JPH09166465A - Oscillatory-type measuring instrument - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain an oscillatory-type measuring instrument in which the influence of an axial force and additional mass is corrected and by which a measurement can be performed with high accuracy by using a specified expression to compute fluid density. SOLUTION: A resonance system is constituted of a straight pipe-shaped measuring pipe 2, sensors 6a, 6b, a drive circuit 8, and a driver 5, and frequency band and phase are adjusted by the circuit 8, and the measuring pipe 2 is resonated in a tertiary mode and a primary mode. Both frequencies are measured by a signal processing circuit 9, and a resonance frequency ratio fr is found. In addition, an axial force T acting on the measuring pipe 2 is found on the basis of the frequency ratio fr . Then, a fluid density ρw is computed by the circuit 9 on the basis of an expression based on the Rayleigh method which finds a resonance angular frequency ω (where E of measuring pipe: Young's modulus; I: cross-section secondary moment; Si: cross-sectional area of hollow part; ρt : density; St: actual cross-sectional area; L: length in axial direction: y: vibrating amplitude in position X; n: number of additional mass pieces; mk and yk : mass and vibrating amplitude of k-th additional mass), and a density measuring error due to the axial force and the additional mass is corrected. Thereby, a measurement can be performed with high accuracy.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a vibration type measuring device for measuring the density of a fluid flowing in at least one straight tubular measuring pipe to be vibrated, and more particularly to a vibration type measuring device capable of improving measurement accuracy. Regarding

[0002]

2. Description of the Related Art FIG. 1 is a block diagram showing a general example of a vibration measuring instrument. Reference numeral 2 in FIG. 1 is a hollow straight tube measuring tube,
The fluid to be measured is connected to an external pipe (not shown) so as to flow through it. Fixing members 3a and 3b are fixed to both ends of the straight tubular measuring tube 2 by a method such as brazing or welding, and 4a and 4b are reinforcing members that are joined to the fixing members 3a and 3b by means such as welding. Material, straight tubular measuring tube 2
It has a sufficiently large rigidity. The straight tubular measuring pipe 2 is fixed by fixing members 3a and 3b and reinforcing members 4a and 4b so that both ends thereof serve as nodes to vibrate.

A driver 5 is provided at the center of the straight measuring tube 2.
The sensors 6a and 6b for detecting the vibration of the measuring pipe 2 are directly located on the measuring pipe 2, and the adapters 7 are provided on the reinforcing members 4a and 4b at positions symmetrical with respect to the driver 5 in the upstream and downstream directions.
It is attached via b and 7c. Here, two sensors 6a and 6b for detecting vibration are attached because when this vibration type measuring instrument is used as a Coriolis mass flowmeter, the density is measured by the method described later and at the same time,
This is because the mass flow rate is measured by the phase difference (time difference) between the two sensors mounted on the upstream side and the downstream side. If this vibration type measuring device is constructed only for density measurement, the sensors 6a and 6b need only be 6a.

The straight tubular measuring tube 2 is composed of a sensor 6a for detecting the vibration of the measuring tube, a drive circuit 8 and a driver 5.
It is oscillated at the resonance frequency. The detection signals of the sensors 6a and 6b and the temperature sensor 10 attached to the measuring tube 2
The temperature of the measuring tube 2 detected by the signal processing circuit 9
Sent to In the signal processing circuit 9, the resonance frequency of the measuring tube 2 is obtained from the detection signals of the sensors 6a and 6b, and the temperature of the measuring tube 2 is subjected to the following calculation, and the density is converted and output.

Generally, the resonance frequency f of the transverse vibration of a beam having a uniform cross section like the measuring tube 2 is EI (∂ ⁴ Y / ∂X ⁴ ) + (ρwSi + ρtSt) (∂ ² Y / ∂t ² ) = 0. (4) However, Y (x, t): indicates the vibration displacement of the measuring pipe at the position x and the time t. By solving the differential equation of the equation (4) expressed as follows under appropriate boundary conditions, f = λ ² √ {EI / (ρwSi + ρtSt)} / (2πL ² ) ... (5) where λ: measuring tube It is a constant determined by the boundary condition and the vibration mode of. Is required.

The above formula (5) can be easily and explicitly solved for ρw, and ρw = {(λ ⁴ EI / 4π ² L ⁴ f ² ) −ρtSt} / Si (6) By substituting the resonance frequency f of the measuring tube into this equation (6) and a value obtained by correcting the temperature change of the Young's modulus E due to the temperature of the measuring tube and the change of I, L, St, Si due to thermal expansion, Can be measured. However, in the case of a structure such as that shown in FIG. 1 using a straight tubular measuring tube, for example, due to changes in the temperature of the fluid or the temperature of the atmosphere,
If a temperature difference occurs between the measuring pipe 2 and the reinforcing members 4a and 4b,
An axial force (axial force) is generated in the measuring pipe 2. As is well known, since such an axial force changes the resonance frequency f of the measuring tube 2, it causes an error in the measurement of the density ρw based on the equation (6).

[0007]

Therefore, conventionally, the measuring tube 2 is a curved tube, or a structure such as a bellows or a diaphragm is inserted at both ends of the measuring tube 2 to prevent the action of axial force, or Measures such as limiting the temperature difference between the fluid and the atmosphere during measurement are taken. However, the use of a curved measuring tube has drawbacks such as liquid pooling and corrosion, which is not good for hygiene, is difficult to clean, and has a large pressure loss, which makes it inconvenient for the user. In addition, a structure using a bellows or a diaphragm has a complicated structure, mechanical strength is lowered and is weak against impact during transportation, and axial force cannot be completely prevented. Furthermore, setting a limit on the temperature difference between the fluid and the atmosphere during measurement imposes a great restriction on the user, especially during online measurement in the field.

As another method for solving the problem of axial force, it acts on the measuring pipe by measuring the temperature difference between the measuring pipe 2 and the reinforcing members 4a and 4b, or by measuring the strain of the measuring pipe with a strain gauge or the like. There is a method of measuring the axial force and correcting the density measurement value. However, this also has the following problems. That is, when the axial force differential equations of the previous (4) (tension) T acts ^{on, EI (∂ 4 Y / ∂X} 4) -T (∂ 2 Y / ∂X 2) + (ρwSi + ρtSt) ( ∂ ² Y / ∂t ² ) = 0 (7).

By solving the equation (7) under appropriate boundary conditions, an equation for obtaining the density as shown in equations (5) and (6) can be obtained. In general, g (f, ρw, T, E, I, Si, ρt, St) = 0 (8) The density ρw is not explicitly included and is given as an extremely complicated function. Therefore, the density ρw cannot be directly obtained as in the equation (6), and the equation is too complicated to apply the numerical analysis such as the iterative approximation to practical use.

In addition to the above, a factor that deteriorates the density measurement accuracy is the mass added to the measuring tube such as the driver 5, the sensors 6a and 6b, and the temperature sensor 10. In such an additional mass, the inertial force acts on the measuring tube as a shearing force, which further complicates the differential equation (7) and thus the function (8), and makes the calculation of the density ρw difficult. Further, in the method of obtaining the axial force from the temperature difference between the measuring pipe 2 and the reinforcing members 4a and 4b, the temperature distribution of the reinforcing member changes due to the heat transfer characteristics of the reinforcing member and the temperature change process of the fluid and atmosphere.
Axial force cannot be calculated accurately. Further, the method of adhering the strain gauge to the measuring tube is not suitable for mass-produced products because there is concern about the adhering technique and long-term reliability. From the above, the object of the present invention is to improve the measurement accuracy while making the measuring tube into a shape convenient for mass production.

[0011]

In order to solve such a problem, the invention of claim 1 provides a vibration type measuring device for measuring the density of a fluid flowing in at least one straight tubular measuring pipe to be vibrated. The resonance angular frequency ω of the straight tubular measuring tube,
A means for measuring the temperature of the straight tubular measuring tube and the axial force T acting on the straight tubular measuring tube is provided, and the density of the fluid is obtained based on the following equation (1).

(Equation 5) However, the meaning of each symbol in the formula (1) is as follows. E: Young's modulus of the measuring tube I: Second moment of area of the measuring tube ρw: Fluid density Si: Cross-sectional area of hollow portion of the measuring tube ρt: Density of the measuring tube St: Actual sectional area of the measuring tube L: Axial direction of the measuring tube Length x: axial position of the measuring tube. Set x = 0 at one end of the measuring tube and x = L at the other end. y: A function with x as a variable, which is the vibration amplitude of the measuring tube at the position x in the axial direction of the measuring tube. n: number of additional masses of measuring tube mk: mass of the kth additional mass (k = 1 to n) yk: vibration amplitude of the kth additional mass (k = 1 to n)

According to a second aspect of the present invention, there is provided a vibration type measuring instrument for measuring a density of a fluid flowing in at least one straight tubular measuring pipe, wherein the resonant angular frequency ω of the straight tubular measuring pipe is A means for measuring the temperature of the straight tubular measuring tube and the axial force T acting on the straight tubular measuring tube is provided, and the density of the fluid is obtained based on the following equation (2).

(Equation 6) However, A, B, and C in the equation (2) are constants determined by the vibration shape of the measuring tube and the added mass.

According to the second aspect of the present invention, a set of values of the variables ρ _W , E, I, ω, L, Si and T in one state is obtained in three different states and substituted into the equation (2). , The constants A, B, and C can be obtained by making three independent equations with unknown variables as unknown variables and solving the simultaneous equations (invention of claim 3), or The variables ρ _W , E, I, ω, L, in one state
A set of values of Si and T is obtained in more than three different states and substituted into the equation (2) to make more than three independent equations with the constants A, B and C as unknown variables, The constants A, B, and C can be obtained by the least-squares method so that the error of these equations becomes the smallest (the invention of claim 4).

In the first to fourth aspects of the invention, the axial force T is
It can be obtained from the ratio of the resonance frequency of the first vibration mode and the resonance frequency of the second vibration mode of the straight tubular measuring tube (the invention of claim 5). In the invention of claim 5, the first vibration mode in the straight tube measuring tube can be a primary mode and the second vibration mode can be a tertiary mode (invention of claim 6), or the straight tube. The first vibration mode and the second vibration mode of the measuring tube can be the third mode and the fifth mode, respectively (the invention of claim 7).

According to the invention of claim 8, at least one of the density and the mass flow rate of the fluid flowing in the at least one straight tubular measuring pipe to be excited is measured, and the axial force T acting on the straight tubular measuring pipe is measured. In the vibration-type measuring instrument, which is obtained from the ratio fr of the resonance frequency of the first vibration mode and the resonance frequency of the second vibration mode of the straight measuring tube, and corrects the measured value based on the axial force T, The axial force T is calculated from the equation (3) of the following expression 7.

(Equation 7) However, u: an integer of 0 or more aj: a coefficient that represents the relationship between the frequency ratio fr and the axial force T and that is applied to fr ^j .

In the invention of claim 8, u = 2 in the equation (3) can be satisfied (invention of claim 9). In the invention according to any one of claims 5 to 7, the axial force T can be obtained from the frequency ratio fr by the equation (3) (invention of claim 10), and in the invention of claim 10 the above (3 In the formula, u = 2 can be satisfied (the invention of claim 11).

[0017]

BEST MODE FOR CARRYING OUT THE INVENTION The embodiment of the present invention is the same as that of FIG. 1, and the processing in the signal processing circuit 9 is different from the general processing. Therefore, the difference will be described below. That is, when the axial force (tension) T acts on the differential equation in the equation (4), the equation becomes as in the equation (7), and even if it is solved under appropriate boundary conditions, the density ρw becomes as in the equation (8). Since it becomes a form that does not explicitly include it and becomes a very complicated function, here, by applying the Rayleigh method to find the angular frequency of resonance to a vibration type measuring instrument with a straight tubular measuring tube, the axial force and the added mass Correct the density measurement error due to.

According to the study by the applicants, it has been confirmed that the formula based on the Rayleigh method is expressed as the following formula (1).

(Equation 8) According to the equation (1), (a) the influence of the axial force and the added mass can be corrected. Since the formula (b) has a simple form, the density ρw can be explicitly solved and the calculation is easy. (C) Practically sufficient density measurement accuracy can be obtained. As a result, it is possible to perform accurate density measurement using a straight tubular measuring tube which is simple and easy to use.

Although equation (1) includes an integral term, it has been found from the study by the applicants that such integral need not be calculated each time in practical use, and may be replaced with a predetermined constant. . Equation (2) shown by the following equation 9 is obtained by converting equation (1) into the density
After explicitly solving for w, the integral term and the summation (summation) term Σ in the equation (1) are replaced with constants A, B, and C. If the constants A, B, and C are obtained and determined in advance, sufficient accuracy can be obtained, which simplifies the form of the equation,
Calculation becomes easy.

(Equation 9)

It is not always practical to actually integrate and obtain the constants A, B and C in the equation (2). That is, FIG.
There is a possibility that dimensional errors, residual stress at the time of assembly, etc. remain in the actual measuring device 1 as shown in FIG. Therefore,
For higher accuracy, it is desirable to actually measure and calibrate the density. The calibration may be performed as follows, for example.

That is, in a certain state, ρw, E,
The values of I, ω, L, Si and T are measured. By substituting this into the equation (2), one equation having A, B, and C as unknowns can be created. By changing the state of such measurements (density, temperature,
It is possible to uniquely obtain the three unknowns by repeating the equation three times (changing the axial force etc.) and creating three equations and solving them simultaneously. According to this method, the constants A, B, and C are determined based on the actual measured values, so that a constant more suitable for the measuring device can be obtained, and the measurement accuracy can be improved. However, if the simultaneous equations are not independent, the unknowns A, B, C cannot be uniquely determined, and if the independence is small, A, B, C can be obtained.
The error of may become large. Therefore, it is desirable to measure in three more independent states.

As another method of calibration, the following can be performed. That is, the same measurement as above is performed in different states, but the number of measurements is made more than three times. In this case, the number of equations becomes larger than the number of unknowns, and in general, there are no A, B, and C that satisfy all equations. Therefore, a constant A, which minimizes the error by the method of least squares,
Determine B and C. Although this method increases the labor of measurement, since the measured values in more cases can be reflected in the constants A, B, and C, when it is desired to obtain the measurement accuracy on average in a wide use range (state). It is valid.

In equations (1) and (2), it is necessary to measure the axial force acting on the measuring tube in order to obtain the density ρw.
The above formula (5) is a formula for obtaining the resonance frequency f of the measuring tube when the axial force is not taken into consideration. Here, when the axial force T acts, the equation (5) is as follows: fv = λv (T) ² √ {EI / (ρwSi + ρtSt)} / (2πL ² ) ... (9) fv: Resonance frequency λv (T): transformed into the mode constant of the v-th mode of the measuring tube (which is a function of T).

Here, the ratio fr of the resonance frequencies fv and fq of the arbitrary v-order mode and q-order mode of the measuring tube is given by the equation (9).
As a result, fr = λv (T) ² / λq (T) ² (10), which is a function of only the axial force. Therefore, the axial force T can be obtained by measuring the ratio of the resonance frequencies of the two modes of the measuring tube.

Since this method measures two resonance frequencies, the drive circuit 8 and the signal processing circuit 9 shown in FIG. 1 are somewhat complicated, but the straight tube measuring tube 2 and the measuring tube in the measuring apparatus 1 are not complicated. Since the existing vibration system including the sensor 6a (6b) for detecting vibration and the driver 5 can be used as it is for measurement, the structure of the measuring apparatus 1 does not have to be complicated. Further, since the axial force can be directly measured, the axial force can be measured by the measuring pipe 2 and the reinforcing member 4.
The accuracy is better than that obtained by the temperature difference between a and 4b. Further, as compared with the method of bonding the strain gauge to the measuring tube, it is suitable for mass production because the troublesome bonding is unnecessary, and the reliability is high.

FIG. 2 shows an example of changes in the vibration shape depending on the mode of the measuring tube. The figure shows the calculation result of the vibration shape in the case of a linear beam with a uniform cross section and fixed at both ends. The figure shows the first order in (a), the third order in (b), and the same ( C) 5
Each of the following modes is shown. In general, the measuring tube 2 as shown in FIG. 1 has an infinite number of vibration modes as shown in FIG. 2, and even if the ratio of the resonance frequencies of any two modes among them is used, the equation (10) More axial force can be obtained. However, when actually measuring the resonance frequency,
Resonate the measuring tube and measure its frequency, or
A method of performing a frequency sweep to measure the transfer function is used, but in any case, when the triber 5 is attached to the center of the straight tubular measuring tube 2 as in the measuring apparatus 1 of FIG. It is desirable to use an odd-order mode that becomes an antinode of vibration and is easily induced. In general, a low-order mode having a low frequency is easier to induce and easier to measure. Applicants' studies have determined that it is convenient to use the ratio of the resonant frequencies of the first-order mode and the third-order mode, or the third-order mode and the fifth-order mode.

FIG. 3 shows an example of the correlation between the ratio of the resonance frequencies of the first-order mode and the third-order mode and the axial force. F1 in the figure is 1
The resonance frequency of the next mode, f3 is the resonance frequency of the third mode, the horizontal axis shows the axial force, and the vertical axis shows the frequency ratio obtained by dividing the resonance frequency of the third mode by the resonance frequency of the first mode. In general, λv (T) in the equation (9) has a complicated function form, and this function is used as it is to calculate the axial force T from the frequency ratio fr.
It is not realistic to ask for. According to the study by the applicants, a method of approximating with a polynomial such as the formula (3) shown in Formula 10 is realistic, and in that case, it is practically sufficient to approximate with u = 2, that is, a quadratic function. It turns out to be.

(Equation 10)

FIG. 4 shows an approximation error when the axial force and the frequency ratio shown in FIG. 3 are approximated by a linear function (linear approximation) and a quadratic function. The coefficient of the quadratic function approximation was derived by the least square method. As is clear from the figure, while the linear function approximation has a relatively large approximation error,
It can be seen that the error is extremely small in the quadratic function approximation. This approximation method is not limited to the case where the above-described density measurement is performed by using the equations (1) and (2), and for example, as a Coriolis mass flowmeter, a straight tubular measuring tube such as the measuring device 1 of FIG. 1 is used. It is also applicable when using. Generally, in a Coriolis mass flowmeter, the mass flow rate is obtained from the phase difference (time difference) between the detection signals of the two upstream and downstream sensors (sensors 6a and 6b in FIG. 1). This phase difference (time difference)
Varies depending on the axial force acting on the measuring tube. In order to correct this, the approximation of the equation (3) can be used when the axial force is obtained from the frequency ratio, and in that case, it is practically sufficient to approximate u = 2, that is, a quadratic function. Is.

[0029]

EXAMPLES From the above viewpoints, examples of actual density measurement will be described below. The apparatus used here is that shown in FIG. Although the number of measuring tubes is one in FIG. 1, the same method can be applied to the case of a plurality of measuring tubes. The resonance frequency ratio for the axial force measurement is the resonance frequency of the third mode is 1
The resonance frequency ratio divided by the resonance frequency of the next mode was used.
To measure the resonance frequency, a resonance system is configured by the straight tubular measuring tube 2, the sensor 6a (6b) for detecting the vibration of the measuring tube, the drive circuit 8 and the driver 5, and the drive circuit 8 adjusts the frequency band and the phase. Thus, the measurement tube 2 was made to resonate in both the third-order mode and the first-order mode, and both frequencies were measured and removed by the signal processing circuit 9. Further, the temperature of the measuring tube 2 was measured by the temperature sensor 10.

Table 1 shows the correspondence between the measured value (true value) and the calculation result by the equation (2). In the table, f1 indicates the resonance frequency of the primary mode, and f3 indicates the resonance frequency of the tertiary mode. Here, the data No. Reference numerals 1 to 3 denote cases in which fluids having different densities are put into the measuring tube 2, and the measuring device 1 is kept at a constant temperature so that no axial force is generated in the measuring tube 2. As a result, the resonance frequency ratio is almost constant.
In addition, data No. 4 to 7 are cases where the density of the fluid in the measuring tube is made constant and the axial force acting on the measuring tube is changed, and it can be seen that the frequency ratio is changed by the axial force.

[Table 1]

Data No. Measured values f1 of 1 to 7
As a procedure for calculating the density from f3 and the measurement tube temperature, first, the axial force is obtained from the frequency ratio fr. Although the value here is different from that in FIG. 3, the axial force T is equal to the frequency ratio f.
Good approximation can be performed with a quadratic function of r (u = 2), and specifically, the following equation (11) is obtained. T = a2 · fr ² + a1 · fr + a0 (11) a2: 1692.2 a1: −20338.7 a0: 59229.3

Next, using the equation (2) as the density calculation equation,
The constants A, B and C were determined. Data No. is used to determine the constant.
Correct the axial force T obtained from equation (11) and the Young's modulus E due to temperature change and I, L, and Si changes due to thermal expansion by measuring tube temperature by using the three types of 1, 2, and 4. Value and
The true value ρw of the fluid density and the angular frequency ω of resonance (= 2
Either πf1 or 2πf3, f1 and f3 may be used, but it is necessary to unify them for all data.
In this example, f3 was used. ) Is substituted into the equation (2),
Make a three-dimensional system of linear equations with A, B, and C as unknowns,
I solved it and asked for it. The data used to determine the constants were selected from the seven data that were considered highly independent. As a result, A = 0.0155343 B = 0.0004201 C = -0.000023 was obtained.

After determining A, B and C in the equation (2) as described above, the data No. is added to the equation (2). The density was calculated by substituting the measurement results of 1 to 7, and the error was calculated by comparing with the true value. Looking at columns 2 to 4 in Table 1, data No. 1,2,
Since 4 was used for determining the constants A, B, and C, the error is naturally 0, but the error is 0.
It is 001 [g / cm ³ ] or less, which means that sufficient measurement accuracy can be obtained.

[0034]

According to the present invention, the equation (1) is applied to the density calculation.
The simple, robust, and easy-to-use structure that uses a straight tubular measuring tube as shown in Fig. 1
The effect of the added mass can be corrected by a simple calculation to obtain an advantage that accurate measurement can be performed. Further, the equation (1) is explicitly solved for the density ρw, and the integral and the summation (Σ)
The calculation can be further facilitated by replacing all of the three with A, B, and C constants. Constant A,
High accuracy can be obtained by calibrating B and C with actual measurement data by solving simultaneous equations or using the least squares method. Further, by obtaining the axial force from the resonance frequency ratio, accurate and suitable for mass production can be measured.
In that case, it is desirable to use the ratio of the resonance frequencies of the first-order mode and the third-order mode or the third-order mode and the fifth-order mode. Furthermore, by approximating the axial force as a polynomial of the resonance frequency ratio as in the formula (3), it can be made practical,
The order is sufficient to be quadratic, and there is an advantage that the calculation can be simplified.

[Brief description of the drawings]

FIG. 1 is a configuration diagram showing an embodiment and a general configuration of the present invention.

FIG. 2 is a waveform diagram showing an example of a change in the vibration shape depending on the mode of the measuring tube.

FIG. 3 is a graph showing an example of the correlation between the ratio of the resonance frequencies of the first-order mode and the third-order mode and the axial force.

FIG. 4 is a graph showing an approximation error when the axial force and the frequency ratio shown in FIG. 3 are approximated by a linear function and a quadratic function.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Measuring device, 2 ... Straight tubular measuring tube, 3a, 3b ... Fixing material, 4a, 4b ... Reinforcing material, 5 ... Driver, 6a, 6b
... sensor, 7a, 7b, 7c ... adapter, 8 ... drive circuit, 9 ... signal processing circuit, 10 ... temperature sensor.

Claims (11)

[Claims] 1. A vibration-type measuring instrument for measuring the density of a fluid flowing in at least one straight tubular measuring tube, wherein the resonance angular frequency ω of said straight tubular measuring tube is equal to that of said straight tubular measuring tube. A vibration type measuring instrument comprising means for measuring a temperature and an axial force T acting on a straight tubular measuring tube, wherein the density of the fluid is obtained based on the following equation (1). [Equation 1] However, the meaning of each symbol in the formula (1) is as follows. E: Young's modulus of the measuring tube I: Second moment of area of the measuring tube ρw: Fluid density Si: Cross-sectional area of hollow portion of the measuring tube ρt: Density of the measuring tube St: Actual sectional area of the measuring tube L: Axial direction of the measuring tube Length x: axial position of the measuring tube. Set x = 0 at one end of the measuring tube and x = L at the other end. y: A function with x as a variable, which is the vibration amplitude of the measuring tube at the position x in the axial direction of the measuring tube. n: number of additional masses of measuring tube mk: mass of the kth additional mass (k = 1 to n) yk: vibration amplitude of the kth additional mass (k = 1 to n) 2. A vibration type measuring instrument for measuring a density of a fluid flowing in at least one straight tubular measuring pipe to be vibrated, wherein the resonance angular frequency ω of the straight tubular measuring pipe, A vibration type measuring instrument comprising means for measuring a temperature and an axial force T acting on a straight tubular measuring tube, wherein the density of the fluid is obtained based on the following equation (2). (Equation 2) However, A, B, and C in the equation (2) are constants determined by the vibration shape of the measuring tube and the added mass. 3. Variables ρ _W , E, I, in one state
A set of values of ω, L, Si, and T is obtained in three different states and is substituted into the equation (2) to make three independent equations with the constants A, B, and C as unknown variables. The vibration-type measuring instrument according to claim 2, wherein the constants A, B, and C are obtained by solving simultaneous equations. 4. The variables ρ _W , E, I, in one state
A set of values of ω, L, Si, and T is obtained in more than three different states and substituted into the equation (2) to obtain the constant A,
It is characterized in that more than three independent equations with B and C as unknown variables are created, and the constants A, B and C are obtained by the least squares method so that the error of these equations is minimized. Item 2. The vibration measuring instrument according to Item 2. 5. The axial force T is the first force of the straight tubular measuring tube.
The vibration-type measuring instrument according to claim 1, wherein the vibration-type measuring instrument is obtained from a ratio between the resonance frequency of the vibration mode and the resonance frequency of the second vibration mode. 6. The vibration-type measuring instrument according to claim 5, wherein the first vibration mode of the straight tubular measuring tube is a first-order mode and the second vibration mode is a third-order mode. 7. The vibration-type measuring instrument according to claim 5, wherein the first vibration mode of the straight pipe measuring tube is a third-order mode and the second vibration mode is a fifth-order mode. 8. The axial force T acting on the straight tubular measuring pipe is measured while measuring at least one of the density and the mass flow rate of a fluid flowing in at least one straight tubular measuring pipe to be excited. In the vibration type measuring device for obtaining the ratio fr of the resonance frequency of the first vibration mode and the resonance frequency of the second vibration mode of the pipe and correcting the measured value based on this axial force T, the axial force T is as follows: A vibration-type measuring instrument characterized by being obtained from the equation (3) of equation 3. (Equation 3) However, u: an integer of 0 or more aj: a coefficient that represents the relationship between the frequency ratio fr and the axial force T and that is applied to fr ^j . 9. The vibration measuring instrument according to claim 8, wherein u = 2 in the equation (3). 10. The vibration measuring instrument according to claim 5, wherein the axial force T is obtained from the frequency ratio fr by the following equation (3). (Equation 4) However, u: an integer of 0 or more aj: a coefficient that represents the relationship between the frequency ratio fr and the axial force T and that is applied to fr ^j . 11. The vibration measuring instrument according to claim 10, wherein u = 2 in the equation (3).