frequency (ω0 + Δω) and (ω0−Δω) will be described. When an excitation current having an angular frequency (ω0 + Δω) is supplied to both the excitation coils 3a and 3b under the phase condition of the first excitation state, the inter-electrode electromotive force detected by the electrodes 2a and 2b is This corresponds to a combined vector Vasp + Vbsp of the vector Vasp of the t component and the vector Vbsp of the v × B component.
Vasp = ra · exp (j · θa)
(B1c [ω0 + Δω] −B2c [ω0 + Δω]) C (ω0 + Δω)
... (35)
Vbsp = rb · exp (j · θb)
(B1c [ω0 + Δω] + B2c [ω0 + Δω]) CV (36)

Next, when an excitation current having an angular frequency (ω0−Δω) is supplied to both excitation coils 3a and 3b under the phase condition of the first excitation state, the inter-electrode electromotive force detected by the electrodes 2a and 2b is as follows: ∂A / ｍt component vector Vasm and v × B component vector Vbsm corresponding to a combined vector Vasm + Vbsm.
Vasm = ra · exp (j · θa)
(B1c [ω0−Δω] −B2c [ω0−Δω]) C / (ω0−Δω)
... (37)
Vbsm = rb · exp (j · θb)
(B1c [ω0−Δω] + B2c [ω0−Δω]) CV (38)

The vector Vasp of the ∂A / ∂t component at the excitation angular frequency (ω0 + Δω) and the vector Vbsp of the v × B component and the vector Vasm of the ∂A / ∂t component at the excitation angular frequency (ω0−Δω) and the vector of the v × B component. From a vector obtained by combining Vbsm, a combined vector Vas0 + Vbs0 to be normalized can be approximately extracted as in the following equation.
Vas0 + Vbs0≈ {(Vasp + Vbsp) + (Vasm + Vbsm)} / 2
... (39)

Here, the reason why the combined vector Vas0 + Vbs0 can be obtained approximately as in Expression (39) will be described. As described in the document “Eta Ota,“ Basics of Magnetic Engineering II ”, Kyoritsu Shuppan Co., Ltd., April 15, 1984, 8th edition, p. Since it is proportional to the magnitude and frequency of the magnetic field, if the loss of the magnetic field generated from the first excitation coil 3a is the same as the loss of the magnetic field generated from the second excitation coil 3b, the following relationship is established.
B1c [ω0] = B1c−B1c · ω0 · ec (40)
B2c [ω0] = B2c−B2c · ω0 · ec (41)
In the equations (40) and (41), ec is a complex coefficient depending on the core material and the core structure of the exciting coils 3a and 3b.

  In the combined vector detected by the electrodes 2a and 2b when the excitation current of the angular frequency (ω0 + Δω) is supplied only to the first excitation coil 3a, the term related to the magnetic field is B1c [ω0 + Δω], and the first A combined vector detected when an excitation current having an angular frequency (ω0−Δω) is supplied only to the excitation coil 3a is a term B1c [ω0−Δω] related to the magnetic field. The following relationship is established between B1c [ω0 + Δω] and B1c [ω0−Δω] from Equation (40) and Equation (41).

B1c [ω0 + Δω] + B1c [ω−Δω]
= B1c−B1c · (ω0 + Δω) · ec + B1c−B1c · (ω0−Δω) · ec
= 2 · B1c · (1−ω0 · ec)
= 2 · B1c [ω0] (42)
B1c [ω0 + Δω] −B1c [ω−Δω]
= B1c-B1c · (ω0 + Δω) · ec-B1c + B1c · (ω0-Δω) · ec
= −B1c · (Δω) · ec + B1c · (−Δω) · ec
= -2 · B1c · Δω · ec (43)

In the combined vector detected when the excitation current having the angular frequency (ω0 + Δω) is supplied only to the second excitation coil 3b, the term related to the magnetic field is B2c [ω0 + Δω], and only the second excitation coil 3b is used. In a combined vector detected when an excitation current having an angular frequency (ω0−Δω) is supplied, a term related to the magnetic field is defined as B2c [ω0−Δω]. Between B2c [ω0 + Δω] and B2c [ω0−Δω], the following relationship is established from Equation (40) and Equation (41).
B2c [ω0 + Δω] + B2c [ω0−Δω] = 2 · B2c [ω0] (44)
B2c [ω0 + Δω] −B2c [ω0−Δω] = − 2 · B2c · Δω · ec (45)

Using the relational expressions (42) to (45), the vector Vasp of ａA / ∂t component at the excitation angular frequency (ω0 + Δω) and the vector of ∂A / ∂t component at the excitation angular frequency (ω0-Δω). A vector obtained by combining Vasm can be transformed as follows.
Vasp + Vasm
= Ra · exp (j · θa) · C
・ {(Ω0 + Δω) ・ (B1c [ω0 + Δω] −B2c [ω0 + Δω])
+ (Ω0−Δω) · (B1c [ω0−Δω] −B2c [ω0−Δω])}
= 2 · ra · exp (j · θa) · C
・ {Ω0 ・ (B1c [ω0] −B2c [ω0])
− (Δω · Δω) · (B1c−B2c) · ec} (46)

Similarly, if the relational expressions (42) to (45) are used, the v × B component vector Vbsp at the excitation angular frequency (ω0 + Δω) and the v × B component vector Vbsm at the excitation angular frequency (ω0−Δω). The vector obtained by combining can be transformed as follows.
Vbsp + Vbsm
= 2 · rb · exp (j · θb) · C · V
(B1c [ω0 + Δω] + B2c [ω0 + Δω]
+ B1c [ω0−Δω] + B2c [ω0−Δω])
= 2 · rb · exp (j · θb) · C · V · (B1c [ω0] + B2c [ω0])
... (47)

The vector Vasp of the ∂A / ∂t component at the excitation angular frequency (ω0 + Δω) and the vector Vbsp of the × A / ∂t component and the vector Vasm of the ∂A / ∂t component and the vector of the v × B component at the excitation angular frequency (ω0-Δω). A vector obtained by synthesizing Vbsm is expressed by the following equation from equations (46) and (47).
Vasp + Vasm + Vbsp + Vbsm
= 2 · ra · exp (j · θa) · C · ω0 · (B1c [ω0] −B2c [ω0])
-2, ra, exp (j, θa), C, (Δω, Δω), (B1c-B2c), ec
+ 2 · rb · exp (j · θb) · C · V · (B1c [ω0] + B2c [ω0])
... (48)

The second term on the right side can be ignored with respect to the first term on the right side and the third term on the right side of Equation (48), and can be approximated as the following equation.
Vasp + Vasm + Vbsp + Vbsm
≈ 2 · ra · exp (j · θa) · C · ω0 · (B1c [ω0] −B2c [ω0])
+ 2 · rb · exp (j · θb) · C · V · (B1c [ω0] + B2c [ω0])
= 2 · (Vas0 + Vbs0) (49)
Thus, the equation (39) can be derived from the equation (49).

Next, normalization of the combined vector Vas0 + Vbs0 will be described. FIG. 9 is a diagram illustrating a first ∂A / ∂t component vector Vas0R and a combined vector Vas0 + Vbs0. FIG. 10 is a diagram illustrating normalization of the combined vector Vas0 + Vbs0 by the first ∂A / ∂t component vector Vas0R. It is the figure which expressed the processing to perform complex vector. A combined vector obtained by normalizing the combined vector Vas0 + Vbs0 and multiplying it by ω0 is expressed as a combined vector Vnas0 + Vnbs0 of the following vector Vnas0 of ∂A / ∂t component and vector Vnbs0 of v × B component.
Vnas0 = (Vas0 / Vas0R) · ω0
= {(B1c [ω0] −B2c [ω0]) / (B1c [ω0] + B2c [ω0])} · ω0
= {(B1c-B2c) / (B1c + B2c)} · ω0 (50)
Vnbs0 = (Vbs0 / Vas0R) · ω0
= (Rb / ra) · exp {j · (θb−θa)} · V (51)

The reason why the normalized composite vector is multiplied by ω0 is to remove ω0 from the coefficient (span) related to the magnitude V of the flow velocity. Substituting Equation (40) and Equation (41) into (B1c [ω0] −B2c [ω0]) / (B1c [ω0] + B2c [ω0]), the shape is transformed into a form not related to the angular frequency ω0 as shown in the following equation. it can.
(B1c [ω0] −B2c [ω0]) / (B1c [ω0] + B2c [ω0])
= (B1c−B1c · ω0 · ec−B2c + B2c · ω0 · ec)
/ (B1c−B1c · ω0 · ec + B2c−B2c · ω0 · ec)
= {(B1c-B2c) · (1-ω0 · ec)}
/ {(B1c + B2c) · (1-ω0 · ec)}
= (B1c-B2c) / (B1c + B2c) (52)
In Expression (50), (B1c [ω0] −B2c [ω0]) / (B1c [ω0] + B2c [ω0]) is transformed into a form not related to the angular frequency ω0 based on Expression (52).

  According to the equation (51), the variation factor (B1c [ω0] + B2c [ω0]) · C is eliminated from the coefficient applied to V of the normalized v × B component vector Vnbs0, and the span is corrected. I understand. In addition, in the normalized vector Vnas0 of ∂A / ∂t component, there is no term related to the frequency in {}, and it is understood that the loss of the magnetic field need not be taken into consideration.

  FIG. 11 is a complex vector representation of the process of extracting the vector Vnas0 of the third ∂A / ∂t component from the normalized composite vector Vnas0 + Vnbs0. As a method for extracting the third ∂A / ∂t component from the normalized composite vector Vnas0 + Vnbs0, a magnetic field having a plurality of excitation frequencies is applied to the fluid to be measured, and a plurality of frequency components included in the inter-electrode electromotive force are output. A method of extracting the ∂A / ∂t component using the difference is used. This method focuses on the fact that the magnitude of the ∂A / ∂t component is proportional to the excitation frequency, and the v × B component does not depend on the excitation frequency. Specifically, a difference between a vector obtained by normalizing a combined vector when excited at a certain angular frequency ω0 and a vector obtained by normalizing a combined vector when excited at another angular frequency ω2 is obtained. Since this difference is a vector that gives only a change in the magnitude of the ∂A / ∂t component, the ∂A / ∂t component can be extracted from this change.

The inter-electrode electromotive force when the excitation current having the angular frequency ω2 is supplied to both the excitation coils 3a and 3b corresponds to the combined vector Vas2 + Vbs2 of the vector ａｓs2 of the following ∂A / ∂t component and the vector Vbs2 of the v × B component. I understand that
Vas2 = ra · exp (j · θa) · (B1c [ω2] −B2c [ω2]) · C · ω2
... (53)
Vbs2 = Vbs0
= Rb · exp (j · θb) · (B1c [ω2] + B2c [ω2]) · C · V
... (54)

  B1c [ω2] is a term related to the magnetic field in the combined vector detected by the electrodes 2a and 2b when the exciting current having the angular frequency ω2 is supplied only to the first exciting coil 3a. B2c [ω2] is a term related to the magnetic field in the combined vector detected when the excitation current having the angular frequency ω2 is supplied only to the second excitation coil 3b.

A first excitation current having an angular frequency ω2 is supplied to the first excitation coil 3a, and a second excitation current having a phase difference of Δθ3 + π and an angular frequency ω2 from the first excitation current is supplied to the second excitation coil 3b. Of the combined vectors detected by the electrodes 2a and 2b when supplied, the vector Vas2R of the ∂A / ∂t component is expressed by the following equation.
Vas2R = ra · exp (j · θa) · (B1c [ω2] + B2c [ω2]) · C · ω2
... (55)
A vector Vas2R represented by Expression (55) is set as a second ∂A / ∂t component.

The composite vector Vas2 + Vbs2 is normalized using the second vector ａｓA / ∂t component Vas2R and multiplied by ω2, and the resultant vector is a combination of the following vector Vnas2 of ∂A / ∂t component and vector Vnbs2 of v × B component. It is represented by the vector Vnas2 + Vnbs2.
Vnas2 = (Vas2 / Vas2R) · ω2
= {(B1c [ω2] -B2c [ω2]) / (B1c [ω2] + B2c [ω2])} · ω2
= {(B1c-B2c) / (B1c + B2c)} · ω2 (56)
Vnbs2 = Vnbs0
= (Vbs2 / Vas2R) · ω2
= (Rb / ra) · exp {j · (θb−θa)} · V (57)

  The normalized v × B component vector Vnbs2 when the excitation angular frequency is ω2 is the same as the vector Vnbs0 shown in the equation (51). On the other hand, the normalized vector Vnas2 of ∂A / ∂t component when the excitation angular frequency is ω2 is obtained by replacing ω0 with ω2 in equation (50).

When the difference between the normalized composite vector Vnas0 + Vnbs0 when the excitation angular frequency is ω0 and the normalized composite vector Vnas2 + Vnbs2 when the excitation angular frequency is ω2, the v × B component is canceled and obtained. The difference obtained by multiplying the difference by ω0 / (ω0−ω2) is the same as the vector Vnas0 as shown in the following equation.
{(Vnas0 + Vnbs0) − (Vnas2 + Vnbs2)} · ω0 / (ω0−ω2)
= (Vnas0−Vnas2) · ω0 / (ω0−ω2)
= {(B1c-B2c) / (B1c + B2c)} · ω0
= Vnas0 (58)

  Therefore, the vector Vnas0 of the ∂A / ∂t component in the normalized combined vector Vnas0 + Vnbs0 can be extracted by using the output difference of different frequency components. The extracted vector Vnas0 of ∂A / ∂t component is set as a third ∂A / ∂t component.

  FIG. 12 is a diagram representing the process of extracting the vector Vnbs0 of the v × B component from the normalized composite vector Vnas0 + Vnbs0 as a complex vector. By subtracting the vector Vnas0 of the third ∂A / ∂t component from the normalized composite vector Vnas0 + Vnbs0, the vector Vnbs0 of the v × B component shown in Expression (51) can be extracted. From equation (51), it can be seen that the vector (Vnbs0) of the v × B component does not include a term related to the angular frequencies ω0 and ω2 (zero point variation factor).

From equation (51), the magnitude V of the flow velocity of the fluid to be measured can be calculated as follows.
V = | Vnbs0 / [(rb / ra) · exp {j · (θb−θa)}] |
= | Vnbs0 | / (rb / ra) (59)

  Next, the principle of an electromagnetic flowmeter having one excitation coil and two pairs of electrodes among the electromagnetic flowmeters based on the basic principle of the present invention will be described with reference to FIG. The electromagnetic flow meter of FIG. 13 is disposed opposite to the measurement tube 1 so as to be orthogonal to both the measurement tube 1, the magnetic field applied to the fluid to be measured, and the measurement tube axis PAX, and to be in contact with the fluid to be measured. 1st electrode 2a, 2b and 2nd electrode 2c, 2d which detect the electromotive force which generate | occur | produced with the magnetic field and the flow of to-be-measured fluid, and 1st electrode 2a, 2b orthogonal to the measurement pipe axis PAX are included. When a plane including PLN1 and the plane including the second electrodes 2c and 2d orthogonal to the measurement tube axis PAX is PLN2, a non-symmetrical time-varying magnetic field is measured before and after the measurement tube 1 with the plane PLN1 as a boundary. At the same time as applying to the fluid, it has an exciting coil 3 that applies a time-varying magnetic field that is asymmetric before and after the measuring tube 1 with the plane PLN2 as a boundary.

  The first electrodes 2a and 2b are arranged at a position separated from the plane PLN3 including the axis of the exciting coil 3 and perpendicular to the direction of the measurement tube axis PAX, for example, by an offset distance d3 upstream. The second electrodes 2c and 2d are disposed at a position separated from the plane PLN3, for example, by an offset distance d4 on the downstream side, and are disposed so as to face the first electrodes 2a and 2b across the plane PLN3.

  When the second electrodes 2c and 2d are disposed so as to face the first electrodes 2a and 2b across the plane PLN3, the exciting coil among the inter-electrode electromotive forces detected by the first electrodes 2a and 2b Among the v × B component caused by the magnetic field generated from the magnetic field 3 and the flow velocity of the fluid and the inter-electrode electromotive force detected by the second electrodes 2c and 2d, the magnetic field generated from the exciting coil 3 and the flow velocity of the fluid The direction is the same as the v × B component. On the other hand, among the inter-electrode electromotive force detected by the first electrodes 2a and 2b, the ∂A / ∂t component caused by the change in the magnetic field generated from the exciting coil 3 and the second electrodes 2c and 2d are detected. In the electromotive force between the electrodes, the ∂A / ∂t component caused by the change in the magnetic field generated from the exciting coil 3 is opposite. Therefore, the ∂A / ∂t component and the v × B component detected by the first electrodes 2a and 2b and the ∂A / ∂t component and the v × B component detected by the second electrodes 2c and 2d are It is necessary to perform correction in consideration of the fact that the variation factor of the v × B component and the variation factor of the ∂A / 全 て t component in all the combined vectors are not equal.

Here, among the magnetic field Bd generated from the excitation coil 3, a magnetic field component (magnetic flux density) B4 orthogonal to both the electrode axis EAX1 and the measurement tube axis PAX on the electrode axis EAX1 connecting the electrodes 2a and 2b, and the excitation coil Among the magnetic fields Bd generated from 3, the magnetic field component (magnetic flux density) B5 orthogonal to both the electrode axis EAX2 and the measurement tube axis PAX on the electrode axis EAX2 connecting the electrodes 2c and 2d is given as follows: And
B4 = b4 · cos (ω0 · t−θ4) (60)
B5 = b5 · cos (ω0 · t−θ5) (61)

  However, since B4 and B5 are generated from one excitation coil 3, b4 and b5 and θ4 and θ5 are related to each other and are not independent variables. In equations (60) and (61), b4 and b5 are the amplitudes of the magnetic flux densities B4 and B5, ω0 is the angular frequency, θ4 is the phase difference (phase lag) between the magnetic flux density B4 and ω0 · t, and θ5 is the magnetic flux. It is a phase difference between the density B5 and ω0 · t. Hereinafter, the magnetic flux density B4 is referred to as a magnetic field B4, and the magnetic flux density B5 is referred to as a magnetic field B5.

  When the flow velocity of the fluid to be measured is 0, the eddy current generated is only a component due to the change in the magnetic field, and the eddy current I due to the change in the magnetic field Bd has a direction as shown in FIG. Therefore, an electromotive force E1 irrelevant to the flow velocity between the electrodes 2a and 2b generated by a change in the magnetic field Bd in a plane including the electrode axis EAX1 and the measurement tube axis PAX, and the electrode axis EAX2 and the measurement tube axis PAX are included. The electromotive force E2 between the electrodes 2c and 2d generated by the change of the magnetic field Bd in the plane is opposite to each other as shown in FIG.

  When the flow velocity of the fluid to be measured is V (V ≠ 0), in addition to the eddy current I when the flow velocity is 0, a component v × Bd due to the flow velocity vector v of the fluid to be measured is generated. Therefore, the eddy current Iv due to the flow velocity vector v and the magnetic field Bd is oriented as shown in FIG. Accordingly, the electromotive force Ev1 of the electrodes 2a and 2b generated by the flow velocity vector v and the magnetic field Bd and the electromotive force Ev2 between the electrodes 2c and 2d generated by the flow velocity vector v and the magnetic field Bd are in the same direction.

In consideration of the direction of the inter-electrode electromotive force described with reference to FIGS. 14 and 15, the electro-electromotive force obtained by converting the electro-electromotive force due to the time change of the magnetic field into a complex vector and the flow velocity of the fluid to be measured. The first inter-electrode electromotive force Eac31 between the electrodes 2a and 2b, which is combined with the electromotive force converted into a complex vector, is obtained by using the equation (18) by using the equations (10), (16), and (17). ) Is represented by the following equation.
Eac31 = rk · ω0 · b4 · exp {j · (π / 2 + θ4 + θ00)}
+ Γ · rk · V · b4 · exp {j · (θ4 + θ01)} (62)

In addition, an electrode 2c, which is a combination of an electromotive force obtained by converting the inter-electrode electromotive force caused by the time change of the magnetic field into a complex vector and an electromotive force obtained by converting the inter-electrode electromotive force caused by the flow velocity of the fluid to be measured into the complex vector. The second inter-electrode electromotive force Eac32 between 2d is expressed by the following equation corresponding to the equation (18) using the equations (10), (16), and (17).
Eac32 = rk · ω0 · b5 · exp {j · (−π / 2 + θ5 + θ00)}
+ Γ · rk · V · b5 · exp {j · (θ5 + θ01)} (63)

  The first term on the right side of Equation (62) is the ∂A / ∂t component detected by the first electrodes 2a and 2b, and the second term on the right side of Equation (62) is v detected by the first electrodes 2a and 2b. × B component. The first term on the right side of Equation (63) is the ∂A / ∂t component detected by the second electrodes 2c and 2d, and the second term on the right side of Equation (63) is v detected by the second electrodes 2c and 2d. × B component.

Here, the relationship between the phase delay θ4 of the magnetic field B4 with respect to ω0 · t and the phase delay θ5 of the magnetic field B5 with respect to ω0 · t is θ5 = θ4 + Δθ5, and the angle θ00 of the ∂A / ∂t component with respect to the imaginary axis and v with respect to the real axis The relationship with the angle θ01 of the × B component is θ01 = θ00 + Δθ01. The first inter-electrode electromotive force Eac31 when θ5 = θ4 + Δθ5 and θ01 = θ00 + Δθ01 are substituted into equation (62), and the second inter-electrode electromotive force when θ5 = θ4 + Δθ5 and θ01 = θ00 + Δθ01 are substituted into equation (63) If the sum with Eac32 is Eac3s, the electromotive force sum Eac3s is expressed by the following equation.
Eac3s = rk · exp {j · (θ4 + θ00)}
Exp (j · π / 2) · {b4-b5 · exp (j · Δθ5)} · ω0
+ Rk · exp {j · (θ4 + θ00)}
Γ · exp (j · Δθ01) · {b4 + b5 · exp (j · Δθ5)} V (64)

Further, the first inter-electrode electromotive force Eac31 when θ5 = θ4 + Δθ5 and θ01 = θ00 + Δθ01 are substituted into the equation (62) and the second interelectrode between when θ5 = θ4 + Δθ5 and θ01 = θ00 + Δθ01 are substituted into the equation (63). If the difference from the electromotive force Eac32 is Eac3d, the electromotive force difference Eac3d is expressed by the following equation.
Eac3d = rk · exp {j · (θ4 + θ00)}
Exp (j · π / 2) · {b4 + b5 · exp (j · Δθ5)} · ω0
+ Rk · exp {j · (θ4 + θ00)}
Γ · exp (j · Δθ01) · {b4-b5 · exp (j · Δθ5)} V (65)

  The first term on the right side of Equation (64) is the ∂A / ∂t component in the electromotive force sum Eac3s, and the second term on the right side of Equation (64) is the v × B component in the electromotive force sum Eac3s. The first term on the right side of Equation (65) is the ∂A / ∂t component in the electromotive force difference Eac3d, and the second term on the right side of Equation (65) is the v × B component in the electromotive force difference Eac3d.

  In the equation (64), the coefficient variation factor relating to the flow velocity V of the v × B component in the electromotive force sum Eac3s and the angular frequency ω0 of the ∂A / ∂t component in the electromotive force sum Eac3s As can be seen from the fact that the coefficient variation factors do not match, in the configuration of the electromagnetic flow meter of FIG. 13, it is possible to perform zero correction and span correction using one ∂A / ∂t component extracted from the combined vector. Can not. Therefore, the variation factor of the coefficient related to the magnitude V of the flow velocity of the v × B component in the electromotive force sum Eac3s shown in Expression (64) and ∂A in the electromotive force difference Eac3d shown in Expression (65). Using the fact that the variation factor of the coefficient related to the angular frequency ω 0 of the / ∂t component becomes equal, by extracting the ∂A / ∂t component in the electromotive force difference Eac3d, 0 correction and span correction can be performed. The same principle as the electromagnetic flow meter of FIG. 1 can be applied to the correction.

  In order to make the content of the principle explained in the case of the electromagnetic flow meter of FIG. 1 correspond to the electromagnetic flow meter of FIG. 13, the electromotive force due to the influence of the magnetic field generated from the first excitation coil 3a is changed to the first electrode 2a. , 2b, the electromotive force Eac31 detected by the second electrodes 2c, 2d is replaced with the electromotive force Eac32 detected by the second electrodes 2c, 2d, and the first electromotive force Eac31 detected by the second excitation coil 3b. The electromotive force detected in the excited state may be replaced with the electromotive force sum Eac3s, and the electromotive force detected in the second excited state may be replaced with the electromotive force difference Eac3d.

[First Embodiment]
Next, a first embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has two excitation coils and a pair of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. The present embodiment uses the first detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The first extraction method described is used. When the second excitation coil is added on the same side as the first excitation coil, the electromagnetic flow meter of FIG. 29 has a redundant configuration. Therefore, the second exciting coil needs to be arranged on a different side from the first exciting coil across the plane including the electrodes.

Of the magnetic field Bb generated from the first exciting coil 3a, a magnetic field component (magnetic flux density) B2 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX connecting the electrodes 2a, 2b, and the second Of the magnetic field Bc generated from the exciting coil 3b, a magnetic field component (magnetic flux density) B3 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX is given as follows.
B2 = b2 · cos (ω0 · t−θ2) (66)
B3 = b3 · cos (ω0 · t−θ3) (67)
In equations (66) and (67), b2 and b3 are the amplitudes of the magnetic flux densities B2 and B3, ω0 is the angular frequency, θ2 is the phase difference (phase lag) between the magnetic flux density B2 and ω0 · t, and θ3 is the magnetic flux. The phase difference between the density B3 and ω0 · t. Hereinafter, the magnetic flux density B2 is defined as the magnetic field B2, and the magnetic flux density B3 is defined as the magnetic field B3.

Considering the loss of the magnetic field, the amplitudes b2 and b3 of the magnetic fields B2 and B3 at the angular frequency ω0 are changed to the function notations b2 [ω0] and b3 [ω0], respectively, and the phase difference θ2 between the magnetic fields B2 and B3 is similarly changed. When θ3 is changed to θ2 [ω0] and θ3 [ω0], respectively, equations (66) and (67) are replaced with equations (68) and (69).
B2 = b2 [ω0] · cos (ω0 · t−θ2 [ω0]) (68)
B3 = b3 [ω0] · cos (ω0 · t−θ3 [ω0]) (69)

Since the electromotive force resulting from the change in the magnetic field is based on the time derivative dB / dt of the magnetic field, the magnetic field B2 generated from the first excitation coil 3a and the magnetic field B3 generated from the second excitation coil 3b are differentiated as follows: To do.
dB2 / dt = ω0 · cos (ω0 · t) · b2 [ω0] · {sin (θ2 [ω0])}
+ Ω0 · sin (ω0 · t) · b2 [ω0] · {−cos (θ2 [ω0])}
... (70)
dB3 / dt = ω0 · cos (ω0 · t) · b3 [ω0] · {sin (θ3 [ω0])}
+ Ω0 · sin (ω0 · t) · b3 [ω0] · {−cos (θ3 [ω0])}
... (71)

When the flow rate of the fluid to be measured is 0, it is generated by the change in the electromotive force E1 between the electrodes that is irrelevant to the flow rate and the change in the magnetic field Bc. The inter-electrode electromotive force E2 irrelevant to the flow velocity is opposite to each other as shown in FIG. At this time, the total inter-electrode electromotive force E obtained by adding the inter-electrode electromotive forces E1 and E2 is the difference between the time derivative of the magnetic field dB2 / dt and the dB3 / dt (−dB2 / dt + dB3 / dt) is multiplied by a proportional coefficient rk, and the phase differences θ2 and θ3 are replaced by θ2 + θ00 and θ3 + θ00, respectively (rk and θ00 are measurements including the conductivity and dielectric constant of the fluid to be measured and the arrangement of the electrodes 2a and 2b). Related to the structure of the tube 1).
E = rk · ω0 · cos (ω0 · t)
・ {−b2 [ω0] · sin (θ2 [ω0] + θ00)
+ B3 [ω0] · sin (θ3 [ω0] + θ00)}
+ Rk · ω0 · sin (ω0 · t)
・ {B2 [ω0] · cos (θ2 [ω0] + θ00)
-B3 [ω0] · cos (θ3 [ω0] + θ00)} (72)

When the magnitude of the flow velocity of the fluid to be measured is V (V ≠ 0), the interelectrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bb, and the interelectrode electromotive force Ev2 generated by the flow velocity vector v and the magnetic field Bc are shown in FIG. As shown in FIG. At this time, the total inter-electrode electromotive force Ev obtained by adding the inter-electrode electromotive forces Ev1 and Ev2 is obtained by multiplying the sum of the magnetic field B2 and the magnetic field B3 by the proportional coefficient rkv to obtain the phase difference θ2, θ3. Are replaced by θ2 + θ01 and θ3 + θ01, respectively (rkv and θ01 relate to the structure of the measuring tube 1 including the magnitude V of the flow velocity, the conductivity and the dielectric constant of the fluid to be measured, and the arrangement of the electrodes 2a and 2b). .
Ev = rkv · cos (ω0 · t)
・ {B2 [ω0] · cos (θ2 [ω0] + θ01)
+ B3 [ω0] · cos (θ3 [ω0] + θ01)}
+ Rkv · sin (ω0 · t)
・ {B2 [ω0] · sin (θ2 [ω0] + θ01)
+ B3 [ω0] · sin (θ3 [ω0] + θ01)} (73)

In consideration of the direction of the electromotive force between the electrodes described in FIGS. 2 and 3, the electromotive force obtained by converting the interelectrode electromotive force due to the time change of the magnetic field into a complex vector and the interelectrode electromotive force due to the flow velocity of the fluid to be measured. Of the whole inter-electrode electromotive force combined with the electromotive force converted into a complex vector, the electromotive force E10c of the component of the angular frequency ω0 applies Equation (17) to Equation (72) and Equation (73). Is expressed by the following equation.
E10c = rk · ω0 · b2 [ω0] · exp {j · (π / 2 + θ2 [ω0] + θ00)}
+ Rk · ω0 · b3 [ω0]
• exp {j · (−π / 2 + θ3 [ω0] + θ00)}
+ Γ · rk · V · b2 [ω0] · exp {j · (θ2 [ω0] + θ01)}
+ Γ · rk · V · b3 [ω0] · exp {j · (θ3 [ω0] + θ01)}
... (74)

Here, the relationship between the phase delay θ2 [ω0] of the magnetic field B2 with respect to ω0 · t and the phase delay θ3 [ω0] of the magnetic field B3 with respect to ω0 · t is θ3 [ω0] = θ2 [ω0] + Δθ3 [ω0] A state in which the relationship between the angle θ00 of the ∂A / ∂t component with respect to the imaginary axis and the angle θ01 of the v × B component with respect to the real axis is θ01 = θ00 + Δθ01 is defined as the first excitation state, and between the electrodes in the first excitation state When the electromotive force E10c is E10, the interelectrode electromotive force E10 is expressed by the following equation.
E10 = rk · exp {j · (θ2 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B2 [ω0] −b3 [ω0] · exp (j · Δθ3 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B2 [ω0] + b3 [ω0] · exp (j · Δθ3 [ω0])}]
... (75)

In addition, the phase difference between the magnetic field B2 and the magnetic field B3 changes from the first excitation state by a constant value π (θ3 [ω2] = π + θ2 [ω2] + Δθ3 [ω2]), and θ01 = θ00 + Δθ01. When the interelectrode electromotive force E10c in the second excitation state is E1π0, the interelectrode electromotive force E1π0 is expressed by the following equation.
E1π0 = rk · exp {j · (θ2 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B2 [ω0] + b3 [ω0] · exp (j · Δθ3 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B2 [ω0] −b3 [ω0] · exp (j · Δθ3 [ω0])}]
... (76)

Further, when the excitation angular frequency is changed from ω0 to ω2 in the first excitation state is defined as the third excitation state, and the interelectrode electromotive force E10c in the third excitation state is E12, the interelectrode electromotive force E12 is From the equation (75), the following equation is obtained.
E12 = rk · exp {j · (θ2 [ω2] + θ00)}
・ [Ω2 ・ exp (j ・ π / 2)
{B2 [ω2] −b3 [ω2] · exp (j · Δθ3 [ω2])}
+ Γ · V · exp (j · Δθ01)
{B2 [ω2] + b3 [ω2] · exp (j · Δθ3 [ω2])}]
... (77)

In addition, when the state in which the excitation angular frequency is changed from ω0 to ω2 in the second excitation state is the fourth excitation state, and the inter-electrode electromotive force E10c in the fourth excitation state is E1π2, the inter-electrode electromotive force E1π2 is From the equation (76), the following equation is obtained.
E1π2 = rk · exp {j · (θ2 [ω2] + θ00)}
・ [Ω2 ・ exp (j ・ π / 2)
{B2 [ω2] + b3 [ω2] · exp (j · Δθ3 [ω2])}
+ Γ · V · exp (j · Δθ01)
{B2 [ω2] -b3 [ω2] · exp (j · Δθ3 [ω2])}]
... (78)

First, correction of the span in the state of the angular frequency ω0 will be described. If the magnetic field B2 generated from the first exciting coil 3a and the magnetic field B3 generated from the second exciting coil 3b are set equal in the initial state (state at the time of calibration), the initial values of the subsequent magnetic fields B2 and B3 are set. The difference from the state becomes small, and the condition of Expression (79) is satisfied.
| B2 [ω0] + b3 [ω0] · exp (j · Δθ3 [ω0]) |
>> | b2 [ω0] −b3 [ω0] · exp (j · Δθ3 [ω0]) | (79)

In addition, since ω0> γ · V is normally satisfied, when the condition of Expression (79) is considered, the condition of Expression (80) is satisfied in Expression (76).
| Ω0 · exp (j · π / 2)
{B2 [ω0] + b3 [ω0] · exp (j · Δθ3 [ω0])} |
≫ ｜ γ ・ V ・ exp (j ・ Δθ01)
{B2 [ω0] −b3 [ω0] · exp (j · Δθ3 [ω0])} |
... (80)

The electromotive force EdA11 that approximates the interelectrode electromotive force E1π0 using the condition of the equation (80) is expressed as the following equation. This electromotive force EdA11 corresponds to the first ∂A / ∂t component in the basic principle.
EdA11≈E1π0 (81)
EdA11 = rk · exp {j · (θ2 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B2 [ω0] + b3 [ω0] · exp (j · Δθ3 [ω0])}
... (82)

Since the electromotive force EdA11 is not related to the magnitude V of the flow velocity, only the component generated by ∂A / ∂t is included. Using this electromotive force EdA11, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the interelectrode electromotive force E10 (combined vector Vas0 + Vbs0) is normalized. When the inter-electrode electromotive force E10 in the equation (75) is normalized by the electromotive force EdA11 in the equation (82) and multiplied by ω0, the result is En10, and the normalized electromotive force En10 is expressed by the following equation.
En10 = (E10 / EdA11) · ω0
= Rk · exp {j · (θ2 [ω0] + θ00)} · [ω0 · exp (j · π / 2)
{B2 [ω0] −b3 [ω0] · exp (j · Δθ3 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B2 [ω0] + b3 [ω0] · exp (j · Δθ3 [ω0])}]
/ [Rk · exp {j · (θ2 [ω0] + θ00)} · ω0 · exp (j · π / 2)
{B2 [ω0] + b3 [ω0] · exp (j · Δθ3 [ω0])}] · ω0
= Ω0 · {b2 [ω0] −b3 [ω0] · exp (j · Δθ3 [ω0])}
/ {B2 [ω0] + b3 [ω0] · exp (j · Δθ3 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (83)

The coefficient {b2 [ω0] −b3 [ω0] · exp (j · Δθ3 [ω0])} / {b2 [ω0] + b3 [ω0] · exp () applied to the angular frequency ω0 of the first term on the right side of the equation (83) j · Δθ3 [ω0])} is also normalized, and is represented by the value {b2−b3 · exp (j · Δθ3)} / {b2 + b3 · exp (j · Δθ3)} not related to the angular frequency ω0. Equation (83) can be replaced by the following equation.
En10 = ω0 · {b2−b3 · exp (j · Δθ3)}
/ {B2 + b3 · exp (j · Δθ3)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (84)

  The second term on the right side of equation (84) is a term obtained by normalizing the component generated by v × B with the component generated by ∂A / ∂t. The reason why the result obtained by normalizing the inter-electrode electromotive force E10 with the electromotive force EdA11 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side related to the magnitude V of the flow velocity. According to the equation (84), the complex coefficient related to the magnitude V of the flow velocity has a magnitude of γ and an angle from the real axis of −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (84) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the ∂A / ∂t component, it is possible to realize span correction that automatically corrects an error due to a magnetic field shift or phase change.

Next, a method for removing the first term on the right side of the equation (84), which is the variation factor of the zero point, will be described. Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. First, an electromotive force EdA12 that approximates the interelectrode electromotive force E1π2 in the equation (78) is expressed by the following equation. This electromotive force EdA12 corresponds to the second ∂A / ∂t component in the basic principle.
EdA12≈E1π2 (85)
EdA12 = rk · exp {j · (θ2 [ω0] + θ00)}
・ Ω2 ・ exp (j ・ π / 2)
{B2 [ω2] + b3 [ω2] · exp (j · Δθ3 [ω2])}
... (86)

If the inter-electrode electromotive force E12 in the equation (77) is normalized by the electromotive force EdA12 and multiplied by ω2 is En12, the normalized electromotive force En12 is expressed by the following equation from the equation (84).
En12 = (E12 / EdA12) · ω2
= Ω2 · {b2 [ω2] −b3 [ω2] · exp (j · Δθ3 [ω2])}
/ {B2 [ω2] + b3 [ω2] · exp (j · Δθ3 [ω2])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
= Ω2 · {b2−b3 · exp (j · Δθ3)}
/ {B2 + b3 · exp (j · Δθ3)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (87)

Taking the difference between the normalized electromotive forces En10 and En12 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA13, the electromotive force difference EdA13 is expressed by the following equation. This electromotive force difference EdA13 corresponds to the third ∂A / ∂t component in the basic principle.
EdA13 = (En10−En12) · ω0 / (ω0−ω2)
= [Ω0 · {b2−b3 · exp (j · Δθ3)}
/ {B2 + b3 · exp (j · Δθ3)}
+ Γ · exp {j · (−π / 2 + Δθ01)} · V
-Ω2 · {b2−b3 · exp (j · Δθ3)}
/ {B2 + b3 · exp (j · Δθ3)}
−γ · exp {j · (−π / 2 + Δθ01)} · V] · ω0 / (ω0−ω2)
= Ω0 · {b2−b3 · exp (j · Δθ3)}
/ {B2 + b3 · exp (j · Δθ3)} (88)

The electromotive force difference EdA13 represents the normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (84). Therefore, if this normalized electromotive force difference EdA13 is used, the normalized v × The B component can be extracted from the normalized electromotive force En10. When the v × B component obtained by subtracting the normalized electromotive force difference EdA13 of equation (88) from the normalized electromotive force En10 of equation (84) is EvBn1, the v × B component EvBn1 is expressed by the following equation: .
EvBn1 = En10-EdA13
= Ω0 · {b2−b3 · exp (j · Δθ3)}
/ {B2 + b3 · exp (j · Δθ3)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
-Ω0 · {b2−b3 · exp (j · Δθ3)}
/ {B2 + b3 · exp (j · Δθ3)}
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (89)

The v × B component EvBn1 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvBn1 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBn1. From the equation (89), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn1 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn1 | / γ (90)

  Table 1 below shows the correspondence between the constants and variables used in the basic principle and the constants and variables of this embodiment. As is clear from Table 1, this embodiment is an example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. FIG. 16 is a block diagram showing the configuration of the electromagnetic flowmeter of the present embodiment, and the same components as those in FIG. The electromagnetic flow meter of the present embodiment supplies excitation current to the measuring tube 1, the electrodes 2a and 2b, the first and second excitation coils 3a and 3b, and the first and second excitation coils 3a and 3b. Power supply unit 4, signal conversion unit 5, and flow rate output unit 6 that calculates the flow rate of the fluid from the v × B component extracted by signal conversion unit 5. The first and second excitation coils 3a and 3b and the power supply unit 4 serve as excitation units that apply a magnetic field that is asymmetric and time-varying with respect to the plane PLN to the fluid to be measured.

  The signal conversion unit 5 obtains the amplitude and phase of the combined electromotive force detected by the electrodes 2a and 2b in each of the first to fourth excitation states, and performs the second excitation based on these amplitudes and phases. The combined electromotive force of the state is extracted as the first ∂A / ∂t component, and the combined electromotive force of the fourth excitation state is extracted as the second ∂A / ∂t component, thereby synthesizing the first excitation state. Using the electromotive force as the first correction target electromotive force, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed based on the first ∂A / ∂t component, The composite electromotive force in the third excitation state is set as the second correction target electromotive force, and the span included in the v × B component in the second correction target electromotive force is based on the second ∂A / ∂t component. The span correction unit 51 for removing the variation factor, the first correction target electromotive force and the span correction subjected to the span correction The difference between the corrected second electromotive force and the second correction target electromotive force is extracted as a third ∂A / ∂t component, and the third ∂A is selected from any one of the two correction target electromotive forces subjected to the span correction. The zero point correction unit 52 extracts the v × B component by removing the / ∂t component.

  The power supply unit 4 supplies the first excitation current having the first angular frequency ω0 to the first excitation coil 3a, and at the same time, the phase difference from the first excitation current is Δθ3 and the first excitation current having the first angular frequency ω0. The first excitation state in which two excitation currents are supplied to the second excitation coil 3b is continued for T1 seconds, and the phase difference between the first excitation current and the second excitation current is determined with respect to the first excitation state. The second excitation state changed to Δθ3 + π is continued for T2 seconds, the third excitation state in which the excitation angular frequency is changed from ω0 to ω2 with respect to the first excitation state is continued for T3 seconds, and further the second excitation state. On the other hand, the fourth excitation state in which the excitation angular frequency is changed from ω0 to ω2 is continued for T4 seconds at a cycle of T seconds. That is, T = T1 + T2 + T3 + T4.

  FIG. 17 is a flowchart showing the operations of the signal conversion unit 5 and the flow rate output unit 6. First, the span correction unit 51 of the signal conversion unit 5 obtains the amplitude r10 of the electromotive force E10 of the component of the angular frequency ω0 among the electromotive forces between the electrodes 2a and 2b in the first excitation state, and the real axis and the electrode A phase difference φ10 with respect to the inter-electromotive force E10 is obtained by a phase detector (not shown) (step 101 in FIG. 17). Subsequently, in the second excitation state, the span correction unit 51 obtains the amplitude r1π0 of the electromotive force E1π0 of the component having the angular frequency ω0 among the electromotive forces between the electrodes 2a and 2b, and the electromotive force E1π0 between the real axis and the electrode. Is obtained by a phase detector (step 102).

  Further, in the third excitation state, the span correction unit 51 obtains the amplitude r12 of the electromotive force E12 of the component of the angular frequency ω2 among the electromotive forces between the electrodes 2a and 2b, and the real axis and the interelectrode electromotive force E12 Is obtained by a phase detector (step 103). Further, in the fourth excitation state, the span correction unit 51 obtains the amplitude r1π2 of the electromotive force E1π2 of the component of the angular frequency ω2 among the electromotive forces between the electrodes 2a and 2b, and the real axis and the interelectrode electromotive force E1π2 Is obtained by a phase detector (step 104). The interelectrode electromotive forces E10, E1π0, E12, and E1π2 can be separated by a band-pass filter, but can be easily separated by actually using a comb-shaped digital filter called a comb filter. Can do.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force EdA11 that approximates the interelectrode electromotive force E1π0 (step 105). The process of step 105 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of Expression (82). The span correction unit 51 calculates the magnitude | EdA11 | of the electromotive force EdA11 as the following equation.
| EdA11 | = r1π0 (91)
Then, the span correction unit 51 calculates the angle ∠EdA11 of the electromotive force EdA11 as the following equation.
∠EdA11 = φ1π0 (92)
This completes the process of step 105.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force En10 obtained by normalizing the interelectrode electromotive force E10 with the electromotive force EdA11 (step 106). The process of step 106 is a process corresponding to the calculation of Expression (84). The span correction unit 51 calculates the magnitude | En10 | of the normalized electromotive force En10 as the following expression.
| En10 | = (r10 / | EdA11 |) · ω0 (93)

Then, the span correction unit 51 calculates the angle ∠En10 of the normalized electromotive force En10 as the following expression.
∠En10 = φ10−∠EdA11 (94)
Further, the span correction unit 51 calculates the real axis component En10x and the imaginary axis component En10y of the normalized electromotive force En10 as the following expression.
En10x = | En10 | .cos (∠En10) (95)
En10y = | En10 | .sin (∠En10) (96)
This completes the process of step 106.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force EdA12 that approximates the interelectrode electromotive force E1π2 (step 107). The process of step 107 is a process corresponding to obtaining the second ∂A / ∂t component, and is a process corresponding to the calculation of Expression (86). The span correction unit 51 calculates the magnitude | EdA12 | of the electromotive force EdA12 as the following equation.
| EdA12 | = r1π2 (97)
Then, the span correction unit 51 calculates the angle ∠EdA12 of the electromotive force EdA12 as the following equation.
∠EdA12 = φ1π2 (98)
This completes the process of step 107.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force En12 obtained by normalizing the inter-electrode electromotive force E12 with the electromotive force EdA12 (step 108). The process of step 108 is a process corresponding to the calculation of Expression (87). The span correction unit 51 calculates the magnitude | En12 | of the normalized electromotive force En12 as the following equation.
| En12 | = (r12 / | EdA12 |) · ω2 (99)

Then, the span correction unit 51 calculates the angle ∠En12 of the normalized electromotive force En12 as the following expression.
∠En12 = φ12−∠EdA12 (100)
Further, the span correction unit 51 calculates the real axis component En12x and the imaginary axis component En12y of the normalized electromotive force En12 as the following expression.
En12x = | En12 | .cos (∠En12) (101)
En12y = | En12 | .sin (∠En12) (102)
This completes the processing of step 108.

Next, the zero point correction unit 52 of the signal conversion unit 5 obtains the magnitude of the electromotive force difference EdA13 between the normalized electromotive forces En10 and En12 (step 109). The process of step 109 is a process corresponding to obtaining the third ∂A / ∂t component, and is a process corresponding to the calculation of Expression (88). The zero point correction unit 52 calculates the real axis component EdA13x and the imaginary axis component EdA13y of the electromotive force difference EdA13 as in the following equation.
EdA13x = (En10x−En12x) · ω0 / (ω0−ω2) (103)
EdA13y = (En10y−En12y) · ω0 / (ω0−ω2) (104)

Then, the zero point correction unit 52 removes the electromotive force difference EdA13 from the normalized electromotive force En10, and obtains the magnitude of the v × B component EvBn1 (step 110). The process of step 110 is a process corresponding to the calculation of Expression (89). The zero point correction unit 52 calculates the magnitude | EvBn1 | of the v × B component EvBn1 as the following equation.
| EvBn1 | = {(En10x−EdA13x) ²
+ (En10y-EdA13y) ² } ^1/2 (105)

The flow rate output unit 6 calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 111). The process of step 111 is a process corresponding to the calculation of Expression (90).
V = | EvBn1 | / γ (106)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5 and the flow rate output unit 6 perform the processing in steps 101 to 111 as described above at regular intervals until the operator instructs the end of measurement (YES in step 112). Note that the processing in steps 104 to 111 is performed in the fourth excitation state.

  As described above, in this embodiment, when the magnetic field B2 generated from the first excitation coil 3a is set to be equal to the magnetic field B3 generated from the second excitation coil 3b, the inter-electrode electromotive force is set. Focusing on the fact that E1π0 can be approximately extracted as the first ∂A / ∂t component and the inter-electrode electromotive force E1π2 can be approximately extracted as the second ∂A / ∂t component, the first ∂A / Using the ∂t component, the span of the flow velocity V of the v × B component in the interelectrode electromotive force E10 in the first excitation state is normalized, and the second ∂A / ∂t component is used. The span of the v × B component flow velocity V in the interelectrode electromotive force E12 in the third excitation state is normalized, and the electromotive force difference EdA13 (third ∂A / ∂t component) is extracted and normalized electromotive force En10 or Since the v × B component is extracted by removing the third ∂A / ∂t component, and the flow rate of the fluid to be measured is calculated from the v × B component, accurate span correction is automatically performed. The zero point of the output of the electromagnetic flow meter can be corrected without setting the flow rate of the fluid to be measured to zero, and the stability of the zero point can be ensured even in high frequency excitation.

  Further, in the present embodiment, in consideration of the difference in magnetic field loss depending on the frequency, the first ∂A / that is obtained by extracting the v × B component of the electromotive force E10 having the angular frequency ω0 from the electromotive force E1π0 having the same angular frequency ω0. Normalize using the ∂t component, normalize the v × B component of the electromotive force E12 of the angular frequency ω2 using the second ∂A / ∂t component extracted from the electromotive force E1π2 of the same angular frequency ω2, Since zero correction is performed based on the difference between the normalized electromotive forces En10 and En12, accurate span correction and zero correction can be performed even when there is an influence due to the loss of the magnetic field.

In the present embodiment, the electromotive force E10 of the component of the angular frequency ω0 is the target of 0 correction and span correction, but the electromotive force E12 of the component of the angular frequency ω2 may be the target of 0 correction and span correction. In this case, the electromotive force difference EdA13 (third ∂A / ∂t component) is obtained from the normalized electromotive forces En12 and En10 as in the following equation.
EdA13 = (En12-En10) · ω2 / (ω2-ω0) (107)
Then, the v × B component EvBn1 may be obtained by subtracting the electromotive force difference EdA13 from the normalized electromotive force En12 as in the following equation. The other processes are the same as the case where the interelectrode electromotive force E10 is subjected to 0 correction and span correction.
| EvBn1 | = | En12-EdA13 | (108)

[Second Embodiment]
Next, a second embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has two excitation coils and a pair of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. The present embodiment uses the first detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The first extraction method described is used.

Of the magnetic field Bb generated from the first exciting coil 3a, a magnetic field component (magnetic flux density) B6 orthogonal to both the electrode axis EAX and the measuring tube axis PAX on the electrode axis EAX connecting the electrodes 2a and 2b, and the second Of the magnetic field Bc generated from the exciting coil 3b, a magnetic field component (magnetic flux density) B7 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX is given as follows.
B6 = b6 · cos (ω0 · t−θ6) + b6 · cos (ω2 · t−θ6)
... (109)
B7 = b7 · cos (ω0 · t−θ7) + b7 · cos (ω2 · t−θ7)
... (110)

  In equations (109) and (110), ω0 and ω2 are different angular frequencies, b6 is the amplitude of the angular frequency ω0 component and the amplitude of the angular frequency ω2 component of the magnetic flux density B6, and b7 is the angular frequency ω0 of the magnetic flux density B7. And θ6 is the phase difference (phase lag) between the angular frequency ω0 component of the magnetic flux density B6 and ω0 · t, and the phase difference between the angular frequency ω2 component and ω2 · t. , Θ7 are the phase difference between the angular frequency ω0 component of the magnetic flux density B7 and ω0 · t, and the phase difference between the angular frequency ω2 component and ω2 · t. Hereinafter, the magnetic flux density B6 is referred to as a magnetic field B6, and the magnetic flux density B7 is referred to as a magnetic field B7.

  Considering the loss of the magnetic field at each angular frequency, the amplitudes b6 and b7 of the components of the angular frequency ω0 of the magnetic fields B6 and B7 are changed to function notations b6 [ω0] and b7 [ω0], respectively. The phase differences θ6 and θ7 of the component of ω0 are changed to θ6 [ω0] and θ7 [ω0], respectively. Further, the amplitudes b6 and b7 of the components of the angular frequency ω2 of the magnetic fields B6 and B7 are changed to function notations b6 [ω2] and b7 [ω2], respectively. Change to θ6 [ω2] and θ7 [ω2]. Thereby, Formula (109) and Formula (110) are replaced with Formula (111) and Formula (112).

B6 = b6 [ω0] · cos (θ6 [ω0]) · cos (ω0 · t)
+ B6 [ω0] · sin (θ6 [ω0]) · sin (ω0 · t)
+ B6 [ω2] · cos (θ6 [ω2]) · cos (ω2 · t)
+ B6 [ω2] · sin (θ6 [ω2]) · sin (ω2 · t) (111)
B7 = b7 [ω0] · cos (θ7 [ω0]) · cos (ω0 · t)
+ B7 [ω0] · sin (θ7 [ω0]) · sin (ω0 · t)
+ B7 [ω2] · cos (θ7 [ω2]) · cos (ω2 · t)
+ B7 [ω2] · sin (θ7 [ω2]) · sin (ω2 · t) (112)

Since the electromotive force resulting from the change of the magnetic field is based on the time differential dB / dt of the magnetic field, the magnetic field B6 generated from the first excitation coil 3a and the magnetic field B7 generated from the second excitation coil 3b are differentiated as follows: To do.
dB6 / dt = ω0 · cos (ω0 · t) · b6 [ω0] · {sin (θ6 [ω0])}
+ Ω0 · sin (ω0 · t) · b6 [ω0] · {−cos (θ6 [ω0])}
+ Ω2 · cos (ω2 · t) · b6 [ω2] · {sin (θ6 [ω2])}
+ Ω2 · sin (ω2 · t) · b6 [ω2] · {−cos (θ6 [ω2])}
... (113)
dB7 / dt = ω0 · cos (ω0 · t) · b7 [ω0] · {sin (θ7 [ω0])}
+ Ω0 · sin (ω0 · t) · b7 [ω0] · {−cos (θ7 [ω0])}
+ Ω2 · cos (ω2 · t) · b7 [ω2] · {sin (θ7 [ω2])}
+ Ω2 · sin (ω2 · t) · b7 [ω2] · {−cos (θ7 [ω2])}
... (114)

  When the flow rate of the fluid to be measured is 0, it is generated by the change in the electromotive force E1 between the electrodes that is irrelevant to the flow rate and the change in the magnetic field Bc. The inter-electrode electromotive force E2 irrelevant to the flow velocity is opposite to each other as shown in FIG. At this time, the total inter-electrode electromotive force E obtained by adding the inter-electrode electromotive forces E1 and E2 is the difference between the time derivative of the magnetic field dB6 / dt and dB7 / dt (−dB6 / dt + dB7 / dt) is multiplied by a proportional coefficient rk for each angular frequency component of ω0, ω2, and the phase differences θ6, θ7 are replaced by θ6 + θ00, θ7 + θ00, respectively (rk, θ00 are the conductivity and dielectric constant of the fluid to be measured. (Related to the structure of the measuring tube 1 including the arrangement of the electrodes 2a, 2b).

E = rk · ω0 · cos (ω0 · t)
・ {-B6 [ω0] · sin (θ6 [ω0] + θ00)
+ B7 [ω0] · sin (θ7 [ω0] + θ00)}
+ Rk · ω0 · sin (ω0 · t)
・ {B6 [ω0] · cos (θ6 [ω0] + θ00)
-B7 [ω0] · cos (θ7 [ω0] + θ00)}
+ Rk · ω2 · cos (ω2 · t)
・ {−b6 [ω2] · sin (θ6 [ω2] + θ00)
+ B7 [ω2] · sin (θ7 [ω2] + θ00)}
+ Rk · ω2 · sin (ω2 · t)
・ {B6 [ω2] · cos (θ6 [ω2] + θ00)
-B7 [ω2] · cos (θ7 [ω2] + θ00)} (115)

  When the magnitude of the flow velocity of the fluid to be measured is V (V ≠ 0), the interelectrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bb, and the interelectrode electromotive force Ev2 generated by the flow velocity vector v and the magnetic field Bc are shown in FIG. As shown in FIG. At this time, the inter-electrode electromotive force Ev obtained by adding the inter-electrode electromotive forces Ev1 and Ev2 is proportional to the sum of the magnetic field B6 and the magnetic field B7 in the angular frequency component of each of ω0 and ω2. Multiply rkv and replace phase differences θ6 and θ7 with θ6 + θ01 and θ7 + θ01, respectively (rkv and θ01 include the velocity V, the conductivity and dielectric constant of the fluid to be measured, and the arrangement of the electrodes 2a and 2b. (Related to the structure of the measuring tube 1).

Ev = rkv · cos (ω0 · t)
・ {B6 [ω0] · cos (θ6 [ω0] + θ01)
+ B7 [ω0] · cos (θ7 [ω0] + θ01)}
+ Rkv · sin (ω0 · t)
・ {B6 [ω0] · sin (θ6 [ω0] + θ01)
+ B7 [ω0] · sin (θ7 [ω0] + θ01)}
+ Rkv · cos (ω2 · t)
・ {B6 [ω2] · cos (θ6 [ω2] + θ01)
+ B7 [ω2] · cos (θ7 [ω2] + θ01)}
+ Rkv · sin (ω2 · t)
・ {B6 [ω2] · sin (θ6 [ω2] + θ01)
+ B7 [ω2] · sin (θ7 [ω2] + θ01)} (116)

In consideration of the direction of the electromotive force between the electrodes described in FIGS. 2 and 3, the electromotive force obtained by converting the interelectrode electromotive force due to the time change of the magnetic field into a complex vector and the interelectrode electromotive force due to the flow velocity of the fluid to be measured. The electromotive force E20c of the component of the angular frequency ω0 out of the total electromotive force combined with the electromotive force obtained by converting into a complex vector is the first term and the second term of Equation (115) and Equation (116). From the first term and the second term and the equation (17), it is expressed by the following equation.
E20c = rk · ω0 · b6 [ω0] · exp {j · (π / 2 + θ6 [ω0] + θ00)}
+ Γ · rk · V · b6 [ω0] · exp {j · (θ6 [ω0] + θ01)}
+ Rk · ω0 · b7 [ω0]
Exp {j · (−π / 2 + θ7 [ω0] + θ00)}
+ Γ · rk · V · b7 [ω0] · exp {j · (θ7 [ω0] + θ01)}
... (117)

In addition, the inter-electrode electromotive force obtained by converting the inter-electrode electromotive force caused by the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force caused by the flow velocity of the fluid to be measured into the complex vector Among the electromotive forces, the electromotive force E22c of the component of the angular frequency ω2 is expressed by the following equation from the third and fourth terms of Equation (115), the third and fourth terms of Equation (116), and Equation (17). It is represented by
E22c = rk · ω2 · b6 [ω2] · exp {j · (π / 2 + θ6 [ω2] + θ00)}
+ Γ · rk · V · b6 [ω2] · exp {j · (θ6 [ω2] + θ01)}
+ Rk · ω2 · b7 [ω2]
• exp {j · (−π / 2 + θ7 [ω2] + θ00)}
+ Γ · rk · V · b7 [ω2] · exp {j · (θ7 [ω2] + θ01)}
... (118)

Here, the relationship between the phase delay θ6 [ω0] of the component of the angular frequency ω0 of the magnetic field B6 and the phase delay θ7 [ω0] of the component of the angular frequency ω0 of the magnetic field B7 is θ7 [ω0] = θ6 [ω0] + Δθ7 [ω0. And the relationship between the angle θ00 of the ∂A / ∂t component with respect to the imaginary axis and the angle θ01 of the v × B component with respect to the real axis is θ01 = θ00 + Δθ01, and is defined as the first excitation state. When the interelectrode electromotive force E20c in the state is E20, the interelectrode electromotive force E20 is expressed by the following equation.
E20 = rk · exp {j · (θ6 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B6 [ω0] −b7 [ω0] · exp (j · Δθ7 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B6 [ω0] + b7 [ω0] · exp (j · Δθ7 [ω0])}]
... (119)

Further, when the interelectrode electromotive force E22c in the first excitation state is E22, the interelectrode electromotive force E22 is expressed by the following equation.
E22 = rk · exp {j · (θ6 [ω2] + θ00)}
・ [Ω2 ・ exp (j ・ π / 2)
{B6 [ω2] −b7 [ω2] · exp (j · Δθ7 [ω2])}
+ Γ · V · exp (j · Δθ01)
{B6 [ω2] + b7 [ω2] · exp (j · Δθ7 [ω2])}]
... (120)

In addition, a state in which the phase difference between the magnetic field B6 and the magnetic field B7 changes from the first excitation state by a constant value π (θ7 [ω0] = π + θ6 [ω0] + Δθ7 [ω0]) and θ01 = θ00 + Δθ01 is the second state. When the interelectrode electromotive force E20c in the second excitation state is E2π0, the interelectrode electromotive force E2π0 is expressed by the following equation.
E2π0 = rk · exp {j · (θ6 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B6 [ω0] + b7 [ω0] · exp (j · Δθ7 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B6 [ω0] −b7 [ω0] · exp (j · Δθ7 [ω0])}]
... (121)

When the interelectrode electromotive force E22c in the second excitation state is E2π2, the interelectrode electromotive force E2π2 is expressed by the following equation.
E2π2 = rk · exp {j · (θ6 [ω2] + θ00)}
・ [Ω2 ・ exp (j ・ π / 2)
{B6 [ω2] + b7 [ω2] · exp (j · Δθ7 [ω2])}
+ Γ · V · exp (j · Δθ01)
{B6 [ω2] −b7 [ω2] · exp (j · Δθ7 [ω2])}]
... (122)

Here, in the magnetic fields B6 and B7 in the initial state (the state at the time of calibration), if b6 [ω0] = b7 [ω0] and Δθ7 [ω0] = 0 are set, even if the subsequent deviation is taken into consideration. b6 [ω0] ≈b7 [ω0] and Δθ7 [ω0] ≈0, and the following conditional expression holds.
| B6 [ω0] + b7 [ω0] · exp (j · Δθ7 [ω0]) |
>> | b6 [ω0] −b7 [ω0] · exp (j · Δθ7 [ω0]) | (123)

In addition, since ω0> γ · V is normally satisfied, the condition of the following expression is satisfied in Expression (121) in consideration of the condition of Expression (123).
| Ω0 · exp (j · π / 2)
{B6 [ω0] + b7 [ω0] · exp (j · Δθ7 [ω0])} |
»| Γ · V · exp (j · Δθ01) · b6 [ω0]
−b7 [ω0] · exp (j · Δθ7 [ω0]) | (124)

The electromotive force EdA21 that approximates the interelectrode electromotive force E2π0 of the equation (121) using the condition of the equation (124) is expressed by the following equation. This electromotive force EdA21 corresponds to the first ∂A / ∂t component in the basic principle.
EdA21≈E2π0 (125)
EdA21 = rk · exp {j · (θ6 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B6 [ω0] + b7 [ω0] · exp (j · Δθ7 [ω0])}
... (126)

Since the electromotive force EdA21 is not related to the magnitude V of the flow velocity, it becomes only a component generated by ∂A / ∂t. Using this electromotive force EdA21, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the interelectrode electromotive force E20 (combined vector Vas0 + Vbs0) is normalized. If the inter-electrode electromotive force E20 is normalized by the electromotive force EdA21 and multiplied by ω0 is En20, the normalized electromotive force En20 is expressed by the following equation.
En20 = (E20 / EdA21) · ω0
= Rk · exp {j · (θ6 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B6 [ω0] −b7 [ω0] · exp (j · Δθ7 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B6 [ω0] + b7 [ω0] · exp (j · Δθ7 [ω0])}]
/ [Rk · exp {j · (θ6 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B6 [ω0] + b7 [ω0] · exp (j · Δθ7 [ω0])}] · ω0
= Ω0 · {b6 [ω0] −b7 [ω0] · exp (j · Δθ7 [ω0])}
/ {B6 [ω0] + b7 [ω0] · exp (j · Δθ7 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (127)

Using Expression (52), the coefficient {b6 [ω0] −b7 [ω0] · exp (j · Δθ7 [ω0])} / {b6 [ω0] applied to the angular frequency ω0 of the first term on the right side of Expression (127). ] + B7 [ω0] · exp (j · Δθ7 [ω0])} is represented by a value {b6-b7 · exp (j · Δθ7)} / {b6 + b7 · exp (j · Δθ7)} not related to the angular frequency ω0. be able to. Therefore, the equation (127) can be replaced by the following equation.
En20 = ω0 · {b6-b7 · exp (j · Δθ7)}
/ {B6 + b7 · exp (j · Δθ7)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (128)

  The second term on the right side of Equation (128) is a term obtained by normalizing the component generated by v × B. The reason why the result obtained by normalizing the inter-electrode electromotive force E20 with the electromotive force EdA21 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side of the magnitude V of the flow velocity. According to the equation (128), the complex coefficient related to the magnitude V of the flow velocity has an angle from the real axis of the magnitude of γ, −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (128) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the ∂A / ∂t component, it is possible to realize span correction that automatically corrects an error due to a magnetic field shift or phase change.

Next, a method for removing the first term on the right side of the equation (128), which is a variation factor of 0 point, will be described. Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. In the equation (124), even if the angular frequency ω0 is replaced with ω2, the same approximation is established. Therefore, the electromotive force EdA22 that approximates the interelectrode electromotive force E2π2 in the equation (122) is expressed by the following equation. This electromotive force EdA22 corresponds to the second ∂A / ∂t component in the basic principle.
EdA22≈E2π2 (129)
EdA22 = rk · exp {j · (θ6 [ω2] + θ00)}
・ Ω2 ・ exp (j ・ π / 2)
{B6 [ω2] + b7 [ω2] · exp (j · Δθ7 [ω2])}
... (130)

When the inter-electrode electromotive force E22 in the equation (120) is normalized by the electromotive force EdA22 in the equation (130) and multiplied by ω2, the result is expressed as En22, from the equation (128). .
En22 = ω2 · {b6-b7 · exp (j · Δθ7)}
/ {B6 + b7 · exp (j · Δθ7)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (131)

Taking the difference between the normalized electromotive forces En20 and En22 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA23, the electromotive force difference EdA23 is expressed by the following equation. This electromotive force difference EdA23 corresponds to the third ∂A / ∂t component in the basic principle.
EdA23 = (En20−En22) · ω0 / (ω0−ω2)
= [{B6-b7 · exp (j · Δθ7)}
/ {B6 + b7 · exp (j · Δθ7)}
.Omega.0 + .gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V
-{B6-b7 · exp (j · Δθ7)}
/ {B6 + b7 · exp (j · Δθ7)}
.Omega.2-.gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V]
・ Ω0 / (ω0−ω2)
= {B6-b7 · exp (j · Δθ7)} / {b6 + b7 · exp (j · Δθ7)}
・ Ω0 (132)

The electromotive force difference EdA23 represents the normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (128). Therefore, if this normalized electromotive force difference EdA23 is used, the normalized v × The B component can be extracted from the normalized electromotive force En20. When the v × B component obtained by subtracting the normalized electromotive force difference EdA23 of equation (132) from the normalized electromotive force En20 of equation (128) is EvBn2, the v × B component EvBn2 is expressed by the following equation: .
EvBn2 = En20-EdA23
= {B6-b7 · exp (j · Δθ7)} / {b6 + b7 · exp (j · Δθ7)}
・ Ω0
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
-{B6-b7 · exp (j · Δθ7)} / {b6 + b7 · exp (j · Δθ7)}
・ Ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (133)

The v × B component EvBn2 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvBn2 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBn2. At this time, the magnitude and direction of the coefficient relating to the magnitude V of the flow velocity are represented by a complex vector [γ · rk · exp {j · (−π / 2 + Δθ01)}]. From the equation (133), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn2 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn2 | / γ (134)

  The correspondence relationship between the constants and variables used in the basic principle and the constants and variables of the present embodiment is as shown in Table 2 below. As is apparent from Table 2, this embodiment is one example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. Since the configuration of the electromagnetic flowmeter of the present embodiment is the same as that of the first embodiment, description will be made using the reference numerals in FIG. The electromagnetic flowmeter of the present embodiment includes a measuring tube 1, electrodes 2a and 2b, first and second exciting coils 3a and 3b, a power supply unit 4, a signal conversion unit 5, and a flow rate output unit 6. Have

  The signal converter 5 obtains the amplitude and phase of the combined electromotive force detected by the electrodes 2a and 2b in each of the first excitation state and the second excitation state, and performs the second excitation based on these amplitudes and phases. The component of the angular frequency ω0 of the combined electromotive force in the state is extracted as the first ∂A / ∂t component, and the component of the angular frequency ω2 of the combined electromotive force in the second excitation state is extracted as the second ∂A / ∂t. The component of the first excitation target electromotive force based on the first ∂A / ∂t component is extracted as a component, and the component of the angular frequency ω0 of the composite electromotive force in the first excitation state is used as the first correction target electromotive force. In addition, the variation factor of the span included in the v × B component is removed, and the component of the angular frequency ω2 of the composite electromotive force in the first excitation state is used as the second correction target electromotive force, so that the second ∂A / ∂ The variation factor of the span included in the v × B component in the second correction target electromotive force based on the t component The span correction unit 51 to be removed, and the difference between the first correction target electromotive force subjected to span correction and the second correction target electromotive force subjected to span correction are extracted as a third ∂A / ∂t component, and this span is extracted. The zero point correction unit 52 extracts a v × B component by removing the third ∂A / ∂t component from any one of the two corrected electromotive forces that have been corrected.

  The power supply unit 4 according to the present embodiment simultaneously supplies a first excitation current including a sine wave component having a first angular frequency ω0 and a sine wave component having a second angular frequency ω2 to the first excitation coil 3a. The second excitation current having a phase difference of Δθ7 from the first excitation current and including the sine wave component of the first angular frequency ω0 and the sine wave component of the second angular frequency ω2 is converted into the second excitation coil 3b. The first excitation state to be supplied to is continued for T1 seconds, and the second excitation state in which the phase difference between the first excitation current and the second excitation current is changed to Δθ7 + π with respect to the first excitation state is T2. Repeat for 2 seconds in a cycle of T seconds. That is, T = T1 + T2.

  FIG. 18 is a flowchart showing the operations of the signal conversion unit 5 and the flow rate output unit 6 of the present embodiment. First, the span correction unit 51 of the signal conversion unit 5 obtains the amplitude r20 of the electromotive force E20 of the component of the angular frequency ω0 among the electromotive forces between the electrodes 2a and 2b in the first excitation state, and the real axis and the electrode A phase difference φ20 with respect to the inter-electromotive force E20 is obtained by a phase detector (not shown). Further, in the first excitation state, the span correction unit 51 obtains the amplitude r22 of the electromotive force E22 of the component of the angular frequency ω2 among the electromotive forces between the electrodes 2a and 2b, and the actual axis and the interelectrode electromotive force E22 Is obtained by a phase detector (step 201 in FIG. 18).

  Subsequently, in the second excitation state, the span correction unit 51 obtains the amplitude r2π0 of the electromotive force E2π0 of the component of the angular frequency ω0 among the electromotive forces between the electrodes 2a and 2b, and the electromotive force E2π0 between the real axis and the electrode. Is obtained by a phase detector. Further, in the second excitation state, the span correction unit 51 obtains the amplitude r2π2 of the electromotive force E2π2 of the component of the angular frequency ω2 among the electromotive forces between the electrodes 2a and 2b, and the real axis and the interelectrode electromotive force E2π2 Is obtained by a phase detector (step 202). The inter-electrode electromotive forces E20, E22, E2π0, E2π2 can be frequency-separated by a bandpass filter or a comb filter.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force EdA21 that approximates the interelectrode electromotive force E2π0 (step 203). The processing of step 203 is processing corresponding to obtaining the first ∂A / ∂t component, and is processing corresponding to the calculation of Expression (126). The span correction unit 51 calculates the magnitude | EdA21 | of the electromotive force EdA21 as the following equation.
| EdA21 | = r2π0 (135)
Then, the span correction unit 51 calculates the angle ∠EdA21 of the electromotive force EdA21 as the following equation.
∠EdA21 = φ2π0 (136)
This completes the process of step 203.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force En20 obtained by normalizing the interelectrode electromotive force E20 with the electromotive force EdA21 (step 204). The process of step 204 is a process corresponding to the calculation of equation (128). The span correction unit 51 calculates the magnitude | En20 | of the normalized electromotive force En20 as the following equation.
| En20 | = (r20 / | EdA21 |) · ω0 (137)

Then, the span correction unit 51 calculates the angle ∠En20 of the normalized electromotive force En20 as the following expression.
∠En20 = φ20−∠EdA21 (138)
Further, the span correction unit 51 calculates the real axis component En20x and the imaginary axis component En20y of the normalized electromotive force En20 as the following expression.
En20x = | En20 | .cos (∠En20) (139)
En20y = | En20 | .sin (∠En20) (140)
This completes the process of step 204.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force EdA22 that approximates the interelectrode electromotive force E2π2 (step 205). The process of step 205 is a process corresponding to obtaining the second ∂A / ∂t component, and is a process corresponding to the calculation of Expression (130). The span correction unit 51 calculates the magnitude | EdA22 | of the electromotive force EdA22 as the following equation.
| EdA22 | = r2π2 (141)
Then, the span correction unit 51 calculates the angle ∠EdA22 of the electromotive force EdA22 as the following equation.
∠EdA22 = φ2π2 (142)
This completes the process of step 205.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force En22 obtained by normalizing the inter-electrode electromotive force E22 with the electromotive force EdA22 (step 206). The process of step 206 is a process corresponding to the calculation of equation (131). The span correction unit 51 calculates the magnitude | En22 | of the normalized electromotive force En22 as the following expression.
| En22 | = (r22 / | EdA22 |) · ω2 (143)

Then, the span correction unit 51 calculates the angle ∠En22 of the normalized electromotive force En22 as the following expression.
∠En22 = φ22−∠EdA22 (144)
Further, the span correction unit 51 calculates the real axis component En22x and the imaginary axis component En22y of the normalized electromotive force En22 as the following expression.
En22x = | En22 | .cos (∠En22) (145)
En22y = | En22 | .sin (∠En22) (146)
This completes the process of step 206.

Next, the zero point correction unit 52 of the signal conversion unit 5 obtains the magnitude of the electromotive force difference EdA23 between the normalized electromotive forces En20 and En22 (step 207). The process of step 207 is a process corresponding to obtaining the third ∂A / ∂t component, and is a process corresponding to the calculation of Expression (132). The zero point correction unit 52 calculates the real axis component EdA23x and the imaginary axis component EdA23y of the electromotive force difference EdA23 as follows.
EdA23x = (En20x−En22x) · ω0 / (ω0−ω2) (147)
EdA23y = (En20y−En22y) · ω0 / (ω0−ω2) (148)

Then, the zero point correction unit 52 removes the electromotive force difference EdA23 from the normalized electromotive force En20, and obtains the magnitude of the v × B component EvBn2 (step 208). The process of step 208 is a process corresponding to the calculation of Expression (133). The zero point correction unit 52 calculates the magnitude | EvBn2 | of the v × B component EvBn2 as follows.
| EvBn2 | = {(En20x−EdA23x) ²
+ (En20y−EdA23y) ² } ^1/2 (149)

The flow rate output unit 6 calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 209). The process of step 209 is a process corresponding to the calculation of equation (134).
V = | EvBn2 | / γ (150)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5 and the flow rate output unit 6 perform the processing in steps 201 to 209 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 210). Note that the processing in steps 202 to 209 is performed in the second excitation state.

  As described above, in the present embodiment, the magnetic field B6 including two components having different frequencies is applied from the first exciting coil 3a to the fluid to be measured, and at the same time, the phase difference from the magnetic field B6 is Δθ7 and the frequencies are different. In the first excitation state in which the magnetic field B7 including two components is applied from the second excitation coil 3b to the fluid to be measured, the electromotive force E20 having the angular frequency ω0 and the electromotive force E22 having the angular frequency ω2 are obtained. In the second excitation state in which the phase difference between the magnetic field B6 and the magnetic field B7 is changed from the first excitation state by a constant value π, the electromotive force E2π0 of the component of the angular frequency ω0 and the electromotive force E2π2 of the component of the angular frequency ω2 And ask. In this embodiment, if the magnetic field B6 and the magnetic field B7 are set to be equal, the interelectrode electromotive force E2π0 can be approximately extracted as the first ∂A / ∂t component, and between the electrodes Focusing on the fact that the electromotive force E2π2 can be approximately extracted as the second ∂A / ∂t component, the flow velocity of the v × B component in the inter-electrode electromotive force E20 using the first ∂A / ∂t component is large. Normalizing the span for V, and normalizing the span for the magnitude V of the flow velocity of the v × B component in the inter-electrode electromotive force E22 using the second ∂A / ∂t component. The electromotive force difference EdA23 (third ∂A / ∂t component) is extracted from the electric powers En20 and En22, and the third ∂A / ∂t component is removed from the normalized electromotive force En20 to obtain the v × B component. Extracted and calculated the flow rate of the fluid to be measured from this v × B component Therefore, accurate span correction can be automatically performed, and the zero point of the output of the electromagnetic flowmeter can be corrected without setting the flow rate of the fluid to be measured to zero, and the zero point is stable even in high frequency excitation. Sex can be secured.

Further, in the present embodiment, in consideration of the difference in magnetic field loss depending on the frequency, the first ∂A / that is obtained by extracting the v × B component of the electromotive force E20 having the angular frequency ω0 from the electromotive force E2π0 having the same angular frequency ω0. Normalize using the ∂t component, normalize the v × B component of the electromotive force E22 of the angular frequency ω2 using the second ∂A / ∂t component extracted from the electromotive force E2π2 of the same angular frequency ω2, Since zero correction is performed based on the difference between the normalized electromotive forces En20 and En22, accurate span correction and zero correction can be performed even when there is an influence due to the loss of the magnetic field.
Further, in the present embodiment, it is not necessary to switch the excitation frequency as in the first embodiment, so that the flow rate can be calculated at a higher speed.

  In the present embodiment, an example in which excitation is performed with two types of frequency components has been shown. However, if excitation is performed with three or more types of frequency components, the accuracy of zero correction can be further improved. As an example of excitation with three or more types of frequency components, modulation can be used. If a carrier wave having an angular frequency ω0 is excited by a modulated wave having an angular frequency ω1, an electromotive force having components of angular frequencies ω0 and ω0 ± ω1 can be obtained in the case of amplitude modulation, and an angular frequency in the case of phase modulation or frequency modulation. The electromotive force of the component of ω0, ω0 ± ζ · ω1 (ζ is a positive integer) can be obtained. Also in this case, it is possible to perform span correction and zero correction by performing excitation while switching the phase difference between the magnetic field generated from the first excitation coil 3a and the magnetic field generated from the second excitation coil 3b. Examples using this modulation are shown in the fourth to seventh embodiments.

Further, in the present embodiment, the electromotive force E20 of the component of the angular frequency ω0 is the target of 0 correction and span correction, but the electromotive force E22 of the component of the angular frequency ω2 may be the target of 0 correction and span correction. In this case, the electromotive force difference EdA23 (third ∂A / ∂t component) is obtained from the normalized electromotive forces En22 and En20 as in the following equation.
EdA23 = (En22-En20) · ω2 / (ω2-ω0) (151)
Then, the v × B component EvBn2 may be obtained by subtracting the electromotive force difference EdA23 from the normalized electromotive force En22 as in the following equation. The other processing is the same as the case where the interelectrode electromotive force E20 is subjected to 0 correction and span correction.
| EvBn2 | = | En22−EdA23 | (152)

[Third Embodiment]
Next, a third embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has two excitation coils and a pair of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. The present embodiment uses the second detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The second extraction method described is used. First, the second extraction method will be described first.

FIG. 19 is a diagram representing the process of extracting the vector Vas0R of the first ∂A / ∂t component as a complex vector. Of the inter-electrode electromotive forces detected by the electrodes 2a and 2b when an excitation current including angular frequency (ω0 + Δω) and (ω0−Δω) components is supplied to both the excitation coils 3a and 3b, the angular frequency (ω0 + Δω) Is equivalent to a combined vector VaspR + VbspR of a vector VaspR of the following ∂A / 成分 t component and a vector VbspR of the v × B component.
VaspR = ra · exp (j · θa)
(B1c [ω0 + Δω] + B2c [ω0 + Δω]) C (ω0 + Δω)
... (153)
VbspR = rb · exp (j · θb)
(B1c [ω0 + Δω] −B2c [ω0 + Δω]) CV
... (154)

Of the inter-electrode electromotive forces detected by the electrodes 2a and 2b when an excitation current including angular frequency (ω0 + Δω) and (ω0−Δω) components is supplied to both the excitation coils 3a and 3b, the angular frequency ( The electromotive force of the component of (ω0−Δω) corresponds to a combined vector VasmR + VbsmR of the following vector VasmR of ∂A / ∂t component and vector VbsmR of v × B component.
VasmR = ra · exp (j · θa)
(B1c [ω0−Δω] + B2c [ω0−Δω]) C / (ω0−Δω)
... (155)
VbsmR = rb · exp (j · θb)
(B1c [ω0−Δω] −B2c [ω0−Δω]) CV
... (156)

From the combined vector at the angular frequency (ω0 + Δω) and the combined vector at the angular frequency (ω0−Δω), a vector Vas0R of the first ∂A / ∂t component equivalent to that when excited at the angular frequency ω0 is approximated as follows: Can be extracted.
Vas0R≈ {(VaspR + VbspR) + (VasmR + VbsmR)} / 2
... (157)

  Thus, it is possible to approximately extract the first ∂A / ∂t component vector Vas0R from the combined vector when excited at the angular frequency (ω0 ± Δω), and efficiently use the frequency band. be able to. Here, the reason why the vector Vas0R of the first ∂A / ∂t component can be approximately obtained as in Expression (157) will be described.

Using the relational expressions (42) to (45), the vector VaspR of ∂A / ∂t component at the angular frequency (ω0 + Δω) and the vector of ∂A / ∂t component at the angular frequency (ω0-Δω). A vector obtained by combining VasmR can be transformed as follows.
VaspR + VasmR
= Ra · exp (j · θa) · C
・ {(Ω0 + Δω) ・ (B1c [ω0 + Δω] + B2c [ω0 + Δω])
+ (Ω0−Δω) · (B1c [ω0−Δω] + B2c [ω0−Δω])}
= Ra · exp (j · θa) · C
・ {Ω0 ・ (B1c [ω0 + Δω] + B1c [ω0−Δω])
+ Ω0 · (B2c [ω0 + Δω] + B2c [ω0−Δω])
+ Δω · (B1c [ω0 + Δω] −B1c [ω0−Δω])
+ Δω · (B2c [ω0 + Δω] −B2c [ω0−Δω])}
= Ra · exp (j · θa) · C
・ {2 ・ ω0 ・ B1c [ω0] +2 ・ ω0 ・ B2c [ω0]
+ Δω · (−2 · B1c · Δω · ec) + Δω · (−2 · B2c · Δω · ec)} = 2 · ra · exp (j · θa) · C
・ {Ω0 ・ (B1c [ω0] + B2c [ω0])
− (Δω · Δω) · (B1c + B2c) · ec} (158)

Similarly, if the relational expressions (42) to (45) are used, the v × B component vector VbspR at the angular frequency (ω0 + Δω) and the v × B component vector VbsmR at the angular frequency (ω0−Δω) are obtained. The combined vector can be transformed as follows.
VbspR + VbsmR
= Rb · exp (j · θb) · C · V
(B1c [ω0 + Δω] −B2c [ω0 + Δω]
+ B1c [ω0−Δω] −B2c [ω0−Δω])
= Rb · exp (j · θb) · C · V
・ {(B1c [ω0 + Δω] + B1c [ω0−Δω])
− (B2c [ω0 + Δω] + B2c [ω0−Δω])}
= 2 · rb · exp (j · θb) · C · V · (B1c [ω0] −B2c [ω0])
... (159)

The combined vector of ∂A / ∂t component and v × B component at the angular frequency (ω0 + Δω) and the combined vector of ∂A / ∂t component and v × B component at the angular frequency (ω0−Δω) is Is expressed by the following equation.
VaspR + VasmR + VbspR + VbsmR
= 2 · ra · exp (j · θa) · C · ω0 · (B1c [ω0] + B2c [ω0])
-2 · ra · exp (j · θa) · C · (Δω · Δω) · (B1c + B2c) · ec}
+ 2 · rb · exp (j · θb) · C · V · (B1c [ω0] −B2c [ω0])
... (160)

The second term and the third term on the right side can be ignored with respect to the first term on the right side of the equation (160), and can be approximated as the following equation using the equation (33).
VaspR + VasmR + VbspR + VbsmR
≒ 2 ・ ra ・ exp (j ・ θa) ・ C ・ ω0 ・ (B1c [ω0] + B2c [ω0])
= 2 · Vas0R (161)
Thus, the equation (157) can be derived from the equation (161).

In the present embodiment, among the magnetic field Bb generated from the first exciting coil 3a, a magnetic field component (magnetic flux density) orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX connecting the electrodes 2a and 2b. ) Of the magnetic field Bc generated from B8 and the second exciting coil 3b, the magnetic field component (magnetic flux density) B9 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX is given as follows: Shall be.
B8 = b8 · cos (ωp · t−θ8) + b8 · cos (ωm · t−θ8)
... (162)
B9 = b9 · cos (ωp · t−θ9) + b9 · cos (ωm · t−θ9)
... (163)

  In the equations (162) and (163), ωp and ωm are different angular frequencies, b8 is the amplitude of the angular frequency ωp component and the amplitude of the angular frequency ωm component of the magnetic flux density B8, and b9 is the angular frequency ωp of the magnetic flux density B9. And θ8 is the phase difference (phase lag) between the angular frequency ωp component of magnetic flux density B8 and ωp · t, and the phase difference between the angular frequency ωm component and ωm · t. , Θ9 is a phase difference between the angular frequency ωp component of the magnetic flux density B9 and ωp · t, and a phase difference between the angular frequency ωm component and ωm · t. Hereinafter, the magnetic flux density B8 is referred to as a magnetic field B8, and the magnetic flux density B9 is referred to as a magnetic field B9.

  In consideration of the loss of the magnetic field at each angular frequency, the amplitudes b8 and b9 of the components of the angular frequency ωp of the magnetic fields B8 and B9 are changed to b8 [ωp] and b9 [ωp], respectively, and the angular frequency is similarly changed. The phase differences θ8 and θ9 of the components of ωp are changed to θ8 [ωp] and θ9 [ωp], respectively. Further, the amplitudes b8 and b9 of the components of the angular frequency ωm of the magnetic fields B8 and B9 are changed to function notations b8 [ωm] and b9 [ωm], respectively, and similarly the phase differences θ8 and θ9 of the components of the angular frequency ωm are respectively set. Change to θ8 [ωm] and θ9 [ωm]. Thereby, Formula (162) and Formula (163) are replaced with Formula (164) and Formula (165).

B8 = b8 [ωp] · cos (θ8 [ωp]) · cos (ωp · t)
+ B8 [ωp] · sin (θ8 [ωp]) · sin (ωp · t)
+ B8 [ωm] · cos (θ8 [ωm]) · cos (ωm · t)
+ B8 [ωm] · sin (θ8 [ωm]) · sin (ωm · t) (164)
B9 = b9 [ωp] · cos (θ9 [ωp]) · cos (ωp · t)
+ B9 [ωp] · sin (θ9 [ωp]) · sin (ωp · t)
+ B9 [ωm] · cos (θ9 [ωm]) · cos (ωm · t)
+ B9 [ωm] · sin (θ9 [ωm]) · sin (ωm · t) (165)

Since the electromotive force resulting from the change in the magnetic field is based on the time differential dB / dt of the magnetic field, the magnetic field B8 generated from the first excitation coil 3a and the magnetic field B9 generated from the second excitation coil 3b are differentiated as follows: To do.
dB8 / dt = ωp · cos (ωp · t) · b8 [ωp] · {sin (θ8 [ωp])}
+ Ωp · sin (ωp · t) · b8 [ωp] · {−cos (θ8 [ωp])}
+ Ωm · cos (ωm · t) · b8 [ωm] · {sin (θ8 [ωm])}
+ Ωm · sin (ωm · t) · b8 [ωm] · {−cos (θ8 [ωm])}
... (166)
dB9 / dt = ωp · cos (ωp · t) · b9 [ωp] · {sin (θ9 [ωp])}
+ Ωp · sin (ωp · t) · b9 [ωp] · {−cos (θ9 [ωp])}
+ Ωm · cos (ωm · t) · b9 [ωm] · {sin (θ9 [ωm])}
+ Ωm · sin (ωm · t) · b9 [ωm] · {−cos (θ9 [ωm])}
... (167)

  When the flow rate of the fluid to be measured is 0, it is generated by the change in the electromotive force E1 between the electrodes that is irrelevant to the flow rate and the change in the magnetic field Bc. The inter-electrode electromotive force E2 irrelevant to the flow velocity is opposite to each other as shown in FIG. At this time, the total inter-electrode electromotive force E obtained by adding the inter-electrode electromotive forces E1 and E2 is the difference between the time derivative of the magnetic field dB8 / dt and dB9 / dt (−dB8 / dt + dB9 / dt) is multiplied by a proportional coefficient rk for each angular frequency component of ωp, ωm, and the phase differences θ8, θ9 are replaced by θ8 + θ00, θ9 + θ00, respectively (rk, θ00 are the conductivity and dielectric constant of the fluid to be measured. (Related to the structure of the measuring tube 1 including the arrangement of the electrodes 2a, 2b).

E = rk · ωp · cos (ωp · t)
{-B8 [ωp] · sin (θ8 [ωp] + θ00)
+ B9 [ωp] · sin (θ9 [ωp] + θ00)}
+ Rk · ωp · sin (ωp · t)
・ {B8 [ωp] · cos (θ8 [ωp] + θ00)
−b9 [ωp] · cos (θ9 [ωp] + θ00)}
+ Rk · ωm · cos (ωm · t)
・ {-B8 [ωm] · sin (θ8 [ωm] + θ00)
+ B9 [ωm] · sin (θ9 [ωm] + θ00)}
+ Rk · ωm · sin (ωm · t)
・ {B8 [ωm] · cos (θ8 [ωm] + θ00)
−b9 [ωm] · cos (θ9 [ωm] + θ00)} (168)

  When the magnitude of the flow velocity of the fluid to be measured is V (V ≠ 0), the interelectrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bb, and the interelectrode electromotive force Ev2 generated by the flow velocity vector v and the magnetic field Bc are shown in FIG. As shown in FIG. At this time, the total inter-electrode electromotive force Ev obtained by adding the inter-electrode electromotive forces Ev1 and Ev2 to the sum of the magnetic field B8 and the magnetic field B9 is proportional to the proportional coefficient rkv in each frequency component of ωp and ωm. The phase differences θ8 and θ9 are replaced with θ8 + θ01 and θ9 + θ01, respectively (rkv and θ01 are measurements including the magnitude V of the flow velocity, the conductivity and dielectric constant of the fluid to be measured, and the arrangement of the electrodes 2a and 2b. Related to the structure of the tube 1).

Ev = rkv · cos (ωp · t)
・ {B8 [ωp] · cos (θ8 [ωp] + θ01)
+ B9 [ωp] · cos (θ9 [ωp] + θ01)}
+ Rkv · sin (ωp · t)
・ {B8 [ωp] · sin (θ8 [ωp] + θ01)
+ B9 [ωp] · sin (θ9 [ωp] + θ01)}
+ Rkv · cos (ωm · t)
・ {B8 [ωm] · cos (θ8 [ωm] + θ01)
+ B9 [ωm] · cos (θ9 [ωm] + θ01)}
+ Rkv · sin (ωm · t)
・ {B8 [ωm] · sin (θ8 [ωm] + θ01)
+ B9 [ωm] · sin (θ9 [ωm] + θ01)} (169)

In consideration of the direction of the electromotive force between the electrodes described in FIGS. 2 and 3, the electromotive force obtained by converting the interelectrode electromotive force due to the time change of the magnetic field into a complex vector and the interelectrode electromotive force due to the flow velocity of the fluid to be measured. Of the total inter-electrode electromotive force combined with the electromotive force converted into a complex vector, the electromotive force E3pc of the component of the angular frequency ωp is expressed by the first term and the second term in the equation (168) and the equation (169). From the first term and the second term and the equation (17), it is expressed by the following equation.
E3pc = rk · ωp · b8 [ωp] · exp {j · (π / 2 + θ8 [ωp] + θ00)}
+ Γ · rk · V · b8 [ωp] · exp {j · (θ8 [ωp] + θ01)}
+ Rk · ωp · b9 [ωp]
Exp {j. (− Π / 2 + θ9 [ωp] + θ00)}
+ Γ · rk · V · b9 [ωp] · exp {j · (θ9 [ωp] + θ01)}
... (170)

In addition, the inter-electrode electromotive force obtained by converting the inter-electrode electromotive force caused by the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force caused by the flow velocity of the fluid to be measured into the complex vector Among the electromotive forces, the electromotive force E3mc of the component of the angular frequency ωm is expressed by the following equation from the third and fourth terms of the equation (168), the third and fourth terms of the equation (169), and the equation (17). It is represented by
E3mc = rk · ωm · b8 [ωm] · exp {j · (π / 2 + θ8 [ωm] + θ00)}
+ Γ · rk · V · b8 [ωm] · exp {j · (θ8 [ωm] + θ01)}
+ Rk · ωm · b9 [ωm]
• exp {j · (−π / 2 + θ9 [ωm] + θ00)}
+ Γ · rk · V · b9 [ωm] · exp {j · (θ9 [ωm] + θ01)}
... (171)

Here, ωp = ω0 + Δω and ωm = ω0−Δω are defined, and further, the phase lag θ8 [ω0] of the component of the angular frequency ω0 of the magnetic field B8 and the phase lag θ9 [ω0] of the component of the angular frequency ω0 of the magnetic field B9. The relationship is θ9 [ω0] = θ8 [ω0] + Δθ9 [ω0], and the relationship between the angle θ00 of the ∂A / ∂t component with respect to the imaginary axis and the angle θ01 of the v × B component with respect to the real axis is θ01 = θ00 + Δθ01. If the state is the first excitation state and the electromotive force E3pc of the component of the angular frequency ωp in the interelectrode electromotive force in the first excitation state is E3p0, the interelectrode electromotive force E3p0 is expressed by the following equation.
E3p0 = rk · exp (j · θ00))
・ [(Ω0 + Δω) · exp (j · π / 2)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
-B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])}
+ Γ · V · exp (j · Δθ01)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
+ B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])}]
... (172)

Further, when the electromotive force E3mc of the component having the angular frequency ωm in the electromotive force between the electrodes in the first excitation state is E3m0, the interelectrode electromotive force E3m0 is expressed by the following equation. However, θ9 [ω0] = θ8 [ω0] + Δθ9 [ω0] is not applied in the equations (172) and (173), and is applied in the later equations.
E3m0 = rk · exp (j · θ00)
・ [(Ω0−Δω) exp (j · π / 2)
{B8 [ω0-Δω] exp (j · θ8 [ω0-Δω])
−b9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}
+ Γ · V · exp (j · Δθ01)
{B8 [ω0-Δω] exp (j · θ8 [ω0-Δω])
+ B9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}]
... (173)

Similarly, ωp = ω0 + Δω and ωm = ω0−Δω are defined, the phase delay θ9 [ω0] of the component of the angular frequency ω0 of the magnetic field B9 is changed to π + θ9 [ω0], and θ01 = θ00 + Δθ01 is the second state. When the electromotive force E3pc of the component of the angular frequency ωp in the second electromotive force is E3πp0, the interelectrode electromotive force E3πp0 is expressed by the following equation.
E3πp0 = rk · exp (j · θ00))
・ [(Ω0 + Δω) · exp (j · π / 2)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
+ B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])}
+ Γ · V · exp (j · Δθ01)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
-B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])}]
... (174)

Further, when the electromotive force E3mc of the component of the angular frequency ωm in the second electromotive force in the second excitation state is E3πm0, the interelectrode electromotive force E3πm0 is expressed by the following equation. However, θ9 [ω0] = θ8 [ω0] + Δθ9 [ω0] is not applied in the equations (174) and (175), and is applied in the later equations.
E3πm0 = rk · exp (j · θ00)
・ [(Ω0−Δω) exp (j · π / 2)
{B8 [ω0-Δω] exp (j · θ8 [ω0-Δω])
+ B9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}
+ Γ · V · exp (j · Δθ01)
{B8 [ω0-Δω] exp (j · θ8 [ω0-Δω])
−b9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}]
... (175)

If the sum of the inter-electrode electromotive forces E3p0 and E3m0 is E3s0, the electromotive force sum E3s0 is expressed by the following equation.
E3s0 = E3p0 + E3m0
= Rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
-B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])
+ B8 [ω0−Δω] · exp (j · θ8 [ω0−Δω])
−b9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}
+ Δω · exp (j · π / 2)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
-B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])
−b8 [ω0−Δω] · exp (j · θ8 [ω0−Δω])
+ B9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}
+ Γ · V · exp (j · Δθ01)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
+ B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])
+ B8 [ω0−Δω] · exp (j · θ8 [ω0−Δω])
+ B9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}]
... (176)

If the sum of the interelectrode electromotive force E3πp0 and E3πm0 is E3πs0, the interelectrode electromotive force E3πs0 is expressed by the following equation.
E3πs0 = E3πp0 + E3πm0
= Rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
+ B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])
+ B8 [ω0−Δω] · exp (j · θ8 [ω0−Δω])
+ B9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}
+ Δω · exp (j · π / 2)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
+ B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])
−b8 [ω0−Δω] · exp (j · θ8 [ω0−Δω])
−b9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}
+ Γ · V · exp (j · Δθ01)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
-B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])
+ B8 [ω0−Δω] · exp (j · θ8 [ω0−Δω])
−b9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])}]
... (177)

Here, since ω0> Δω is normally satisfied, the conditional expressions (178) to (181) are satisfied.
2 ・ b8 [ω0] ・ exp (j ・ θ8 [ω0])
≒ b8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
+ B8 [ω0−Δω] · exp (j · θ8 [ω0−Δω]) (178)
2 · b9 [ω0] · exp (j · θ9 [ω0])
≒ b9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])
+ B9 [ω0−Δω] · exp (j · θ9 [ω0−Δω]) (179)

| Ω0 · exp (j · π / 2) · {2 · b8 [ω0] · exp (j · θ8 [ω0])} |
>> | ± Δω · exp (j · π / 2)
・ {B8 [ω0 + Δω] · exp (j · θ8 [ω0 + Δω])
−b8 [ω0−Δω] · exp (j · θ8 [ω0−Δω])} | (180)
| Ω0 · exp (j · π / 2) · {2 · b9 [ω0] · exp (j · θ9 [ω0])} |
>> | ± Δω · exp (j · π / 2)
・ {B9 [ω0 + Δω] · exp (j · θ9 [ω0 + Δω])
−b9 [ω0−Δω] · exp (j · θ9 [ω0−Δω])} | (181)

When E3s0a is an approximation of the electromotive force sum E3s0 by applying the conditions of the equations (178) to (181) to the equation (176), the electromotive force sum E3s0a is expressed by the following equation.
E3s0a≈E3s0 (182)
E3s0a = rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {2 ・ b8 [ω0] ・ exp (j ・ θ8 [ω0])
-2 · b9 [ω0] · exp (j · θ9 [ω0])}
+ Γ · V · exp (j · Δθ01)
・ {2 ・ b8 [ω0] ・ exp (j ・ θ8 [ω0])
+ 2 · b9 [ω0] · exp (j · θ9 [ω0])} (183)

Similarly, when E3πs0a is obtained by applying the conditions of equations (178) to (181) to equation (177) and approximating the electromotive force sum E3πs0, the electromotive force sum E3πs0a is expressed by the following equation.
E3πs0a≈E3πs0 (184)
E3πs0a = rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {2 ・ b8 [ω0] ・ exp (j ・ θ8 [ω0])
+ 2 · b9 [ω0] · exp (j · θ9 [ω0])}
+ Γ · V · exp (j · Δθ01)
・ {2 ・ b8 [ω0] ・ exp (j ・ θ8 [ω0])
-2 · b9 [ω0] · exp (j · θ9 [ω0])}]
... (185)

If E3s0b is obtained by substituting θ9 [ω0] = θ8 [ω0] + Δθ9 [ω0] into the electromotive force sum E3s0a, the electromotive force sum E3s0b is expressed by the following equation.
E3s0b = 2 · rk · exp {j · (θ8 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B8 [ω0] −b9 [ω0] · exp (j · Δθ9 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B8 [ω0] + b9 [ω0] · exp (j · Δθ9 [ω0])}]
... (186)

Further, if E3πs0b is obtained by substituting θ9 [ω0] = θ8 [ω0] + Δθ9 [ω0] into the electromotive force sum E3πs0a, the electromotive force sum E3πs0b is expressed by the following equation.
E3πs0b = 2 · rk · exp {j · (θ8 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B8 [ω0] + b9 [ω0] · exp (j · Δθ9 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B8 [ω0] −b9 [ω0] · exp (j · Δθ9 [ω0])}]
... (187)

Here, if b8 [ω0] = b9 [ω0] and Δθ9 [ω0] = 0 are set in the magnetic fields B8 and B9 in the initial state (the state at the time of calibration), even if the subsequent deviation is taken into consideration. b8 [ω0] ≈b9 [ω0] and Δθ9 [ω0] ≈0, and the following conditional expression holds.
| B8 [ω0] + b9 [ω0] · exp (j · Δθ9 [ω0]) |
>> | b8 [ω0] −b9 [ω0] · exp (j · Δθ9 [ω0]) | (188)

Since ω0> γ · V is normally satisfied, the following condition is satisfied in Expression (187) in consideration of the condition of Expression (188).
| Ω0 · exp (j · π / 2)
{B8 [ω0] + b9 [ω0] · exp (j · Δθ9 [ω0])} |
≫ ｜ γ ・ V ・ exp (j ・ Δθ01)
B8 [ω0] −b9 [ω0] · exp (j · Δθ9 [ω0]) | (189)

An electromotive force sum EdA31 obtained by approximating the electromotive force sum E3πs0b of the equation (187) using the condition of the equation (189) is expressed by the following equation. This electromotive force sum EdA31 corresponds to the first ∂A / ∂t component in the basic principle.
EdA31≈E3πs0b≈E3πs0 (190)
EdA31 = 2 · rk · exp {j · (θ8 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B8 [ω0] + b9 [ω0] · exp (j · Δθ9 [ω0])}
... (191)

Since the electromotive force sum EdA31 is not related to the magnitude V of the flow velocity, it becomes only the component generated by ∂A / ∂t. Using this electromotive force sum EdA31, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the electromotive force sum E3s0b (synthesis vector Vas0 + Vbs0) is normalized. If the electromotive force sum E3s0b is normalized by the electromotive force sum EdA31 and multiplied by ω0 is En30, the normalized electromotive force sum En30 is expressed by the following equation.
En30 = (E3s0b / EdA31) · ω0
= 2 · rk · exp {j · (θ8 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B8 [ω0] −b9 [ω0] · exp (j · Δθ9 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B8 [ω0] + b9 [ω0] · exp (j · Δθ9 [ω0])}]
/ [2 · rk · exp {j · (θ8 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B8 [ω0] + b9 [ω0] · exp (j · Δθ9 [ω0])}] · ω0
= Ω0 · {b8 [ω0] −b9 [ω0] · exp (j · Δθ9 [ω0])}
/ {B8 [ω0] + b9 [ω0] · exp (j · Δθ9 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (192)

Using the equation (52), the coefficient {b8 [ω0] −b9 [ω0] · exp (j · Δθ9 [ω0])} / {b8 [ω0] applied to the angular frequency ω0 of the first term on the right side of the equation (192) ] + B9 [ω0] · exp (j · Δθ9 [ω0])} is represented by a value {b8−b9 · exp (j · Δθ9)} / {b8 + b9 · exp (j · Δθ9)} not related to the angular frequency ω0. be able to. Therefore, equation (192) can be replaced by the following equation.
En30 = ω0 · {b8−b9 · exp (j · Δθ9)}
/ {B8 + b9 · exp (j · Δθ9)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (193)

  The second term on the right side of Equation (193) is a term obtained by normalizing the component generated by v × B. The reason why the result obtained by normalizing the electromotive force sum E3s0b with the electromotive force sum EdA31 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side of the magnitude V of the flow velocity. According to the equation (193), the complex coefficient related to the magnitude V of the flow velocity has a magnitude of γ and an angle from the real axis of −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (193) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the component ∂A / ∂t, it is possible to realize span correction that automatically corrects errors due to magnetic field shifts and phase changes.

Next, a method for removing the first term on the right side of the equation (193), which is a variation factor of 0 point, will be described. When ωc and ωd are used instead of the excitation angular frequencies ωp and ωm in the equations (164) and (165), the magnetic fields B8 and B9 are expressed by the following equations.
B8 = b8 [ωc] · cos (θ8 [ωc]) · cos (ωc · t)
+ B8 [ωc] · sin (θ8 [ωc]) · sin (ωc · t)
+ B8 [ωd] · cos (θ8 [ωd]) · cos (ωd · t)
+ B8 [ωd] · sin (θ8 [ωd]) · sin (ωd · t) (194)
B9 = b9 [ωc] · cos (θ9 [ωc]) · cos (ωc · t)
+ B9 [ωc] · sin (θ9 [ωc]) · sin (ωc · t)
+ B9 [ωd] · cos (θ9 [ωd]) · cos (ωd · t)
+ B9 [ωd] · sin (θ9 [ωd]) · sin (ωd · t) (195)

  Here, the angular frequencies ωc and ωd are set to have a relationship of ωc = ω2 + Δω and ωd = ω2−Δω. Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. The electromotive force sum E3s2 to be subjected to span correction at the angular frequency ω2 is the inter-electrode electromotive force E3p2 in which the angular frequency ω0 is replaced with ω2 in the equation (172), and the electrode in which the angular frequency ω0 is replaced with ω2 in the equation (173). It is represented by the sum E3p2 + E3m2 with the inter-electromotive force E3m2. Further, the electromotive force sum E3πs2 which is the basis of the second ∂A / ∂t component is obtained by calculating the interelectrode electromotive force E3πp2 obtained by replacing the angular frequency ω0 with ω2 in the equation (174) and the angular frequency ω0 in the equation (175). It is represented by the sum E3πp2 + E3πm2 with the interelectrode electromotive force E3πm2 replaced by ω2. Furthermore, the electromotive force sum EdA32 that is the second ∂A / ∂t component is obtained by replacing the angular frequency ω0 with ω2 in the equation (191).

If the result obtained by normalizing the electromotive force sum E3s2 by the electromotive force sum EdA32 and multiplying it by ω2 is denoted by En32, the normalized electromotive force sum En32 is expressed by the following equation from the equation (193).
En32 = ω2 · {b8−b9 · exp (j · Δθ9)}
/ {B8 + b9 · exp (j · Δθ9)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (196)

Taking the difference between the normalized electromotive force sums En30 and En32 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA33, the difference EdA33 is expressed by the following equation. This electromotive force sum difference EdA33 corresponds to the third ∂A / ∂t component in the basic principle.
EdA33 = (En30−En32) · ω0 / (ω0−ω2)
= [{B8−b9 · exp (j · Δθ9)}
/ {B8 + b9 · exp (j · Δθ9)}
.Omega.0 + .gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V
− {B8−b9 · exp (j · Δθ9)}
/ {B8 + b9 · exp (j · Δθ9)}
.Omega.2-.gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V]
・ Ω0 / (ω0−ω2)
= {B8-b9 · exp (j · Δθ9)}
/ {B8 + b9 · exp (j · Δθ9)} · ω0 (197)

The difference EdA33 represents the normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (193). Therefore, if this difference EdA33 is used, the normalized v × B component is normalized. It can be taken out from the power sum En30. When the v × B component obtained by subtracting the difference EdA33 of the equation (197) from the normalized electromotive force sum En30 of the equation (193) is EvBn3, the v × B component EvBn3 is expressed by the following equation.
EvBn3 = En30-EdA33
= {B8-b9 · exp (j · Δθ9)}
/ {B8 + b9 · exp (j · Δθ9)} · ω0
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
− {B8−b9 · exp (j · Δθ9)}
/ {B8 + b9 · exp (j · Δθ9)} · ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (198)

The v × B component EvBn3 is not related to the angular frequency ω. As can be seen from the fact that the v × B component EvBn3 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBn3. From the equation (198), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn3 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn3 | / γ (199)

  Table 3 below shows the correspondence between the constants and variables used in the basic principle and the constants and variables of the present embodiment. As is apparent from Table 3, this embodiment is one example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. Since the configuration of the electromagnetic flowmeter of the present embodiment is the same as that of the first embodiment, description will be made using the reference numerals in FIG. The electromagnetic flowmeter of the present embodiment includes a measuring tube 1, electrodes 2a and 2b, first and second exciting coils 3a and 3b, a power supply unit 4, a signal conversion unit 5, and a flow rate output unit 6. Have

  The signal conversion unit 5 obtains the amplitude and phase of the combined electromotive force detected by the electrodes 2a and 2b in each of the first to fourth excitation states, and performs the second excitation based on these amplitudes and phases. The sum of electromotive forces of the component of the angular frequency ω0 + Δω and the component of the angular frequency ω0-Δω of the combined electromotive force in the state is extracted as the first ∂A / ∂t component, and the angle of the combined electromotive force in the fourth excitation state The sum of electromotive forces of the component of frequency ω2 + Δω and the component of angular frequency ω2-Δω is extracted as the second ∂A / ∂t component, and the component of angular frequency ω0 + Δω and the angular frequency ω0 of the composite electromotive force in the first excitation state are extracted. The sum of electromotive forces with the component of -Δω is used as the first correction target electromotive force, and the span included in the v × B component in the first correction target electromotive force based on the first ∂A / ∂t component While removing the fluctuation factor, the angular frequency ω2 + Δω of the composite electromotive force in the third excitation state The v × B component in the second correction target electromotive force based on the second ∂A / ∂t component with the electromotive force sum of the component and the component of the angular frequency ω2−Δω as the second correction target electromotive force The span correction unit 51 that removes the variation factor of the span included in the first correction target electromotive force that has been subjected to the span correction and the second correction target electromotive force that has been subjected to the span correction is calculated as a third ∂A / ∂. A zero-point correction unit 52 that extracts the v × B component by extracting the third ∂A / ∂t component from either one of the two correction target electromotive forces that have been subjected to span correction and extracted as the t component. It consists of.

  The power supply unit 4 of the present embodiment simultaneously supplies the first excitation current including the sine wave component of the angular frequency (ω0 + Δω) and the sine wave component of the angular frequency (ω0−Δω) to the first excitation coil 3a. The second excitation current having a phase difference of Δθ9 from the first excitation current and including a sine wave component of the angular frequency (ω0 + Δω) and a sine wave component of the angular frequency (ω0−Δω) is supplied to the second excitation coil 3b. The first excitation state to be supplied to is continued for T1 seconds, and the second excitation state in which the phase difference between the first excitation current and the second excitation current is changed to Δθ9 + π with respect to the first excitation state is T2. The second exciting current is supplied to the first exciting coil 3a at the same time as the third exciting current including the sine wave component of the angular frequency (ω2 + Δω) and the sine wave component of the angular frequency (ω2−Δω). Is the phase difference Δθ9, the sine wave component of the angular frequency (ω2 + Δω) and the angular frequency (ω The third excitation state in which the fourth excitation current including the sine wave component of 2-Δω) is supplied to the second excitation coil 3b is continued for T3 seconds, and the third excitation state is applied to the third excitation state. The fourth excitation state in which the phase difference between the current and the fourth excitation current is changed to Δθ9 + π is repeated for T4 seconds at a cycle of T seconds. That is, T = T1 + T2 + T3 + T4.

  FIG. 20 is a flowchart showing the operations of the signal conversion unit 5 and the flow rate output unit 6 of the present embodiment. First, the span correction unit 51 of the signal conversion unit 5 generates an angular frequency (ω0 + Δω) component and an angular frequency (ω0−Δω) component of the electromotive force between the electrodes 2a and 2b in the first excitation state. The amplitude r3s0 of the power sum E3s0 is obtained, and the phase difference φ3s0 between the real axis and the electromotive force sum E3s0 is obtained by a phase detector (not shown) (step 301 in FIG. 20). Subsequently, in the second excitation state, the span correction unit 51 has an electromotive force sum E3πs0 of the angular frequency (ω0 + Δω) component and the angular frequency (ω0−Δω) component of the electromotive force between the electrodes 2a and 2b. The amplitude r3πs0 is obtained, and the phase difference φ3πs0 between the real axis and the electromotive force sum E3πs0 is obtained by the phase detector (step 302).

  Further, in the third excitation state, the span correction unit 51 has an amplitude of the electromotive force sum E3s2 of the angular frequency (ω2 + Δω) component and the angular frequency (ω2-Δω) component of the electromotive force between the electrodes 2a and 2b. In addition to obtaining r3s2, the phase difference φ3s2 between the real axis and the electromotive force sum E3s2 is obtained by the phase detector (step 303). Furthermore, in the fourth excitation state, the span correction unit 51 has an amplitude of an electromotive force sum E3πs2 of the angular frequency (ω2 + Δω) component and the angular frequency (ω2-Δω) component of the electromotive force between the electrodes 2a and 2b. While obtaining r3πs2, the phase difference φ3πs2 between the real axis and the electromotive force sum E3πs2 is obtained by the phase detector (step 304). The electromotive force sums E3s0, E3πs0, E3s2, and E3πs2 can be frequency-separated by a bandpass filter or a comb filter.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force sum EdA31 that approximates the electromotive force sum E3πs0 (step 305). The process of step 305 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of equation (191). The span correction unit 51 calculates the magnitude | EdA31 | of the electromotive force sum EdA31 as follows.
| EdA31 | = r3πs0 (200)
Then, the span correction unit 51 calculates the angle ∠EdA31 of the electromotive force sum EdA31 as the following equation.
∠EdA31 = φ3πs0 (201)
This completes the process of step 305.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force sum En30 obtained by normalizing the electromotive force sum E3s0 with the electromotive force sum EdA31 (step 306). The process of step 306 is a process corresponding to the calculation of equation (193). The span correction unit 51 calculates the magnitude | En30 | of the normalized electromotive force sum En30 as the following equation.
| En30 | = (r3s0 / | EdA31 |) · ω0 (202)

Then, the span correction unit 51 calculates the angle ∠En30 of the normalized electromotive force sum En30 as the following expression.
∠En30 = φ3s0−∠EdA31 (203)
Further, the span correction unit 51 calculates the real axis component En30x and the imaginary axis component En30y of the normalized electromotive force sum En30 as in the following equation.
En30x = | En30 | .cos (∠En30) (204)
En30y = | En30 | .sin (∠En30) (205)
This completes the process of step 306.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force sum EdA32 that approximates the electromotive force sum E3πs2 (step 307). The processing of step 307 is processing corresponding to obtaining the second ∂A / ∂t component. The span correction unit 51 calculates the magnitude | EdA32 | of the electromotive force sum EdA32 as follows.
| EdA32 | = r3πs2 (206)
Then, the span correction unit 51 calculates the angle ∠EdA32 of the electromotive force sum EdA32 as the following equation.
∠EdA32 = φ3πs2 (207)
This completes the process of step 307.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force sum En32 obtained by normalizing the electromotive force sum E3s2 with the electromotive force sum EdA32 (step 308). The process of step 308 is a process corresponding to the calculation of equation (196). The span correction unit 51 calculates the magnitude | En32 | of the normalized electromotive force sum En32 as the following equation.
| En32 | = (r3s2 / | EdA32 |) · ω2 (208)

Then, the span correction unit 51 calculates the angle ∠En32 of the normalized electromotive force sum En32 as the following equation.
∠En32 = φ3s2-∠EdA32 (209)
Further, the span correction unit 51 calculates the real axis component En32x and the imaginary axis component En32y of the normalized electromotive force sum En32 as in the following equation.
En32x = | En32 | .cos (∠En32) (210)
En32y = | En32 | .sin (∠En32) (211)
This completes the processing in step 308.

Next, the zero point correction unit 52 of the signal conversion unit 5 obtains the magnitude of the difference EdA33 between the normalized electromotive force sums En30 and En32 (step 309). The process of step 309 is a process corresponding to obtaining the third ∂A / ∂t component, and is a process corresponding to the calculation of Expression (197). The zero point correction unit 52 calculates the real axis component EdA33x and the imaginary axis component EdA33y of the difference EdA33 as in the following equation.
EdA33x = (En30x−En32x) · ω0 / (ω0−ω2) (212)
EdA33y = (En30y−En32y) · ω0 / (ω0−ω2) (213)

Then, the zero point correction unit 52 removes the difference EdA33 from the normalized electromotive force sum En30 and obtains the magnitude of the v × B component EvBn3 (step 310). The process of step 310 is a process corresponding to the calculation of equation (198). The zero point correction unit 52 calculates the magnitude | EvBn3 | of the v × B component EvBn3 as the following equation.
| EvBn3 | = {(En30x−EdA33x) ²
+ (En30y−EdA33y) ² } ^1/2 (214)

The flow rate output unit 6 calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 311). The process of step 311 is a process corresponding to the calculation of equation (199).
V = | EvBn3 | / γ (215)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5 and the flow rate output unit 6 perform the processing in steps 301 to 311 as described above at regular intervals until the operator instructs the end of measurement (YES in step 312). Note that the processing of steps 304 to 311 is performed in the fourth excitation state.

  As described above, in the present embodiment, the electromotive force sum E3s0 of the component of the angular frequency (ω0 + Δω) and the component of the angular frequency (ω0−Δω) is obtained in the first excitation state, and the angle is calculated in the second excitation state. An electromotive force sum E3πs0 of the frequency (ω0 + Δω) component and the angular frequency (ω0−Δω) component is obtained, and the angular frequency (ω2 + Δω) component and the angular frequency (ω2−Δω) component in the third excitation state are obtained. An electromotive force sum E3s2 is obtained, and an electromotive force sum E3πs2 of the angular frequency (ω2 + Δω) component and the angular frequency (ω2-Δω) component is obtained in the fourth excitation state. In this embodiment, if the magnetic field B8 generated from the first excitation coil 3a is set to be equal to the magnetic field B9 generated from the second excitation coil 3b, the electromotive force sum E3πs0 is approximate. Can be extracted as the first ∂A / ∂t component, and the electromotive force sum E3πs2 can be approximately extracted as the second ∂A / ∂t component, and the first ∂A / ∂t component is used. Normalizing the span of the velocity V of the v × B component in the electromotive force sum E3s0 and using the second ∂A / ∂t component, the flow velocity of the v × B component in the electromotive force sum E3s2 Is normalized, the difference EdA33 (third ∂A / ∂t component) is extracted from the normalized electromotive force sums En30 and En32, and the third ∂ is calculated from the normalized electromotive force sum En30. Extract v / B component by removing A / ∂t component Since the flow rate of the fluid to be measured is calculated from the v × B component, accurate span correction can be automatically performed, and the output of the electromagnetic flowmeter can be output without setting the flow rate of the fluid to be measured to zero. The zero point can be corrected, and the stability of the zero point can be secured even in high-frequency excitation.

  In the present embodiment, the first ∂A / ∂t component obtained by extracting the v × B component of the electromotive force sum E3s0 from the electromotive force sum E3πs0 of the same angular frequency in consideration of the difference in magnetic field loss depending on the frequency. , And the v × B component of the electromotive force sum E3s2 is normalized using the second ∂A / 角 t component extracted from the electromotive force sum E3πs2 of the same angular frequency, and the normalized electromotive force, respectively. Since zero correction is performed based on the difference between the sums En30 and En32, accurate span correction and zero correction can be performed even when there is an influence due to the loss of the magnetic field. Further, in the present embodiment, since excitation is performed with the frequencies dispersed, the frequency band can be used efficiently.

  Note that modulation can be used as another example of the present embodiment. If a carrier wave having an angular frequency ω0 is excited by a modulated wave having an angular frequency ω1, an electromotive force having components of angular frequencies ω0 and ω0 ± ω1 can be obtained in the case of amplitude modulation, and an angular frequency in the case of phase modulation or frequency modulation. The electromotive force of the component of ω0, ω0 ± ζ · ω1 (ζ is a positive integer) can be obtained. Also in this case, it is possible to perform span correction and zero correction by performing excitation while switching the phase difference between the magnetic field generated from the first excitation coil 3a and the magnetic field generated from the second excitation coil 3b. Examples using this modulation are shown in the fourth to seventh embodiments.

Further, in the present embodiment, the electromotive force sum E3s0 is set as an object of 0 correction and span correction, but the electromotive force sum E3s2 may be set as an object of 0 correction and span correction. In this case, the difference EdA33 (third ∂A / ∂t component) is obtained from the normalized electromotive force sums En32 and En30 as in the following equation.
EdA33 = (En32-En30) · ω2 / (ω2-ω0) (216)
Then, the v × B component EvBn3 may be obtained by subtracting the difference EdA33 from the normalized electromotive force sum En32 as in the following equation. The other processes are the same as the case where the electromotive force sum E3s0 is the target of 0 correction and span correction.
| EvBn3 | = | En32-EdA33 | (217)

[Fourth Embodiment]
Next, a fourth embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has two excitation coils and a pair of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. The present embodiment uses the second detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The second extraction method described is used.

Of the magnetic field Bb generated from the first exciting coil 3a, a magnetic field component (magnetic flux density) B10 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX connecting the electrodes 2a and 2b, Of the magnetic field Bc generated from the excitation coil 3b, a magnetic field component (magnetic flux density) B11 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX is given as follows.
B10 = b10 · {1 + ma · cos (ω1 · t)} · cos (ω0 · t−θ10) (218)
B11 = b11 · {1-ma · cos (ω1 · t)} · cos (ω0 · t−θ11) (219)

  In equations (218) and (219), b10 and b11 are the amplitudes of the magnetic flux densities B10 and B11, respectively, ω0 is the angular frequency of the carrier wave, ω1 is the angular frequency of the modulation wave, and θ10 is the magnetic flux density B10 and ω0 · t. The phase difference (phase lag), θ11 is the phase difference between the magnetic flux density B11 and ω0 · t, and ma is the amplitude modulation index. Hereinafter, the magnetic flux density B10 is referred to as a magnetic field B10, and the magnetic flux density B11 is referred to as a magnetic field B11. Expressions (218) and (219) can be transformed as follows.

B10 = b10 · {1 + ma · cos (ω1 · t)} · cos (ω0 · t−θ10)
= B10 · cos (θ10) · cos (ω0 · t)
+ B10 · sin (θ10) · sin (ω0 · t)
+ (1/2) · ma · b10 · cos (θ10) · cos {(ω0 + ω1) · t}
+ (1/2) · ma · b10 · sin (θ10) · sin {(ω0 + ω1) · t}
+ (1/2) · ma · b10 · cos (θ10) · cos {(ω0−ω1) · t}
+ (1/2) · ma · b10 · sin (θ10) · sin {(ω0−ω1) · t}
... (220)

B11 = b11 · {1-ma · cos (ω1 · t)} · cos (ω0 · t−θ11)
= B11 · cos (θ11) · cos (ω0 · t)
+ B11 · sin (θ11) · sin (ω0 · t)
+ (1/2) · ma · b11 · {−cos (θ11)}
Cos {(ω0 + ω1) · t}
+ (1/2) · ma · b11 · {−sin (θ11)}
Sin {(ω0 + ω1) · t}
+ (1/2) · ma · b11 · {−cos (θ11)}
Cos {(ω0−ω1) · t}
+ (1/2) · ma · b11 · {−sin (θ11)}
Sin {(ω0−ω1) · t} (221)

  Considering the loss of the magnetic field at each angular frequency, the amplitudes b10 and b11 of the components of the angular frequency ω0 of the magnetic fields B10 and B11 are changed to function notations b10 [ω0] and b11 [ω0], respectively. The phase differences θ10 and θ11 of the component of ω0 are changed to θ10 [ω0] and θ11 [ω0], respectively. In addition, the amplitudes b10 and b11 of the components of the angular frequency (ω0 + ω1) of the magnetic fields B10 and B11 are changed to b10 [ω0 + ω1] and b11 [ω0 + ω1], respectively, and the phase difference θ10 of the components of the angular frequency (ω0 + ω1) is similarly changed. , Θ11 are changed to θ10 [ω0 + ω1] and θ11 [ω0 + ω1], respectively. Further, the amplitudes b10 and b11 of the components of the angular frequencies (ω0−ω1) of the magnetic fields B10 and B11 are changed to b10 [ω0−ω1] and b11 [ω0−ω1], respectively, and the angular frequencies (ω0− The phase differences θ10 and θ11 of the components of ω1) are changed to θ10 [ω0−ω1] and θ11 [ω0−ω1], respectively. Thereby, Formula (220) and Formula (221) are replaced with Formula (222) and Formula (223).

B10 = b10 · {1 + ma · cos (ω1 · t)} · cos (ω0 · t−θ10)
= B10 [ω0] · cos (θ10 [ω0]) · cos (ω0 · t)
+ B10 [ω0] · sin (θ10 [ω0]) · sin (ω0 · t)
+ (1/2) · ma · b10 [ω0 + ω1] · cos (θ10 [ω0 + ω1])
Cos {(ω0 + ω1) · t}
+ (1/2) · ma · b10 [ω0 + ω1] · sin (θ10 [ω0 + ω1])
Sin {(ω0 + ω1) · t}
+ (1/2) · ma · b10 [ω0−ω1] · cos (θ10 [ω0−ω1])
Cos {(ω0−ω1) · t}
+ (1/2) · ma · b10 [ω0−ω1] · sin (θ10 [ω0−ω1])
Sin {(ω0−ω1) · t} (222)

B11 = b11 · {1-ma · cos (ω1 · t)} · cos (ω0 · t−θ11)
= B11 [ω0] · cos (θ11 [ω0]) · cos (ω0 · t)
+ B11 [ω0] · sin (θ11 [ω0]) · sin (ω0 · t)
+ (1/2) · ma · b11 [ω0 + ω1] · {−cos (θ11 [ω0 + ω1])}
Cos {(ω0 + ω1) · t}
+ (1/2) · ma · b11 [ω0 + ω1] · {−sin (θ11 [ω0 + ω1])}
Sin {(ω0 + ω1) · t}
+ (1/2) · ma · b11 [ω0−ω1] · {−cos (θ11 [ω0−ω1])}
Cos {(ω0−ω1) · t}
+ (1/2) · ma · b11 [ω0−ω1] · {−sin (θ11 [ω0−ω1])}
Sin {(ω0−ω1) · t} (223)

Since the electromotive force resulting from the change of the magnetic field is based on the time differential dB / dt of the magnetic field, the magnetic field B10 generated from the first excitation coil 3a and the magnetic field B11 generated from the second excitation coil 3b are differentiated as follows: To do.
dB10 / dt = ω0 · cos (ω0 · t)
B10 [ω0] · {sin (θ10 [ω0])}
+ Ω0 · sin (ω0 · t)
B10 [ω0] · {−cos (θ10 [ω0])}
+ (1/2) · ma · (ω0 + ω1) · cos {(ω0 + ω1) · t}
B10 [ω0 + ω1] • {sin (θ10 [ω0 + ω1])}
+ (1/2) · ma · (ω0 + ω1) · sin {(ω0 + ω1) · t
B10 [ω0 + ω1] · {−cos (θ10 [ω0 + ω1])}
+ (1/2) · ma · (ω0−ω1) · cos {(ω0−ω1) · t}
B10 [ω0−ω1] • {sin (θ10 [ω0−ω1])}
+ (1/2) · ma · (ω0−ω1) · sin {(ω0−ω1) · t}
B10 [ω0−ω1] • {−cos (θ10 [ω0−ω1])}
... (224)

dB11 / dt = ω0 · cos (ω0 · t)
B11 [ω0] · {sin (θ11 [ω0])}
+ Ω0 · sin (ω0 · t)
B11 [ω0] · {−cos (θ11 [ω0])}
+ (1/2) · ma · (ω0 + ω1) · cos {(ω0 + ω1) · t}
B11 [ω0 + ω1] · {−sin (θ11 [ω0 + ω1])}
+ (1/2) · ma · (ω0 + ω1) · sin {(ω0 + ω1) · t}
B11 [ω0 + ω1] · {cos (θ11 [ω0 + ω1])}
+ (1/2) · ma · (ω0−ω1) · cos {(ω0−ω1) · t}
B11 [ω0−ω1] • {−sin (θ11 [ω0−ω1])}
+ (1/2) · ma · (ω0−ω1) · sin {(ω0−ω1) · t}
B11 [ω0−ω1] • {cos (θ11 [ω0−ω1])}
... (225)

  When the flow rate of the fluid to be measured is 0, it is generated by the change in the electromotive force E1 between the electrodes that is irrelevant to the flow rate and the change in the magnetic field Bc. The inter-electrode electromotive force E2 irrelevant to the flow velocity is opposite to each other as shown in FIG. At this time, the total inter-electrode electromotive force E obtained by adding the inter-electrode electromotive forces E1 and E2 is the difference between the time derivative of the magnetic field dB10 / dt and dB11 / dt (−dB10 / dt + dB11 / dt) is multiplied by the proportional coefficient rk for each angular frequency component of ω0, (ω0−ω1), (ω0 + ω1), and the phase differences θ10 and θ11 are replaced by θ10 + θ00 and θ11 + θ00, respectively (rk and θ00 are measured). (Related to the structure of the measuring tube 1 including the conductivity and dielectric constant of the fluid and the arrangement of the electrodes 2a, 2b).

E = rk · ω0 · cos (ω0 · t)
・ {−b10 [ω0] · sin (θ10 [ω0] + θ00)
+ B11 [ω0] · sin (θ11 [ω0] + θ00)}
+ Rk · ω0 · sin (ω0 · t)
・ {B10 [ω0] · cos (θ10 [ω0] + θ00)
−b11 [ω0] · cos (θ11 [ω0] + θ00)}
+ (1/2) · ma · rk · (ω0 + ω1) · cos {(ω0 + ω1) · t}
・ {−b10 [ω0 + ω1] · sin (θ10 [ω0 + ω1] + θ00)
-B11 [ω0 + ω1] · sin (θ11 [ω0 + ω1] + θ00)}
+ (1/2) · ma · rk · (ω0 + ω1) · sin {(ω0 + ω1) · t}
・ {B10 [ω0 + ω1] · cos (θ10 [ω0 + ω1] + θ00)
+ B11 [ω0 + ω1] · cos (θ11 [ω0 + ω1] + θ00)}
+ (1/2) · ma · rk · (ω0−ω1) · cos {(ω0−ω1) · t}
{-B10 [ω0−ω1] · sin (θ10 [ω0−ω1] + θ00)
−b11 [ω0−ω1] · sin (θ11 [ω0−ω1] + θ00)}
+ (1/2) · ma · rk · (ω0−ω1) · sin {(ω0−ω1) · t}
{B10 [ω0−ω1] · cos (θ10 [ω0−ω1] + θ00)
+ B11 [ω0−ω1] · cos (θ11 [ω0−ω1] + θ00)}
... (226)

  When the magnitude of the flow velocity of the fluid to be measured is V (V ≠ 0), the interelectrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bb, and the interelectrode electromotive force Ev2 generated by the flow velocity vector v and the magnetic field Bc are shown in FIG. As shown in FIG. At this time, the total inter-electrode electromotive force Ev obtained by adding the inter-electrode electromotive forces Ev1 and Ev2 is ω0, (ω0−ω1), (ω0 + ω1) as the sum of the magnetic field B10 and the magnetic field B11 as shown in the following equation. The proportional coefficient rkv is applied to each angular frequency component, and the phase differences θ10 and θ11 are replaced by θ10 + θ01 and θ11 + θ01, respectively (rkv and θ01 are the flow velocity magnitude V, the conductivity and dielectric constant of the fluid to be measured, (Related to the structure of the measuring tube 1 including the arrangement of the electrodes 2a, 2b).

Ev = rkv · cos (ω0 · t)
・ {B10 [ω0] · cos (θ10 [ω0] + θ01)
+ B11 [ω0] · cos (θ11 [ω0] + θ01)}
+ Rkv · sin (ω0 · t)
・ {B10 [ω0] · sin (θ10 [ω0] + θ01)
+ B11 [ω0] · sin (θ11 [ω0] + θ01)}
+ (1/2) · ma · rkv · cos {(ω0 + ω1) · t}
{B10 [ω0 + ω1] · cos (θ10 [ω0 + ω1] + θ01)
−b11 [ω0 + ω1] · cos (θ11 [ω0 + ω1] + θ01)}
+ (1/2) · ma · rkv · sin {(ω0 + ω1) · t}
{B10 [ω0 + ω1] · sin (θ10 [ω0 + ω1] + θ01)
-B11 [ω0 + ω1] · sin (θ11 [ω0 + ω1] + θ01)}
+ (1/2) · ma · rkv · cos {(ω0−ω1) · t}
{B10 [ω0−ω1] · cos (θ10 [ω0−ω1] + θ01)
−b11 [ω0−ω1] · cos (θ11 [ω0−ω1] + θ01)}
+ (1/2) · ma · rkv · sin {(ω0−ω1) · t}
{B10 [ω0−ω1] · sin (θ10 [ω0−ω1] + θ01)
−b11 [ω0−ω1] · sin (θ11 [ω0−ω1] + θ01)}
... (227)

In consideration of the direction of the electromotive force between the electrodes described in FIGS. 2 and 3, the electromotive force obtained by converting the interelectrode electromotive force due to the time change of the magnetic field into a complex vector and the interelectrode electromotive force due to the flow velocity of the fluid to be measured. The electromotive force E40c of the component of the angular frequency ω0 out of the total inter-electrode electromotive force combined with the electromotive force converted into a complex vector is expressed by the first term, the second term of the equation (226), and the equation (227). From the first term and the second term and the equation (17), it is expressed by the following equation.
E40c = rk · ω0 · b10 [ω0]
Exp {j. (Π / 2 + θ10 [ω0] + θ00)}
+ Γ · rk · V · b10 [ω0] · exp {j · (θ10 [ω0] + θ01)}
+ Rk · ω0 · b11 [ω0]
Exp {j · (−π / 2 + θ11 [ω0] + θ00)}
+ Γ · rk · V · b11 [ω0] · exp {j · (θ11 [ω0] + θ01)}
... (228)

In addition, the inter-electrode electromotive force obtained by converting the inter-electrode electromotive force caused by the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force caused by the flow velocity of the fluid to be measured into the complex vector Among the electromotive forces, the electromotive force E4pc of the component of the angular frequency (ω0 + ω1) is obtained from the third and fourth terms of Equation (226), the third and fourth terms of Equation (227), and Equation (17). It is expressed by the following formula.
E4pc = (1/2) · ma · rk · (ω0 + ω1) · b10 [ω0 + ω1]
Exp {j · (π / 2 + θ10 [ω0 + ω1] + θ00)}
+ (1/2) · ma · γ · rk · V · b10 [ω0 + ω1]
Exp {j · (θ10 [ω0 + ω1] + θ01)}
+ (1/2) · ma · rk · (ω0 + ω1) · b11 [ω0 + ω1]
Exp {j · (π / 2 + θ11 [ω0 + ω1] + θ00)}
+ (1/2) · ma · γ · rk · V · b11 [ω0 + ω1]
Exp {j · (π + θ11 [ω0 + ω1] + θ01)} (229)

In addition, the inter-electrode electromotive force obtained by converting the inter-electrode electromotive force caused by the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force caused by the flow velocity of the fluid to be measured into the complex vector Among the electromotive forces, the electromotive force E4mc of the component of the angular frequency (ω0−ω1) is the fifth term and the sixth term of the equation (226) and the fifth term, the sixth term of the equation (227), and the equation (17). And is expressed by the following equation.
E4mc = (1/2) · ma · rk · (ω0−ω1) · b10 [ω0−ω1]
Exp {j · (π / 2 + θ10 [ω0−ω1] + θ00)}
+ (1/2) · ma · γ · rk · V · b10 [ω0−ω1]
Exp {j. (Θ10 [ω0−ω1] + θ01)}
+ (1/2) · ma · rk · (ω0−ω1) · b11 [ω0−ω1]
Exp {j · (π / 2 + θ11 [ω0−ω1] + θ00)}
+ (1/2) · ma · γ · rk · V · b10 [ω0−ω1]
Exp {j · (π + θ11 [ω0−ω1] + θ01)} (230)

Here, the relationship between the phase delay θ10 [ω0] of the component of the angular frequency ω0 of the magnetic field B10 and the phase delay θ11 [ω0] of the component of the angular frequency ω0 of the magnetic field B11 is θ11 [ω0] = θ10 [ω0] + Δθ11 [ω0. ], And the relationship between the angle θ00 of the ∂A / 成分 t component with respect to the imaginary axis and the angle θ01 of the v × B component with respect to the real axis is θ01 = θ00 + Δθ01, θ01 = θ00 + Δθ01 and θ11 [ω0 in equation (228) ] = Θ10 [ω0] + Δθ11 [ω0] is substituted, and the inter-electrode electromotive force E40 is expressed by the following equation.
E40 = rk · exp {j · (θ10 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}]
... (231)

The inter-electrode electromotive force E4p0 when θ01 = θ00 + Δθ01 is substituted into the equation (229) is expressed by the following equation.
E4p0 = (1/2) · ma · rk · exp (j · θ00)
・ [(Ω0 + ω1) · exp (j · π / 2)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
+ B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
−b11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])}]
... (232)

The inter-electrode electromotive force E4m0 when θ01 = θ00 + Δθ01 is substituted into the equation (230) is expressed by the following equation.
E4m0 = (1/2) · ma · rk · exp (j · θ00)
・ [(Ω0−ω1) · exp (j · π / 2)
{B10 [ω0-ω1] exp (j · θ10 [ω0-ω1])
+ B11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0-ω1] exp (j · θ10 [ω0-ω1])
−b11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}]
... (233)

Here, when the sum of the inter-electrode electromotive forces E4p0 and E4m0 is E4s0, the electromotive force sum E4s0 is expressed by the following equation.
E4s0 = E4p0 + E4m0
= (1/2) · ma · rk · exp (j · θ00)
・ [(Ω0 + ω1) · exp (j · π / 2)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
+ B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
−b11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])}]
+ (1/2) · ma · rk · exp (j · θ00)
・ [(Ω0−ω1) · exp (j · π / 2)
{B10 [ω0-ω1] exp (j · θ10 [ω0-ω1])
+ B11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0-ω1] exp (j · θ10 [ω0-ω1])
−b11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}]
= (1/2) · ma · rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
+ B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])
+ B10 [ω0−ω1] · exp (j · θ10 [ω0−ω1])
+ B11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}
+ Ω1 · exp (j · π / 2)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
+ B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])
−b10 [ω0−ω1] · exp (j · θ10 [ω0−ω1])
−b11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
-B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])
+ B10 [ω0−ω1] · exp (j · θ10 [ω0−ω1])
−b11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}]
... (234)

Here, since ω0> ω1 is normally satisfied, the conditional expressions (235) to (238) are satisfied.
2 · b10 [ω0] · exp (j · θ10 [ω0])
≒ b10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
+ B10 [ω0−ω1] · exp (j · θ10 [ω0−ω1]) (235)
2 · b11 [ω0] · exp (j · θ11 [ω0])
≒ b11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])
+ B11 [ω0−ω1] · exp (j · θ11 [ω0−ω1]) (236)

| Ω0 · exp (j · π / 2) · {2 · b10 [ω0]
Exp (j · θ10 [ω0])} |
>> | ω1 · exp (j · π / 2)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
−b10 [ω0−ω1] · exp (j · θ10 [ω0−ω1])} |
... (237)
| Ω0 · exp (j · π / 2) · {2 · b11 [ω0]
Exp (j · θ11 [ω0])} |
>> | ω1 · exp (j · π / 2)
・ {B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])
−b11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])} |
... (238)

When E4s0a is obtained by approximating the electromotive force sum E4s0 by applying the conditions of the equations (235) to (238) to the equation (234), the electromotive force sum E4s0a is expressed by the equations (239) and (240). Is done.
E4s0a≈E4s0 (239)
E4s0a = (1/2) · ma · rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {2 ・ b10 [ω0] ・ exp (j ・ θ10 [ω0])
+ 2 · b11 [ω0] · exp (j · θ11 [ω0])}
+ Γ · V · exp (j · Δθ01)
・ {2 ・ b10 [ω0] ・ exp (j ・ θ10 [ω0])
-2 · b11 [ω0] · exp (j · θ11 [ω0])} (240)

As in equation (231), if θ11 [ω0] = θ10 [ω0] + Δθ11 [ω0] is substituted into the electromotive force sum E4s0a in equation (240), E4s0b is obtained, and the electromotive force sum E4s0b is expressed by the following equation: .
E4s0b = ma · rk · exp {j · (θ10 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])}]
... (241)

Further, if b10 [ω0] = b11 [ω0] and Δθ11 [ω] = 0 are set in the magnetic fields B10 and B11 in the initial state (the state at the time of calibration), even if the subsequent deviation is considered, b10 [ω0] ≈b11 [ω0] and Δθ11 [ω] ≈0, and the following conditional expression holds.
| B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0]) |
»| B10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0]) |
... (242)

Further, since ω0> γ · V is normally satisfied, when the condition of the equation (242) is considered, the following equation is satisfied in the equation (241).
| Ω0 · exp (j · π / 2)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])} |
»| Γ · V · exp (j · Δθ01) · b10 [ω0]
−b11 [ω0] · exp (j · Δθ11 [ω0]) | (243)

An electromotive force sum EdA41 obtained by multiplying an approximation of the electromotive force sum E4s0b of the equation (241) by (1 / ma) using the condition of the equation (243) is expressed by the following equation. This electromotive force sum EdA41 corresponds to the first ∂A / ∂t component in the basic principle.
EdA41≈E4s0b · (1 / ma) ≈E4s0 · (1 / ma) (244)
EdA41 = rk · exp {j · (θ10 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}
... (245)

Since the electromotive force sum EdA41 is not related to the magnitude V of the flow velocity, it becomes only the component generated by ∂A / ∂t. Using this electromotive force sum EdA41, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the interelectrode electromotive force E40 (the combined vector Vas0 + Vbs0) is normalized. If the inter-electrode electromotive force E40 is normalized by the electromotive force sum EdA41 and multiplied by ω0 to be En40, the normalized electromotive force En40 is expressed by the following equation.
En40 = (E40 / EdA41) · ω0
= Rk · exp {j · (θ10 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}]
/ [Rk · exp {j · (θ10 [ω0] + θ00)} · ω0 · exp (j · π / 2)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}] · ω0
= Ω0 · {b10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])}
/ {B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (246)

Using equation (52), the coefficient {b10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])} / {b10 [ω0] applied to the angular frequency ω0 of the first term on the right-hand side of equation (246) ] + B11 [ω0] · exp (j · Δθ11 [ω0])} is represented by a value {b10−b11 · exp (j · Δθ11)} / {b10 + b11 · exp (j · Δθ11)} not related to the angular frequency ω0. be able to. Therefore, the equation (246) can be replaced by the following equation.
En40 = ω0 · {b10−b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (247)

  The second term on the right side of Equation (247) is a term obtained by normalizing the component generated by v × B. The reason why the result obtained by normalizing the inter-electrode electromotive force E40 with the electromotive force sum EdA41 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side of the magnitude V of the flow velocity. The complex coefficient relating to the magnitude V of the flow velocity has an angle from the real axis of the magnitude of γ, −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (247) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the component ∂A / ∂t, it is possible to realize span correction that automatically corrects errors due to magnetic field shifts and phase changes.

Next, a method for removing the first term on the right side of the equation (247), which is a factor of variation at 0 point, will be described. If the angular frequency of the carrier wave is ω2 instead of ω0 in equations (218) and (228), the magnetic fields B10 and B11 are expressed by the following equations.
B10 = b10 · {1 + ma · cos (ω1 · t)} · cos (ω2 · t−θ10) (248)
B11 = b11 · {1−ma · cos (ω1 · t)} · cos (ω2 · t−θ11) (249)

  Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. The inter-electrode electromotive force E42 subjected to span correction at the angular frequency ω2 is obtained by replacing the angular frequency ω0 with ω2 in the equation (231). The electromotive force sum E4s2 that is the basis of the second ∂A / ∂t component is the interelectrode electromotive force E4p2 in which the angular frequency ω0 is replaced with ω2 in Equation (232), and the angular frequency ω0 in ω2 in Equation (233). It is represented by the sum E4p2 + E4m2 with the interelectrode electromotive force E4m2. The electromotive force sum EdA42 as the second ∂A / ∂t component is obtained by replacing the angular frequency ω0 with ω2 in the equation (245).

If the result obtained by normalizing the inter-electrode electromotive force E42 by the electromotive force sum EdA42 and multiplying it by ω2 is taken as En42, the normalized electromotive force En42 is expressed by the following equation from the equation (247).
En42 = ω2 · {b10−b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (250)

Taking the difference between the normalized electromotive forces En40 and En42 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA43, the electromotive force difference EdA43 is expressed by the following equation. This electromotive force difference EdA43 corresponds to the third ∂A / ∂t component in the basic principle.
EdA43 = (En40−En42) · ω0 / (ω0−ω2)
= [{B10−b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)}
.Omega.0 + .gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V
-{B10-b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)}
.Omega.2-.gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V]
・ Ω0 / (ω0−ω2)
= {B10-b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)} · ω0 ·· (251)

The electromotive force difference EdA43 represents a normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (247). Therefore, if this electromotive force difference EdA43 is used, the normalized v × B component Can be extracted from the normalized electromotive force En40. When the v × B component obtained by subtracting the electromotive force difference EdA43 of the equation (251) from the normalized electromotive force En40 of the equation (247) is EvBn4, the v × B component EvBn4 is expressed by the following equation.
EvBn4 = En40-EdA43
= {B10-b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)} · ω0
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
-{B10-b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)} · ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (252)

The v × B component EvBn4 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvBn4 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBn4. From the equation (252), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn4 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn4 | / γ (253)

  The correspondence between the constants and variables used in the basic principle and the constants and variables of the present embodiment is as shown in Table 4 below. As is apparent from Table 4, this embodiment is an example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. Since the configuration of the electromagnetic flowmeter of the present embodiment is the same as that of the first embodiment, description will be made using the reference numerals in FIG. The electromagnetic flowmeter of the present embodiment includes a measuring tube 1, electrodes 2a and 2b, first and second exciting coils 3a and 3b, a power supply unit 4, a signal conversion unit 5, and a flow rate output unit 6. Have

  The signal conversion unit 5 obtains the amplitude and phase of the combined electromotive force detected by the electrodes 2a and 2b in each of the first excitation state and the second excitation state, and performs the first excitation based on these amplitudes and phases. The sum of electromotive forces of the component of the angular frequency ω0 + ω1 and the component of the angular frequency ω0−ω1 of the combined electromotive force in the state is extracted as the first ∂A / ∂t component, and the angle of the combined electromotive force in the second excitation state The sum of electromotive forces of the component of frequency ω2 + ω1 and the component of angular frequency ω2-ω1 is extracted as the second ∂A / ∂t component, and the component of angular frequency ω0 of the composite electromotive force in the first excitation state is the first. As a correction target electromotive force, based on the first ∂A / ∂t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the second excitation state Using the component of the angular frequency ω2 of the combined electromotive force as the second correction target electromotive force, A span correction unit 51 that removes a variation factor of the span included in the v × B component in the second correction target electromotive force based on the A / ∂t component, and the first correction target electromotive force that has been subjected to span correction A difference from the second correction target electromotive force subjected to the span correction is extracted as a third ∂A / ∂t component, and the third one of the two correction target electromotive forces subjected to the span correction is extracted. The zero point correction unit 52 extracts the v × B component by removing the ∂A / ∂t component.

  The power supply unit 4 according to the present embodiment supplies a first excitation current obtained by amplitude-modulating a sine wave carrier wave having an angular frequency ω0 with a sine wave modulation wave having an angular frequency ω1 to the first excitation coil 3a, and at the same time, the angular frequency. First excitation for supplying a second excitation current obtained by amplitude-modulating a sine wave carrier wave of ω0 with a modulated wave having the same angular frequency and opposite phase to the modulated wave of the first excitation current to the second excitation coil 3b. The state continues for T1 seconds, and a third excitation current obtained by amplitude-modulating a sine wave carrier wave having an angular frequency ω2 with a sine wave modulation wave having an angular frequency ω1 is supplied to the first excitation coil 3a, and at the same time, the sine wave having the angular frequency ω2 is supplied. A second excitation state in which a fourth excitation current obtained by amplitude-modulating a wave carrier wave with a modulation wave having the same angular frequency and an opposite phase with respect to the modulation wave of the third excitation current is supplied to the second excitation coil 3b. To last seconds Repeated at T second period. That is, T = T1 + T2. The amplitude modulation index ma is an arbitrary value.

  FIG. 21 is a flowchart showing the operations of the signal conversion unit 5 and the flow rate output unit 6 of the present embodiment. First, the span correction unit 51 of the signal conversion unit 5 obtains the amplitude r40 of the electromotive force E40 of the component of the angular frequency ω0 among the electromotive forces between the electrodes 2a and 2b in the first excitation state, and the real axis and the electrode A phase difference φ40 with respect to the inter-electromotive force E40 is obtained by a phase detector (not shown) (step 401 in FIG. 21). Further, the span correction unit 51 obtains the amplitude r4s0 of the sum E4s0 of the angular frequency (ω0 + ω1) component and the angular frequency (ω0−ω1) component of the electromotive force between the electrodes 2a and 2b in the first excitation state. At the same time, a phase difference φ4s0 between the real axis and the electromotive force sum E4s0 is obtained by the phase detector (step 402).

  Subsequently, in the second excitation state, the span correction unit 51 obtains the amplitude r42 of the electromotive force E42 of the component of the angular frequency ω2 among the electromotive forces between the electrodes 2a and 2b, and at the same time, the real axis and the interelectrode electromotive force E42. Is obtained by a phase detector (step 403). Further, the span correction unit 51 obtains the amplitude r4s2 of the sum E4s2 of the angular frequency (ω2 + ω1) component and the angular frequency (ω2−ω1) component of the electromotive force between the electrodes 2a and 2b in the second excitation state. At the same time, a phase difference φ4s2 between the real axis and the electromotive force sum E4s2 is obtained by the phase detector (step 404). The components of the inter-electrode electromotive force E40, E42 and the inter-electrode electromotive force angular frequency (ω0 + ω1), (ω0-ω1), (ω2 + ω1), (ω2-ω1) may be frequency separated by a bandpass filter or a comb filter. it can.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force sum EdA41 that approximates the electromotive force sum E4s0 (step 405). The process of step 405 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of Expression (245). The span correction unit 51 calculates the magnitude | EdA41 | of the electromotive force sum EdA41 as follows.
| EdA41 | = r4s0 (254)
Then, the span correction unit 51 calculates the angle ∠EdA41 of the electromotive force sum EdA41 as the following equation.
∠EdA41 = φ4s0 (255)
This completes the process of step 405.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force En40 obtained by normalizing the inter-electrode electromotive force E40 with the electromotive force sum EdA41 (step 406). The process of step 406 is a process corresponding to the calculation of equation (247). The span correction unit 51 calculates the magnitude | En40 | of the normalized electromotive force En40 as the following equation.
| En40 | = (r40 / | EdA41 |) · ω0 (256)

Then, the span correction unit 51 calculates the angle ∠En40 of the normalized electromotive force En40 as the following expression.
∠En40 = φ40−∠EdA41 (257)
Further, the span correction unit 51 calculates the real axis component En40x and the imaginary axis component En40y of the normalized electromotive force En40 as the following expression.
En40x = | En40 | .cos (∠En40) (258)
En40y = | En40 | .sin (∠En40) (259)
This completes the process of step 406.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force sum EdA42 that approximates the electromotive force sum E4s2 (step 407). The processing in step 407 is processing corresponding to obtaining the second ∂A / ∂t component. The span correction unit 51 calculates the magnitude | EdA42 | of the electromotive force sum EdA42 as follows.
| EdA42 | = r4s2 (260)
Then, the span correction unit 51 calculates the angle ∠EdA42 of the electromotive force sum EdA42 as the following equation.
∠EdA42 = φ4s2 (261)
This completes the process of step 407.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force En42 obtained by normalizing the interelectrode electromotive force E42 with the electromotive force sum EdA42 (step 408). The process of step 408 is a process corresponding to the calculation of Expression (250). The span correction unit 51 calculates the magnitude | En42 | of the normalized electromotive force En42 as the following expression.
| En42 | = (r42 / | EdA42 |) · ω2 (262)

Then, the span correction unit 51 calculates the angle ∠En42 of the normalized electromotive force En42 as the following expression.
∠En42 = φ42−∠EdA42 (263)
Further, the span correction unit 51 calculates the real axis component En42x and the imaginary axis component En42y of the normalized electromotive force En42 as the following expression.
En42x = | En42 | .cos (∠En42) (264)
En42y = | En42 | .sin (∠En42) (265)
This completes the process of step 408.

Next, the zero point correction unit 52 of the signal conversion unit 5 obtains the magnitude of the electromotive force difference EdA43 between the normalized electromotive forces En40 and En42 (step 409). The process of step 409 is a process corresponding to obtaining the third ∂A / ∂t component, and is a process corresponding to the calculation of Expression (251). The zero point correction unit 52 calculates the real axis component EdA43x and the imaginary axis component EdA43y of the electromotive force difference EdA43 as follows.
EdA43x = (En40x−En42x) · ω0 / (ω0−ω2) (266)
EdA43y = (En40y−En42y) · ω0 / (ω0−ω2) (267)

Then, the zero point correction unit 52 removes the electromotive force difference EdA43 from the normalized electromotive force En40 and obtains the magnitude of the v × B component EvBn4 (step 410). The process of step 410 is a process corresponding to the calculation of equation (252). The zero point correction unit 52 calculates the magnitude | EvBn4 | of the v × B component EvBn4 as follows.
| EvBn4 | = {(En40x−EdA43x) ²
+ (En40y−EdA43y) ² } ^1/2 (268)

The flow rate output unit 6 calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 411). The process of step 411 is a process corresponding to the calculation of Expression (253).
V = | EvBn4 | / γ (269)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5 and the flow rate output unit 6 perform the processes in steps 401 to 411 as described above at regular intervals until the operator instructs the end of measurement (YES in step 412). Note that the processing in steps 403 to 411 is performed in the second excitation state.

  As described above, in the present embodiment, in the first excitation state, the electromotive force E40 of the component of the angular frequency ω0, the electromotive force sum of the component of the angular frequency (ω0 + ω1) and the angular frequency (ω0−ω1) component. E4s0 is obtained, and in the second excitation state, an electromotive force E42 of the component of the angular frequency ω2, and an electromotive force sum E4s2 of the angular frequency (ω2 + ω1) component and the angular frequency (ω2-ω1) component are obtained. In this embodiment, if the magnetic field B10 generated from the first excitation coil 3a is set to be equal to the magnetic field B11 generated from the second excitation coil 3b, the electromotive force sum E4s0 is approximate. The first 抽出 A / 起 t component can be extracted as the first ∂A / ∂t component, and the electromotive force sum E4s2 can be approximately extracted as the second 、 A / ∂t component. Normalizing the span of the flow velocity V of the v × B component in the interelectrode electromotive force E40 and using the second ∂A / ∂t component, the v × B component in the interelectrode electromotive force E42 Normalization is performed on the span of the flow velocity V, the electromotive force difference EdA43 (third ∂A / ∂t component) is extracted from the normalized electromotive forces En40 and En42, and the normalized electromotive force En40 is used as the third. By removing the ∂A / ∂t component of Since the flow rate of the fluid to be measured is calculated from the v × B component, accurate span correction can be automatically performed, and the flow rate of the electromagnetic flow meter can be reduced without reducing the flow rate of the fluid to be measured to zero. The zero point of the output can be corrected, and the stability of the zero point can be ensured even in high frequency excitation.

In the present embodiment, in consideration of the difference in magnetic field loss depending on the frequency, the first ∂A / of the same angular frequency obtained by extracting the v × B component of the electromotive force E40 having the angular frequency ω0 from the electromotive force sum E4s0. Normalize using the ∂t component and normalize the v × B component of the electromotive force E42 of the angular frequency ω2 using the second ∂A / ∂t component of the same angular frequency extracted from the electromotive force sum E4s2. Since zero correction is performed based on the difference between the normalized electromotive forces En40 and En42, accurate span correction and zero correction can be performed even when there is an influence of magnetic field loss.
In the present embodiment, it is not necessary to switch the phase difference of the magnetic field only by switching the frequency of the carrier wave, and it is not necessary to use the four excitation states as in the first embodiment. Can be calculated.

In the present embodiment, the electromotive force E40 of the component of the angular frequency ω0 is the target of 0 correction and span correction, but the electromotive force E42 of the component of the angular frequency ω2 may be the target of 0 correction and span correction. In this case, the electromotive force difference EdA43 (third ∂A / ∂t component) is obtained from the normalized electromotive forces En42 and En40 as in the following equation.
EdA43 = (En42−En40) · ω2 / (ω2−ω0) (270)
Then, the v × B component EvBn4 may be obtained by subtracting the electromotive force difference EdA43 from the normalized electromotive force En42 as in the following equation. The other processes are the same as those in the case where the interelectrode electromotive force E40 is subjected to 0 correction and span correction.
| EvBn4 | = | En42−EdA43 | (271)

[Fifth Embodiment]
Next, a fifth embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has two excitation coils and a pair of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. The present embodiment uses the second detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The second extraction method described is used.

The excitation conditions in the present embodiment are the same as those in the fourth embodiment. In the equation (228), the phase difference θ11 [ω0] of the component of the angular frequency ω0 of the magnetic field B11 is replaced with π + θ11 [ω0], and the inter-electrode electromotive force E5π0 when θ01 = θ00 + Δθ01 is substituted is expressed by the following equation. The
E5π0 = rk · exp {j · (θ10 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])}]
... (272)

In the equation (229), the inter-electrode electromotive force E5πp0 when the phase difference θ11 [ω0] is replaced by π + θ11 [ω0] and θ01 = θ00 + Δθ01 is substituted is expressed by the following equation.
E5πp0 = (1/2) · ma · rk · exp (j · θ00)
・ [(Ω0 + ω1) · exp (j · π / 2)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
-B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
+ B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])}]
... (273)

In the equation (230), the inter-electrode electromotive force E5πm0 when the phase difference θ11 [ω0] is replaced by π + θ11 [ω0] and θ01 = θ00 + Δθ01 is substituted is expressed by the following equation. However, in the equations (272), (273), and (274), θ11 [ω0] = θ10 [ω0] + Δθ11 [ω0] is not applied, and is applied in the later equations. Also, it should be noted that the phase difference of the modulation part is originally opposite, so that it is the same phase.
E5πm0 = (1/2) · ma · rk · exp (j · θ00)
・ [(Ω0−ω1) · exp (j · π / 2)
{B10 [ω0-ω1] exp (j · θ10 [ω0-ω1])
−b11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0-ω1] exp (j · θ10 [ω0-ω1])
+ B11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}]
... (274)

If the sum of the interelectrode electromotive forces E5πp0 and E5πm0 is E5πs0, the electromotive force sum E5πs0 is expressed by the following equation.
E5πs0 = E5πp0 + E5πm0
= (1/2) · ma · rk · exp (j · θ00)
・ [(Ω0 + ω1) · exp (j · π / 2)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
-B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
+ B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])}]
+ (1/2) · ma · rk · exp (j · θ00)
・ [(Ω0−ω1) · exp (j · π / 2)
{B10 [ω0-ω1] exp (j · θ10 [ω0-ω1])
−b11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0-ω1] exp (j · θ10 [ω0-ω1])
+ B11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}]
= (1/2) · ma · rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
-B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])
+ B10 [ω0−ω1] · exp (j · θ10 [ω0−ω1])
−b11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}
+ Ω1 · exp (j · π / 2)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
-B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])
−b10 [ω0−ω1] · exp (j · θ10 [ω0−ω1])
+ B11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B10 [ω0 + ω1] · exp (j · θ10 [ω0 + ω1])
+ B11 [ω0 + ω1] · exp (j · θ11 [ω0 + ω1])
+ B10 [ω0−ω1] · exp (j · θ10 [ω0−ω1])
+ B11 [ω0−ω1] · exp (j · θ11 [ω0−ω1])}]
... (275)

When E5πs0a is obtained by approximating the electromotive force sum E5πs0 by applying the conditions of the equations (235) to (238) to the equation (275), the electromotive force sum E5πs0a is expressed by the equations (276) and (277). Is done.
E5πs0a≈E5πs0 (276)
E5πs0a = (1/2) · ma · rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {2 ・ b10 [ω0] ・ exp (j ・ θ10 [ω0])
-2 · b11 [ω0] · exp (j · θ11 [ω0])}
+ Γ · V · exp (j · Δθ01)
・ {2 ・ b10 [ω0] ・ exp (j ・ θ10 [ω0])
+ 2 · b11 [ω0] · exp (j · θ11 [ω0])}
... (277)

Here, if the value obtained by substituting θ11 [ω0] = θ10 [ω0] + Δθ11 [ω0] into the electromotive force sum E5πs0a of the equation (277) is E5πs0b, the electromotive force sum E5πs0b is expressed by the following equation.
E5πs0b = ma · rk · exp {j · (θ10 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}]
... (278)

In the initial state (calibration state) of the magnetic fields B10 and B11, if b10 [ω0] = b11 [ω0] and Δθ11 [ω0] = 0 are set, b10 [ω0 ] ≈b11 [ω0], Δθ11 [ω0] ≈0, and the conditional expression (243) shown in the third embodiment holds.
An electromotive force EdA51 obtained by multiplying an approximation of the interelectrode electromotive force E5π0 of the equation (272) using the condition of the equation (243) is expressed by the following equation. This electromotive force EdA51 corresponds to the first ∂A / ∂t component in the basic principle.
EdA51≈E5π0 · ma (279)
EdA51 = ma · rk · exp {j · (θ10 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}
... (280)

Since the electromotive force EdA51 is not related to the magnitude V of the flow velocity, only the component generated by ∂A / ∂t is included. Using this electromotive force EdA51, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the electromotive force sum E5πs0b (combined vector Vas0 + Vbs0) is normalized. When the electromotive force sum E5πs0b is normalized by the electromotive force EdA51 and multiplied by ω0 is En50, the normalized electromotive force sum En50 is expressed by the following equation.
En50 = (E5πs0b / EdA51) · ω0
= Ma · rk · exp {j · (θ10 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}]
/ [Ma · rk · exp {j · (θ10 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}] · ω0
= Ω0 · {b10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])}
/ {B10 [ω0] + b11 [ω0] · exp (j · Δθ11 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (281)

Using the equation (52), the coefficient {b10 [ω0] −b11 [ω0] · exp (j · Δθ11 [ω0])} / {b10 [ω0] applied to the angular frequency ω0 of the first term on the right side of the equation (281). ] + B11 [ω0] · exp (j · Δθ11 [ω0])} is represented by a value {b10−b11 · exp (j · Δθ11)} / {b10 + b11 · exp (j · Δθ11)} not related to the angular frequency ω0. be able to. Therefore, the equation (281) can be replaced by the following equation.
En50 = ω0 · {b10−b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (282)

  The second term on the right side of Expression (282) is a term obtained by normalizing the component generated by v × B. The reason why the result obtained by normalizing the electromotive force sum E5πs0b with the electromotive force EdA51 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side of the magnitude V of the flow velocity. The complex coefficient relating to the magnitude V of the flow velocity has an angle from the real axis of the magnitude of γ, −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (282) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the component ∂A / ∂t, it is possible to realize span correction that automatically corrects errors due to magnetic field shifts and phase changes.

  Next, a method for removing the first term on the right side of the equation (282), which is a variation factor of the zero point, will be described. When the angular frequency of the carrier wave is ω2 instead of ω0, the magnetic fields B10 and B11 are expressed by the equations in which θ11 is replaced by π + θ11 in the equations (248) and (249). Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. The electromotive force sum E5πs2 to be subjected to span correction at the angular frequency ω2 is the inter-electrode electromotive force E5πp2 in which the angular frequency ω0 is replaced with ω2 in the equation (273) and the interelectrode between the electrodes in which the angular frequency ω0 is replaced with ω2 in the equation (274). It is represented by the sum E5πp2 + E5πm2 with the electromotive force E5πm2. The interelectrode electromotive force E5π2 that is the basis of the second ∂A / ∂t component is expressed by the equation (272) in which the angular frequency ω0 is replaced with ω2. The electromotive force EdA52 serving as the second ∂A / ∂t component is obtained by replacing the angular frequency ω0 with ω2 in the equation (280).

If the result of normalizing the electromotive force sum E5πs2 with the electromotive force EdA52 and multiplying it by ω2 is En52, the normalized electromotive force sum En52 is expressed by the following equation from the equation (282).
En52 = ω2 · {b10−b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (283)

Taking the difference between the normalized electromotive force sums En50 and En52 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA53, the difference EdA53 is expressed by the following equation. This difference EdA53 corresponds to the third ∂A / ∂t component in the basic principle.
EdA53 = (En50−En52) · ω0 / (ω0−ω2)
= [{B10−b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)}
.Omega.0 + .gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V
-{B10-b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)}
.Omega.2-.gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V]
・ Ω0 / (ω0−ω2)
= {B10-b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)} · ω0 ·· (284)

The difference EdA53 represents the normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (282). Therefore, if this difference EdA53 is used, the normalized v × B component is normalized. It can be taken out from the power sum En50. When the v × B component obtained by subtracting the difference EdA53 of the equation (284) from the normalized electromotive force sum En50 of the equation (282) is EvBn5, the v × B component EvBn5 is expressed by the following equation.
EvBn5 = En50-EdA53
= {B10-b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)} · ω0
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
-{B10-b11 · exp (j · Δθ11)}
/ {B10 + b11 · exp (j · Δθ11)} · ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (285)

The v × B component EvBn5 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvBn5 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBn5. From the equation (285), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn5 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn5 | / γ (286)

  Table 5 below shows the correspondence between the constants and variables used in the basic principle and the constants and variables in the present embodiment. As is apparent from Table 5, this embodiment is one example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. Since the configuration of the electromagnetic flowmeter of the present embodiment is the same as that of the first embodiment, description will be made using the reference numerals in FIG. The electromagnetic flowmeter of the present embodiment includes a measuring tube 1, electrodes 2a and 2b, first and second exciting coils 3a and 3b, a power supply unit 4, a signal conversion unit 5, and a flow rate output unit 6. Have

  The signal conversion unit 5 obtains the amplitude and phase of the combined electromotive force detected by the electrodes 2a and 2b in each of the first excitation state and the second excitation state, and performs the first excitation based on these amplitudes and phases. The component of the angular frequency ω0 of the combined electromotive force in the state is extracted as the first ∂A / ∂t component, and the component of the angular frequency ω2 of the combined electromotive force in the second excitation state is extracted as the second ∂A / ∂t. The first electromotive force sum of the component of the angular frequency ω0 + ω1 and the component of the angular frequency ω0−ω1 of the composite electromotive force in the first excitation state is extracted as a first correction target electromotive force. Based on the t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the angular frequency ω2 + ω1 component and the angular frequency ω2 of the composite electromotive force in the second excitation state are removed. The sum of the electromotive force with the component of −ω1 is set as the second correction target electromotive force, and the second power A span correction unit 51 that removes a variation factor of the span included in the v × B component in the second correction target electromotive force based on the A / ∂t component, and the first correction target electromotive force that has been subjected to span correction A difference from the second correction target electromotive force subjected to the span correction is extracted as a third ∂A / ∂t component, and the third one of the two correction target electromotive forces subjected to the span correction is extracted. The zero point correction unit 52 extracts the v × B component by removing the ∂A / ∂t component.

  The operation of the power supply unit 4 is the same as that of the fourth embodiment. FIG. 22 is a flowchart showing the operations of the signal conversion unit 5 and the flow rate output unit 6 of the present embodiment. First, the span correction unit 51 of the signal conversion unit 5 has the amplitude of the electromotive force E5π0 of the component of the angular frequency ω0 in the electromotive force between the electrodes 2a and 2b in the first excitation state described in the fourth embodiment. In addition to obtaining r5π0, a phase difference φ5π0 between the real axis and the interelectrode electromotive force E5π0 is obtained by a phase detector (not shown) (step 501 in FIG. 22). Further, the span correction unit 51 obtains the amplitude r5πs0 of the sum E5πs0 of the angular frequency (ω0 + ω1) component and the angular frequency (ω0−ω1) component of the electromotive force between the electrodes 2a and 2b in the first excitation state. At the same time, a phase difference φ5πs0 between the real axis and the electromotive force sum E5πs0 is obtained by the phase detector (step 502).

  Subsequently, the span correction unit 51 obtains the amplitude r5π2 of the electromotive force E5π2 of the component of the angular frequency ω2 among the electromotive forces between the electrodes 2a and 2b in the second excitation state described in the fourth embodiment. Then, a phase difference φ5π2 between the real axis and the inter-electrode electromotive force E5π2 is obtained by a phase detector (step 503). The span correction unit 51 obtains the amplitude r5πs2 of the sum E5πs2 of the angular frequency (ω2 + ω1) component and the angular frequency (ω2-ω1) component of the electromotive force between the electrodes 2a and 2b in the second excitation state. At the same time, a phase difference φ5πs2 between the real axis and the electromotive force sum E5πs2 is obtained by the phase detector (step 504).

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force EdA51 that approximates the interelectrode electromotive force E5π0 (step 505). The process of step 505 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of Expression (280). The span correction unit 51 calculates the magnitude | EdA51 | of the electromotive force EdA51 as the following equation.
| EdA51 | = r5π0 (287)
Then, the span correction unit 51 calculates the angle ∠EdA51 of the electromotive force EdA51 as the following equation.
∠EdA51 = φ5π0 (288)
This completes the process of step 505.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force sum En50 obtained by normalizing the electromotive force sum E5πs0 with the electromotive force EdA51 (step 506). The process of step 506 is a process corresponding to the calculation of equation (282). The span correction unit 51 calculates the magnitude | En50 | of the normalized electromotive force sum En50 as the following equation.
| En50 | = (r5πs0 / | EdA51 |) · ω0 (289)

Then, the span correction unit 51 calculates the angle ∠En50 of the normalized electromotive force sum En50 as the following expression.
∠En50 = φ5πs0−∠EdA51 (290)
Further, the span correction unit 51 calculates the real axis component En50x and the imaginary axis component En50y of the normalized electromotive force sum En50 as the following equation.
En50x = | En50 | .cos (∠En50) (291)
En50y = | En50 | .sin (∠En50) (292)
This completes the processing in step 506.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force EdA52 that approximates the interelectrode electromotive force E5π2 (step 507). The processing in this step 507 is processing corresponding to obtaining the second ∂A / ∂t component. The span correction unit 51 calculates the magnitude | EdA52 | of the electromotive force EdA52 as follows.
| EdA52 | = r5π2 (293)
Then, the span correction unit 51 calculates the angle ∠EdA52 of the electromotive force EdA52 as the following equation.
∠EdA52 = φ5π2 (294)
This completes the processing in step 507.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force sum En52 obtained by normalizing the electromotive force sum E5πs2 with the electromotive force EdA52 (step 508). The process of step 508 is a process corresponding to the calculation of Expression (283). The span correction unit 51 calculates the magnitude | En52 | of the normalized electromotive force sum En52 as follows.
| En52 | = (r5πs2 / | EdA52 |) · ω2 (295)

Then, the span correction unit 51 calculates the angle ∠En52 of the normalized electromotive force sum En52 as the following equation.
∠En52 = φ5πs2-∠EdA52 (296)
Further, the span correction unit 51 calculates the real axis component En52x and the imaginary axis component En52y of the normalized electromotive force sum En52 as the following expression.
En52x = | En52 | .cos (∠En52) (297)
En52y = | En52 | .sin (∠En52) (298)
This completes the processing in step 508.

Next, the zero point correction unit 52 of the signal conversion unit 5 obtains the magnitude of the difference EdA53 between the normalized electromotive force sums En50 and En52 (step 509). The process of step 509 is a process corresponding to obtaining the third ∂A / ∂t component, and is a process corresponding to the calculation of Expression (284). The zero point correction unit 52 calculates the real axis component EdA53x and the imaginary axis component EdA53y of the difference EdA53 as in the following equation.
EdA53x = (En50x−En52x) · ω0 / (ω0−ω2) (299)
EdA53y = (En50y−En52y) · ω0 / (ω0−ω2) (300)

Then, the zero point correction unit 52 removes the difference EdA53 from the normalized electromotive force sum En50 and obtains the magnitude of the v × B component EvBn5 (step 510). The process of step 510 is a process corresponding to the calculation of equation (285). The zero point correction unit 52 calculates the magnitude | EvBn5 | of the v × B component EvBn5 as the following equation.
| EvBn5 | = {(En50x−EdA53x) ²
+ (En50y−EdA53y) ² } ^1/2 (301)

The flow rate output unit 6 calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 511). The process of step 511 is a process corresponding to the calculation of equation (286).
V = | EvBn5 | / γ (302)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5 and the flow rate output unit 6 perform the processing in steps 501 to 511 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 512). Note that the processing in steps 503 to 511 is performed in the second excitation state.

  As described above, in the present embodiment, in the first excitation state, the electromotive force E5π0 of the component of the angular frequency ω0, the electromotive force sum of the component of the angular frequency (ω0 + ω1) and the angular frequency (ω0−ω1) component. E5πs0 is obtained, and in the second excitation state, the electromotive force E5π2 of the component of the angular frequency ω2, and the electromotive force sum E5πs2 of the component of the angular frequency (ω2 + ω1) and the angular frequency (ω2-ω1) component are obtained. In this embodiment, if the magnetic field B10 generated from the first excitation coil 3a is set to be equal to the magnetic field B11 generated from the second excitation coil 3b, the interelectrode electromotive force E5π0 is approximated. Focusing on the fact that the first ∂A / ∂t component can be extracted, and the interelectrode electromotive force E5π2 can be approximately extracted as the second ∂A / ∂t component, the first ∂A / ∂t component Is used to normalize the span of the velocity V of the v × B component in the electromotive force sum E5πs0 and v × B component in the electromotive force sum E5πs2 using the second ∂A / ∂t component. Normalization is performed on the span of the flow velocity magnitude V, and a difference EdA53 (third ∂A / ∂t component) is extracted from the normalized electromotive force sums En50 and En52 to obtain a third from the normalized electromotive force sum En50. V × B by removing the ∂A / ∂t component of Since the flow rate of the fluid to be measured is calculated from this v × B component, accurate span correction can be automatically performed, and the electromagnetic flow can be obtained without reducing the flow rate of the fluid to be measured to zero. The zero point of the output of the flow meter can be corrected, and the stability of the zero point can be ensured even in high frequency excitation.

In the present embodiment, the first ∂A / ∂t component having the same angular frequency obtained by extracting the v × B component of the electromotive force sum E5πs0 from the electromotive force E5π0 in consideration of the difference in magnetic field loss depending on the frequency. And normalizing the v × B component of the electromotive force sum E5πs2 using the second ∂A / ∂t component of the same angular frequency extracted from the electromotive force E5π2, and respectively normalizing the electromotive force sum En50. Since the zero correction is performed based on the difference between En and 52, accurate span correction and zero correction can be performed even when there is an influence due to the loss of the magnetic field.
In the present embodiment, it is not necessary to switch the phase difference of the magnetic field only by switching the frequency of the carrier wave, and it is not necessary to use the four excitation states as in the first embodiment. Can be calculated.

In the present embodiment, the electromotive force sum E5πs0 is the target of 0 correction and span correction, but the electromotive force sum E5πs2 may be the target of 0 correction and span correction. In this case, the difference EdA53 (third ∂A / ∂t component) is obtained from the normalized electromotive force sums En52 and En50 as in the following equation.
EdA53 = (En52-En50) · ω2 / (ω2-ω0) (303)
Then, the v × B component EvBn5 may be obtained by subtracting the difference EdA53 from the normalized electromotive force sum En52 as in the following equation. The other processes are the same as those in the case where the electromotive force sum E5πs0 is the target of 0 correction and span correction.
| EvBn5 | = | En52-EdA53 | (304)

[Sixth Embodiment]
Next, a sixth embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has two excitation coils and a pair of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. The present embodiment uses the second detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The second extraction method described is used.

Of the magnetic field Bb generated from the first exciting coil 3a, a magnetic field component (magnetic flux density) B12 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX connecting the electrodes 2a and 2b, The magnetic field component (magnetic flux density) B13 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX among the magnetic field Bc generated from the excitation coil 3b is given as follows.
B12 = b12 · cos {ω0 · t-mp · cos (ω1 · t) −θ12} (305)
B13 = b13 · cos {ω0 · t + mp · cos (ω1 · t) −θ13} (306)

  In equations (305) and (306), b12 and b13 are the amplitudes of the magnetic flux densities B12 and B13, ω0 is the angular frequency of the carrier wave, ω1 is the angular frequency of the modulated wave, and θ12 is the magnetic flux density B12 and ω0 · t-mp ·. The phase difference (phase lag) from cos (ω1 · t), θ13 is the phase difference between the magnetic flux density B13 and ω0 · t-mp · cos (ω1 · t), and mp is the phase modulation index. Hereinafter, the magnetic flux density B12 is referred to as a magnetic field B12, and the magnetic flux density B13 is referred to as a magnetic field B13. Expressions (305) and (306) can be transformed as follows.

B12 = b12 · cos {ω0 · t-mp · cos (ω1 · t) −θ12}
= B12 · cos (ω0 · t−θ12) · cos {−mp · cos (ω1 · t)}
−b12 · sin (ω0 · t−θ12) · sin {−mp · cos (ω1 · t)}
= B12 · cos {mp · cos (ω1 · t)}
・ {Cos (ω0 · t) ・ cos (−θ12)
-Sin (ω0 · t) · sin (-θ12)}
+ B12 · sin {mp · cos (ω1 · t)}
・ {Sin (ω0 · t) ・ cos (−θ12)
+ Cos (ω0 · t) · sin (−θ12)} (307)

B13 = b13 · cos {ω0 · t + mp · cos (ω1 · t) −θ13}
= B13 · cos (ω0 · t−θ13) · cos {mp · cos (ω1 · t)}
−b13 · sin (ω0 · t−θ13) · sin {mp · cos (ω1 · t)}
= −b13 · cos {mp · cos (ω1 · t)}
・ {Cos (ω0 · t) ・ cos (−θ13)
-Sin (ω0 · t) · sin (-θ13)}
-B13 · sin {mp · cos (ω1 · t)}
・ {Sin (ω0 ・ t) ・ cos (−θ13)
+ Cos (ω0 · t) · sin (−θ13)} (308)

  Here, cos {mp · cos (ω1 · t)} and sin {mp · cos (ω1 · t)} in the equations (307) and (308) can be converted as the following equations.

In the expressions (309) and (310), J _n (mp) (n = 0, 1, 2,...) Is known as a first kind Bessel function, and this first kind Bessel function J _n ( mp) is given by:

In equation (311), k! Means the factorial of k. If only n = 0 and 1 are employed in the equations (309) and (310), the equations (307) and (308) can be modified as follows.
B12 = J ₀ (mp) · b12 · {cos (θ12)} · cos (ω0 · t)
+ J ₀ (mp) · b12 · {sin (θ12)} · sin (ω0 · t)
+ J ₁ (mp) · b12 · {−sin (θ12)} · cos {(ω0 + ω1) · t}
+ J ₁ (mp) · b12 · {cos (θ12)} · sin {(ω0 + ω1) · t}
+ J ₁ (mp) · b12 · {−sin (θ12)} · cos {(ω0−ω1) · t}
+ J ₁ (mp) · b12 · {cos (θ12)} · sin {(ω0−ω1) · t}
... (312)

B13 = J ₀ (mp) · b13 · {cos (θ13)} · cos (ω0 · t)
+ J ₀ (mp) · b13 · {sin (θ13)} · sin (ω0 · t)
+ J ₁ (mp) · b13 · {sin (θ13)} · cos {(ω0 + ω1) · t}
+ J ₁ (mp) · b13 · {−cos (θ13)} · sin {(ω0 + ω1) · t}
+ J ₁ (mp) · b13 · {sin (θ13)} · cos {(ω0−ω1) · t}
+ J ₁ (mp) · b13 · {−cos (θ13)} · sin {(ω0−ω1) · t}
... (313)

  Considering the loss of the magnetic field at each angular frequency, the amplitudes b12 and b13 of the components of the angular frequency ω0 of the magnetic fields B12 and B13 are changed to function notations b12 [ω0] and b13 [ω0], respectively. The phase differences θ12 and θ13 of the component of ω0 are changed to θ12 [ω0] and θ13 [ω0], respectively. In addition, the amplitudes b12 and b13 of the components of the angular frequencies (ω0 + ω1) of the magnetic fields B12 and B13 are changed to b12 [ω0 + ω1] and b13 [ω0 + ω1], respectively, in the function notation. , Θ13 are changed to θ12 [ω0 + ω1] and θ13 [ω0 + ω1], respectively. Further, the amplitudes b12 and b13 of the components of the angular frequencies (ω0−ω1) of the magnetic fields B12 and B13 are changed to b12 [ω0−ω1] and b13 [ω0−ω1], respectively, and the angular frequencies (ω0− The phase differences θ12 and θ13 of the components of ω1) are changed to θ12 [ω0−ω1] and θ13 [ω0−ω1], respectively. As a result, Expression (312) and Expression (313) are replaced with Expression (314) and Expression (315).

B12 = J ₀ (mp) · b12 [ω0]
{Cos (θ12 [ω0])} · cos (ω0 · t)
+ J ₀ (mp) · b12 [ω0] · {sin (θ12 [ω0])} · sin (ω0 · t)
+ J ₁ (mp) · b12 [ω0 + ω1] · {−sin (θ12 [ω0 + ω1])}
Cos {(ω0 + ω1) · t}
+ J ₁ (mp) · b12 [ω0 + ω1] · {cos (θ12 [ω0 + ω1])}
Sin {(ω0 + ω1) · t}
+ J ₁ (mp) · b12 [ω0−ω1] · {−sin (θ12 [ω0−ω1])}
Cos {(ω0−ω1) · t}
+ J ₁ (mp) · b12 [ω0−ω1] · {cos (θ12 [ω0−ω1])}
Sin {(ω0−ω1) · t} (314)

B13 = J ₀ (mp) · b13 [ω0]
{Cos (θ13 [ω0])} · cos (ω0 · t)
+ J ₀ (mp) · b13 [ω0] · {sin (θ13 [ω0])} · sin (ω0 · t)
+ J ₁ (mp) · b13 [ω0 + ω1] · {sin (θ13 [ω0 + ω1])}
Cos {(ω0 + ω1) · t}
+ J ₁ (mp) · b13 [ω0 + ω1] · {−cos (θ13 [ω0 + ω1])}
Sin {(ω0 + ω1) · t}
+ J ₁ (mp) · b13 [ω0−ω1] · {sin (θ13 [ω0−ω1])}
Cos {(ω0−ω1) · t}
+ J ₁ (mp) · b13 [ω0−ω1] · {−cos (θ13 [ω0−ω1])}
Sin {(ω0−ω1) · t} (315)

Since the electromotive force resulting from the change in the magnetic field is based on the time derivative dB / dt of the magnetic field, the magnetic field B12 generated from the first excitation coil 3a and the magnetic field B13 generated from the second excitation coil 3b are differentiated as follows: To do.
dB12 / dt = J ₀ (mp) · ω0 · cos (ω0 · t)
B12 [ω0] · {sin (θ12 [ω0])}
+ J ₀ (mp) · ω0 · sin (ω0 · t)
B12 [ω0] • {−cos (θ12 [ω0])}
+ J ₁ (mp) · (ω0 + ω1) · cos {(ω0 + ω1) · t}
B12 [ω0 + ω1] · {cos (θ12 [ω0 + ω1])}
+ J ₁ (mp) · (ω0 + ω1) · sin {(ω0 + ω1) · t}
B12 [ω0 + ω1] · {sin (θ12 [ω0 + ω1])}
+ J ₁ (mp) · (ω0−ω1) · cos {(ω0−ω1) · t}
B12 [ω0−ω1] • {cos (θ12 [ω0−ω1])}
+ J ₁ (mp) · (ω 0 −ω 1) · sin {(ω 0 −ω 1) · t}
B12 [ω0−ω1] • {sin (θ12 [ω0−ω1])}
... (316)

dB13 / dt = J ₀ (mp) · ω0 · cos (ω0 · t)
B13 [ω0] · {sin (θ13 [ω0])}
+ J ₀ (mp) · ω0 · sin (ω0 · t)
B13 [ω0] · {−cos (θ13 [ω0])}
+ J ₁ (mp) · (ω0 + ω1) · cos {(ω0 + ω1) · t}
B13 [ω0 + ω1] • {−cos (θ13 [ω0 + ω1])}
+ J ₁ (mp) · (ω0 + ω1) · sin {(ω0 + ω1) · t}
B13 [ω0 + ω1] • {−sin (θ13 [ω0 + ω1])}
+ J ₁ (mp) · (ω0−ω1) · cos {(ω0−ω1) · t}
B13 [ω0−ω1] • {−cos (θ13 [ω0−ω1])}
+ J ₁ (mp) · (ω 0 −ω 1) · sin {(ω 0 −ω 1) · t}
B13 [ω0−ω1] • {−sin (θ13 [ω0−ω1])}
... (317)

  When the flow rate of the fluid to be measured is 0, it is generated by the change in the electromotive force E1 between the electrodes that is irrelevant to the flow rate and the change in the magnetic field Bc. The inter-electrode electromotive force E2 irrelevant to the flow velocity is opposite to each other as shown in FIG. At this time, the total inter-electrode electromotive force E obtained by adding the inter-electrode electromotive forces E1 and E2 is the difference (−dB12 / dt + dB13 / dt) is multiplied by the proportional coefficient rk for each angular frequency component of ω0, (ω0−ω1), (ω0 + ω1), and the phase differences θ12 and θ13 are replaced by θ12 + θ00 and θ13 + θ00, respectively (rk and θ00 are measured). (Related to the structure of the measuring tube 1 including the conductivity and dielectric constant of the fluid and the arrangement of the electrodes 2a, 2b).

E = J ₀ (mp) · rk · ω0 · cos (ω0 · t)
{-B12 [ω0] · sin (θ12 [ω0] + θ00)
+ B13 [ω0] · sin (θ13 [ω0] + θ00)}
+ J ₀ (mp) · rk · ω0 · sin (ω0 · t)
・ {B12 [ω0] · cos (θ12 [ω0] + θ00)
−b13 [ω0] · cos (θ13 [ω0] + θ00)}
+ J ₁ (mp) · rk · (ω0 + ω1) · cos {(ω0 + ω1) · t}
・ {−b12 [ω0 + ω1] · cos (θ12 [ω0 + ω1] + θ00)
-B13 [ω0 + ω1] · cos (θ13 [ω0 + ω1] + θ00)}
+ J ₁ (mp) · rk · (ω0 + ω1) · sin {(ω0 + ω1) · t}
{-B12 [ω0 + ω1] · sin (θ12 [ω0 + ω1] + θ00)
-B13 [ω0 + ω1] · sin (θ13 [ω0 + ω1] + θ00)}
+ J ₁ (mp) · rk · (ω0−ω1) · cos {(ω0−ω1) · t}
{-B12 [ω0-ω1] · cos (θ12 [ω0-ω1] + θ00)
−b13 [ω0−ω1] · cos (θ13 [ω0−ω1] + θ00)}
+ J ₁ (mp) · rk · (ω0−ω1) · sin {(ω0−ω1) · t}
{-B12 [ω0−ω1] · sin (θ12 [ω0−ω1] + θ00)
−b13 [ω0−ω1] · sin (θ13 [ω0−ω1] + θ00)}
... (318)

  When the magnitude of the flow velocity of the fluid to be measured is V (V ≠ 0), the interelectrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bb, and the interelectrode electromotive force Ev2 generated by the flow velocity vector v and the magnetic field Bc are shown in FIG. As shown in FIG. At this time, the total inter-electrode electromotive force Ev obtained by adding the inter-electrode electromotive forces Ev1 and Ev2 is ω0, (ω0−ω1), (ω0 + ω1) as the sum of the magnetic field B12 and the magnetic field B13, as shown in the following equation. The proportional coefficient rkv is applied to each angular frequency component, and the phase differences θ12 and θ13 are replaced with θ12 + θ01 and θ13 + θ01, respectively (rkv and θ01 are the flow velocity magnitude V, the conductivity and dielectric constant of the fluid to be measured, (Related to the structure of the measuring tube 1 including the arrangement of the electrodes 2a, 2b).

Ev = J ₀ (mp) · rkv · cos (ω0 · t)
・ {B12 [ω0] · cos (θ12 [ω0] + θ01)
+ B13 [ω0] · cos (θ13 [ω0] + θ01)}
+ J ₀ (mp) · rkv · sin (ω0 · t)
・ {B12 [ω0] · sin (θ12 [ω0] + θ01)
+ B13 [ω0] · sin (θ13 [ω0] + θ01)}
+ J ₁ (mp) · rkv · cos {(ω0 + ω1) · t}
{-B12 [ω0 + ω1] · sin (θ12 [ω0 + ω1] + θ01)
+ B13 [ω0 + ω1] · sin (θ13 [ω0 + ω1] + θ01)}
+ J ₁ (mp) · rkv · sin {(ω0 + ω1) · t}
・ {B12 [ω0 + ω1] · cos (θ12 [ω0 + ω1] + θ01)
-B13 [ω0 + ω1] · cos (θ13 [ω0 + ω1] + θ01)}
+ J ₁ (mp) · rkv · cos {(ω0−ω1) · t}
{-B12 [ω0−ω1] · sin (θ12 [ω0−ω1] + θ01)
+ B13 [ω0−ω1] · sin (θ13 [ω0−ω1] + θ01)}
+ J ₁ (mp) · rkv · sin {(ω0−ω1) · t}
{B12 [ω0−ω1] · cos (θ12 [ω0−ω1] + θ01)
−b13 [ω0−ω1] · cos (θ13 [ω0−ω1] + θ01)}
... (319)

In consideration of the direction of the electromotive force between the electrodes described in FIGS. 2 and 3, the electromotive force obtained by converting the interelectrode electromotive force due to the time change of the magnetic field into a complex vector and the interelectrode electromotive force due to the flow velocity of the fluid under measurement Of the total inter-electrode electromotive force obtained by combining the electromotive force converted into a complex vector, the electromotive force E60c of the component of the angular frequency ω0 is expressed by the first term and the second term of the equation (318) and the equation (319). From the first term and the second term and the equation (17), it is expressed by the following equation.
E60c = J ₀ (mp) · rk · ω0 · b12 [ω0]
Exp {j · (π / 2 + θ12 [ω0] + θ00)}
+ J ₀ (mp) · γ · rk · V · b12 [ω0]
Exp {j. (Θ12 [ω0] + θ01)}
+ J ₀ (mp) · rk · ω0 · b13 [ω0]
Exp {j · (−π / 2 + θ13 [ω0] + θ00)}
+ J ₀ (mp) · γ · rk · V · b13 [ω0]
Exp {j. (Θ13 [ω0] + θ01)} (320)

In addition, the inter-electrode electromotive force obtained by converting the inter-electrode electromotive force caused by the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force caused by the flow velocity of the fluid to be measured into the complex vector Among the electromotive forces, the electromotive force E6pc of the component of the angular frequency (ω0 + ω1) is obtained from the third and fourth terms of Equation (318), the third and fourth terms of Equation (319), and Equation (17). It is expressed by the following formula.
E6pc = J ₁ (mp) · rk · (ω0 + ω1) · b12 [ω0 + ω1]
Exp {j · (π + θ12 [ω0 + ω1] + θ00)}
+ J ₁ (mp) · γ · rk · V · b12 [ω0 + ω1]
Exp {j · (π / 2 + θ12 [ω0 + ω1] + θ01)}
+ J ₁ (mp) · rk · (ω0 + ω1) · b13 [ω0 + ω1]
• exp {j · (π + θ13 [ω0 + ω1] + θ00)}
+ J ₁ (mp) · γ · rk · V · b13 [ω0 + ω1]
Exp {j. (− Π / 2 + θ13 [ω0 + ω1] + θ01)}
... (321)

In addition, the inter-electrode electromotive force obtained by converting the inter-electrode electromotive force caused by the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force caused by the flow velocity of the fluid to be measured into the complex vector Among the electromotive forces, the electromotive force E6mc of the component of the angular frequency (ω0−ω1) is the fifth term and the sixth term of the equation (318) and the fifth term, the sixth term of the equation (319), and the equation (17). And is expressed by the following equation.
E6mc = J ₁ (mp) · rk · (ω0−ω1) · b12 [ω0−ω1]
Exp {j · (π + θ12 [ω0−ω1] + θ00)}
+ J ₁ (mp) · γ · rk · V · b12 [ω0−ω1]
Exp {j. (Π / 2 + θ12 [ω0−ω1] + θ01)}
+ J ₁ (mp) · rk · (ω0−ω1) · b13 [ω0−ω1]
Exp {j. (Π + θ13 [ω0−ω1] + θ00)}
+ J ₁ (mp) · γ · rk · V · b12 [ω0−ω1]
Exp {j · (−π / 2 + θ13 [ω0−ω1] + θ01)}
... (322)

Here, the relationship between the phase delay θ12 [ω0] of the component of the angular frequency ω0 of the magnetic field B12 and the phase delay θ13 [ω0] of the component of the angular frequency ω0 of the magnetic field B13 is θ13 [ω0] = θ12 [ω0] + Δθ13 [ω0. ], And the relationship between the angle θ00 of the ∂A / ∂t component with respect to the imaginary axis and the angle θ01 of the v × B component with respect to the real axis is θ01 = θ00 + Δθ01, θ01 = θ00 + Δθ01 and θ13 [ω0 in Equation (320) ] = Θ12 [ω0] + Δθ13 [ω0] is substituted, and the inter-electrode electromotive force E60 is expressed by the following equation.
E60 = J ₀ (mp) · rk · exp {j · (θ12 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}]
... (323)

The interelectrode electromotive force E6p0 when θ01 = θ00 + Δθ01 is substituted into the equation (321) is expressed by the following equation.
E6p0 = J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [(Ω0 + ω1) · exp (j · π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
+ B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
−b13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])}]
... (324)

The inter-electrode electromotive force E6m0 when θ01 = θ00 + Δθ01 is substituted into the equation (322) is expressed by the following equation.
E6m0 = J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [(Ω0−ω1) · exp (j · π / 2)
{B12 [ω0-ω1] · exp (j · θ12 [ω0-ω1])
+ B13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0-ω1] · exp (j · θ12 [ω0-ω1])
−b13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}]
... (325)

When the sum of the inter-electrode electromotive forces E6p0 and E6m0 is E6s0, the electromotive force sum E6s0 is expressed by the following equation.
E6s0 = E6p0 + E6m0
= J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [(Ω0 + ω1) · exp (j · π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
+ B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
−b13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])}]
+ J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [(Ω0−ω1) · exp (j · π / 2)
{B12 [ω0-ω1] · exp (j · θ12 [ω0-ω1])
+ B13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0-ω1] · exp (j · θ12 [ω0-ω1])
−b13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}]
= J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
+ B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
+ B12 [ω0−ω1] · exp (j · θ12 [ω0−ω1])
+ B13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}
+ Ω1 · exp (j · π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
+ B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
−b12 [ω0−ω1] · exp (j · θ12 [ω0−ω1])
−b13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
-B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
+ B12 [ω0−ω1] · exp (j · θ12 [ω0−ω1])
−b13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}]
... (326)

Here, since ω0> ω1 is normally satisfied, the conditional expressions (327) to (330) are satisfied.
2 · b12 [ω0] · exp (j · θ12 [ω0])
≒ b12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
+ B12 [ω0−ω1] · exp (j · θ12 [ω0−ω1]) (327)
2 · b13 [ω0] · exp (j · θ13 [ω0])
≒ b13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
+ B13 [ω0−ω1] · exp (j · θ13 [ω0−ω1]) (328)

| Ω0 · exp (j · π / 2)
{2 · b12 [ω0] · exp (j · θ12 [ω0])} |
>> | ω1 · exp (j · π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
−b12 [ω0−ω1] · exp (j · θ12 [ω0−ω1])} |
... (329)
| Ω0 · exp (j · π / 2)
{2 · b13 [ω0] · exp (j · θ13 [ω0])} |
>> | ω1 · exp (j · π / 2)
· {B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
−b13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])} |
... (330)

When E6s0a is obtained by approximating the electromotive force sum E6s0 by applying the conditions of Equations (327) to (330) to Equation (326), the electromotive force sum E6s0a is expressed by Equations (331) and (332). Is done.
E6s0a≈E6s0 (331)
E6s0a = J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
・ {2 ・ b12 [ω0] ・ exp (j ・ θ12 [ω0])
+ 2 · b13 [ω0] · exp (j · θ13 [ω0])}
+ Γ · V · exp (j · Δθ01)
・ {2 ・ b12 [ω0] ・ exp (j ・ θ12 [ω0])
-2 · b13 [ω0] · exp (j · θ13 [ω0])} (332)

As in equation (323), if θ13 [ω0] = θ12 [ω0] + Δθ13 [ω0] is substituted for the electromotive force sum E6s0a in equation (332), E6s0b, the electromotive force sum E6s0b is expressed by the following equation: .
E6s0b = 2 · J ₁ (mp) · rk
Exp {j · (π / 2 + θ12 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])}]
... (333)

Further, if b12 [ω0] = b13 [ω0] and Δθ13 [ω] = 0 are set in the magnetic fields B12 and B13 in the initial state (the state at the time of calibration), b12 [ω0] = b13 [ω0] = 0. [ω0] ≈b13 [ω0] and Δθ13 [ω] ≈0, and the following conditional expression holds.
| B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0]) |
»| B12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0]) |
... (334)

Further, since ω0> γ · V is normally satisfied, when the condition of the equation (334) is considered, the following equation is satisfied in the equation (333).
| Ω0 · exp (j · π / 2)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])} |
»| Γ · V · exp (j · Δθ01) · b12 [ω0]
−b13 [ω0] · exp (j · Δθ13 [ω0]) | (335)

Using the condition of Expression (335), the approximation of the electromotive force sum E6s0b of Expression (333) was multiplied by J ₀ (mp) / {2 · J ₁ (mp) · exp (j · π / 2)}. The electromotive force sum EdA61 is expressed by the following equation. This electromotive force sum EdA61 corresponds to the first ∂A / ∂t component in the basic principle.
EdA61≈E6s0b · [J ₀ (mp)
/ {2 · J ₁ (mp) · exp (j · π / 2)}] (336)
EdA61 = J ₀ (mp) · rk · exp {j · (θ12 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}
... (337)

Since the electromotive force sum EdA61 is not related to the magnitude V of the flow velocity, it becomes only a component generated by ∂A / ∂t. Using this electromotive force sum EdA61, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the interelectrode electromotive force E60 (the combined vector Vas0 + Vbs0) is normalized. When the inter-electrode electromotive force E60 in the equation (323) is normalized by the electromotive force sum EdA61 in the equation (337) and multiplied by ω0 is represented as En60, the normalized electromotive force En60 is expressed by the following equation.
En60 = (E60 / EdA61) · ω0
= J ₀ (mp) · rk · exp {j · (θ12 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}]
/ [J ₀ (mp) · rk · exp {j · (θ12 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}] · ω0
= Ω0 · {b12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])}
/ {B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (338)

Using equation (52), the coefficient {b12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])} / {b12 [ω0] applied to the angular frequency ω0 of the first term on the right side of equation (338). ] + B13 [ω0] · exp (j · Δθ13 [ω0])} is represented by a value {b12−b13 · exp (j · Δθ13)} / {b12 + b13 · exp (j · Δθ13)} not related to the angular frequency ω0. be able to. Therefore, equation (338) can be replaced as:
En60 = ω0 · {b12−b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (339)

  The second term on the right side of Equation (339) is a term obtained by normalizing the component generated by v × B. The reason why the result obtained by normalizing the inter-electrode electromotive force E60 with the electromotive force sum EdA61 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side related to the magnitude V of the flow velocity. The complex coefficient relating to the magnitude V of the flow velocity has an angle from the real axis of the magnitude of γ, −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (339) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the component ∂A / ∂t, it is possible to realize span correction that automatically corrects errors due to magnetic field shifts and phase changes.

Next, a method for removing the first term on the right side of the equation (339), which is a variation factor of 0 point, will be described. When the angular frequency of the carrier wave is ω2 instead of ω0 in equations (305) and (306), the magnetic fields B12 and B13 are expressed by the following equations.
B12 = b12 · cos {ω2 · t-mp · cos (ω1 · t) −θ12} (340)
B13 = b13 · cos {ω2 · t + mp · cos (ω1 · t) −θ13} (341)

  Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. The inter-electrode electromotive force E62 subjected to span correction at the angular frequency ω2 is obtained by replacing the angular frequency ω0 with ω2 in the equation (323). The electromotive force sum E6s2 that is the basis of the second ∂A / ∂t component is the interelectrode electromotive force E6p2 in which the angular frequency ω0 is replaced with ω2 in the equation (324) and the angular frequency ω0 in ω2 in the equation (325). It is expressed as the sum E6p2 + E6m2 with the inter-electrode electromotive force E6m2. The electromotive force sum EdA62 as the second ∂A / ∂t component is obtained by replacing the angular frequency ω0 with ω2 in the equation (337).

If the inter-electrode electromotive force E62 is normalized by the electromotive force sum EdA62 and the result obtained by multiplying by ω2 is En62, the normalized electromotive force En62 is expressed by the following equation from the equation (339).
En62 = ω2 · {b12−b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (342)

Taking the difference between the normalized electromotive forces En60 and En62 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA63, the electromotive force difference EdA63 is expressed by the following equation. This electromotive force difference EdA63 corresponds to the third ∂A / ∂t component in the basic principle.
EdA63 = (En60−En62) · ω0 / (ω0−ω2)
= [{B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)}
.Omega.0 + .gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V
-{B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)}
.Omega.2-.gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V]
・ Ω0 / (ω0−ω2)
= {B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)} · ω0 ·· (343)

The electromotive force difference EdA63 represents a normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (339). Therefore, if this electromotive force difference EdA63 is used, the normalized v × B component Can be extracted from the normalized electromotive force En60. When the v × B component obtained by subtracting the electromotive force difference EdA63 of equation (343) from the normalized electromotive force En60 of equation (339) is EvBn6, the v × B component EvBn6 is expressed by the following equation.
EvBn6 = En60-EdA63
= {B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)} · ω0
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
-{B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)} · ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (344)

The v × B component EvBn6 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvBn6 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBn6. From the equation (344), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn6 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn6 | / γ (345)

  Table 6 below shows the correspondence between the constants and variables used in the basic principle and the constants and variables of the present embodiment. As is apparent from Table 6, this embodiment is an example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. Since the configuration of the electromagnetic flowmeter of the present embodiment is the same as that of the first embodiment, description will be made using the reference numerals in FIG. The electromagnetic flowmeter of the present embodiment includes a measuring tube 1, electrodes 2a and 2b, first and second exciting coils 3a and 3b, a power supply unit 4, a signal conversion unit 5, and a flow rate output unit 6. Have

  The signal conversion unit 5 obtains the amplitude and phase of the combined electromotive force detected by the electrodes 2a and 2b in each of the first excitation state and the second excitation state, and performs the first excitation based on these amplitudes and phases. The sum of electromotive forces of the component of the angular frequency ω0 + ω1 and the component of the angular frequency ω0−ω1 of the combined electromotive force in the state is extracted as the first ∂A / ∂t component, and the angle of the combined electromotive force in the second excitation state The sum of electromotive forces of the component of frequency ω2 + ω1 and the component of angular frequency ω2-ω1 is extracted as the second ∂A / ∂t component, and the component of angular frequency ω0 of the composite electromotive force in the first excitation state is the first. As a correction target electromotive force, based on the first ∂A / ∂t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the second excitation state Using the component of the angular frequency ω2 of the combined electromotive force as the second correction target electromotive force, A span correction unit 51 that removes a variation factor of the span included in the v × B component in the second correction target electromotive force based on the A / ∂t component, and the first correction target electromotive force that has been subjected to span correction A difference from the second correction target electromotive force subjected to the span correction is extracted as a third ∂A / ∂t component, and the third one of the two correction target electromotive forces subjected to the span correction is extracted. The zero point correction unit 52 extracts the v × B component by removing the ∂A / ∂t component.

  The power supply unit 4 of the present embodiment supplies a first excitation current obtained by phase-modulating a sine wave carrier wave having an angular frequency ω0 with a sine wave modulation wave having an angular frequency ω1 to the first excitation coil 3a, and at the same time, the angular frequency First excitation that supplies a second excitation current obtained by phase-modulating a sine wave carrier wave of ω0 with a modulation wave having the same angular frequency and an opposite phase with respect to the modulation wave of the first excitation current to the second excitation coil 3b. The state continues for T1 seconds, and a third excitation current obtained by phase-modulating a sine wave carrier wave having an angular frequency ω2 with a sine wave modulation wave having an angular frequency ω1 is supplied to the first excitation coil 3a, and at the same time, the sine wave having the angular frequency ω2 is supplied. A second excitation state in which a fourth excitation current obtained by phase-modulating a wave carrier wave with a modulation wave having the same angular frequency and an opposite phase with respect to the modulation wave of the third excitation current is supplied to the second excitation coil 3b. To last seconds Repeated at T second period. That is, T = T1 + T2. The phase modulation index mp is an arbitrary value.

  Since the processing flow of the signal conversion unit 5 and the flow rate output unit 6 of this embodiment is the same as that of the fourth embodiment, the operations of the signal conversion unit 5 and the flow rate output unit 6 will be described using the reference numerals in FIG. explain. First, the span correction unit 51 of the signal conversion unit 5 obtains the amplitude r60 of the electromotive force E60 of the component of the angular frequency ω0 out of the electromotive force between the electrodes 2a and 2b in the first excitation state, and the real axis and the electrode A phase difference φ60 with respect to the inter-electromotive force E60 is obtained by a phase detector (not shown) (step 401 in FIG. 21). Further, the span correction unit 51 obtains the amplitude r6s0 of the sum E6s0 of the angular frequency (ω0 + ω1) component and the angular frequency (ω0−ω1) component of the electromotive force between the electrodes 2a and 2b in the first excitation state. At the same time, a phase difference φ6s0 between the real axis and the electromotive force sum E6s0 is obtained by the phase detector (step 402).

  Subsequently, in the second excitation state, the span correction unit 51 obtains the amplitude r62 of the electromotive force E62 of the component of the angular frequency ω2 among the electromotive forces between the electrodes 2a and 2b, and at the same time the inter-electrode electromotive force E62. Is obtained by a phase detector (step 403). Further, the span correction unit 51 obtains the amplitude r6s2 of the sum E6s2 of the angular frequency (ω2 + ω1) component and the angular frequency (ω2-ω1) component of the electromotive force between the electrodes 2a and 2b in the second excitation state. At the same time, the phase difference φ6s2 between the real axis and the electromotive force sum E6s2 is obtained by the phase detector (step 404). The components of the interelectrode electromotive forces E60 and E62 and the angular frequencies (ω0 + ω1), (ω0−ω1), (ω2 + ω1), and (ω2−ω1) of the interelectrode electromotive force may be frequency separated by a bandpass filter or a comb filter. it can.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force sum EdA61 that approximates the electromotive force sum E6s0 (step 405). The process of step 405 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of Expression (337). The span correction unit 51 calculates the magnitude | EdA61 | of the electromotive force sum EdA61 as follows.
| EdA61 | = r6s0 (346)
Then, the span correction unit 51 calculates the angle ∠EdA61 of the electromotive force sum EdA61 as the following equation.
∠EdA61 = φ6s0 (347)
This completes the process of step 405.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force En60 obtained by normalizing the interelectrode electromotive force E60 with the electromotive force sum EdA61 (step 406). The process of step 406 is a process corresponding to the calculation of equation (339). The span correction unit 51 calculates the magnitude | En60 | of the normalized electromotive force En60 as the following expression.
| En60 | = (r60 / | EdA61 |) · ω0 (348)

Then, the span correction unit 51 calculates the angle ∠En60 of the normalized electromotive force En60 as the following equation.
∠En60 = φ60−∠EdA61 (349)
Further, the span correction unit 51 calculates the real axis component En60x and the imaginary axis component En60y of the normalized electromotive force En60 as the following expression.
En60x = | En60 | .cos (∠En60) (350)
En60y = | En60 | .sin (∠En60) (351)
This completes the process of step 406.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force sum EdA62 that approximates the electromotive force sum E6s2 (step 407). The processing in step 407 is processing corresponding to obtaining the second ∂A / ∂t component. The span correction unit 51 calculates the magnitude | EdA62 | of the electromotive force sum EdA62 as follows.
| EdA62 | = r6s2 (352)
Then, the span correction unit 51 calculates the angle ∠EdA62 of the electromotive force sum EdA62 as the following equation.
∠EdA62 = φ6s2 (353)
This completes the process of step 407.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force En62 obtained by normalizing the interelectrode electromotive force E62 with the electromotive force sum EdA62 (step 408). The process of step 408 is a process corresponding to the calculation of equation (342). The span correction unit 51 calculates the magnitude | En62 | of the normalized electromotive force En62 as the following equation.
| En62 | = (r62 / | EdA62 |) · ω2 (354)

Then, the span correction unit 51 calculates the angle ∠En62 of the normalized electromotive force En62 as the following expression.
∠En62 = φ62−∠EdA62 (355)
Further, the span correction unit 51 calculates the real axis component En62x and the imaginary axis component En62y of the normalized electromotive force En62 as the following expression.
En62x = | En62 | .cos (∠En62) (356)
En62y = | En62 | .sin (∠En62) (357)
This completes the process of step 408.

Next, the zero point correction unit 52 of the signal conversion unit 5 obtains the magnitude of the electromotive force difference EdA63 between the normalized electromotive forces En60 and En62 (step 409). The process of step 409 is a process corresponding to obtaining the third ∂A / ∂t component, and is a process corresponding to the calculation of Expression (343). The zero point correction unit 52 calculates the real axis component EdA63x and the imaginary axis component EdA63y of the electromotive force difference EdA63 as follows.
EdA63x = (En60x−En62x) · ω0 / (ω0−ω2) (358)
EdA63y = (En60y−En62y) · ω0 / (ω0−ω2) (359)

Then, the zero point correction unit 52 removes the electromotive force difference EdA63 from the normalized electromotive force En60 and obtains the magnitude of the v × B component EvBn6 (step 410). The process of step 410 is a process corresponding to the calculation of equation (344). The zero point correction unit 52 calculates the magnitude | EvBn6 | of the v × B component EvBn6 as the following equation.
| EvBn6 | = {(En60x−EdA63x) ²
+ (En60y−EdA63y) ² } ^1/2 (360)

The flow rate output unit 6 calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 411). The process of step 411 is a process corresponding to the calculation of Expression (345).
V = | EvBn6 | / γ (361)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5 and the flow rate output unit 6 perform the processes in steps 401 to 411 as described above at regular intervals until the operator instructs the end of measurement (YES in step 412). Note that the processing in steps 403 to 411 is performed in the second excitation state.

  As described above, in the present embodiment, in the first excitation state, the electromotive force E60 of the component of the angular frequency ω0, the sum of the electromotive forces of the component of the angular frequency (ω0 + ω1) and the component of the angular frequency (ω0−ω1). E6s0 is obtained, and in the second excitation state, an electromotive force E62 of the component of the angular frequency ω2, and an electromotive force sum E6s2 of the angular frequency (ω2 + ω1) component and the angular frequency (ω2-ω1) component are obtained. In this embodiment, if the magnetic field B12 generated from the first excitation coil 3a is set to be equal to the magnetic field B13 generated from the second excitation coil 3b, the electromotive force sum E6s0 is approximate. The first で き る A / 起 t component can be extracted as the first ∂A / ∂t component, and the electromotive force sum E6s2 can be approximately extracted as the second ∂A / ∂t component. Normalizing the span of the velocity V of the v × B component in the interelectrode electromotive force E60 and using the second ∂A / ∂t component, the v × B component in the interelectrode electromotive force E62 Normalization is performed on the span of the flow velocity V, and the electromotive force difference EdA63 (third ∂A / ∂t component) is extracted from the normalized electromotive forces En60 and En62. By removing the ∂A / ∂t component of Since the flow rate of the fluid to be measured is calculated from the v × B component, accurate span correction can be automatically performed, and the flow rate of the electromagnetic flow meter can be reduced without reducing the flow rate of the fluid to be measured to zero. The zero point of the output can be corrected, and the stability of the zero point can be ensured even in high frequency excitation.

In the present embodiment, in consideration of the difference in magnetic field loss depending on the frequency, the first ∂A / of the same angular frequency obtained by extracting the v × B component of the electromotive force E60 of the angular frequency ω0 from the electromotive force sum E6s0. Normalize using the ∂t component and normalize the v × B component of the electromotive force E62 of the angular frequency ω2 using the second ∂A / ∂t component of the same angular frequency extracted from the electromotive force sum E6s2. Since zero correction is performed based on the difference between the normalized electromotive forces En60 and En62, accurate span correction and zero correction can be performed even when there is an influence due to magnetic field loss.
In the present embodiment, it is not necessary to switch the phase difference of the magnetic field only by switching the frequency of the carrier wave, and it is not necessary to use the four excitation states as in the first embodiment. Can be calculated.

In the present embodiment, the electromotive force E60 of the component of the angular frequency ω0 is the target of 0 correction and span correction, but the electromotive force E62 of the component of the angular frequency ω2 may be the target of 0 correction and span correction. In this case, the electromotive force difference EdA63 (third ∂A / ∂t component) is obtained from the normalized electromotive forces En62 and En60 as in the following equation.
EdA63 = (En62−En60) · ω2 / (ω2−ω0) (362)
Then, the v × B component EvBn6 may be obtained by subtracting the electromotive force difference EdA63 from the normalized electromotive force En62 as in the following equation. The other processes are the same as those in the case where the interelectrode electromotive force E60 is subjected to 0 correction and span correction.
| EvBn6 | = | En62−EdA63 | (363)

  In this embodiment, the exciting current obtained by phase-modulating the carrier wave with the modulated wave is supplied to the exciting coils 3a and 3b. However, the present invention is not limited to this. You may make it supply to coil 3a, 3b.

Hereinafter, the fact that frequency modulation can be handled in the same way as phase modulation will be described. In FIG. 1, of the magnetic field Bb generated from the first exciting coil 3a, the magnetic field component (magnetic flux density) B12 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX connecting the electrodes 2a and 2b. Is given as follows.
B12 = b12 · cos {ω0 · t-mf · sin (ω1 · t) −θ12}
... (364)
In Expression (364), b12 is the amplitude of the magnetic field B12, ω0 is the angular frequency of the carrier wave, ω1 is the angular frequency of the modulated wave, and θ12 is the position of the carrier wave of the magnetic field B12 and ω0 · t−mf · sin (ω1 · t). Phase difference (phase lag), mf is a frequency modulation index.

The frequency modulation index mf is expressed by the following equation.
mf = Δω1 / ω1 (365)
In Expression (365), Δω1 represents an angular frequency band, and Δω1 = 2π · ΔF, where ΔF is a frequency shift amount at the maximum amplitude of the modulated wave. Equation (364) can be transformed as:

B12 = b12 · cos {ω0 · t-mf · sin (ω1 · t) −θ12}
= B12 · cos (ω0 · t−θ12) · cos {−mf · sin (ω1 · t)}
−b12 · sin (ω0 · t−θ12) · sin {−mf · sin (ω1 · t)}
= B12 · cos {mf · sin (ω1 · t)}
・ {Cos (ω0 · t) ・ cos (−θ12)
-Sin (ω0 · t) · sin (-θ12)}
+ B12 · sin {mf · sin (ω1 · t)}
・ {Sin (ω0 · t) ・ cos (−θ12)
+ Cos (ω0 · t) · sin (−θ12)} (366)

  Here, cos {mf · sin (ω1 · t)} and sin {mf · sin (ω1 · t)} in the equation (366) can be converted as follows.

In the expressions (367) and (368), J _n (mf) (n = 0, 1, 2,...) Is known as a first kind Bessel function, and this first kind Bessel function J _n ( mf) is given by:

In formula (369), k! Means the factorial of k. When only n = 0 and 1 are employed in Expression (367) and Expression (368), Expression (366) can be modified as follows.
B12 = b12 · J ₀ (mf)
・ {Cos (ω0 · t) ・ cos (−θ12)
-Sin (ω0 · t) · sin (-θ12)}
+ B12 · 2 · J ₁ (mf) · cos (ω1 · t)
・ {Sin (ω0 · t) ・ cos (−θ12)
+ Cos (ω0 · t) · sin (−θ12)}
= J ₀ (mf) · b12 · {cos (θ12)} · cos (ω0 · t)
+ J ₀ (mf) · b12 · {sin (θ12)} · sin (ω0 · t)
+ J ₁ (mf) · b12 · {−sin (θ12)} · cos {(ω0 + ω1) · t}
+ J ₁ (mf) · b12 · {cos (θ12)} · sin {(ω0 + ω1) · t}
+ J ₁ (mf) · b12 · {−sin (θ12)} · cos {(ω0−ω1) · t}
+ J ₁ (mf) · b12 · {cos (θ12)} · sin {(ω0−ω1) · t}
... (370)

  If mf = mp in equation (370), the equation is exactly the same as equation (312), and it can be seen that frequency modulation can be handled equivalent to phase modulation. Also in the following embodiments in which an excitation current obtained by phase-modulating a carrier wave is supplied to the excitation coil, frequency modulation can be handled in the same manner as in the case of phase modulation, and thus description of frequency modulation is omitted.

[Seventh Embodiment]
Next, a seventh embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has two excitation coils and a pair of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. The present embodiment uses the second detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The second extraction method described is used.

The excitation conditions in this embodiment are the same as those in the sixth embodiment. In the above equation (320), when the phase difference θ13 [ω0] of the component of the angular frequency ω0 of the magnetic field B13 is replaced with π + θ13 [ω0] and θ01 = θ00 + Δθ01 is substituted, the interelectrode electromotive force E7π0 is expressed by the following equation. The
E7π0 = J ₀ (mp) · rk · exp {j · (θ12 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])}]
... (371)

In the equation (321), the interelectrode electromotive force E7πp0 when the phase difference θ13 [ω0] is replaced by π + θ13 [ω0] and θ01 = θ00 + Δθ01 is substituted is expressed by the following equation.
E7πp0 = J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [(Ω0 + ω1) · exp (j · π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
-B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
+ B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])}]
... (372)

In the equation (322), the inter-electrode electromotive force E7πm0 when the phase difference θ13 [ω0] is replaced by π + θ13 [ω0] and θ01 = θ00 + Δθ01 is substituted is expressed by the following equation. However, θ13 [ω0] = θ12 [ω0] + Δθ13 [ω0] is not applied in the equations (371), (372), and (373), and is applied in the later equations. Also, it should be noted that the phase difference of the modulation part is originally opposite, so that it is the same phase.
E7πm0 = J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [(Ω0−ω1) · exp (j · π / 2)
{B12 [ω0-ω1] · exp (j · θ12 [ω0-ω1])
−b13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0-ω1] · exp (j · θ12 [ω0-ω1])
+ B13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}]
... (373)

If the sum of the interelectrode electromotive forces E7πp0 and E7πm0 is E7πs0, the electromotive force sum E7πs0 is expressed by the following equation.
E7πs0 = E7πp0 + E7πm0
= J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [(Ω0 + ω1) · exp (j · π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
-B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
+ B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])}]
+ J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [(Ω0−ω1) · exp (j · π / 2)
{B12 [ω0-ω1] · exp (j · θ12 [ω0-ω1])
−b13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0-ω1] · exp (j · θ12 [ω0-ω1])
+ B13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}]
= J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
-B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
+ B12 [ω0−ω1] · exp (j · θ12 [ω0−ω1])
−b13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}
+ Ω1 · exp (j · π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
-B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
−b12 [ω0−ω1] · exp (j · θ12 [ω0−ω1])
+ B13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}
+ Γ · V · exp (j · Δθ01)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
+ B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
+ B12 [ω0−ω1] · exp (j · θ12 [ω0−ω1])
+ B13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])}]
... (374)

Here, since ω0> ω1 is normally satisfied, the conditional expressions of Expressions (375) to (378) are satisfied.
2 · b12 [ω0] · exp (j · θ12 [ω0])
≒ b12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
+ B12 [ω0−ω1] · exp (j · θ12 [ω0−ω1]) (375)
2 · b13 [ω0] · exp (j · θ13 [ω0])
≒ b13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
+ B13 [ω0−ω1] · exp (j · θ13 [ω0−ω1]) (376)

| Ω0 · exp (j · π / 2)
{2 · b12 [ω0] · exp (j · θ12 [ω0])} |
>> | ω1 · exp (j · π / 2)
・ {B12 [ω0 + ω1] · exp (j · θ12 [ω0 + ω1])
−b12 [ω0−ω1] · exp (j · θ12 [ω0−ω1])} |
... (377)
| Ω0 · exp (j · π / 2)
{2 · b13 [ω0] · exp (j · θ13 [ω0])} |
>> | ω1 · exp (j · π / 2)
· {B13 [ω0 + ω1] · exp (j · θ13 [ω0 + ω1])
−b13 [ω0−ω1] · exp (j · θ13 [ω0−ω1])} |
... (378)

When E7πs0a is obtained by approximating the electromotive force sum E7πs0 by applying the conditions of the equations (375) to (378) to the equation (374), the electromotive force sum E7πs0a is expressed by the equations (379) and (380). Is done.
E7πs0a≈E7πs0 (379)
E7πs0a = J ₁ (mp) · rk · exp {j · (π / 2 + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
・ {2 ・ b12 [ω0] ・ exp (j ・ θ12 [ω0])
-2 · b13 [ω0] · exp (j · θ13 [ω0])}
+ Γ · V · exp (j · Δθ01)
・ {2 ・ b12 [ω0] ・ exp (j ・ θ12 [ω0])
+ 2 · b13 [ω0] · exp (j · θ13 [ω0])}
... (380)

Here, if the value obtained by substituting θ13 [ω0] = θ12 [ω0] + Δθ13 [ω0] into the electromotive force sum E7πs0a of the equation (380) is E7πs0b, the electromotive force sum E7πs0b is expressed by the following equation.
E7πs0b = 2 · J ₁ (mp) · rk
Exp {j · (π / 2 + θ12 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}]
... (381)

In the initial state (calibration state) of magnetic fields B12 and B13, if b12 [ω0] = b13 [ω0] and Δθ13 [ω0] = 0 are set, b12 [ω0 ] ≈b13 [ω0], Δθ13 [ω0] ≈0, and the following conditional expression holds.
| B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0]) |
»| B12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0]) |
... (382)

Since ω0> γ · V is normally satisfied, the following condition is satisfied in Expression (371) when the condition of Expression (382) is taken into consideration.
| Ω0 · exp (j · π / 2)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])} |
»| Γ · V · exp (j · Δθ01) · b12 [ω0]
−b13 [ω0] · exp (j · Δθ13 [ω0]) | (383)

Using the condition of the equation (383), the approximation of the interelectrode electromotive force E7π0 of the equation (371) is multiplied by 2 · {J ₁ (mp) / J ₀ (mp)} · exp (j · π / 2) times. The electromotive force EdA71 is expressed by the following equation. This electromotive force EdA71 corresponds to the first ∂A / ∂t component in the basic principle.
EdA71≈E7π0 · 2 · {J ₁ (mp) / J ₀ (mp)} · exp (j · π / 2)
... (384)
EdA71 = 2 · J ₁ (mp) · rk
Exp {j · (π / 2 + θ12 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}
... (385)

Since the electromotive force EdA71 is not related to the magnitude V of the flow velocity, only the component generated by ∂A / ∂t is included. Using this electromotive force EdA71, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the electromotive force sum E7πs0b (combined vector Vas0 + Vbs0) is normalized. If the electromotive force sum E7πs0b in the equation (381) is normalized by the electromotive force EdA71 in the equation (385) and multiplied by ω0 is En70, the normalized electromotive force sum En70 is expressed by the following equation.
En70 = (E7πs0b / EdA71) · ω0
= 2 · J ₁ (mp) · rk · exp {j · (π / 2 + θ12 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}]
/ [2 · J ₁ (mp) · rk · exp {j · (π / 2 + θ12 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}] · ω0
= Ω0 · {b12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])}
/ {B12 [ω0] + b13 [ω0] · exp (j · Δθ13 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (386)

Using the equation (52), the coefficient {b12 [ω0] −b13 [ω0] · exp (j · Δθ13 [ω0])} / {b12 [ω0] applied to the angular frequency ω0 of the first term on the right side of the equation (386). ] + B13 [ω0] · exp (j · Δθ13 [ω0])} is represented by a value {b12−b13 · exp (j · Δθ13)} / {b12 + b13 · exp (j · Δθ13)} not related to the angular frequency ω0. be able to. Therefore, the equation (386) can be replaced by the following equation.
En70 = ω0 · {b12−b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (387)

  The second term of Expression (387) is a term obtained by normalizing the component generated by v × B. The reason why the result obtained by normalizing the electromotive force sum E7πs0b with the electromotive force EdA71 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side of the magnitude V of the flow velocity. The complex coefficient related to the magnitude V of the flow velocity has an angle from the real axis of the magnitude of γ, −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (387) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the component ∂A / ∂t, it is possible to realize span correction that automatically corrects errors due to magnetic field shifts and phase changes.

  Next, a method for removing the first term on the right side of the equation (387), which is a variation factor of 0 point, will be described. When the angular frequency of the carrier wave is ω2 instead of ω0, the magnetic fields B12 and B13 are expressed by the equations in which θ13 is replaced by π + θ13 in the equations (340) and (341). Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. The electromotive force sum E7πs2 to be subjected to span correction at the angular frequency ω2 is the inter-electrode electromotive force E7πp2 in which the angular frequency ω0 is replaced with ω2 in the equation (372) and the interelectrode between the electrodes in which the angular frequency ω0 is replaced with ω2 in the equation (373). It is represented by the sum E7πp2 + E7πm2 with the electromotive force E7πm2. The interelectrode electromotive force E7π2 that is the basis of the second ∂A / ∂t component is represented by the equation (371) in which the angular frequency ω0 is replaced with ω2. The electromotive force EdA72 as the second ∂A / ∂t component is obtained by replacing the angular frequency ω0 with ω2 in the equation (385).

If the electromotive force sum E7πs2 is normalized by the electromotive force EdA72 and multiplied by ω2 is En72, the normalized electromotive force sum En72 is expressed by the following equation from the equation (387).
En72 = ω2 · {b12−b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (388)

Taking the difference between the normalized electromotive force sums En70 and En72 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA73, the difference EdA73 is expressed by the following equation. This difference EdA73 corresponds to the third ∂A / ∂t component in the basic principle.
EdA73 = (En70−En72) · ω0 / (ω0−ω2)
= [{B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)}
.Omega.0 + .gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V
-{B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)}
.Omega.2-.gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V]
・ Ω0 / (ω0−ω2)
= {B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)} · ω0 ·· (389)

The difference EdA73 represents the normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (387). Therefore, if this difference EdA73 is used, the normalized v × B component is normalized. It can be taken out from the power sum En70. When the v × B component obtained by subtracting the difference EdA73 of equation (389) from the normalized electromotive force sum En70 of equation (387) is EvBn7, the v × B component EvBn7 is expressed by the following equation.
EvBn7 = En70-EdA73
= {B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)} · ω0
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
-{B12-b13 · exp (j · Δθ13)}
/ {B12 + b13 · exp (j · Δθ13)} · ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (390)

The v × B component EvBn7 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvBn7 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBn7. The magnitude and direction of the coefficient relating to the magnitude V of the flow velocity are represented by a complex vector [γ · rk · exp {j · (−π / 2 + Δθ01)}]. From the equation (390), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn7 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn7 | / γ (391)

  Table 7 below shows the correspondence between the constants and variables used in the basic principle and the constants and variables in the present embodiment. As is apparent from Table 7, the present embodiment is one example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. Since the configuration of the electromagnetic flowmeter of the present embodiment is the same as that of the first embodiment, description will be made using the reference numerals in FIG. The electromagnetic flowmeter of the present embodiment includes a measuring tube 1, electrodes 2a and 2b, first and second exciting coils 3a and 3b, a power supply unit 4, a signal conversion unit 5, and a flow rate output unit 6. Have

  The signal conversion unit 5 obtains the amplitude and phase of the combined electromotive force detected by the electrodes 2a and 2b in each of the first excitation state and the second excitation state, and performs the first excitation based on these amplitudes and phases. The component of the angular frequency ω0 of the combined electromotive force in the state is extracted as the first ∂A / ∂t component, and the component of the angular frequency ω2 of the combined electromotive force in the second excitation state is extracted as the second ∂A / ∂t. The first electromotive force sum of the component of the angular frequency ω0 + ω1 and the component of the angular frequency ω0−ω1 of the composite electromotive force in the first excitation state is extracted as a first correction target electromotive force. Based on the t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the angular frequency ω2 + ω1 component and the angular frequency ω2 of the composite electromotive force in the second excitation state are removed. The sum of the electromotive force with the component of −ω1 is set as the second correction target electromotive force, and the second power A span correction unit 51 that removes a variation factor of the span included in the v × B component in the second correction target electromotive force based on the A / ∂t component, and the first correction target electromotive force that has been subjected to span correction A difference from the second correction target electromotive force subjected to the span correction is extracted as a third ∂A / ∂t component, and the third one of the two correction target electromotive forces subjected to the span correction is extracted. The zero point correction unit 52 extracts the v × B component by removing the ∂A / ∂t component.

  The operation of the power supply unit 4 is the same as that in the sixth embodiment. Since the processing flow of the signal conversion unit 5 and the flow rate output unit 6 of the present embodiment is the same as that of the fifth embodiment, the operations of the signal conversion unit 5 and the flow rate output unit 6 are performed using the reference numerals in FIG. explain. First, the span correction unit 51 of the signal conversion unit 5 has the amplitude of the electromotive force E7π0 of the component of the angular frequency ω0 in the electromotive force between the electrodes 2a and 2b in the first excitation state described in the sixth embodiment. In addition to obtaining r7π0, a phase difference φ7π0 between the real axis and the interelectrode electromotive force E7π0 is obtained by a phase detector (not shown) (step 501 in FIG. 22). Further, the span correction unit 51 obtains the amplitude r7πs0 of the sum E7πs0 of the angular frequency (ω0 + ω1) component and the angular frequency (ω0−ω1) component of the electromotive force between the electrodes 2a and 2b in the first excitation state. At the same time, a phase difference φ7πs0 between the real axis and the electromotive force sum E7πs0 is obtained by the phase detector (step 502).

  Subsequently, the span correction unit 51 obtains the amplitude r7π2 of the electromotive force E7π2 of the component of the angular frequency ω2 among the electromotive forces between the electrodes 2a and 2b in the second excitation state described in the sixth embodiment. Then, the phase difference φ7π2 between the real axis and the inter-electrode electromotive force E7π2 is obtained by the phase detector (step 503). The span correction unit 51 obtains the amplitude r7πs2 of the sum E7πs2 of the angular frequency (ω2 + ω1) component and the angular frequency (ω2-ω1) component of the electromotive force between the electrodes 2a and 2b in the second excitation state. At the same time, a phase difference φ7πs2 between the real axis and the electromotive force sum E7πs2 is obtained by the phase detector (step 504).

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force EdA71 that approximates the interelectrode electromotive force E7π0 (step 505). The process of step 505 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of Expression (385). The span correction unit 51 calculates the magnitude | EdA71 | of the electromotive force EdA71 as follows.
| EdA71 | = r7π0 (392)
Then, the span correction unit 51 calculates the angle ∠EdA71 of the electromotive force EdA71 as the following equation.
∠EdA71 = φ7π0 (393)
This completes the process of step 505.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force sum En70 obtained by normalizing the electromotive force sum E7πs0 with the electromotive force EdA71 (step 506). The process of step 506 is a process corresponding to the calculation of Expression (387). The span correction unit 51 calculates the magnitude | En70 | of the normalized electromotive force sum En70 as follows.
| En70 | = (r7πs0 / | EdA71 |) · ω0 (394)

Then, the span correction unit 51 calculates the angle ∠En70 of the normalized electromotive force sum En70 as the following expression.
∠En70 = φ7πs0−∠EdA71 (395)
Further, the span correction unit 51 calculates the real axis component En70x and the imaginary axis component En70y of the normalized electromotive force sum En70 as the following equation.
En70x = | En70 | .cos (∠En70) (396)
En70y = | En70 | .sin (∠En70) (397)
This completes the processing in step 506.

Next, the span correction unit 51 obtains the magnitude and angle of the electromotive force EdA72 that approximates the interelectrode electromotive force E7π2 (step 507). The processing in this step 507 is processing corresponding to obtaining the second ∂A / ∂t component. The span correction unit 51 calculates the magnitude | EdA72 | of the electromotive force EdA72 as follows.
| EdA72 | = r7π2 (398)
Then, the span correction unit 51 calculates the angle ∠EdA72 of the electromotive force EdA72 as the following equation.
∠EdA72 = φ7π2 (399)
This completes the processing in step 507.

Subsequently, the span correction unit 51 obtains the magnitude and angle of the normalized electromotive force sum En72 obtained by normalizing the electromotive force sum E7πs2 with the electromotive force EdA72 (step 508). The processing in step 508 is processing equivalent to the calculation of equation (388). The span correction unit 51 calculates the magnitude | En72 | of the normalized electromotive force sum En72 as the following equation.
| En72 | = (r7πs2 / | EdA72 |) · ω2 (400)

Then, the span correction unit 51 calculates the angle ∠En72 of the normalized electromotive force sum En72 as the following equation.
∠En72 = φ7πs2-∠EdA72 (401)
Further, the span correction unit 51 calculates the real axis component En72x and the imaginary axis component En72y of the normalized electromotive force sum En72 as in the following equation.
En72x = | En72 | .cos (∠En72) (402)
En72y = | En72 | .sin (∠En72) (403)
This completes the processing in step 508.

Next, the zero point correction unit 52 of the signal conversion unit 5 obtains the magnitude of the difference EdA73 between the normalized electromotive force sums En70 and En72 (step 509). The processing in step 509 is processing corresponding to obtaining the third ∂A / ∂t component, and is processing corresponding to the calculation of equation (389). The zero point correction unit 52 calculates the real axis component EdA73x and the imaginary axis component EdA73y of the difference EdA73 as in the following equation.
EdA73x = (En70x−En72x) · ω0 / (ω0−ω2) (404)
EdA73y = (En70y−En72y) · ω0 / (ω0−ω2) (405)

Then, the zero point correction unit 52 removes the difference EdA73 from the normalized electromotive force sum En70 and obtains the magnitude of the v × B component EvBn7 (step 510). The process of step 510 is a process corresponding to the calculation of equation (390). The zero point correction unit 52 calculates the magnitude | EvBn7 | of the v × B component EvBn7 as follows.
| EvBn7 | = {(En70x−EdA73x) ²
+ (En70y−EdA73y) ² } ^1/2 (406)

The flow rate output unit 6 calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 511). The process of step 511 is a process corresponding to the calculation of equation (391).
V = | EvBn7 | / γ (407)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5 and the flow rate output unit 6 perform the processing in steps 501 to 511 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 512). Note that the processing in steps 503 to 511 is performed in the second excitation state.

  As described above, in the present embodiment, in the first excitation state, the electromotive force E7π0 of the component of the angular frequency ω0, the electromotive force sum of the component of the angular frequency (ω0 + ω1) and the angular frequency (ω0−ω1) component. E7πs0 is obtained, and in the second excitation state, the electromotive force E7π2 of the component of the angular frequency ω2, and the electromotive force sum E7πs2 of the component of the angular frequency (ω2 + ω1) and the angular frequency (ω2-ω1) component are obtained. In this embodiment, if the magnetic field B12 generated from the first exciting coil 3a and the magnetic field B13 generated from the second exciting coil 3b are set to be equal, the interelectrode electromotive force E7π0 is approximated. Focusing on the fact that the first ∂A / ∂t component can be extracted and the interelectrode electromotive force E7π2 can be approximately extracted as the second ∂A / ∂t component, the first ∂A / ∂t component Is used to normalize the span of the flow velocity V of the v × B component in the electromotive force sum E7πs0 and v × B component in the electromotive force sum E7πs2 using the second ∂A / ∂t component. Normalization is performed on the span of the flow velocity V, and the difference EdA73 (third ∂A / ∂t component) is extracted from the normalized electromotive force sums En70 and En72, and the normalized electromotive force sum En70 V × B by removing the ∂A / ∂t component of Since the minute is extracted and the flow rate of the fluid to be measured is calculated from this v × B component, accurate span correction can be automatically performed, and the electromagnetic flow can be obtained without reducing the flow rate of the fluid to be measured to zero. The zero point of the output of the flow meter can be corrected, and the stability of the zero point can be ensured even in high frequency excitation.

In the present embodiment, the first ∂A / ∂t component having the same angular frequency obtained by extracting the v × B component of the electromotive force sum E7πs0 from the electromotive force E7π0 in consideration of the difference in magnetic field loss depending on the frequency. And normalizing the v × B component of the electromotive force sum E7πs2 using the second ∂A / ∂t components of the same angular frequency extracted from the electromotive force E7π2, and respectively normalizing the electromotive force sum En70. Since the zero correction is performed based on the difference between En and 72, accurate span correction and zero correction can be performed even when there is an influence due to the loss of the magnetic field.
In the present embodiment, it is not necessary to switch the phase difference of the magnetic field only by switching the frequency of the carrier wave, and it is not necessary to use the four excitation states as in the first embodiment. Can be calculated.

In the present embodiment, the electromotive force sum E7πs0 is the target of 0 correction and span correction, but the electromotive force sum E7πs2 may be the target of 0 correction and span correction. In this case, the difference EdA73 (third ∂A / ∂t component) is obtained from the normalized electromotive force sums En72 and En70 as in the following equation.
EdA73 = (En72-En70) · ω2 / (ω2-ω0) (408)
Then, the v × B component EvBn7 may be obtained by subtracting the difference EdA73 from the normalized electromotive force sum En72 as in the following equation. The other processes are the same as those in the case where the electromotive force sum E7πs0 is the target of 0 correction and span correction.
| EvBn7 | = | En72−EdA73 | (409)

[Eighth Embodiment]
Next, an eighth embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has one excitation coil and two pairs of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. When the newly added second electrode is added on the same side as the existing first electrode, the redundant configuration of the first embodiment is obtained. Therefore, it is necessary to arrange the second electrode on a different side from the first electrode with the exciting coil interposed therebetween. The present embodiment uses the first detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The first extraction method described is used.

Of the magnetic field Bd generated from the excitation coil 3, a magnetic field component (magnetic flux density) B4 orthogonal to both the electrode axis EAX1 and the measurement tube axis PAX on the electrode axis EAX1 connecting the electrodes 2a and 2b, and generated from the excitation coil 3 The magnetic field component (magnetic flux density) B5 orthogonal to both the electrode axis EAX2 and the measurement tube axis PAX on the electrode axis EAX2 connecting the electrodes 2c and 2d is assumed to be given as follows.
B4 = b4 · cos (ω0 · t−θ4) (410)
B5 = b5 · cos (ω0 · t−θ5) (411)

  However, since B4 and B5 are generated from one excitation coil 3, b4 and b5 and θ4 and θ5 are related to each other and are not independent variables. In equations (410) and (411), b4 and b5 are the amplitudes of the magnetic flux densities B4 and B5, ω0 is the angular frequency, θ4 is the phase difference (phase lag) between the magnetic flux density B4 and ω0 · t, and θ5 is the magnetic flux. It is the phase difference between the density B5 and ω0 · t. Hereinafter, the magnetic flux density B4 is referred to as a magnetic field B4, and the magnetic flux density B5 is referred to as a magnetic field B5.

Considering the loss of the magnetic field, the amplitudes b4 and b5 of the magnetic fields B4 and B5 at the angular frequency ω0 are changed to the function notations b4 [ω0] and b5 [ω0], respectively, and similarly the phase difference θ4 of the magnetic fields B4 and B5. When θ5 is changed to θ4 [ω0] and θ5 [ω0], respectively, equations (410) and (411) are replaced with equations (412) and (413).
B4 = b4 [ω0] · cos (ω0 · t−θ4 [ω0]) (412)
B5 = b5 [ω0] · cos (ω0 · t−θ5 [ω0]) (413)

Since the electromotive force resulting from the change of the magnetic field is based on the time derivative dB / dt of the magnetic field, B4 and B5 of the magnetic field Bd generated from the exciting coil 3 are differentiated as follows.
dB4 / dt = ω0 · cos (ω0 · t) · b4 [ω0] · {sin (θ4 [ω0])}
+ Ω0 · sin (ω0 · t) · b4 [ω0] · {−cos (θ4 [ω0])}
... (414)
dB5 / dt = ω0 · cos (ω0 · t) · b5 [ω0] · {sin (θ5 [ω0])}
+ Ω0 · sin (ω0 · t) · b5 [ω0] · {−cos (θ5 [ω0])}
... (415)

  When the flow rate of the fluid to be measured is 0, the first inter-electrode electromotive force E1 that is generated by the change of the magnetic field Bd and is independent of the flow velocity and the electrode axis EAX2 in the plane including the electrode axis EAX1 and the measurement tube axis PAX. In the plane including the measurement tube axis PAX, the second inter-electrode electromotive force E2 generated by the change of the magnetic field Bd is irrelevant to each other as shown in FIG. At this time, the first inter-electrode electromotive force E1 and the second inter-electrode electromotive force E2 are time differentials (−dB4 / dt, dB5 / dt) of the magnetic field added with the direction of the electromotive force, as shown in the following equation. Is multiplied by a proportionality factor rk, and the phase differences θ4 and θ5 are respectively replaced by θ4 + θ00 and θ5 + θ00 (rk and θ00 are the conductivity and dielectric constant of the fluid to be measured and the arrangement of the electrodes 2a, 2b, 2c and 2d, respectively. (Related to the structure of the measuring tube 1).

E1 = rk · ω0 · cos (ω0 · t) · b4 [ω0]
・ {-Sin (θ4 [ω0] + θ00)}
+ Rk · ω0 · sin (ω0 · t) · b4 [ω0]
{Cos (θ4 [ω0] + θ00)} (416)
E2 = rk · ω0 · cos (ω0 · t) · b5 [ω0]
・ {Sin (θ5 [ω0] + θ00)}
+ Rk · ω0 · sin (ω0 · t) · b5 [ω0]
{-Cos (θ5 [ω0] + θ00)} (417)

  When the magnitude of the flow velocity of the fluid to be measured is V (V ≠ 0), the first inter-electrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bd, and the second electrode generated by the flow velocity vector v and the magnetic field Bd. The electromotive force Ev2 has the same direction as shown in FIG. At this time, the first inter-electrode electromotive force Ev1 and the second inter-electrode electromotive force Ev2 are obtained by multiplying the magnetic field (B4, B5) to which the direction of the electromotive force is added by the proportional coefficient rkv as shown in the following equation. The phase differences θ4 and θ5 are respectively replaced by θ4 + θ01 and θ5 + θ01 (rkv and θ01 are measurements including the magnitude V of the flow velocity, the conductivity and dielectric constant of the fluid to be measured, and the arrangement of the electrodes 2a, 2b, 2c and 2d. Related to the structure of the tube 1).

Ev1 = rkv · cos (ω0 · t) · b4 [ω0] · cos (θ4 [ω0] + θ01)
+ Rkv · sin (ω0 · t) · b4 [ω0] · sin (θ4 [ω0] + θ01)
... (418)
Ev2 = rkv · cos (ω0 · t) · b5 [ω0] · cos (θ5 [ω0] + θ01)
+ Rkv · sin (ω0 · t) · b5 [ω0] · sin (θ5 [ω0] + θ01)
... (419)

In consideration of the direction of the inter-electrode electromotive force described with reference to FIGS. 14 and 15, the electro-electromotive force obtained by converting the electro-electromotive force due to the time change of the magnetic field into a complex vector and the flow velocity of the fluid to be measured. The electromotive force E810c of the component of the angular frequency ω0 of the first inter-electrode electromotive force between the electrodes 2a and 2b, which is combined with the electromotive force converted into a complex vector, is expressed by Equations (416) and (418). By applying (17), it is expressed by the following equation.
E810c = rk · ω0 · b4 [ω0]
• exp {j · (π / 2 + θ4 [ω0] + θ00)}
+ Γ · rk · V · b4 [ω0] · exp {j · (θ4 [ω0] + θ01)}
... (420)

Between the electrodes 2c and 2d, which combines the electromotive force obtained by converting the electromotive force between the electrodes due to the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the electromotive force between the electrodes caused by the flow velocity of the fluid to be measured into the complex vector. The electromotive force E82c of the component having the angular frequency ω0 of the second inter-electrode electromotive force is expressed by the following equation by applying the equation (17) to the equations (417) and (419).
E820c = rk · ω0 · b5 [ω0]
Exp {j. (− Π / 2 + θ5 [ω0] + θ00)}
+ Γ · rk · V · b5 [ω0] · exp {j · (θ5 [ω0] + θ01)}
... (421)

Here, the relationship between the phase delay θ4 [ω0] of the component of the angular frequency ω0 of the magnetic field B4 and the phase delay θ5 [ω0] of the component of the angular frequency ω0 of the magnetic field B5 is expressed as θ5 [ω0] = θ4 [ω0] + Δθ5 [ω0 And the relationship between the angle θ00 of the ∂A / ∂t component with respect to the imaginary axis and the angle θ01 of the v × B component with respect to the real axis is θ01 = θ00 + Δθ01. Θ5 [ω0] = θ4 [ω0] + Δθ5 [ω0], θ01 = θ00 + Δθ01 when substituting θ5 [ω0] = θ4 [ω0] into equation (420), component E810c of the angular frequency ω0 of the first interelectrode electromotive force, and θ5 [ω0 into equation (421). ] = Θ4 [ω0] + Δθ5 [ω0], θ01 = θ00 + Δθ01 and substituting E8s0 with the component E820c of the angular frequency ω0 of the second electrode electromotive force, the electromotive force sum E8s0 is given by expressed.
E8s0 = rk · exp {j · (θ4 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B4 [ω0] −b5 [ω0] · exp (j · Δθ5 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B4 [ω0] + b5 [ω0] · exp (j · Δθ5 [ω0])}]
... (422)

In addition, when θ5 [ω0] = θ4 [ω0] + Δθ5 [ω0] and θ01 = θ00 + Δθ01 are substituted into Equation (420), the component E810c of the angular frequency ω0 of the first inter-electrode electromotive force and θ5 into Equation (421). If the difference from the component E820c of the angular frequency ω0 of the second electrode electromotive force when substituting [ω0] = θ4 [ω0] + Δθ5 [ω0] and θ01 = θ00 + Δθ01 is E8d0, the electromotive force difference E8d0 is It is expressed by a formula.
E8d0 = rk · exp {j · (θ4 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B4 [ω0] + b5 [ω0] · exp (j · Δθ5 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B4 [ω0] −b5 [ω0] · exp (j · Δθ5 [ω0])}]
... (423)

If the magnetic fields B4 and B5 generated from the exciting coil 3 are set to be equal in the initial state (the state at the time of calibration), the difference from the initial state of the subsequent magnetic fields B4 and B5 becomes small, and the condition of the following equation is satisfied: It holds.
| B4 [ω0] + b5 [ω0] · exp (j · Δθ5 [ω0]) |
>> | b4 [ω0] −b5 [ω0] · exp (j · Δθ5 [ω0]) | (424)

Further, since ω0> γ · V is normally satisfied, when the condition of the equation (424) is considered, the following equation is satisfied in the equation (423).
| Ω0 · exp (j · π / 2)
{B4 [ω0] + b5 [ω0] · exp (j · Δθ5 [ω0])} |
≫ ｜ γ ・ V ・ exp (j ・ Δθ01)
{B4 [ω0] −b5 [ω0] · exp (j · Δθ5 [ω0])} |
... (425)

The electromotive force difference EdA81 that approximates the electromotive force difference E8d0 using the condition of the equation (425) is expressed by the following equation. This electromotive force EdA81 corresponds to the first ∂A / ∂t component in the basic principle.
EdA81≈E8d0 (426)
EdA81 = rk · exp {j · (θ4 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B4 [ω0] + b5 [ω0] · exp (j · Δθ5 [ω0])}
... (427)

Since the electromotive force difference EdA81 is not related to the magnitude V of the flow velocity, it is only a component generated by の み A / ∂t. Using this electromotive force difference EdA81, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the electromotive force sum E8s0 is normalized. Normalizing the electromotive force sum E8s0 in the equation (422) with the electromotive force difference EdA81 in the equation (426) and multiplying the result by ω0 is En80, the normalized electromotive force sum En80 is expressed by the following equation.
En80 = (E8s0 / EdA81) · ω0
= Rk · exp {j · (θ4 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B4 [ω0] −b5 [ω0] · exp (j · Δθ5 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B4 [ω0] + b5 [ω0] · exp (j · Δθ5 [ω0])}]
/ [Rk · exp {j · (θ4 [ω0] + θ00)} · ω0 · exp (j · π / 2)
{B4 [ω0] + b5 [ω0] · exp (j · Δθ5 [ω0])}] · ω0
= Ω0 · {b4 [ω0] −b5 [ω0] · exp (j · Δθ5 [ω0])}
/ {B4 [ω0] + b5 [ω0] · exp (j · Δθ5 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (428)

Using equation (52), the coefficient {b4 [ω0] −b5 [ω0] · exp (j · Δθ5 [ω0])} / {b4 [ω0] applied to the angular frequency ω0 of the first term on the right side of equation (428) ] + B5 [ω0] · exp (j · Δθ5 [ω0])} is represented by a value {b4-b5 · exp (j · Δθ5)} / {b4 + b5 · exp (j · Δθ5)} not related to the angular frequency ω0. be able to. Therefore, the equation (428) can be replaced by the following equation.
En80 = ω0 · {b4-b5 · exp (j · Δθ5)}
/ {B4 + b5 · exp (j · Δθ5)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (429)

  The second term on the right side of Equation (429) is a term obtained by normalizing the component generated by v × B with the component generated by ∂A / ∂t. The reason why the result obtained by normalizing the electromotive force sum E8s0 by the electromotive force difference EdA81 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side of the magnitude V of the flow velocity. According to the equation (429), the complex coefficient related to the magnitude V of the flow velocity has a magnitude of γ and an angle from the real axis of −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (429) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the ∂A / ∂t component, it is possible to realize span correction that automatically corrects an error due to a magnetic field shift or phase change.

Next, a method for removing the first term on the right side of the equation (429), which is a variation factor of 0 point, will be described. When the excitation angular frequency is ω2 instead of ω0 in the equations (412) and (413), the magnetic fields B4 and B5 are expressed by the following equations.
B4 = b4 [ω2] · cos (ω2 · t−θ4 [ω2]) (430)
B5 = b5 [ω2] · cos (ω2 · t−θ5 [ω2]) (431)

  Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. The electromotive force sum E8s2 to be subjected to span correction at the angular frequency ω2 is represented by the expression (422) in which the angular frequency ω0 is replaced with ω2. The electromotive force difference E8d2 that is the basis of the second ∂A / ∂t component is expressed by the equation (423) in which the angular frequency ω0 is replaced with ω2. The electromotive force difference EdA82 serving as the second ∂A / ∂t component is obtained by replacing the angular frequency ω0 with ω2 in the equation (427).

Normalizing the electromotive force sum E8s2 with the electromotive force difference EdA82 and multiplying the result by ω2 to En82, the normalized electromotive force sum En82 is expressed by the following equation from Equation (429).
En82 = ω2 · {b4-b5 · exp (j · Δθ5)}
/ {B4 + b5 · exp (j · Δθ5)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (432)

If the difference between the normalized electromotive force sums En80 and En82 is taken and the obtained difference is multiplied by ω0 / (ω0−ω2) as EdA83, the difference EdA83 is expressed by the following equation. This electromotive force sum difference EdA83 corresponds to the third ∂A / ∂t component in the basic principle.
EdA83 = (En20−En22) · ω0 / (ω0−ω2)
= [Ω0 · {b4-b5 · exp (j · Δθ5)}
/ {B4 + b5 · exp (j · Δθ5)}
+ Γ · exp {j · (−π / 2 + Δθ01)} · V
-Ω2 · {b4-b5 · exp (j · Δθ5)}
/ {B4 + b5 · exp (j · Δθ5)}
−γ · exp {j · (−π / 2 + Δθ01)} · V]
・ Ω0 / (ω0−ω2)
= Ω0 · {b4-b5 · exp (j · Δθ5)}
/ {B4 + b5 · exp (j · Δθ5)} (433)

The difference EdA83 represents the normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (429). Therefore, if this difference EdA83 is used, the normalized v × B component is normalized. It can be taken out from the power sum En80. When the v × B component obtained by subtracting the difference EdA83 of the equation (433) from the normalized electromotive force sum En80 of the equation (429) is EvBn8, the v × B component EvBn8 is expressed by the following equation.
EvBn8 = En80-EdA83
= Ω0 · {b4-b5 · exp (j · Δθ5)}
/ {B4 + b5 · exp (j · Δθ5)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
-Ω0 · {b4-b5 · exp (j · Δθ5)}
/ {B4 + b5 · exp (j · Δθ5)}
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (434)

The v × B component EvBn8 is not related to the angular frequency ω0. As can be seen from the fact that the v × B component EvBn8 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBn8. From the equation (434), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn8 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn8 | / γ (435)

  Table 8 below shows the correspondence between the constants and variables used in the basic principle and the constants and variables in the present embodiment. As is apparent from Table 8, this embodiment is one example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. FIG. 23 is a block diagram showing the configuration of the electromagnetic flowmeter of the present embodiment, and the same components as those in FIG. 13 are denoted by the same reference numerals. The electromagnetic flow meter of the present embodiment includes a measuring tube 1, first electrodes 2a and 2b, second electrodes 2c and 2d, an excitation coil 3, a power supply unit 4a, a signal conversion unit 5a, a signal A flow rate output unit 6a that calculates the flow rate of the fluid from the v × B component extracted by the conversion unit 5a.

  The signal converter 5a is configured to detect the first combined electromotive force detected by the first electrodes 2a and 2b and the second electrodes 2c and 2d detected in the first excitation state and the second excitation state, respectively. 2 is obtained, and based on these amplitudes and phases, the sum of electromotive forces in the same excitation state and the difference in electromotive forces in the same excitation state of the first composite electromotive force and the second composite electromotive force are obtained. Each of the first excitation state and the second excitation state is obtained, and the electromotive force difference in the first excitation state is extracted as the first ∂A / ∂t component, and the electromotive force difference in the second excitation state is calculated. Extracted as the second ∂A / ∂t component, the sum of electromotive forces in the first excitation state as the first correction target electromotive force, and the first correction target electromotive force based on the first ∂A / ∂t component. While removing the span variation factor included in the v × B component of the power, the electromotive force sum of the second excitation state is As a correction target electromotive force, a span correction unit 51a that removes a span variation factor included in the v × B component in the second correction target electromotive force based on the second ∂A / ∂t component, and a span The difference between the corrected first correction target electromotive force and the second corrected correction target electromotive force is extracted as a third ∂A / ∂t component, and the two corrected correction target electromotive forces with span correction are extracted. The zero point correction unit 52a that extracts the v × B component by removing the third ∂A / ∂t component from any one of them.

  The power supply unit 4a continues the first excitation state in which the excitation current having the angular frequency ω0 is supplied to the excitation coil 3 for T1 seconds, and subsequently performs the second excitation state in which the excitation current having the angular frequency ω2 is supplied to the excitation coil 3. The T2 second duration is repeated at a T second cycle. That is, T = T1 + T2.

  FIG. 24 is a flowchart showing the operations of the signal conversion unit 5a and the flow rate output unit 6a. First, the span correction unit 51a of the signal conversion unit 5a is the sum of the first inter-electrode electromotive force between the electrodes 2a and 2b and the second inter-electrode electromotive force between the electrodes 2c and 2d in the first excitation state. The amplitude r8s0 of E8s0 is obtained, and the phase difference φ8s0 between the real axis and the electromotive force sum E8s0 is obtained by a phase detector (not shown). Further, in the first excitation state, the span correction unit 51a obtains the amplitude r8d0 of the difference E8d0 between the first inter-electrode electromotive force and the second inter-electrode electromotive force, and between the real axis and the electromotive force difference E8d0. A phase difference φ8d0 is obtained by a phase detector (step 601 in FIG. 24).

  Subsequently, in the second excitation state, the span correction unit 51a obtains the amplitude r8s2 of the sum E8s2 of the first interelectrode electromotive force and the second interelectrode electromotive force, and the real axis and the electromotive force sum E8s2. Is obtained by a phase detector. Further, in the second excitation state, the span correction unit 51a obtains the amplitude r8d2 of the difference E8d2 between the first inter-electrode electromotive force and the second inter-electrode electromotive force, and between the real axis and the electromotive force difference E8d2. A phase difference φ8d2 is obtained by a phase detector (step 602).

Next, the span correction unit 51a obtains the magnitude and angle of the electromotive force difference EdA81 that approximates the electromotive force difference E8d0 (step 603). The process of step 603 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of equation (427). The span correction unit 51a calculates the magnitude | EdA81 | of the electromotive force difference EdA81 as follows.
| EdA81 | = r8d0 (436)
Then, the span correction unit 51a calculates the angle ∠EdA81 of the electromotive force difference EdA81 as the following equation.
∠EdA81 = φ8d0 (437)
This completes the processing in step 603.

Subsequently, the span correction unit 51a obtains the magnitude and angle of the normalized electromotive force sum En80 obtained by normalizing the electromotive force sum E8s0 with the electromotive force difference EdA81 (step 604). The process of step 604 is a process corresponding to the calculation of equation (429). The span correction unit 51a calculates the magnitude | En80 | of the normalized electromotive force sum En80 as the following equation.
| En80 | = (r8s0 / | EdA81 |) · ω0 (438)

Then, the span correction unit 51a calculates the angle ∠En80 of the normalized electromotive force sum En80 as the following equation.
∠En80 = φ8s0−∠EdA81 (439)
Further, the span correction unit 51a calculates the real axis component En80x and the imaginary axis component En80y of the normalized electromotive force sum En80 as the following expression.
En80x = | En80 | .cos (∠En80) (440)
En80y = | En80 | .sin (∠En80) (441)
This completes the process of step 604.

Next, the span correction unit 51a obtains the magnitude and angle of the electromotive force difference EdA82 that approximates the electromotive force difference E8d2 (step 605). The processing in step 605 is processing corresponding to obtaining the second ∂A / ∂t component. The span correction unit 51a calculates the magnitude | EdA82 | of the electromotive force difference EdA82 as follows.
| EdA82 | = r8d2 (442)
Then, the span correction unit 51a calculates the angle ∠EdA82 of the electromotive force difference EdA82 as the following equation.
∠EdA82 = φ8d2 (443)
This completes the processing in step 605.

Subsequently, the span correction unit 51a obtains the magnitude and angle of the normalized electromotive force sum En82 obtained by normalizing the electromotive force sum E8s2 with the electromotive force difference EdA82 (step 606). The process of step 606 is a process corresponding to the calculation of equation (432). The span correction unit 51a calculates the magnitude | En82 | of the normalized electromotive force sum En82 as follows.
| En82 | = (r8s2 / | EdA82 |) · ω2 (444)

Then, the span correction unit 51a calculates the angle ∠En82 of the normalized electromotive force sum En82 as the following equation.
∠En82 = φ8s2-∠EdA82 (445)
Further, the span correction unit 51a calculates the real axis component En82x and the imaginary axis component En82y of the normalized electromotive force sum En82 as in the following equation.
En82x = | En82 | .cos (∠En82) (446)
En82y = | En82 | .sin (∠En82) (447)
This completes the processing in step 606.

Next, the zero point correction unit 52a of the signal conversion unit 5a obtains the magnitude of the difference EdA83 between the normalized electromotive force sums En80 and En82 (step 607). The process of step 607 is a process corresponding to obtaining the third ∂A / ∂t component, and is a process corresponding to the calculation of Expression (433). The zero point correction unit 52a calculates the real axis component EdA83x and the imaginary axis component EdA83y of the difference EdA83 as follows.
EdA83x = (En80x−En82x) · ω0 / (ω0−ω2) (48)
EdA83y = (En80y−En82y) · ω0 / (ω0−ω2) (449)

Then, the zero point correction unit 52a removes the difference EdA83 from the normalized electromotive force sum En80, and obtains the magnitude of the v × B component EvBn8 (step 608). The processing in step 608 is processing equivalent to the calculation of equation (434). The zero point correction unit 52a calculates the magnitude | EvBn8 | of the v × B component EvBn8 as follows.
| EvBn8 | = {(En80x−EdA83x) ²
+ (En80y−EdA83y) ² } ^1/2 (450)

The flow rate output unit 6a calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 609). The process of step 609 is a process corresponding to the calculation of equation (435).
V = | EvBn8 | / γ (451)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5a and the flow rate output unit 6a perform the processing in steps 601 to 609 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 610). Note that the processing in steps 602 to 609 is performed in the second excitation state.

  As described above, in the present embodiment, the electromotive force sum E8s0 and the electromotive force difference E8d0 are obtained in the first excitation state, and the electromotive force sum E8s2 and the electromotive force difference E8d2 are obtained in the second excitation state. In this embodiment, if the magnetic fields B4 and B5 generated from the exciting coil 3 are set to be equal, the electromotive force difference E8d0 can be approximately extracted as the first ∂A / ∂t component. Further, focusing on the fact that the electromotive force difference E8d2 can be approximately extracted as the second ∂A / ∂t component, the flow velocity of the v × B component in the electromotive force sum E8s0 using the first ∂A / ∂t component. Normalizing the span for the magnitude V of V, and normalizing the span for the magnitude V of the flow velocity of the v × B component in the electromotive force sum E8s2 using the second ∂A / ∂t component The difference EdA83 (third ∂A / ∂t component) is extracted from the electromotive force sums En80 and En82, and the third ∂A / ∂t component is removed from the normalized electromotive force sum En80 to obtain the v × B component. And the flow rate of the fluid to be measured is calculated from this v × B component. As a result, accurate span correction can be performed automatically, and the zero point of the output of the electromagnetic flowmeter can be corrected without setting the flow rate of the fluid to be measured to zero. Can be ensured.

  In the present embodiment, the first ∂A / 磁場 t component of the same angular frequency obtained by extracting the v × B component of the electromotive force sum E8s0 from the electromotive force difference E8d0 in consideration of the difference in magnetic field loss depending on the frequency. Is normalized using the second ∂A / ∂t component of the same angular frequency extracted from the electromotive force difference E8d2, and the electromotive force obtained by normalizing the v × B component of the electromotive force sum E8s2 is normalized. Since zero correction is performed based on the difference between the sums En80 and En82, accurate span correction and zero correction can be performed even when there is an influence due to the loss of the magnetic field.

In the present embodiment, the electromotive force sum E8s0 is the target of 0 correction and span correction, but the electromotive force sum E8s2 may be the target of 0 correction and span correction. In this case, the difference EdA83 (third ∂A / ∂t component) is obtained from the normalized electromotive force sums En82 and En80 as in the following equation.
EdA83 = (En82−En80) · ω2 / (ω2−ω0) (452)
Then, the v × B component EvBn8 may be obtained by subtracting the difference EdA83 from the normalized electromotive force sum En82 as in the following equation. The other processes are the same as those in the case where the electromotive force sum E8s0 is the target of zero correction and span correction.
| EvBn8 | = | En82-EdA83 | (453)

[Ninth Embodiment]
Next, a ninth embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has one excitation coil and two pairs of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. The present embodiment uses the first detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The first extraction method described is used.

Of the magnetic field Bd generated from the excitation coil 3, the magnetic field component (magnetic flux density) B14 orthogonal to both the electrode axis EAX1 and the measurement tube axis PAX on the electrode axis EAX1 connecting the electrodes 2a and 2b and the excitation coil 3 The magnetic field component (magnetic flux density) B15 orthogonal to both the electrode axis EAX2 and the measurement tube axis PAX on the electrode axis EAX2 connecting the electrodes 2c and 2d is assumed to be given as follows.
B14 = b14 · cos (ω0 · t−θ14) + b14 · cos (ω2 · t−θ14) (454)
B15 = b15 · cos (ω0 · t−θ15) + b15 · cos (ω2 · t−θ15) (455)

  However, since B14 and B15 are generated from one excitation coil 3, b14 and b15 and θ14 and θ15 are related to each other and are not independent variables. In Expressions (454) and (455), ω0 and ω2 are different angular frequencies, b14 is the amplitude of the angular frequency ω0 component and the amplitude of the angular frequency ω2 component of the magnetic flux density B14, and b15 is the angular frequency ω0 of the magnetic flux density B15. And θ14 are the phase difference (phase lag) between the angular frequency ω0 component of magnetic flux density B14 and ω0 · t, and the phase difference between the angular frequency ω2 component and ω2 · t. , Θ15 is the phase difference between the angular frequency ω0 component of the magnetic flux density B15 and ω0 · t, and the phase difference between the angular frequency ω2 component and ω2 · t. Hereinafter, the magnetic flux density B14 is referred to as a magnetic field B14, and the magnetic flux density B15 is referred to as a magnetic field B15.

  Considering the loss of the magnetic field at each angular frequency, the amplitudes b14 and b15 of the components of the angular frequency ω0 of the magnetic fields B14 and B15 are changed to b14 [ω0] and b15 [ω0], respectively, and the angular frequency is similarly changed. The phase differences θ14 and θ15 of the component of ω0 are changed to θ14 [ω0] and θ15 [ω0], respectively. Further, the amplitudes b14 and b15 of the components of the angular frequency ω2 of the magnetic fields B14 and B15 are changed to function notations b14 [ω2] and b15 [ω2], respectively, and similarly the phase differences θ14 and θ15 of the components of the angular frequency ω2 are respectively set. They are changed to θ14 [ω2] and θ15 [ω2]. As a result, Expression (454) and Expression (455) are replaced with Expression (456) and Expression (457).

B14 = b14 [ω0] · cos (θ14 [ω0]) · cos (ω0 · t)
+ B14 [ω0] · sin (θ14 [ω0]) · sin (ω0 · t)
+ B14 [ω2] · cos (θ14 [ω2]) · cos (ω2 · t)
+ B14 [ω2] · sin (θ14 [ω2]) · sin (ω2 · t)
... (456)
B15 = b15 [ω0] · cos (θ15 [ω0]) · cos (ω0 · t)
+ B15 [ω0] · sin (θ15 [ω0]) · sin (ω0 · t)
+ B15 [ω2] · cos (θ15 [ω2]) · cos (ω2 · t)
+ B15 [ω2] · sin (θ15 [ω2]) · sin (ω2 · t)
... (457)

Since the electromotive force resulting from the change of the magnetic field is based on the time differential dB / dt of the magnetic field, B14 and B15 of the magnetic field Bd generated from the exciting coil 3 are differentiated as follows.
dB14 / dt = ω0 · cos (ω0 · t) · b14 [ω0]
・ {Sin (θ14 [ω0])}
+ Ω0 · sin (ω0 · t) · b14 [ω0]
・ {-Cos (θ14 [ω0])}
+ Ω2 · cos (ω2 · t) · b14 [ω2]
・ {Sin (θ14 [ω2])}
+ Ω2 · sin (ω2 · t) · b14 [ω2]
{-Cos (θ14 [ω2])} (458)

dB15 / dt = ω0 · cos (ω0 · t) · b15 [ω0]
・ {Sin (θ15 [ω0])}
+ Ω0 · sin (ω0 · t) · b15 [ω0]
・ {-Cos (θ15 [ω0])}
+ Ω2 · cos (ω2 · t) · b15 [ω2]
・ {Sin (θ15 [ω2])}
+ Ω2 · sin (ω2 · t) · b15 [ω2]
{-Cos (θ15 [ω2])} (459)

  When the flow rate of the fluid to be measured is 0, the first inter-electrode electromotive force E1 that is generated by the change of the magnetic field Bd and is independent of the flow velocity and the electrode axis EAX2 in the plane including the electrode axis EAX1 and the measurement tube axis PAX. In the plane including the measurement tube axis PAX, the second inter-electrode electromotive force E2 generated by the change of the magnetic field Bd is irrelevant to each other as shown in FIG. At this time, the first inter-electrode electromotive force E1 and the second inter-electrode electromotive force E2 are time differentials (−dB14 / dt, dB15 / dt) of the magnetic field added with the direction of the electromotive force, as shown in the following equation. Is multiplied by a proportional coefficient rk for each angular frequency component of ω0 and ω2, and the phase differences θ14 and θ15 are replaced by θ14 + θ00 and θ15 + θ00, respectively (rk and θ00 are the conductivity and dielectric constant of the fluid to be measured and the electrode 2a. , 2b, 2c, 2d, related to the structure of the measuring tube 1).

E1 = rk · ω0 · cos (ω0 · t) · b14 [ω0]
・ {-Sin (θ14 [ω0] + θ00)}
+ Rk · ω0 · sin (ω0 · t) · b14 [ω0]
・ {Cos (θ14 [ω0] + θ00)}
+ Rk · ω2 · cos (ω2 · t) · b14 [ω2]
・ {-Sin (θ14 [ω2] + θ00)}
+ Rk · ω2 · sin (ω2 · t) · b14 [ω2]
{Cos (θ14 [ω2] + θ00)} (460)

E2 = rk · ω0 · cos (ω0 · t) · b15 [ω0]
・ {Sin (θ15 [ω0] + θ00)}
+ Rk · ω0 · sin (ω0 · t) · b15 [ω0]
・ {-Cos (θ15 [ω0] + θ00)}
+ Rk · ω2 · cos (ω2 · t) · b15 [ω2]
・ {Sin (θ15 [ω2] + θ00)}
+ Rk · ω2 · sin (ω2 · t) · b15 [ω2]
{-Cos (θ15 [ω2] + θ00)} (461)

  When the magnitude of the flow velocity of the fluid to be measured is V (V ≠ 0), the first inter-electrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bd, and the second electrode generated by the flow velocity vector v and the magnetic field Bd. The electromotive force Ev2 has the same direction as shown in FIG. At this time, the first inter-electrode electromotive force Ev1 and the second inter-electrode electromotive force Ev2 are represented by the following equations, and the angular frequency of each of ω0 and ω2 is added to the magnetic field (B14, B15) obtained by adding the direction of the electromotive force. The proportional coefficient rkv is applied to the components, and the phase differences θ14 and θ15 are replaced with θ14 + θ01 and θ15 + θ01, respectively (rkv and θ01 are the flow velocity magnitude V, the conductivity and dielectric constant of the fluid to be measured, and the electrodes 2a and 2b. , 2c, 2d related to the structure of the measuring tube 1).

Ev1 = rkv · cos (ω0 · t) · b14 [ω0]
・ Cos (θ14 [ω0] + θ01)
+ Rkv · sin (ω0 · t) · b14 [ω0]
・ Sin (θ14 [ω0] + θ01)
+ Rkv · cos (ω2 · t) · b14 [ω2]
・ Cos (θ14 [ω2] + θ01)
+ Rkv · sin (ω2 · t) · b14 [ω2]
Sin (θ14 [ω2] + θ01) (462)

Ev2 = rkv · cos (ω0 · t) · b15 [ω0]
・ Cos (θ15 [ω0] + θ01)
+ Rkv · sin (ω0 · t) · b15 [ω0]
・ Sin (θ15 [ω0] + θ01)
+ Rkv · cos (ω2 · t) · b15 [ω2]
・ Cos (θ15 [ω2] + θ01)
+ Rkv · sin (ω2 · t) · b15 [ω2]
Sin (θ15 [ω2] + θ01) (463)

In consideration of the direction of the inter-electrode electromotive force described with reference to FIGS. 14 and 15, the electro-electromotive force obtained by converting the electro-electromotive force due to the time change of the magnetic field into a complex vector and the flow velocity of the fluid to be measured. The electromotive force E910c of the component of the angular frequency ω0 of the first interelectrode electromotive force between the electrodes 2a and 2b, which is combined with the electromotive force obtained by converting the signal into a complex vector, is expressed by the first term and the second term in the equation (460). From the term, the first term of the formula (462), the second term, and the formula (17), it is expressed by the following formula.
E910c = rk · ω0 · b14 [ω0]
Exp {j. (Π / 2 + θ14 [ω0] + θ00)}
+ Γ · rk · V · b14 [ω0] · exp {j · (θ14 [ω0] + θ01)}
... (464)

Between the electrodes 2a and 2b, which is a combination of the electromotive force obtained by converting the electromotive force between the electrodes due to the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the electromotive force between the electrodes caused by the flow velocity of the fluid to be measured into the complex vector The electromotive force E912c of the component of the angular frequency ω2 in the first inter-electrode electromotive force of the first term is expressed by the third term, the fourth term, and the third term, the fourth term, and the formula (17) of the formula (462). ) And the following formula.
E912c = rk · ω2 · b14 [ω2]
Exp {j. (Π / 2 + θ14 [ω2] + θ00)}
+ Γ · rk · V · b14 [ω2] · exp {j · (θ14 [ω2] + θ01)}
... (465)

Between the electrodes 2c and 2d, which is a combination of the electromotive force obtained by converting the electromotive force between the electrodes due to the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the electromotive force between the electrodes caused by the flow velocity of the fluid to be measured into the complex vector The electromotive force E920c of the component of the angular frequency ω0 among the second inter-electrode electromotive force of the first term and the second term of the equation (461) and the first and second terms of the equation (463) and the equation (17) ) And the following formula.
E920c = rk · (ω0) · b15 [ω0]
Exp {j. (− Π / 2 + θ15 [ω0] + θ00)}
+ Γ · rk · V · b15 [ω0] · exp {j · (θ15 [ω0] + θ01)}
... (466)

Between the electrodes 2c and 2d, which combines the electromotive force obtained by converting the electromotive force between the electrodes due to the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the electromotive force between the electrodes caused by the flow velocity of the fluid to be measured into the complex vector. The electromotive force E922c of the component of the angular frequency ω2 in the second inter-electrode electromotive force of the second term is expressed by the third term, the fourth term, and the third term, the fourth term, and the formula (17) of the formula (463). ) And the following formula.
E922c = rk · (ω2) · b15 [ω2]
Exp {j · (−π / 2 + θ15 [ω2] + θ00)}
+ Γ · rk · V · b15 [ω2] · exp {j · (θ15 [ω2] + θ01)}
... (467)

Here, the relationship between the phase delay θ14 [ω0] of the component of the angular frequency ω0 of the magnetic field B14 and the phase delay θ15 [ω0] of the component of the angular frequency ω0 of the magnetic field B15 is expressed as θ15 [ω0] = θ14 [ω0] + Δθ15 [ω0. And the relationship between the angle θ00 of the ∂A / ∂t component with respect to the imaginary axis and the angle θ01 of the v × B component with respect to the real axis is θ01 = θ00 + Δθ01. The component E910c of the angular frequency ω0 of the first inter-electrode electromotive force when θ01 = θ00 + Δθ01, θ15 [ω0] = θ14 [ω0] + Δθ15 [ω0] is substituted into the equation (464), and θ01 = θ00 + Δθ01 into the equation (466). , Θ15 [ω0] = θ14 [ω0] + Δθ15 [ω0] is substituted, and the sum of the second inter-electrode electromotive force and the component E920c of the angular frequency ω0 is E9s0, the electromotive force sum E9s0 is expressed.
E9s0 = rk · exp {j · (θ14 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B14 [ω0] −b15 [ω0] · exp (j · Δθ15 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B14 [ω0] + b15 [ω0] · exp (j · Δθ15 [ω0])}]
... (468)

In addition, when θ01 = θ00 + Δθ01 and θ15 [ω0] = θ14 [ω0] + Δθ15 [ω0] are substituted into Expression (464), the component E910c of the angular frequency ω0 of the first inter-electrode electromotive force and θ01 into Expression (466) = Θ00 + Δθ01, θ15 [ω0] = θ14 [ω0] + Δθ15 [ω0] When the difference between the second electrode electromotive force and the component E920c of the angular frequency ω0 is E9d0, the electromotive force difference E9d0 is It is expressed by a formula.
E9d0 = rk · exp {j · (θ14 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B14 [ω0] + b15 [ω0] · exp (j · Δθ15 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B14 [ω0] −b15 [ω0] · exp (j · Δθ15 [ω0])}]
... (469)

Further, the relationship between the phase delay θ14 [ω2] of the component of the angular frequency ω2 of the magnetic field B14 and the phase delay θ15 [ω2] of the component of the angular frequency ω2 of the magnetic field B15 is expressed as θ15 [ω2] = θ14 [ω2] + Δθ15 [ω2]. And The component E912c of the angular frequency ω2 of the first inter-electrode electromotive force when θ01 = θ00 + Δθ01 and θ15 [ω2] = θ14 [ω2] + Δθ15 [ω2] are substituted into the equation (465) and θ01 = θ00 + Δθ01 into the equation (467). , Θ15 [ω2] = θ14 [ω2] + Δθ15 [ω2] is substituted, and the sum of the component E922c of the angular frequency ω2 of the second inter-electrode electromotive force is E9s2, the electromotive force sum E9s2 is given by expressed.
E9s2 = rk · exp {j · (θ14 [ω2] + θ00)}
・ [Ω2 ・ exp (j ・ π / 2)
{B14 [ω2] -b15 [ω2] · exp (j · Δθ15 [ω2])}
+ Γ · V · exp (j · Δθ01)
{B14 [ω2] + b15 [ω2] · exp (j · Δθ15 [ω2])}]
... (470)

Further, when θ01 = θ00 + Δθ01 and θ15 [ω2] = θ14 [ω2] + Δθ15 [ω2] are substituted into Expression (465), the component E912c of the angular frequency ω2 of the first inter-electrode electromotive force and θ01 into Expression (467) = Θ00 + Δθ01, θ15 [ω2] = θ14 [ω2] + Δθ15 [ω2] When the difference from the component E922c of the angular frequency ω2 of the second electrode electromotive force is E9d2, the electromotive force difference E9d2 is It is expressed by a formula.
E9d2 = rk · exp {j · (θ14 [ω2] + θ00)}
・ [Ω2 ・ exp (j ・ π / 2)
{B14 [ω2] + b15 [ω2] · exp (j · Δθ15 [ω2])}
+ Γ · V · exp (j · Δθ01)
{B14 [ω2] -b15 [ω2] · exp (j · Δθ15 [ω2])}]
... (471)

If the magnetic fields B14 and B15 generated from the exciting coil 3 are set to be equal in the initial state (the state at the time of calibration), the difference from the initial state of the subsequent magnetic fields B14 and B15 becomes small. It holds.
| B14 [ω0] + b15 [ω0] · exp (j · Δθ15 [ω0]) |
»| B14 [ω0] −b15 [ω0] · exp (j · Δθ15 [ω0]) |
... (472)
B14 [ω2] + b15 [ω2] · exp (j · Δθ15 [ω2]) |
»| B15 [ω2] −b15 [ω2] · exp (j · Δθ15 [ω2]) |
... (473)

Further, since ω0> γ · V and ω2> γ · V are normally satisfied, when the condition of Expression (472) is considered, the condition of Expression (474) is satisfied in Expression (469), and the condition of Expression (473) is satisfied. In consideration, the condition of the expression (475) is established in the expression (471).
| Ω0 · exp (j · π / 2)
{B14 [ω0] + b15 [ω0] · exp (j · Δθ15 [ω0])} |
≫ ｜ γ ・ V ・ exp (j ・ Δθ01)
{B14 [ω0] −b15 [ω0] · exp (j · Δθ15 [ω0])} |
... (474)
| Ω2 · exp (j · π / 2)
{B14 [ω2] + b15 [ω2] · exp (j · Δθ15 [ω2])} |
≫ ｜ γ ・ V ・ exp (j ・ Δθ01)
{B14 [ω2] -b15 [ω2] · exp (j · Δθ15 [ω2])} |
... (475)

If an approximation of the electromotive force difference E9d0 in the equation (469) using the condition of the equation (474) as EdA91, the electromotive force difference EdA91 is expressed by the following equation. This electromotive force difference EdA91 corresponds to the first ∂A / ∂t component in the basic principle.
EdA91≈E9d0 (476)
EdA91 = rk · exp {j · (θ14 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B14 [ω0] + b15 [ω0] · exp (j · Δθ15 [ω0])}
... (477)

Since the electromotive force difference EdA91 is not related to the magnitude V of the flow velocity, it becomes only a component generated by ∂A / ∂t. Using this electromotive force difference EdA91, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the electromotive force sum E9s0 is normalized. If the electromotive force sum E9s0 is normalized by the electromotive force difference EdA91 and multiplied by ω0 is En90, the normalized electromotive force sum En90 is expressed by the following equation.
En90 = (E9s0 / EdA91) · ω0
= Rk · exp {j · (θ1 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B14 [ω0] −b15 [ω0] · exp (j · Δθ15 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B14 [ω0] + b15 [ω0] · exp (j · Δθ15 [ω0])}]
/ [Rk · exp {j · (θ14 [ω0] + θ00)} · ω0 · exp (j · π / 2)
{B14 [ω0] + b15 [ω0] · exp (j · Δθ15 [ω0])}] · ω0
= Ω0 · {b14 [ω0] −b15 [ω0] · exp (j · Δθ15 [ω0])}
/ {B14 [ω0] + b15 [ω0] · exp (j · Δθ15 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (478)

Using equation (52), the coefficient {b14 [ω0] −b15 [ω0] · exp (j · Δθ15 [ω0])} / {b14 [ω0] applied to the angular frequency ω0 of the first term on the right side of equation (478) ] + B15 [ω0] · exp (j · Δθ15 [ω0])} is represented by a value {b14−b15 · exp (j · Δθ15)} / {b14 + b15 · exp (j · Δθ15)} not related to the angular frequency ω0. be able to. Therefore, the equation (478) can be replaced by the following equation.
En90 = ω0 · {b14−b15 · exp (j · Δθ15)}
/ {B14 + b15 · exp (j · Δθ15)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (479)

  The second term on the right side of Equation (479) is a term obtained by normalizing the component generated by v × B. The reason why the result obtained by normalizing the electromotive force sum E9s0 by the electromotive force difference EdA91 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side of the magnitude V of the flow velocity. The complex coefficient related to the magnitude V of the flow velocity has an angle from the real axis of the magnitude of γ, −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (479) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the ∂A / ∂t component, it is possible to realize span correction that automatically corrects an error due to a magnetic field shift or phase change.

Next, a method for removing the first term on the right side of Equation (479), which is a factor of variation at 0 point, will be described. Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. If an approximation of the electromotive force difference E9d2 in the equation (471) using the condition of the equation (475) is taken as EdA92, the electromotive force difference EdA92 is expressed by the following equation. This electromotive force EdA92 corresponds to the second ∂A / ∂t component in the basic principle.
EdA92≈E9d2 (480)
EdA92 = rk · exp {j · (θ14 [ω2] + θ00)}
・ Ω2 ・ exp (j ・ π / 2)
{B14 [ω2] + b15 [ω2] · exp (j · Δθ15 [ω2])}
... (481)

If the result obtained by normalizing the electromotive force sum E9s2 of the equation (470) by the electromotive force difference EdA92 of the equation (481) and multiplying it by ω2 is En92, the normalized electromotive force sum En92 is expressed by the following equation from the equation (479). The
En92 = ω2 · {b14−b15 · exp (j · Δθ15)}
/ {B14 + b15 · exp (j · Δθ15)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (482)

Taking the difference between the normalized electromotive force sums En90 and En92 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA93, the difference EdA93 is expressed by the following equation. This difference EdA93 corresponds to the third ∂A / ∂t component in the basic principle.
EdA93 = (En9a−En9b) · ω0 / (ω0−ω2)
= [Ω0 · {b14−b15 · exp (j · Δθ15)}
/ {B14 + b15 · exp (j · Δθ15)}
+ Γ · exp {j · (−π / 2 + Δθ01)} · V
−ω2 · {b14−b15 · exp (j · Δθ15)}
/ {B14 + b15 · exp (j · Δθ15)}
−γ · exp {j · (−π / 2 + Δθ01)} · V]
・ Ω0 / (ω0−ω2)
= Ω0 · {b14−b15 · exp (j · Δθ15)}
/ {B14 + b15 · exp (j · Δθ15)} (483)

The difference EdA93 represents the normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (479). Therefore, if this difference EdA93 is used, the normalized v × B component is normalized. It can be taken out from the power sum En90. When the v × B component obtained when the difference EdA93 of the equation (483) is subtracted from the normalized electromotive force sum En90 of the equation (479) is EvBn9, the v × B component EvBn9 is expressed by the following equation.
EvBn9 = En90-EdA93
= Ω0 · {b14−b15 · exp (j · Δθ15)}
/ {B14 + b15 · exp (j · Δθ15)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
-Ω0 · {b14-b15 · exp (j · Δθ15)}
/ {B14 + b15 · exp (j · Δθ15)}
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (484)

The v × B component EvBn9 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvBn9 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBn9. From the equation (484), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn9 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn9 | / γ (485)

  Table 9 below shows the correspondence between the constants and variables used in the basic principle and the constants and variables in the present embodiment. As is apparent from Table 9, this embodiment is one example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. Since the configuration of the electromagnetic flowmeter of the present embodiment is the same as that of the eighth embodiment, description will be made using the reference numerals in FIG. The electromagnetic flow meter of the present embodiment includes a measurement tube 1, first electrodes 2a and 2b, second electrodes 2c and 2d, an excitation coil 3, a power supply unit 4a, a signal conversion unit 5a, a flow rate. And an output unit 6a.

  The signal converter 5a obtains the amplitude and phase of the first combined electromotive force detected by the first electrodes 2a and 2b and the second combined electromotive force detected by the second electrodes 2c and 2d. Based on the amplitude and phase, the sum of the electromotive forces of the same frequency components and the electromotive force difference of the same frequency components of the first composite electromotive force and the second composite electromotive force are obtained for each of the angular frequencies ω0 and ω2, and the angular frequency ω0 The electromotive force difference is extracted as the first ∂A / ∂t component, the electromotive force difference at the angular frequency ω2 is extracted as the second ∂A / ∂t component, and the electromotive force sum of the angular frequency ω0 is calculated as the first ∂A / ∂t component. As a correction target electromotive force, based on the first ∂A / ∂t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the electromotive force at the angular frequency ω2 Based on the second ∂A / ∂t component, the sum is taken as the second correction target electromotive force. A span correction unit 51a that removes a span variation factor included in the v × B component in the target electromotive force, a first correction target electromotive force that is subjected to span correction, and a second correction target electromotive force that is subjected to span correction Is extracted as the third ∂A / ∂t component, and v × is obtained by removing the third ∂A / い ず れ t component from any one of the two correction target electromotive forces subjected to the span correction. And a zero point correction unit 52a for extracting the B component.

  The power supply unit 4a of the present embodiment supplies an excitation current including a sine wave component having an angular frequency ω0 and a sine wave component having an angular frequency ω2 to the excitation coil 3. At this time, the amplitude of the angular frequency ω0 component and the angular frequency ω2 component in the excitation current is the same.

  FIG. 25 is a flowchart showing the operations of the signal conversion unit 5a and the flow rate output unit 6a of the present embodiment. First, the span correction unit 51a of the signal converting unit 5a sets the amplitude r9s0 of the sum E9s0 of the component E910c of the angular frequency ω0 of the first interelectrode electromotive force and the component E920c of the angular frequency ω0 of the second interelectrode electromotive force. At the same time, the phase difference φ9s0 between the real axis and the electromotive force sum E9s0 is obtained by a phase detector (not shown). The span correction unit 51a obtains the amplitude r9d0 of the difference E9d0 between the component E910c of the angular frequency ω0 of the first inter-electrode electromotive force and the component E920c of the angular frequency ω0 of the second inter-electrode electromotive force, and the real axis And a phase difference φ9d0 between the electromotive force difference E9d0 and the phase detector. The span correction unit 51a obtains the amplitude r9s2 of the sum E9s2 of the component E912c of the angular frequency ω2 of the first inter-electrode electromotive force and the component E922c of the angular frequency ω2 of the second inter-electrode electromotive force, and the real axis And a phase detector φ9s2 is obtained by the phase detector. Furthermore, the span correction unit 51a obtains the amplitude r9d2 of the difference E9d2 between the component E912c of the angular frequency ω2 of the first inter-electrode electromotive force and the component E922c of the angular frequency ω2 of the second inter-electrode electromotive force, and the real axis And a phase difference φ9d2 between the electromotive force difference E9d2 and the phase detector (step 701 in FIG. 25). The inter-electrode electromotive forces E910c, E920c, E912c, and E922c can be frequency-separated by a bandpass filter or a comb filter.

Next, the span correction unit 51a obtains the magnitude and angle of the electromotive force difference EdA91 that approximates the electromotive force difference E9d0 (step 702). The process of step 702 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of Expression (477). The span correction unit 51a calculates the magnitude | EdA91 | of the electromotive force difference EdA91 as follows.
| EdA91 | = r9d0 (486)
Then, the span correction unit 51a calculates the angle ∠EdA91 of the electromotive force difference EdA91 as the following equation.
∠EdA91 = φ9d0 (487)
This completes the processing in step 702.

Subsequently, the span correction unit 51a obtains the magnitude and angle of the normalized electromotive force sum En90 obtained by normalizing the electromotive force sum E9s0 with the electromotive force difference EdA91 (step 703). The processing in step 703 is processing equivalent to the calculation of equation (479). The span correction unit 51a calculates the magnitude | En90 | of the normalized electromotive force sum En90 as the following equation.
| En90 | = (r9s0 / | EdA91 |) · ω0 (488)

Then, the span correction unit 51a calculates the angle ∠En90 of the normalized electromotive force sum En90 as the following equation.
∠En90 = φ9s0−∠EdA91 (489)
Further, the span correction unit 51a calculates the real axis component En90x and the imaginary axis component En90y of the normalized electromotive force sum En90 as in the following equation.
En90x = | En90 | .cos (∠En90) (490)
En90y = | En90 | .sin (∠En90) (491)
This completes the processing in step 703.

Next, the span correction unit 51a obtains the magnitude and angle of the electromotive force difference EdA92 that approximates the electromotive force difference E9d2 (step 704). The process of step 704 is a process corresponding to obtaining the second ∂A / ∂t component, and is a process corresponding to the calculation of equation (481). The span correction unit 51a calculates the magnitude | EdA92 | of the electromotive force difference EdA92 as the following equation.
| EdA92 | = r9d2 (492)
Then, the span correction unit 51a calculates the angle ∠EdA92 of the electromotive force difference EdA92 as the following equation.
∠EdA92 = φ9d2 (493)
This completes the process of step 704.

Subsequently, the span correction unit 51a obtains the magnitude and angle of the normalized electromotive force sum En92 obtained by normalizing the electromotive force sum E9s2 with the electromotive force difference EdA92 (step 705). The process of step 705 is a process corresponding to the calculation of equation (482). The span correction unit 51a calculates the magnitude | En92 | of the normalized electromotive force sum En92 as the following equation.
| En92 | = (r9s2 / | EdA92 |) · ω2 (494)

Then, the span correction unit 51a calculates the angle ∠En92 of the normalized electromotive force sum En92 as the following equation.
∠En92 = φ9s2-∠EdA92 (495)
Further, the span correction unit 51a calculates the real axis component En92x and the imaginary axis component En92y of the normalized electromotive force sum En92 as the following expression.
En92x = | En92 | .cos (∠En92) (496)
En92y = | En92 | .sin (∠En92) (497)
This completes the process of step 705.

Next, the zero point correction unit 52a of the signal conversion unit 5a obtains the magnitude of the difference EdA93 between the normalized electromotive force sums En90 and En92 (step 706). The process of step 706 is a process corresponding to obtaining the third ∂A / ∂t component, and is a process corresponding to the calculation of Expression (483). The zero point correction unit 52a calculates the real axis component EdA93x and the imaginary axis component EdA93y of the difference EdA93 as in the following equation.
EdA93x = (En90x-En92x) .omega.0 / (. Omega.0-.omega.2) .. (498)
EdA93y = (En90y−En92y) · ω0 / (ω0−ω2) (499)

Then, the zero point correction unit 52a removes the difference EdA93 from the normalized electromotive force sum En90, and obtains the magnitude of the v × B component EvBn9 (step 707). The process of step 707 is a process corresponding to the calculation of equation (484). The zero point correction unit 52a calculates the magnitude | EvBn9 | of the v × B component EvBn9 as the following equation.
| EvBn9 | = {(En90x−EdA93x) ²
+ (En90y−EdA93y) ² } ^1/2 (500)

The flow rate output unit 6a calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 708). The processing in step 708 is processing equivalent to the calculation of equation (485).
V = | EvBn9 | / γ (501)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5a and the flow rate output unit 6a perform the processing in steps 701 to 708 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 709).

  As described above, in the present embodiment, the electromotive force sum E9s0 and the electromotive force difference E9d0 at the angular frequency ω0 are obtained, and the electromotive force sum E9s2 and the electromotive force difference E9d2 at the angular frequency ω2 are obtained. In this embodiment, when the magnetic fields B14 and B15 generated from the exciting coil 3 are set to be equal, the electromotive force difference E9d0 can be approximately extracted as the first ∂A / ∂t component. Also, focusing on the fact that the electromotive force difference E9d2 can be approximately extracted as the second ∂A / ∂t component, the flow velocity of the v × B component in the electromotive force sum E9s0 using the first ∂A / ∂t component. Normalizing the span over the magnitude V of V, and normalizing the span over the magnitude V of the flow velocity of the v × B component in the electromotive force sum E9s2 using the second ∂A / ∂t component The difference EdA93 (third ∂A / ∂t component) is extracted from the electromotive force sums En90 and En92, and the third ∂A / ∂t component is removed from the normalized electromotive force sum En90 to obtain the v × B component. And the flow rate of the fluid to be measured is calculated from this v × B component As a result, accurate span correction can be performed automatically, and the zero point of the output of the electromagnetic flowmeter can be corrected without reducing the flow rate of the fluid to be measured. The stability of 0 point can be ensured.

In the present embodiment, the first ∂A / 磁場 t component having the same angular frequency obtained by extracting the v × B component of the electromotive force sum E9s0 from the electromotive force difference E9d0 in consideration of the difference in the loss of the magnetic field due to the frequency. Is normalized using the second ∂A / ∂t component of the same angular frequency extracted from the electromotive force difference E9d2, and the electromotive force obtained by normalizing the v × B component of the electromotive force sum E9s2 is normalized. Since zero correction is performed based on the difference between the sums En90 and En92, accurate span correction and zero correction can be performed even when there is an influence due to magnetic field loss.
Further, in this embodiment, it is not necessary to switch the excitation frequency as in the eighth embodiment, so that the flow rate can be calculated at a higher speed.

  In the present embodiment, an example in which excitation is performed with two types of frequency components has been described. However, if excitation is performed with three or more types of frequency components, the accuracy of zero correction can be further improved. As an example of excitation with three or more types of frequency components, modulation can be used. If a carrier wave having an angular frequency ω0 is excited by a modulated wave having an angular frequency ω1, the electromotive force of the components having angular frequencies ω0 and ω0 ± ω1 can be obtained in the case of amplitude modulation, and the angular frequency in the case of phase modulation or frequency modulation. The electromotive force of the component of ω0, ω0 ± ζ · ω1 (ζ is a positive integer) can be obtained. An example in which this modulation is used is equivalent to that shown in the fourth to seventh embodiments, and a detailed description thereof will be omitted.

Further, in the present embodiment, the electromotive force sum E9s0 is set as an object of 0 correction and span correction, but the electromotive force sum E9s2 may be set as an object of 0 correction and span correction. In this case, the difference EdA93 (third ∂A / ∂t component) is obtained from the normalized electromotive force sums En92 and En90 as in the following equation.
EdA93 = (En92-En90) · ω2 / (ω2-ω0) (502)
Then, the v × B component EvBn9 may be obtained by subtracting the difference EdA93 from the normalized electromotive force sum En92 as in the following equation. The other processes are the same as the case where the electromotive force sum E9s0 is the target of 0 correction and span correction.
| EvBn9 | = | En92-EdA93 | (503)

[Tenth embodiment]
Next, a tenth embodiment of the present invention will be described. The electromagnetic flow meter of the present embodiment has one excitation coil and two pairs of electrodes, and the configuration excluding the signal processing system is the same as that of the electromagnetic flow meter shown in FIG. The principle of this embodiment will be described using reference numerals. The present embodiment uses the second detection method described in the basic principle as a method for detecting the composite vector Vas0 + Vbs0 to be normalized, and uses the basic principle as a method for extracting the first ∂A / ∂t component. The second extraction method described is used.

Of the magnetic field Bd generated from the excitation coil 3, the magnetic field component (magnetic flux density) B16 orthogonal to both the electrode axis EAX1 and the measurement tube axis PAX on the electrode axis EAX1 connecting the electrodes 2a and 2b, and the excitation coil 3 The magnetic field component (magnetic flux density) B17 orthogonal to both the electrode axis EAX2 and the measurement tube axis PAX on the electrode axis EAX2 connecting the electrodes 2c and 2d is assumed to be given as follows.
B16 = b16 · cos (ωp · t−θ16) + b16 · cos (ωm · t−θ16) (504)
B17 = b17 · cos (ωp · t−θ17) + b17 · cos (ωm · t−θ17) (505)

  However, since B16 and B17 are generated from one excitation coil 3, b16 and b17 and θ16 and θ17 are related to each other and are not independent variables. In equations (504) and (505), ωp and ωm are different angular frequencies, b16 is the amplitude of the angular frequency ωp component and the amplitude of the angular frequency ωm component of the magnetic flux density B16, and b17 is the angular frequency ωp of the magnetic flux density B17. And θ16 is the phase difference (phase lag) between the angular frequency ωp component and ωp · t of the magnetic flux density B16, and the phase difference between the angular frequency ωm component and ωm · t. , Θ17 are the phase difference between the angular frequency ωp component of the magnetic flux density B17 and ωp · t, and the phase difference between the angular frequency ωm component and ωm · t. Hereinafter, the magnetic flux density B16 is referred to as a magnetic field B16, and the magnetic flux density B17 is referred to as a magnetic field B17.

  Considering the loss of the magnetic field at each angular frequency, the amplitudes b16 and b17 of the components of the angular frequency ωp of the magnetic fields B16 and B17 are changed to b16 [ωp] and b17 [ωp], respectively, and the angular frequency is similarly changed. The phase differences θ16 and θ17 of the components of ωp are changed to θ16 [ωp] and θ17 [ωp], respectively. Furthermore, the amplitudes b16 and b17 of the components of the angular frequency ωm of the magnetic fields B16 and B17 are changed to b16 [ωm] and b17 [ωm], respectively, and the function notations are similarly obtained, and the phase differences θ16 and θ17 of the components of the angular frequency ωm are respectively set. They are changed to θ16 [ωm] and θ17 [ωm]. Thereby, Formula (504) and Formula (505) are replaced with Formula (506) and Formula (507).

B16 = b16 [ωp] · cos (θ16 [ωp]) · cos (ωp · t)
+ B16 [ωp] · sin (θ16 [ωp]) · sin (ωp · t)
+ B16 [ωm] · cos (θ16 [ωm]) · cos (ωm · t)
+ B16 [ωm] · sin (θ16 [ωm]) · sin (ωm · t)
... (506)
B17 = b17 [ωp] · cos (θ17 [ωp]) · cos (ωp · t)
+ B17 [ωp] · sin (θ17 [ωp]) · sin (ωp · t)
+ B17 [ωm] · cos (θ17 [ωm]) · cos (ωm · t)
+ B17 [ωm] · sin (θ17 [ωm]) · sin (ωm · t)
... (507)

Since the electromotive force resulting from the change of the magnetic field is based on the time derivative dB / dt of the magnetic field, B16 and B17 of the magnetic field Bd generated from the exciting coil 3 are differentiated as follows.
dB16 / dt = ωp · cos (ωp · t) · b16 [ωp]
・ {Sin (θ16 [ωp])}
+ Ωp · sin (ωp · t) · b16 [ωp]
・ {-Cos (θ16 [ωp])}
+ Ωm · cos (ωm · t) · b16 [ωm]
・ {Sin (θ16 [ωm])}
+ Ωm · sin (ωm · t) · b16 [ωm]
{-Cos (θ16 [ωm])} (508)

dB17 / dt = ωp · cos (ωp · t) · b17 [ωp]
・ {Sin (θ17 [ωp])}
+ Ωp · sin (ωp · t) · b17 [ωp]
・ {-Cos (θ17 [ωp])}
+ Ωm · cos (ωm · t) · b17 [ωm]
・ {Sin (θ17 [ωm])}
+ Ωm · sin (ωm · t) · b17 [ωm]
{-Cos (θ17 [ωm])} (509)

  When the flow rate of the fluid to be measured is 0, the first inter-electrode electromotive force E1 that is generated by the change of the magnetic field Bd and is independent of the flow velocity and the electrode axis EAX2 in the plane including the electrode axis EAX1 and the measurement tube axis PAX. In the plane including the measurement tube axis PAX, the second inter-electrode electromotive force E2 generated by the change of the magnetic field Bd is irrelevant to each other as shown in FIG. At this time, the first inter-electrode electromotive force E1 and the second inter-electrode electromotive force E2 are time differentials (−dB16 / dt, dB17 / dt) of the magnetic field added with the direction of the electromotive force, as shown in the following equation. Is multiplied by a proportional coefficient rk in the angular frequency components of ωp and ωm, and the phase differences θ16 and θ17 are replaced with θ16 + θ00 and θ17 + θ00, respectively (rk and θ00 are the conductivity and dielectric constant of the fluid to be measured and the electrode 2a. , 2b, 2c, 2d, related to the structure of the measuring tube 1).

E1 = rk · ωp · cos (ωp · t) · b16 [ωp]
・ {-Sin (θ16 [ωp] + θ00)}
+ Rk · ωp · sin (ωp · t) · b16 [ωp]
・ {Cos (θ16 [ωp] + θ00)}
+ Rk · ωm · cos (ωm · t) · b16 [ωm]
・ {-Sin (θ16 [ωm] + θ00)}
+ Rk · ωm · sin (ωm · t) · b16 [ωm]
{Cos (θ16 [ωm] + θ00)} (510)

E2 = rk · ωp · cos (ωp · t) · b17 [ωp]
・ {Sin (θ17 [ωp] + θ00)}
+ Rk · ωp · sin (ωp · t) · b17 [ωp]
・ {-Cos (θ17 [ωp] + θ00)}
+ Rk · ωm · cos (ωp · t) · b17 [ωm]
・ {Sin (θ17 [ωm] + θ00)}
+ Rk · ωm · sin (ωm · t) · b17 [ωm]
{-Cos (θ17 [ωm] + θ00)} (511)

  When the magnitude of the flow velocity of the fluid to be measured is V (V ≠ 0), the first inter-electrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bd, and the second electrode generated by the flow velocity vector v and the magnetic field Bd. The electromotive force Ev2 has the same direction as shown in FIG. At this time, the first inter-electrode electromotive force Ev1 and the second inter-electrode electromotive force Ev2 are respectively frequency components of ω0 and ω2 to the magnetic field (B16, B17) obtained by adding the direction of the electromotive force, as shown in the following equation. The phase differences θ16 and θ17 are respectively replaced by θ16 + θ01 and θ17 + θ01 (rkv and θ01 are the flow velocity magnitude V, the conductivity and dielectric constant of the fluid to be measured, and the electrodes 2a, 2b, (Related to the structure of the measuring tube 1 including the arrangement of 2c, 2d).

Ev1 = rkv · cos (ωp · t) · b16 [ωp]
・ Cos (θ16 [ωp] + θ01)
+ Rkv · sin (ωp · t) · b16 [ωp]
・ Sin (θ16 [ωp] + θ01)
+ Rkv · cos (ωm · t) · b16 [ωm]
・ Cos (θ16 [ωm] + θ01)
+ Rkv · sin (ωm · t) · b16 [ωm]
Sin (θ16 [ωm] + θ01) (512)

Ev2 = rkv · cos (ωp · t) · b17 [ωp]
・ Cos (θ17 [ωp] + θ01)
+ Rkv · sin (ωp · t) · b17 [ωp]
・ Sin (θ17 [ωp] + θ01)
+ Rkv · cos (ωm · t) · b17 [ωm]
・ Cos (θ17 [ωm] + θ01)
+ Rkv · sin (ωm · t) · b17 [ωm]
Sin (θ17 [ωm] + θ01) (513)

In consideration of the direction of the electromotive force between the electrodes described in FIGS. 14 and 15, the electromotive force obtained by converting the interelectrode electromotive force due to the time change of the magnetic field into a complex vector and the interelectrode electromotive force due to the flow velocity of the fluid to be measured. The electromotive force EX1pc of the component of the angular frequency ωp of the first interelectrode electromotive force between the electrodes 2a and 2b, which is combined with the electromotive force obtained by converting the signal into a complex vector, is expressed by the first term and the second term of the equation (510). From the term, the first term and the second term of equation (512), and equation (17),
EX1pc = rk · ωp · b16 [ωp]
Exp {j. (Π / 2 + θ16 [ωp] + θ00)}
+ Γ · rk · V · b16 [ωp] · exp {j · (θ16 [ωp] + θ01)}
... (514)

Between the electrodes 2a and 2b, which is a combination of the electromotive force obtained by converting the electromotive force between the electrodes due to the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the electromotive force between the electrodes caused by the flow velocity of the fluid to be measured into the complex vector The electromotive force EX1mc of the component of the angular frequency ωm of the first inter-electrode electromotive force of the first term is expressed by the third term, the fourth term, and the third term, the fourth term, and the formula (17) of the formula (512). ) And the following formula.
EX1mc = rk · ωm · b16 [ωm]
• exp {j · (π / 2 + θ16 [ωm] + θ00)}
+ Γ · rk · V · b16 [ωm] · exp {j · (θ16 [ωm] + θ01)}
... (515)

Between the electrodes 2c and 2d, which is a combination of the electromotive force obtained by converting the electromotive force between the electrodes due to the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the electromotive force between the electrodes caused by the flow velocity of the fluid to be measured into the complex vector The electromotive force EX2pc of the component of the angular frequency ωp of the second inter-electrode electromotive force is expressed by the first term, the second term of the equation (511), the first term, the second term of the equation (513), and the equation (17). ) And the following formula.
EX2pc = rk · (ωp) · b17 [ωp]
Exp {j · (−π / 2 + θ17 [ωp] + θ00)}
+ Γ · rk · V · b17 [ωp] · exp {j · (θ17 [ωp] + θ01)}
... (516)

Between the electrodes 2c and 2d, which is a combination of the electromotive force obtained by converting the electromotive force between the electrodes due to the time change of the magnetic field into a complex vector and the electromotive force obtained by converting the electromotive force between the electrodes caused by the flow velocity of the fluid to be measured into the complex vector The electromotive force EX2mc of the component of the angular frequency ωm in the second inter-electrode electromotive force of the second term is expressed by the third term, the fourth term, and the third term, the fourth term, and the formula (17) of the formula (513). ) And the following formula.
EX2mc = rk · (ωm) · b17 [ωm]
Exp {j · (−π / 2 + θ17 [ωm] + θ00)}
+ Γ · rk · V · b17 [ωm] · exp {j · (θ17 [ωm] + θ01)}
... (517)

  Here, ωp = ω0 + Δω and ωm = ω0−Δω are defined, and further, the phase delay θ16 [ω0] of the component of the angular frequency ω0 of the magnetic field B16 and the phase delay θ17 [ω0] of the component of the angular frequency ω0 of the magnetic field B17. The relationship is θ17 [ω0] = θ16 [ω0] + Δθ17 [ω0], and the relationship between the angle θ00 of the ∂A / ∂t component with respect to the imaginary axis and the angle θ01 of the v × B component with respect to the real axis is θ01 = θ00 + Δθ01. . The component EX1pc of the angular frequency ωp of the first inter-electrode electromotive force when ωp = ω0 + Δω and θ01 = θ00 + Δθ01 are substituted into the equation (514), and when ωp = ω0 + Δω and θ01 = θ00 + Δθ01 are substituted into the equation (516). If the sum of the second electrode electromotive force and the component EX2pc of the angular frequency ωp is EXsp0, the electromotive force sum EXsp0 is expressed by the following equation.

EXsp0 = rk · exp (j · θ00))
・ [(Ω0 + Δω) · exp (j · π / 2)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
-B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])}
+ Γ · V · exp (j · Δθ01)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
+ B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])}]
... (518)

Further, the component EX1mc of the angular frequency ωm of the first inter-electrode electromotive force when ωm = ω0−Δω and θ01 = θ00 + Δθ01 are substituted into the equation (515), and ωm = ω0−Δω, θ01 = in the equation (517). If the sum of the angular frequency ωm of the second inter-electrode electromotive force and the component EX2mc when substituting θ00 + Δθ01 is EXsm0, the electromotive force sum EXsm0 is expressed by the following equation.
EXsm0 = rk · exp (j · θ00)
・ [(Ω0−Δω) exp (j · π / 2)
{B16 [ω0-Δω] exp (j · θ16 [ω0-Δω])
−b17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}
+ Γ · V · exp (j · Δθ01)
{B16 [ω0-Δω] exp (j · θ16 [ω0-Δω])
+ B17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}]
... (519)

Also, the component EX1pc of the angular frequency ωp of the first inter-electrode electromotive force when ωp = ω0 + Δω and θ01 = θ00 + Δθ01 are substituted into the equation (514), and ωp = ω0 + Δω, θ01 = θ00 + Δθ01 are substituted into the equation (516). If the difference between the second electrode electromotive force and the component EX2pc of the angular frequency ωp is EXdp0, the electromotive force difference EXdp0 is expressed by the following equation.
EXdp0 = rk · exp (j · θ00))
・ [(Ω0 + Δω) · exp (j · π / 2)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
+ B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])}
+ Γ · V · exp (j · Δθ01)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
-B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])}]
... (520)

Further, the component EX1mc of the angular frequency ωm of the first inter-electrode electromotive force when ωm = ω0−Δω and θ01 = θ00 + Δθ01 are substituted into the equation (515), and ωm = ω0−Δω, θ01 = in the equation (517). If the difference from the component EX2mc of the angular frequency ωm of the second electrode electromotive force when θ00 + Δθ01 is substituted is EXdm0, the electromotive force difference EXdm0 is expressed by the following equation. However, in the equations (518) to (521), θ17 [ω0] = θ16 [ω0] + Δθ17 [ω0] is not applied, and is applied in the later equation.
EXdm0 = rk · exp (j · θ00)
・ [(Ω0−Δω) exp (j · π / 2)
{B16 [ω0-Δω] exp (j · θ16 [ω0-Δω])
+ B17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}
+ Γ · V · exp (j · Δθ01)
{B16 [ω0-Δω] exp (j · θ16 [ω0-Δω])
−b17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}]
... (521)

If the sum of the electromotive force sums EXsp0 and EXsm0 is EXss0, the sum of the electromotive force sums EXss0 is expressed by the following equation.
EXss0 = EXsp0 + EXsm0
= Rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
-B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])
+ B16 [ω0−Δω] · exp (j · θ16 [ω0−Δω])
−b17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}
+ Δω · exp (j · π / 2)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
-B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])
−b16 [ω0−Δω] · exp (j · θ16 [ω0−Δω])
+ B17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}
+ Γ · V · exp (j · Δθ01)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
+ B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])
+ B16 [ω0−Δω] · exp (j · θ16 [ω0−Δω])
+ B17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}]
... (522)

If the sum of the electromotive force differences EXdp0 and EXdm0 is EXds0, the sum of electromotive force differences EXds0 is expressed by the following equation.
EXds0 = EXdp0 + EXdm0
= Rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
+ B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])
+ B16 [ω0−Δω] · exp (j · θ16 [ω0−Δω])
+ B17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}
+ Δω · exp (j · π / 2)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
+ B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])
−b16 [ω0−Δω] · exp (j · θ16 [ω0−Δω])
−b17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}
+ Γ · V · exp (j · Δθ01)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
-B17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])
+ B16 [ω0−Δω] · exp (j · θ16 [ω0−Δω])
−b17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])}]
... (523)

Here, since ω0> Δω is normally satisfied, the conditional expressions of Expressions (524) to (527) are satisfied.
2 · b16 [ω0] · exp (j · θ16 [ω0])
≒ b16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
+ B16 [ω0−Δω] · exp (j · θ16 [ω0−Δω]) (524)
2 · b17 [ω0] · exp (j · θ17 [ω0])
≒ b17 [ω0 + Δω] · exp (j · θ17 [ω0 + Δω])
+ B17 [ω0−Δω] · exp (j · θ17 [ω0−Δω]) (525)

| Ω0 · exp (j · π / 2)
{2 · b16 [ω0] · exp (j · θ16 [ω0])} |
>> | ± Δω · exp (j · π / 2)
・ {B16 [ω0 + Δω] · exp (j · θ16 [ω0 + Δω])
−b16 [ω0−Δω] · exp (j · θ16 [ω0−Δω])} |
... (526)
| Ω0 · exp (j · π / 2)
{2 · b17 [ω0] · exp (j · θ17 [ω0])} |
>> | ± Δω · exp (j · π / 2)
{B17 [ω0 + Δω] exp (j · θ17 [ω0 + Δω])
−b17 [ω0−Δω] · exp (j · θ17 [ω0−Δω])} |
... (527)

When the condition of equations (524) to (527) is applied to equation (522) and the sum EXss0 is approximated as EXss0a, the sum of electromotive forces EXss0a is expressed by the following equation.
EXss0a≈EXss0 (528)
EXss0a = rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {2 ・ b16 [ω0] ・ exp (j ・ θ16 [ω0])
-2 · b17 [ω0] · exp (j · θ17 [ω0])}
+ Γ · V · exp (j · Δθ01)
・ {2 ・ b16 [ω0] ・ exp (j ・ θ16 [ω0])
+ 2 · b17 [ω0] · exp (j · θ17 [ω0])}
... (529)

Further, when EXds0a is obtained by applying the conditions of Expressions (524) to (527) to Expression (523) and approximating the sum EXds0, the sum of electromotive force differences EXds0a is expressed by the following expression.
EXds0a≈EXds0 (530)
EXds0a = rk · exp (j · θ00)
・ [Ω0 ・ exp (j ・ π / 2)
・ {2 ・ b16 [ω0] ・ exp (j ・ θ16 [ω0])
+ 2 · b17 [ω0] · exp (j · θ17 [ω0])}
+ Γ · V · exp (j · Δθ01)
・ {2 ・ b16 [ω0] ・ exp (j ・ θ16 [ω0])
-2 · b17 [ω0] · exp (j · θ17 [ω0])}]
... (531)

When EXss0b is obtained by substituting θ17 [ω0] = θ16 [ω0] + Δθ17 [ω0] into the sum of electromotive forces EXss0a, the sum of electromotive force EXss0b is expressed by the following equation.
EXss0b = 2 · rk · exp {j · (θ16 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B16 [ω0] −b17 [ω0] · exp (j · Δθ17 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B16 [ω0] + b17 [ω0] · exp (j · Δθ17 [ω0])}]
... (532)

Further, if EXds0b is obtained by substituting θ17 [ω0] = θ16 [ω0] + Δθ17 [ω0] into the sum of electromotive forces EXds0a, the sum of electromotive force differences EXds0b is expressed by the following equation.
EXds0b = 2 · rk · exp {j · (θ16 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B16 [ω0] + b17 [ω0] · exp (j · Δθ17 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B16 [ω0] −b17 [ω0] · exp (j · Δθ17 [ω0])}]
... (533)

Here, if the magnetic fields B16 and B17 generated from the exciting coil 3 are set equal in the initial state (the state at the time of calibration), the difference from the initial state of the subsequent magnetic fields B16 and B17 becomes small. The following conditions hold.
| B16 [ω0] + b17 [ω0] · exp (j · Δθ17 [ω0]) |
»| B16 [ω0] −b17 [ω0] · exp (j · Δθ17 [ω0]) |
... (534)

In general, since ω0> γ · V is satisfied, when the condition of the equation (534) is considered, the following equation is satisfied in the equation (533).
| Ω0 · exp (j · π / 2)
{B16 [ω0] + b17 [ω0] · exp (j · Δθ17 [ω0])} |
»| Γ · V · exp (j · Δθ01) · b16 [ω0]
-B17 [ω0] · exp (j · Δθ17 [ω0]) | (535)

Assuming that EdAX1 is an approximation of the sum EXds0b of the electromotive force difference of the equation (533) using the condition of the equation (535), the sum of electromotive force differences EdAX1 is expressed by the following equation. This sum of electromotive force differences EdAX1 corresponds to the first ∂A / ∂t component in the basic principle.
EdAX1≈EXds0b≈EXds0 (536)
EdAX1 = 2 · rk · exp {j · (θ16 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B16 [ω0] + b17 [ω0] · exp (j · Δθ17 [ω0])}
... (537)

Since the sum of the electromotive force differences EdAX1 is not related to the magnitude V of the flow velocity, it becomes only the component generated by ∂A / な る t. Using this sum EdAX1, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component in the sum of electromotive forces EXss0b (combined vector Vas0 + Vbs0) is normalized. If the sum of electromotive forces EXss0b is normalized by the sum of electromotive force differences EdAX1 and multiplied by ω0 is EnX0, the normalized electromotive force sum EnX0 is expressed by the following equation.
EnX0 = (EXss0b / EdAX1) · ω0
= 2 · rk · exp {j · (θ16 [ω0] + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B16 [ω0] −b17 [ω0] · exp (j · Δθ17 [ω0])}
+ Γ · V · exp (j · Δθ01)
{B16 [ω0] + b17 [ω0] · exp (j · Δθ17 [ω0])}]
/ [2 · rk · exp {j · (θ16 [ω0] + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B16 [ω0] + b17 [ω0] · exp (j · Δθ17 [ω0])}] · ω0
= Ω0 · {b16 [ω0] −b17 [ω0] · exp (j · Δθ17 [ω0])}
/ {B16 [ω0] + b17 [ω0] · exp (j · Δθ17 [ω0])}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (538)

Using equation (52), the coefficient {b16 [ω0] −b17 [ω0] · exp (j · Δθ17 [ω0])} / {b16 [ω0] applied to the angular frequency ω0 of the first term on the right side of equation (538). ] + B17 [ω0] · exp (j · Δθ17 [ω0])} is represented by a value {b16−b17 · exp (j · Δθ17)} / {b16 + b17 · exp (j · Δθ17)} not related to the angular frequency ω0. be able to. Therefore, equation (538) can be replaced as:
EnX0 = ω0 · {b16−b17 · exp (j · Δθ17)}
/ {B16 + b17 · exp (j · Δθ17)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (539)

  The second term on the right side of Equation (539) is a term obtained by normalizing the component generated by v × B. The reason why the result of normalizing the sum of electromotive forces EXss0b with the sum of electromotive force differences EdAX1 is multiplied by ω0 is to eliminate the excitation angular frequency ω0 from the second term on the right side of the magnitude V of the flow velocity. The complex coefficient related to the magnitude V of the flow velocity has an angle from the real axis of the magnitude of γ, −π / 2 + Δθ01. The coefficient γ and the angle Δθ01 are constants that can be obtained in advance by calibration or the like, and the second term on the right side of the equation (539) is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by performing the normalization of the v × B component using the component ∂A / ∂t, it is possible to realize span correction that automatically corrects errors due to magnetic field shifts and phase changes.

Next, a method for removing the first term on the right side of the equation (539), which is a variation factor of 0 point, will be described. When ωc and ωd are taken instead of the excitation angular frequencies ωp and ωm in the equations (506) and (507), the magnetic fields B16 and B17 are expressed by the following equations.
B16 = b16 [ωc] · cos (θ16 [ωc]) · cos (ωc · t)
+ B16 [ωc] · sin (θ16 [ωc]) · sin (ωc · t)
+ B16 [ωd] · cos (θ16 [ωd]) · cos (ωd · t)
+ B16 [ωd] · sin (θ16 [ωd]) · sin (ωd · t)
... (540)
B17 = b17 [ωc] · cos (θ17 [ωc]) · cos (ωc · t)
+ B17 [ωc] · sin (θ17 [ωc]) · sin (ωc · t)
+ B17 [ωd] · cos (θ17 [ωd]) · cos (ωd · t)
+ B17 [ωd] · sin (θ17 [ωd]) · sin (ωd · t)
... (541)

  Here, the angular frequencies ωc and ωd are set to have a relationship of ωc = ω2 + Δω and ωd = ω2−Δω. Normalization is performed at the angular frequency ω2 as in the normalization at the angular frequency ω0. The sum of electromotive forces EXss2 to be subjected to span correction at the angular frequency ω2 is the sum of electromotive forces EXsp2 in which the angular frequency ω0 is replaced with ω2 in Equation (518) and the sum of the electromotive forces EXsp2 in Equation (519) with ω2. It is represented by the sum EXsp2 + EXsm2 with the power sum EXsm2. The sum EXds2 of the electromotive force difference that is the basis of the second ∂A / ∂t component is the electromotive force difference EXdp2 obtained by replacing the angular frequency ω0 with ω2 in the equation (520) and the angular frequency ω0 in the equation (521) with ω2. This is expressed as a sum EXdp2 + EXdm2 with the replaced electromotive force difference EXdm2. The sum EdAX2 of the electromotive force difference as the second ∂A / ∂t component is obtained by replacing the angular frequency ω0 with ω2 in the equation (537).

When the sum of electromotive forces EXss2 is normalized by the sum of electromotive force differences EdAX2 and multiplied by ω2 is EnX2, the normalized electromotive force sum EnX2 is expressed by the following equation from Equation (539).
EnX2 = ω2 · {b16−b17 · exp (j · Δθ17)}
/ {B16 + b17 · exp (j · Δθ17)}
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V (542)

Taking the difference between the normalized electromotive force sums EnX0 and EnX2 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdAX3, the difference EdAX3 is expressed by the following equation. This difference EdAX3 corresponds to the third ∂A / ∂t component in the basic principle.
EdAX3 = (EnX0−EnX2) · ω0 / (ω0−ω2)
= [{B16−b17 · exp (j · Δθ17)}
/ {B16 + b17 · exp (j · Δθ17)}
.Omega.0 + .gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V
-{B16-b17 · exp (j · Δθ17)}
/ {B16 + b17 · exp (j · Δθ17)}
.Omega.2-.gamma.exp {j. (-. Pi./2+.DELTA..theta.01)}.V]
・ Ω0 / (ω0−ω2)
= {B16-b17 · exp (j · Δθ17)}
/ {B16 + b17 · exp (j · Δθ17)} · ω0 ·· (543)

The difference EdAX3 represents a normalized ∂A / ∂t component and is equal to the first term on the right side of the equation (539). Therefore, if this difference EdAX3 is used, the normalized v × B component is normalized. It can be taken out from the power sum EnX0. When the v × B component obtained by subtracting the difference EdAX3 of the equation (543) from the normalized electromotive force sum EnX0 of the equation (539) is EvBnX, the v × B component EvBnX is expressed by the following equation.
EvBnX = EnX0-EdAX3
= {B16-b17 · exp (j · Δθ17)}
/ {B16 + b17 · exp (j · Δθ17)} · ω0
+ [Γ · exp {j · (−π / 2 + Δθ01)}] · V
-{B16-b17 · exp (j · Δθ17)}
/ {B16 + b17 · exp (j · Δθ17)} · ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (544)

The v × B component EvBnX is not related to the angular frequency ω. As can be seen from the fact that the v × B component EvBnX becomes 0 when the magnitude V of the flow velocity is 0, an output in which the span is corrected and the zero point is corrected can be obtained from the v × B component EvBnX. From the equation (544), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBnX / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBnX | / γ (545)

  The correspondence relationship between the constants and variables used in the basic principle and the constants and variables of the present embodiment is as shown in Table 10 below. As is apparent from Table 10, the present embodiment is an example that specifically realizes the basic principle described above.

  Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. Since the configuration of the electromagnetic flowmeter of the present embodiment is the same as that of the eighth embodiment, description will be made using the reference numerals in FIG. The electromagnetic flow meter of the present embodiment includes a measurement tube 1, first electrodes 2a and 2b, second electrodes 2c and 2d, an excitation coil 3, a power supply unit 4a, a signal conversion unit 5a, a flow rate. And an output unit 6a.

  The signal converter 5a is configured to detect the first combined electromotive force detected by the first electrodes 2a and 2b and the second electrodes 2c and 2d detected in the first excitation state and the second excitation state, respectively. 2 is obtained, and based on these amplitudes and phases, the sum of the electromotive forces of the same frequency components and the electromotive force difference of the same frequency components of the first composite electromotive force and the second composite electromotive force are obtained. The angular frequency ω0 ± Δω in the first excitation state and the angular frequency ω2 ± Δω in the second excitation state are obtained, and the difference in electromotive force between the angular frequency ω0 + Δω and the occurrence of the angular frequency ω0−Δω in the first excitation state is obtained. The sum of the power difference is extracted as the first ∂A / 成分 t component, and the sum of the electromotive force difference at the angular frequency ω2 + Δω and the electromotive force difference at the angular frequency ω2-Δω in the second excitation state is Extracted as ∂A / ∂t component, sum of electromotive force and angular circumference of angular frequency ω0 + Δω in the first excitation state The sum of the wave number ω0−Δω and the sum of electromotive forces is used as the first correction target electromotive force, and is included in the v × B component in the first correction target electromotive force based on the first ∂A / ∂t component. In addition to removing the variation factor of the span, the sum of the electromotive force of the angular frequency ω2 + Δω and the electromotive force sum of the angular frequency ω2-Δω in the second excitation state is used as the second correction target electromotive force. / Span correction unit 51a for removing a span variation factor included in the v × B component of the second correction target electromotive force based on the ∂t component, and the first correction target electromotive force and the span corrected. The difference from the corrected second correction target electromotive force is extracted as a third ∂A / ∂t component, and the third ∂ from two of the two correction target electromotive forces subjected to span correction is extracted. It is composed of a zero point correction unit 52a that extracts the v × B component by removing the A / ∂t component. That.

  The power supply unit 4a according to the present embodiment performs a first excitation state in which the excitation current including the sine wave component of the angular frequency (ω0 + Δω) and the sine wave component of the angular frequency (ω0−Δω) is supplied to the excitation coil T1. The second excitation state in which the excitation current including the sine wave component of the angular frequency (ω2 + Δω) and the sine wave component of the angular frequency (ω2−Δω) is supplied to the excitation coil 3 is continued for T2 seconds. Is repeated every T seconds. That is, T = T1 + T2.

  FIG. 26 is a flowchart showing the operation of the signal conversion unit 5a and the flow rate output unit 6a of the present embodiment. First, the span correction unit 51a of the signal conversion unit 5a, in the first excitation state, the component of the angular frequency (ω0 + Δω) of the first inter-electrode electromotive force between the electrodes 2a and 2b and the second between the electrodes 2c and 2d. The sum EXsp0 with the component of the angular frequency (ω0 + Δω) of the interelectrode electromotive force and the angular frequency (ω0− of the component of the angular frequency (ω0−Δω) of the first interelectrode electromotive force and the second electrode electromotive force. Δs) and the sum EXsm0 of the electromotive force sums EXsp0 and EXsm0, the amplitude rXss0 of the sum EXs0, and the phase difference φXss0 between the real axis and the sum of the electromotive force EXss0 are obtained by a phase detector (not shown). (Step 801 in FIG. 26).

  Further, in the first excitation state, the span correction unit 51a has a difference EXdp0 between the component of the angular frequency (ω0 + Δω) of the first interelectrode electromotive force and the component of the angular frequency (ω0 + Δω) of the second interelectrode electromotive force. And the difference EXdm0 between the component of the angular frequency (ω0−Δω) of the first inter-electrode electromotive force and the component of the angular frequency (ω0−Δω) of the second inter-electrode electromotive force is obtained, and the electromotive force difference EXdp0 and EXdm0 The amplitude rXds0 of the sum EXds0 is calculated, and the phase difference φXds0 between the real axis and the sum EXds0 of the electromotive force difference is obtained by the phase detector (step 802).

  Subsequently, in the second excitation state, the span correction unit 51a sums the component of the angular frequency (ω2 + Δω) of the first interelectrode electromotive force and the component of the angular frequency (ω2 + Δω) of the second interelectrode electromotive force. EXsp2 and the sum EXsm2 of the component of the angular frequency (ω2-Δω) of the first inter-electrode electromotive force and the component of the angular frequency (ω2-Δω) of the second inter-electrode electromotive force are obtained, and the electromotive force sum EXsp2 The amplitude rXss2 of the sum EXsm2 with EXsm2 is obtained, and the phase difference φXss2 between the real axis and the sum of electromotive forces EXss2 is obtained with a phase detector (step 803).

  Further, in the second excitation state, the span correction unit 51a has a difference EXdp2 between the component of the angular frequency (ω2 + Δω) of the first interelectrode electromotive force and the component of the angular frequency (ω2 + Δω) of the second interelectrode electromotive force. , And the difference EXdm2 between the component of the angular frequency (ω2−Δω) of the first inter-electrode electromotive force and the component of the angular frequency (ω2-Δω) of the second inter-electrode electromotive force, and the electromotive force difference EXdp2 and EXdm2 The amplitude rXds2 of the sum EXds2 is obtained, and the phase difference φXds2 between the real axis and the sum EXds2 of the electromotive force difference is obtained by the phase detector (step 804).

Next, the span correction unit 51a calculates the magnitude and angle of the electromotive force difference sum EdAX1 that approximates the electromotive force difference sum EXds0 (step 805). The process in step 805 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of Expression (537). The span correction unit 51a calculates the magnitude | EdAX1 | of the sum of electromotive force differences EdAX1 as the following equation.
| EdAX1 | = rXds0 (546)
Then, the span correction unit 51a calculates an angle ∠EdAX1 of the sum of electromotive force differences EdAX1 as the following equation.
∠EdAX1 = φXds0 (547)
This completes the process of step 805.

Subsequently, the span correction unit 51a obtains the magnitude and angle of the normalized electromotive force sum EnX0 obtained by normalizing the sum of electromotive forces EXss0 with the sum of electromotive force differences EdAX1 (step 806). The process of step 806 is a process corresponding to the calculation of equation (539). The span correction unit 51a calculates the magnitude | EnX0 | of the normalized electromotive force sum EnX0 as the following equation.
| EnX0 | = (rXss0 / | EdAX1 |) · ω0 (548)

Then, the span correction unit 51a calculates the angle ∠EnX0 of the normalized electromotive force sum EnX0 as the following equation.
∠EnX0 = φXss0−∠EdAX1 (549)
Further, the span correction unit 51a calculates the real axis component EnX0x and the imaginary axis component EnX0y of the normalized electromotive force sum EnX0 as in the following equation.
EnX0x = | EnX0 | .cos (∠EnX0) (550)
EnX0y = | EnX0 | .sin (∠EnX0) (551)
This completes the processing in step 806.

Next, the span correction unit 51a obtains the magnitude and angle of the electromotive force difference sum EdAX2 that approximates the electromotive force difference sum EXds2 (step 807). The processing in step 807 is processing corresponding to obtaining the second ∂A / ∂t component. The span correction unit 51a calculates the magnitude | EdAX2 | of the sum of electromotive force differences EdAX2 as the following equation.
| EdAX2 | = rXds2 (552)
Then, the span correction unit 51a calculates the angle ∠EdAX2 of the sum of electromotive force differences EdAX2 as the following equation.
∠EdAX2 = φXds2 (553)
This completes the processing in step 807.

Subsequently, the span correction unit 51a obtains the magnitude and angle of the normalized electromotive force sum EnX2 obtained by normalizing the sum of electromotive forces EXss2 with the sum of electromotive force differences EdAX2 (step 808). The process of step 808 is a process corresponding to the calculation of Expression (542). The span correction unit 51a calculates the magnitude | EnX2 | of the normalized electromotive force sum EnX2 as follows.
| EnX2 | = (rXss2 // EdAX2 |) · ω2 (554)

Then, the span correction unit 51a calculates the angle ∠EnX2 of the normalized electromotive force sum EnX2 as the following equation.
∠EnX2 = φXss2-∠EdAX2 (555)
Further, the span correction unit 51a calculates the real axis component EnX2x and the imaginary axis component EnX2y of the normalized electromotive force sum EnX2 as follows.
EnX2x = | EnX2 | .cos (∠EnX2) (556)
EnX2y = | EnX2 | .sin (∠EnX2) (557)
This completes the processing in step 808.

Next, the zero point correction unit 52a of the signal conversion unit 5a calculates the magnitude of the difference EdAX3 between the normalized electromotive force sums EnX0 and EnX2 (step 809). The process of step 809 is a process corresponding to obtaining the third ∂A / ∂t component, and is a process corresponding to the calculation of Expression (543). The zero point correction unit 52a calculates the real axis component EdAX3x and the imaginary axis component EdAX3y of the difference EdAX3 as follows.
EdAX3x = (EnX0x−EnX2x) · ω0 / (ω0−ω2) (558)
EdAX3y = (EnX0y−EnX2y) · ω0 / (ω0−ω2) (559)

Then, the zero point correction unit 52a removes the difference EdAX3 from the normalized electromotive force sum EnX0 and obtains the magnitude of the v × B component EvBnX (step 810). The process of step 810 is a process corresponding to the calculation of Expression (544). The zero point correction unit 52a calculates the magnitude | EvBnX | of the v × B component EvBnX as the following equation.
| EvBnX | = {(EnX0x−EdAX3x) ²
+ (EnX0y-EdAX3y) ² } ^1/2 (560)

The flow rate output unit 6a calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 811). The process of step 811 is a process corresponding to the calculation of equation (545).
V = | EvBnX | / γ (561)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5a and the flow rate output unit 6a perform the processing in steps 801 to 811 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 812). Note that the processing in steps 803 to 811 is performed in the second excitation state.

  As described above, in the present embodiment, the sum of electromotive forces EXss0 and the sum of electromotive force differences EXds0 are obtained in the first excitation state, and the sum of electromotive force EXss2 and the difference between the electromotive force differences in the second excitation state. The sum EXds2 is obtained. In this embodiment, if the magnetic fields B16 and B17 generated from the exciting coil 3 are set to be equal, the sum EXds0 of the electromotive force difference is approximately set as the first ∂A / ∂t component. Focusing on the fact that the sum EXds2 of the electromotive force difference can be approximately extracted as the second ∂A / ∂t component, and using the first ∂A / ∂t component, Normalize the span of the flow velocity V of the v × B component V, and use the second ∂A / ∂t component to obtain the flow velocity V of the v × B component in the sum of electromotive forces EXss2. The span is normalized, the difference EdAX3 (third ∂A / ∂t component) is extracted from the normalized electromotive force sums EnX0 and EnX2, and the third ∂A / ∂t component is extracted from the normalized electromotive force sum EnX0. V × B component is extracted by removing the v × B component. Since the flow rate of the fluid to be measured is calculated, accurate span correction can be automatically performed, and the zero point of the output of the electromagnetic flowmeter can be corrected without reducing the flow rate of the fluid to be measured. Thus, stability at zero point can be ensured even in high frequency excitation.

  Further, in the present embodiment, in consideration of the difference in magnetic field loss depending on the frequency, the first 同 じ A having the same angular frequency obtained by extracting the v × B component of the electromotive force sum EXss0 from the electromotive force difference sum EXds0. Normalize using the second ∂A / ∂t component of the same angular frequency extracted from the sum of electromotive force differences EXds2 Since zero correction is performed based on the difference between the normalized electromotive force sums EnX0 and EnX2, respectively, accurate span correction and zero correction can be performed even when there is an influence due to magnetic field loss. Further, in the present embodiment, since excitation is performed with the frequencies dispersed, the frequency band can be used efficiently.

  Note that modulation can be used as another example of the present embodiment. If a carrier wave having an angular frequency ω0 is excited by a modulated wave having an angular frequency ω1, the electromotive force of the components having angular frequencies ω0 and ω0 ± ω1 can be obtained in the case of amplitude modulation, and the angular frequency in the case of phase modulation or frequency modulation. The electromotive force of the component of ω0, ω0 ± ζ · ω1 (ζ is a positive integer) can be obtained. As described at the end of the basic principle, an example of using this modulation is the fourth embodiment to the fourth embodiment, if the configuration of the electromagnetic flow meter of FIG. 1 is converted to the configuration of the electromagnetic flow meter of FIG. The detailed description is omitted because it is the same as that shown in the seventh embodiment.

In the present embodiment, the sum of electromotive forces EXss0 is the target of 0 correction and span correction, but the sum of electromotive forces EXss2 may be the target of 0 correction and span correction. In this case, the difference EdAX3 (third ∂A / ∂t component) is obtained from the normalized electromotive force sums EnX2 and EnX0 as in the following equation.
EdAX3 = (EnX2-EnX0) · ω2 / (ω2-ω0) (562)
Then, the v × B component EvBnX may be obtained by subtracting the difference EdAX3 from the normalized electromotive force sum EnX2 as in the following equation. The other processes are the same as the case where the sum of electromotive forces EXss0 is the target of 0 correction and span correction.
| EvBnX | = | EnX2-EdAX3 | (563)

  In the first to tenth embodiments, a sine wave excitation method using a sine wave as an excitation current is employed, but in the case of a rectangular wave, it can be considered as a combination of sine waves. A rectangular wave excitation method using a rectangular wave as the excitation current may be employed. As shown in FIG. 27, the electrodes 2a, 2b, 2c, and 2d used in the first to tenth embodiments are exposed from the inner wall of the measuring tube 1 and come into contact with the fluid to be measured. 28, or a capacitively coupled electrode that does not contact the fluid to be measured as shown in FIG. In the case of the capacitive coupling type, the electrodes 2a, 2b, 2c and 2d are covered with a lining 10 made of ceramic, Teflon (registered trademark) or the like formed on the inner wall of the measuring tube 1.

  In the first to tenth embodiments, the pair of electrodes 2a and 2b is used as the first electrode, and the pair of electrodes 2c and 2d is used as the second electrode. However, the present invention is not limited to this, and one each of the first electrode and the second electrode may be provided. When there is only one electrode, a grounding ring and a grounding electrode for setting the potential of the fluid to be measured to the grounding potential are provided in the measuring tube 1, and an electromotive force (grounding potential and grounding potential) generated in one electrode is provided. The signal converters 5, 5a, and 5b may detect the potential difference. The electrode axis is a straight line connecting the pair of electrodes when a pair of electrodes is used. On the other hand, when there is only one electrode, when it is assumed that a virtual electrode is arranged at a position facing the real electrode across the measurement tube axis PAX on the plane PLN including this single real electrode, A straight line connecting the imaginary electrode and the virtual electrode becomes the electrode axis.

  In the sixth embodiment and the seventh embodiment, only the case of n = 0, 1 is applied in the expansion of the first-order Bessel function, and the angular frequency ω0 ± ω1, ω2 ± of the electromotive force between the electrodes is applied. Although the component of ω1 is used, the present invention is not limited to this, and components of ω0 + ζ1 · ω1 (ζ1 is a positive integer) and ω2 + ζ2 · ω1 (ζ2 is a positive integer) may be used. When ζ1 and ζ2 are integers of 2 or more, the flow velocity magnitude V can be calculated by applying n = 2 or later in the expansion of the first-order Bessel function.

  The present invention can be applied to flow measurement of a fluid to be measured flowing in a measurement tube.

It is a block diagram for demonstrating the principle of the electromagnetic flowmeter which has two excitation coils and one pair of electrodes among the electromagnetic flowmeters based on the basic principle of this invention. It is a figure which shows the eddy current and electromotive force between electrodes when the flow volume of the fluid to be measured is 0 in the electromagnetic flow meter of FIG. It is a figure which shows the eddy current and electromotive force between electrodes when the flow volume of the fluid to be measured is not 0 in the electromagnetic flow meter of FIG. It is a figure which shows the vector of (A) / (t) component, the vector of vxB component, and a synthetic | combination vector at the time of exciting only with the 1st excitation coil in the electromagnetic flowmeter of FIG. It is a figure which shows the vector of (A) / (t) component, the vector of vxB component, and a synthetic | combination vector at the time of exciting only with the 2nd excitation coil in the electromagnetic flowmeter of FIG. It is a figure which shows the vector of (A) / (t) component, the vector of vxB component, and a synthetic | combination vector at the time of exciting with two exciting coils in the electromagnetic flowmeter of FIG. It is a figure which shows the vector of (A) / (t) component, the vector of vxB component, and a synthetic | combination vector at the time of exciting only by the 2nd excitation coil in the 2nd excitation state in the electromagnetic flowmeter of FIG. It is a figure which shows the vector of (A) / (t) component, the vector of vxB component, and a synthetic | combination vector at the time of exciting two excitation coils in the 2nd excitation state in the electromagnetic flowmeter of FIG. It is a figure which shows the vector of the 1st (A) / (t) component in the electromagnetic flowmeter of FIG. 1, and the synthetic | combination vector used as the object of normalization. It is the figure which expressed the complex vector expression of the process which normalizes the synthetic | combination vector detected with an electrode in the electromagnetic flowmeter of FIG. 1 by the 1st ∂A / ∂t component. It is the figure which expressed the complex vector representation of the process which extracts the 3rd ∂A / ∂t component from the synthetic vector normalized in the electromagnetic flow meter of FIG. It is the figure which expressed the complex vector expression about the process which extracts the vxB component from the synthetic | combination vector normalized in the electromagnetic flowmeter of FIG. It is a block diagram for demonstrating the principle of the electromagnetic flowmeter which has one excitation coil and two pairs of electrodes among the electromagnetic flowmeters based on the basic principle of this invention. It is a figure which shows the eddy current and electromotive force between electrodes when the flow volume of the fluid to be measured is 0 in the electromagnetic flow meter of FIG. It is a figure which shows the eddy current and electromotive force between electrodes when the flow volume of the fluid to be measured is not 0 in the electromagnetic flow meter of FIG. It is a block diagram which shows the structure of the electromagnetic flowmeter of the 1st Embodiment of this invention. It is a flowchart which shows operation | movement of the signal converter in the 1st Embodiment of this invention, and a flow volume output part. It is a flowchart which shows operation | movement of the signal converter in the 2nd Embodiment of this invention, and a flow volume output part. It is the figure which expressed complex vector expression about the processing which extracts the vector of the 1st ∂A / ∂t component in the 3rd embodiment of the present invention. It is a flowchart which shows operation | movement of the signal conversion part and flow volume output part in the 3rd Embodiment of this invention. It is a flowchart which shows operation | movement of the signal conversion part and flow volume output part in the 4th Embodiment of this invention. It is a flowchart which shows operation | movement of the signal conversion part and flow volume output part in the 5th Embodiment of this invention. It is a block diagram which shows the structure of the electromagnetic flowmeter of the 8th Embodiment of this invention. It is a flowchart which shows operation | movement of the signal conversion part and flow volume output part in the 8th Embodiment of this invention. It is a flowchart which shows operation | movement of the signal conversion part and flow volume output part in the 9th Embodiment of this invention. It is a flowchart which shows operation | movement of the signal conversion part and flow volume output part in the 10th Embodiment of this invention. It is sectional drawing which shows one example of the electrode used with the electromagnetic flowmeter of this invention. It is sectional drawing which shows the other example of the electrode used with the electromagnetic flowmeter of this invention. It is a block diagram for demonstrating the principle of the conventional electromagnetic flowmeter. It is a figure which shows the eddy current and electromotive force between electrodes when the flow volume of the fluid to be measured is 0 in a conventional electromagnetic flow meter. It is a figure which shows the eddy current and electromotive force between electrodes when the flow volume of the fluid to be measured is not 0 in a conventional electromagnetic flow meter. It is a figure for demonstrating the shift of the span in an electromagnetic flowmeter. It is a figure for demonstrating the zero point shift in an electromagnetic flowmeter. It is a figure for demonstrating the problem of the conventional electromagnetic flowmeter.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Measuring tube, 2a, 2b, 2c, 2d ... Electrode 3, 3a, 3b ... Excitation coil, 4, 4a ... Power supply part 5, 5a ... Signal conversion part, 6, 6a ... Flow output part, 51, 51a ... Span correction unit, 52, 52a ... 0 point correction unit.

Claims (21)

A measuring tube through which the fluid to be measured flows;
An electrode disposed in the measuring tube and detecting an electromotive force generated by the magnetic field applied to the fluid and the flow of the fluid;
An excitation unit for applying to the fluid a magnetic field that is asymmetric and time-varying with respect to a first plane perpendicular to the axial direction of the measuring tube, including the electrode
From the combined electromotive force of the 電極 A / ∂t component electromotive force detected by the electrode and the v × B component electromotive force caused by the fluid flow velocity, which is irrelevant to the fluid flow velocity, the first frequency The first ∂A / ∂t component and the first correction target electromotive force at the second frequency are extracted, and the second ∂A / ∂t component and the second correction target electromotive force at the second frequency are extracted. And removing a variation factor of the span, which is a coefficient applied to the magnitude V of the flow velocity of the v × B component in the first correction target electromotive force based on the extracted first ∂A / ∂t component. , A span for removing a variation factor of the span, which is a coefficient relating to the flow velocity V of the v × B component in the second correction target electromotive force based on the extracted second 前 記 A / ∂t component A span correction unit that performs correction,
Based on the span-corrected first correction target electromotive force and the span-corrected second correction target electromotive force, the flow rate of the fluid is irrelevant and the third is caused by the time change of the magnetic field. By extracting the ∂A / ∂t component and removing the extracted third ∂A / ∂t component from any one of the two correction target electromotive forces subjected to the span correction, the v × B component A zero point correction unit for extracting
An electromagnetic flow meter comprising: a flow rate output unit that calculates a flow rate of the fluid from the extracted v × B component. The electromagnetic flowmeter according to claim 1,
The excitation section includes a first excitation coil disposed at a position away from a first plane perpendicular to the axial direction of the measurement tube, including the electrode, with a first offset, and the first excitation coil A second excitation coil disposed at a position away from the plane by providing a second offset so as to face the first excitation coil across the first plane; and the first excitation coil And a power supply unit for supplying excitation current to the first excitation coil and the second excitation coil while switching the phase difference and excitation angular frequency of the excitation current supplied to the second excitation coil and the excitation current supplied to the second excitation coil. An electromagnetic flow meter characterized by that. The electromagnetic flow meter according to claim 2,
The span correction unit has a first phase difference between the first magnetic field generated by the first exciting coil and the second magnetic field generated by the second exciting coil by Δθ3 and an exciting angular frequency of ω0. An excitation state, a second excitation state in which the phase difference between the first magnetic field and the second magnetic field is changed to Δθ3 + π with respect to the first excitation state, and an excitation angle with respect to the first excitation state. A combination detected by the electrodes in each of four excitation states, a third excitation state in which the frequency is changed to ω2 and a fourth excitation state in which the excitation angular frequency is changed to ω2 with respect to the second excitation state. The amplitude and phase of the electromotive force are obtained, and based on these amplitude and phase, the combined electromotive force in the second excitation state is extracted as the first ∂A / ∂t component, and the fourth excitation state Extracting the combined electromotive force as the second ∂A / ∂t component, The combined electromotive force in the first excitation state is set as the first correction target electromotive force, and the v × B component in the first correction target electromotive force is based on the extracted first ∂A / ∂t component. The variation factor of the included span is removed, and the combined electromotive force in the third excitation state is set as the second correction target electromotive force based on the extracted second ∂A / ∂t component. Perform span correction to remove the span variation factor included in the v × B component in the correction target electromotive force,
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flowmeter according to claim 1,
The excitation section includes a first excitation coil disposed at a position away from a first plane perpendicular to the axial direction of the measurement tube, including the electrode, with a first offset, and the first excitation coil A second excitation coil disposed at a position away from the plane by providing a second offset so as to face the first excitation coil across the first plane; and the first excitation coil A power supply that supplies excitation currents that simultaneously provide a plurality of excitation angular frequencies to the first excitation coil and the second excitation coil while switching the phase difference between the excitation current supplied to the first excitation coil and the excitation current supplied to the second excitation coil. An electromagnetic flow meter comprising a part. The electromagnetic flow meter according to claim 4, wherein
The power supply unit supplies an excitation current that simultaneously gives two excitation angular frequencies having different angular frequencies ω0 and ω2 to the first excitation coil and the second excitation coil,
The span correction unit has a phase difference of Δθ7 between the first magnetic field generated by the first excitation coil and the second magnetic field generated by the second excitation coil, and excitation angular frequencies of ω0 and ω2. In each of the two excitation states, one excitation state and a second excitation state in which the phase difference between the first magnetic field and the second magnetic field is changed to Δθ7 + π with respect to the first excitation state. The amplitude and phase of the detected composite electromotive force are obtained, and the component of the angular frequency ω0 of the composite electromotive force in the second excitation state is extracted as the first ∂A / ∂t component based on these amplitude and phase. In addition, the component of the angular frequency ω2 of the synthetic electromotive force in the second excitation state is extracted as the second ∂A / ∂t component, and the component of the angular frequency ω0 of the synthetic electromotive force in the first excitation state As the first correction target electromotive force, the extracted first ∂A Based on the ∂t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the component of the angular frequency ω2 of the composite electromotive force in the first excitation state is As a second correction target electromotive force, a span for removing a variation factor of the span included in the v × B component in the second correction target electromotive force based on the extracted second ∂A / ∂t component Make corrections
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flowmeter according to claim 1,
The excitation section includes a first excitation coil disposed at a position away from a first plane perpendicular to the axial direction of the measurement tube, including the electrode, with a first offset, and the first excitation coil A second excitation coil disposed at a position away from the plane by providing a second offset so as to face the first excitation coil across the first plane; and the first excitation coil An excitation current that simultaneously gives a plurality of excitation angular frequencies to the first excitation coil and the second excitation coil while switching the phase difference and excitation angular frequency of the excitation current supplied to the second excitation coil and the excitation current supplied to the second excitation coil An electromagnetic flow meter comprising: a power supply unit that supplies electric power. The electromagnetic flow meter according to claim 6, wherein
The power supply unit supplies an excitation current that simultaneously supplies two excitation angular frequencies having different angular frequencies ω0 ± Δω to the first excitation coil and the second excitation coil, and two different angular frequencies ω2 ± Δω. Supplying an excitation current to the excitation coil while switching between excitation states for supplying the excitation current to the first excitation coil and the second excitation coil at the same time.
The span correction unit has a first phase difference between the first magnetic field generated by the first excitation coil and the second magnetic field generated by the second excitation coil by Δθ9 and an excitation angular frequency of ω0 ± Δω. 1 excitation state, a second excitation state in which the phase difference between the first magnetic field and the second magnetic field is changed to Δθ9 + π with respect to the first excitation state, and the first excitation state. A third excitation state in which the excitation angular frequency is changed to ω2 ± Δω, and a fourth excitation state in which the phase difference between the first magnetic field and the second magnetic field is changed to Δθ9 + π with respect to the third excitation state. The amplitude and phase of the composite electromotive force detected by the electrode in each of the four excitation states are obtained, and the component and angle of the angular frequency ω0 + Δω of the composite electromotive force in the second excitation state are determined based on these amplitudes and phases. The electromotive force sum with the component of the frequency ω0−Δω is the first ∂A / ∂t And the sum of electromotive forces of the component of angular frequency ω2 + Δω and the component of angular frequency ω2-Δω of the synthetic electromotive force in the fourth excitation state is extracted as the second ∂A / ∂t component, The extracted first ∂A / ∂t component using the sum of electromotive forces of the component of angular frequency ω0 + Δω and the component of angular frequency ω0-Δω of the composite electromotive force in the first excitation state as the first correction target electromotive force. Based on this, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the angular frequency ω2 + Δω component and the angular frequency ω2 of the composite electromotive force in the third excitation state are removed. A sum of electromotive forces with a component of -Δω is set as a second correction target electromotive force, and a v × B component in the second correction target electromotive force is calculated based on the extracted second ∂A / ∂t component. Perform span correction to remove the included span fluctuation factors,
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flowmeter according to claim 1,
The excitation section includes a first excitation coil disposed at a position away from a first plane perpendicular to the axial direction of the measurement tube, including the electrode, with a first offset, and the first excitation coil A second excitation coil disposed at a position away from the plane by providing a second offset so as to face the first excitation coil across the first plane; and the first excitation coil And a power supply unit that supplies an excitation current that simultaneously or alternately gives a plurality of excitation angular frequencies to the second excitation coil. The electromagnetic flow meter according to claim 8,
The power supply unit supplies an excitation current that simultaneously or alternately supplies a plurality of components obtained by modulating a plurality of carrier waves with a frequency different from that of the carrier waves to the first excitation coil and the second excitation coil. An electromagnetic flow meter characterized by The electromagnetic flow meter according to claim 9, wherein
The power supply unit supplies a first excitation current obtained by amplitude-modulating a carrier wave having an angular frequency ω0 with a modulated wave having an angular frequency ω1 to the first excitation coil, and simultaneously, a carrier wave having the angular frequency ω0 is supplied to the first excitation coil. A first excitation state in which a second excitation current amplitude-modulated by a modulation wave having the same angular frequency and an opposite phase with respect to the modulation wave of the current is supplied to the second excitation coil, and a carrier wave having an angular frequency ω2 is an angular frequency. A third exciting current amplitude-modulated by the modulated wave of ω1 is supplied to the first exciting coil, and at the same time, the carrier wave of the angular frequency ω2 is opposite in phase to the modulated wave of the third exciting current at the same angular frequency. The excitation current is supplied to the first excitation coil and the second excitation coil while switching between the second excitation state in which the fourth excitation current amplitude-modulated by the modulated wave is supplied to the second excitation coil. ,
The span correction unit obtains an amplitude and a phase of a composite electromotive force detected by the electrode in each of the first excitation state and the second excitation state, and the first excitation based on these amplitudes and phases. The sum of electromotive forces of the component of the angular frequency ω0 + ω1 and the component of the angular frequency ω0−ω1 of the combined electromotive force in the state is extracted as the first ∂A / ∂t component, and the combined electromotive force in the second excitation state The sum of electromotive forces of the component of the angular frequency ω2 + ω1 and the component of the angular frequency ω2-ω1 is extracted as the second ∂A / ∂t component, and the component of the angular frequency ω0 of the composite electromotive force in the first excited state is extracted. Is used as the first correction target electromotive force, and the variation factor of the span included in the v × B component in the first correction target electromotive force is removed based on the extracted first ∂A / ∂t component. In addition, the angular frequency ω2 of the composite electromotive force in the second excitation state is Using the component as the second correction target electromotive force, the variation factor of the span included in the v × B component in the second correction target electromotive force is removed based on the extracted second ∂A / ∂t component Perform span correction to
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flow meter according to claim 9, wherein
The power supply unit supplies a first excitation current obtained by amplitude-modulating a carrier wave having an angular frequency ω0 with a modulated wave having an angular frequency ω1 to the first excitation coil, and simultaneously, a carrier wave having the angular frequency ω0 is supplied to the first excitation coil. A first excitation state in which a second excitation current amplitude-modulated by a modulated wave having the same angular frequency and an opposite phase with respect to a modulated wave of current is supplied to the second exciting coil, and a carrier wave having an angular frequency ω2 is angular frequency. A third exciting current amplitude-modulated by the modulated wave of ω1 is supplied to the first exciting coil, and at the same time, the carrier wave of the angular frequency ω2 is opposite in phase to the modulated wave of the third exciting current at the same angular frequency. The excitation current is supplied to the first excitation coil and the second excitation coil while switching between the second excitation state in which the fourth excitation current amplitude-modulated by the modulated wave is supplied to the second excitation coil. ,
The span correction unit obtains an amplitude and a phase of a composite electromotive force detected by the electrode in each of the first excitation state and the second excitation state, and the first excitation based on these amplitudes and phases. The component of the angular frequency ω0 of the combined electromotive force in the state is extracted as the first ∂A / ∂t component, and the component of the angular frequency ω2 of the synthetic electromotive force in the second excitation state is extracted as the second ∂A. /? T component, and the extracted electromotive force sum of the component of the angular frequency ω0 + ω1 and the component of the angular frequency ω0-ω1 of the composite electromotive force in the first excitation state is extracted as the first correction target electromotive force. Based on the first ∂A / ∂t component, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed, and the combined electromotive force in the second excitation state is removed. Electromotive force between the component of angular frequency ω2 + ω1 and the component of angular frequency ω2-ω1 Using the sum of the forces as the second correction target electromotive force, the variation factor of the span included in the v × B component in the second correction target electromotive force based on the extracted second ∂A / ∂t component Perform span correction to be removed,
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flow meter according to claim 9, wherein
The power supply unit supplies a first excitation current obtained by phase-modulating or frequency-modulating a carrier wave having an angular frequency ω0 with a modulated wave having an angular frequency ω1 to the first excitation coil, and simultaneously supplying the carrier wave having the angular frequency ω0 to the first excitation coil. A first excitation state in which a second excitation current phase-modulated or frequency-modulated with a modulation wave of the same angular frequency and opposite phase with respect to the modulation wave of one excitation current is supplied to the second excitation coil; A third excitation current obtained by phase-modulating or frequency-modulating a carrier wave of ω2 with a modulated wave of angular frequency ω1 is supplied to the first excitation coil, and at the same time, a carrier wave of angular frequency ω2 is modulated by the third excitation current. While switching between a second excitation state in which a fourth excitation current phase-modulated or frequency-modulated with a modulated wave having the same angular frequency and opposite phase is supplied to the second excitation coil, The exciting current is supplied to the first exciting coil and the second exciting coil,
The span correction unit obtains an amplitude and a phase of a composite electromotive force detected by the electrode in each of the first excitation state and the second excitation state, and the first excitation based on these amplitudes and phases. The sum of electromotive forces of the component of the angular frequency ω0 + ζ1 · ω1 (ζ1 is a positive integer) and the component of the angular frequency ω0−ζ1 · ω1 of the combined electromotive force in the state is extracted as the first ∂A / ∂t component. , The sum of electromotive forces of the component of the angular frequency ω2 + ζ2 · ω1 (ζ2 is a positive integer) and the component of the angular frequency ω2−ζ2 · ω1 of the combined electromotive force in the second excitation state is the second ∂A / ∂. Extracted as a t component, and a component of the angular frequency ω0 of the composite electromotive force in the first excitation state is used as a first correction target electromotive force, based on the extracted first ∂A / ∂t component. Of span variation included in the v × B component of the correction target electromotive force And the second correction target based on the extracted second ∂A / ∂t component with the component of the angular frequency ω2 of the composite electromotive force in the second excitation state as the second correction target electromotive force. Perform span correction to remove the span variation factor included in the v × B component of the electromotive force,
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flow meter according to claim 9, wherein
The power supply unit supplies a first excitation current obtained by phase-modulating or frequency-modulating a carrier wave having an angular frequency ω0 with a modulated wave having an angular frequency ω1 to the first excitation coil, and simultaneously supplying the carrier wave having the angular frequency ω0 to the first excitation coil. A first excitation state in which a second excitation current phase-modulated or frequency-modulated with a modulation wave of the same angular frequency and opposite phase with respect to the modulation wave of one excitation current is supplied to the second excitation coil; A third excitation current obtained by phase-modulating or frequency-modulating a carrier wave of ω2 with a modulated wave of angular frequency ω1 is supplied to the first excitation coil, and at the same time, a carrier wave of angular frequency ω2 is modulated by the third excitation current. While switching between a second excitation state in which a fourth excitation current phase-modulated or frequency-modulated with a modulated wave having the same angular frequency and opposite phase is supplied to the second excitation coil, The exciting current is supplied to the first exciting coil and the second exciting coil,
The span correction unit obtains an amplitude and a phase of a composite electromotive force detected by the electrode in each of the first excitation state and the second excitation state, and the first excitation based on these amplitudes and phases. The component of the angular frequency ω0 of the combined electromotive force in the state is extracted as the first ∂A / ∂t component, and the component of the angular frequency ω2 of the synthetic electromotive force in the second excitation state is extracted as the second ∂A. /? T component, and the electromotive force sum of the component of the angular frequency ω0 + ζ1 · ω1 (ζ1 is a positive integer) and the component of the angular frequency ω0−ζ1 · ω1 of the composite electromotive force in the first excitation state As a correction target electromotive force of 1, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed based on the extracted first ∂A / ∂t component, and Angular frequency ω2 + ζ2 · ω1 (ζ2 of the synthetic electromotive force in the second excitation state Is a positive integer) and the sum of electromotive forces of the components of the angular frequency ω2-ζ2 · ω1 as a second correction target electromotive force, based on the extracted second ∂A / ∂t component, Perform span correction to remove the span variation factor included in the v × B component of the correction target electromotive force of
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flowmeter according to claim 1,
The excitation unit includes an excitation coil that applies a magnetic field to the fluid, and a power supply unit that supplies an excitation current while switching the excitation angular frequency to the excitation coil.
The electrode includes a first electrode disposed at a position spaced apart from a second plane perpendicular to the axial direction of the measurement tube, including the axis of the excitation coil, and the second electrode. And a second electrode disposed so as to face the first electrode across the second plane at a position away from the plane by providing a second offset. Flowmeter. The electromagnetic flow meter according to claim 14, wherein
The power supply unit switches the excitation coil while switching between a first excitation state in which an excitation current having an angular frequency ω0 is supplied to the excitation coil and a second excitation state in which an excitation current having an angular frequency ω2 is supplied to the excitation coil. Supply excitation current to
The span correction unit includes a first composite electromotive force detected by the first electrode and a second composite detected by the second electrode in each of the first excitation state and the second excitation state. The amplitude and phase of the electromotive force are obtained, and based on these amplitude and phase, the sum of the electromotive forces in the same excitation state and the electromotive force difference in the same excitation state of the first combined electromotive force and the second combined electromotive force are calculated. Each of the first excitation state and the second excitation state is obtained, the electromotive force difference between the first excitation states is extracted as the first ∂A / ∂t component, and the second excitation state is started. The power difference is extracted as the second ∂A / ∂t component, and the sum of electromotive forces in the first excitation state is used as the first correction target electromotive force to the extracted first ∂A / ∂t component. Based on this, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed. In addition, the sum of electromotive forces in the second excitation state is set as a second correction target electromotive force, and v in the second correction target electromotive force based on the extracted second ∂A / ∂t component. X Perform span correction to remove the span fluctuation factor included in the B component,
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flowmeter according to claim 1,
The excitation unit includes an excitation coil that applies a magnetic field to the fluid, and a power supply unit that supplies an excitation current that simultaneously provides a plurality of excitation angular frequencies to the excitation coil.
The electrode includes a first electrode disposed at a position spaced apart from a second plane perpendicular to the axial direction of the measurement tube, including the axis of the excitation coil, and the second electrode. And a second electrode disposed so as to face the first electrode across the second plane at a position away from the plane by providing a second offset. Flowmeter. The electromagnetic flow meter according to claim 16, wherein
The power supply unit supplies an excitation current that simultaneously gives two excitation angular frequencies having different angular frequencies ω0 and ω2 to the excitation coil,
The span correction unit obtains the amplitude and phase of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and uses these amplitudes and phases. Based on each of the angular frequencies ω 0 and ω 2, an electromotive force sum of the same frequency components and an electromotive force difference of the same frequency components of the first combined electromotive force and the second combined electromotive force are obtained for each of the angular frequencies ω 0 and ω 2. The difference is extracted as the first ∂A / ∂t component, the electromotive force difference at the angular frequency ω2 is extracted as the second ∂A / ∂t component, and the electromotive force sum of the angular frequency ω0 is As a correction target electromotive force of 1, the variation factor of the span included in the v × B component in the first correction target electromotive force is removed based on the extracted first ∂A / ∂t component, and The sum of electromotive forces of the angular frequency ω2 as a second correction target electromotive force, Perform span correction to eliminate variable factors of the span included in the v × B component in said second correction target electromotive force based on the second ∂A / ∂t component out,
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flow meter according to claim 14, wherein
The electromagnetic power meter, wherein the power supply unit supplies an excitation current that simultaneously gives two different excitation angular frequencies to the excitation coil. The electromagnetic flow meter according to claim 18,
The power supply unit simultaneously performs a first excitation state in which excitation currents that simultaneously provide two excitation angular frequencies having different angular frequencies ω0 ± Δω are supplied to the excitation coil, and two excitation angular frequencies having different angular frequencies ω2 ± Δω. Supplying an excitation current to the excitation coil while switching between a second excitation state in which the excitation current to be supplied is supplied to the excitation coil;
The span correction unit includes a first composite electromotive force detected by the first electrode and a second composite detected by the second electrode in each of the first excitation state and the second excitation state. The amplitude and phase of the electromotive force are obtained, and based on these amplitude and phase, the sum of electromotive forces of the same frequency component and the electromotive force difference of the same frequency component of the first combined electromotive force and the second combined electromotive force are Each of the angular frequency ω0 ± Δω in the first excitation state and the angular frequency ω2 ± Δω in the second excitation state is obtained, and an electromotive force difference between the angular frequency ω0 + Δω in the first excitation state and the angular frequency ω0−Δω The sum of the electromotive force difference is extracted as the first ∂A / ∂t component, and the sum of the electromotive force difference at the angular frequency ω2 + Δω and the electromotive force difference at the angular frequency ω2-Δω in the second excitation state is calculated. Extracted as the second ∂A / ∂t component, and the angular frequency of the first excitation state The sum of the electromotive force sum of several ω0 + Δω and the sum of electromotive forces of the angular frequencies ω0−Δω is used as a first correction target electromotive force, and the first correction target is based on the extracted first ∂A / ∂t component. In addition to removing the span fluctuation factor included in the v × B component of the electromotive force, the sum of the electromotive force sum of the angular frequency ω2 + Δω and the electromotive force sum of the angular frequency ω2-Δω in the second excitation state is As the second correction target electromotive force, the span correction for removing the variation factor of the span included in the v × B component in the second correction target electromotive force based on the extracted second ∂A / ∂t component And
The zero point correction unit extracts a difference between the first correction target electromotive force subjected to the span correction and the second correction target electromotive force subjected to the span correction as the third ∂A / ∂t component, An electromagnetic flow rate characterized in that a v × B component is extracted by removing the extracted third ∂A / ∂t component from any one of the two corrected electromotive forces subjected to span correction Total. The electromagnetic flowmeter according to claim 1,
The excitation unit includes an excitation coil that applies a magnetic field to the fluid and a power supply unit that supplies an excitation current that simultaneously or alternately provides a plurality of excitation angular frequencies to the excitation coil.
The electrode includes a first electrode disposed at a position spaced apart from a second plane perpendicular to the axial direction of the measurement tube, including the axis of the excitation coil, and the second electrode. And a second electrode disposed so as to face the first electrode across the second plane at a position away from the plane by providing a second offset. Flowmeter. The electromagnetic flow meter according to claim 20, wherein
The said power supply part supplies the exciting current which gives the several component which modulated the several frequency carrier wave with the modulated wave of a different frequency from this carrier wave simultaneously or alternately to the said excitation coil, The electromagnetic flowmeter characterized by the above-mentioned.

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