JP4555023B2 - Electromagnetic flow meter - Google Patents

Electromagnetic flow meter Download PDF

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JP4555023B2
JP4555023B2 JP2004241476A JP2004241476A JP4555023B2 JP 4555023 B2 JP4555023 B2 JP 4555023B2 JP 2004241476 A JP2004241476 A JP 2004241476A JP 2004241476 A JP2004241476 A JP 2004241476A JP 4555023 B2 JP4555023 B2 JP 4555023B2
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electromotive force
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electrode
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友繁 山本
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Azbil Corp
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Description

本発明は、電磁流量計に係り、特に電極で検出される電極間起電力のうち被測定流体の流量に起因する成分の流速にかかる係数を自動的に補正するスパン補正と、磁場の変動に起因する０点のずれを自動的に補正する０補正の技術に関するものである。   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.

従来技術と本発明を理解するために必要な両者に共通する理論的前提部分について説明する。まず、一般に知られている数学的基礎知識について説明する。
同一周波数で異なる振幅の余弦波Ｐ・ｃｏｓ（ω・ｔ）、正弦波Ｑ・ｓｉｎ（ω・ｔ）は、以下のような余弦波に合成される。Ｐ，Ｑは振幅、ωは角周波数である。
Ｐ・ｃｏｓ（ω・ｔ）＋Ｑ・ｓｉｎ（ω・ｔ）＝（Ｐ2＋Ｑ2）1/2 ・ｃｏｓ（ω・ｔ−ε）
ただし、ε＝ｔａｎ-1（Ｑ／Ｐ） ・・・（１） 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 synthesized 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)

式（１）の合成を分析するには、余弦波Ｐ・ｃｏｓ（ω・ｔ）の振幅Ｐを実軸、正弦波Ｑ・ｓｉｎ（ω・ｔ）の振幅Ｑを虚軸にとるように複素座標平面に写像すると都合がよい。すなわち、複素座標平面上において、原点からの距離（Ｐ2＋Ｑ2）1/2 が合成波の振幅を与え、実軸との角度ε＝ｔａｎ-1（Ｑ／Ｐ）が合成波とω・ｔとの位相差を与えることになる。 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.

また、複素座標平面上においては、以下の関係式が成り立つ。
Ｌ・ｅｘｐ（ｊ・ε）＝Ｌ・ｃｏｓ（ε）＋ｊ・Ｌ・ｓｉｎ（ε） ・・・（２）
式（２）は複素ベクトルに関する表記であり、ｊは虚数単位である。Ｌは複素ベクトルの長さを与え、εは複素ベクトルの方向を与える。したがって、複素座標平面上の幾何学的関係を分析するには、複素ベクトルへの変換を活用すると都合がよい。
以下の説明では、電極間起電力がどのような挙動を示し、従来技術はこの挙動をどのように利用しているかを説明するために、上記のような複素座標平面への写像と、複素ベクトルによる幾何学的分析を採用する。 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

次に、発明者が提案した電磁流量計（特許文献１参照）におけるコイル１組、電極１対の場合の複素ベクトル配置について説明する。
図３０は、特許文献１の電磁流量計の原理を説明するためのブロック図である。この電磁流量計は、被測定流体が流れる測定管１と、被測定流体に印加される磁場および測定管１の軸ＰＡＸの双方と直交し、かつ被測定流体と接触するように測定管１に対向配置され、前記磁場と被測定流体の流れとによって生じた起電力を検出する一対の電極２ａ，２ｂと、測定管軸ＰＡＸの方向と直交する、電極２ａ，２ｂを含む平面ＰＬＮを測定管１の境としたとき、この平面ＰＬＮを境とする測定管１の前後で非対称な、時間変化する磁場を被測定流体に印加する励磁コイル３とを有する。 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. 30 is a block diagram for explaining the principle of the electromagnetic flow meter 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 so as to be orthogonal to and in contact with 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.

ここで、励磁コイル３から発生する磁場のうち、電極２ａ，２ｂ間を結ぶ電極軸ＥＡＸ上において電極軸ＥＡＸおよび測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ１は、以下のように与えられるものとする。
Ｂ１＝ｂ１・ｃｏｓ（ω０・ｔ−θ１） ・・・（３）
式（３）において、ｂ１は振幅、ω０は角周波数、θ１はω０・ｔとの位相差（位相遅れ）である。以下、磁束密度Ｂ１を磁場Ｂ１とする。 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 lag) from ω0 · t. Hereinafter, the magnetic flux density B1 is referred to as a magnetic field B1.

まず、磁場の変化に起因し、被測定流体の流速とは無関係な電極間起電力について説明する。磁場の変化に起因する起電力は、磁場の時間微分ｄＢ／ｄｔによるので、励磁コイル３から発生する磁場Ｂ１を次式のように微分する。
ｄＢ１／ｄｔ＝−ω０・ｂ１・ｓｉｎ（ω０・ｔ−θ１） ・・・（４）
被測定流体の流速が０の場合、発生する渦電流は、磁場の変化に起因する成分のみとなり、磁場Ｂａの変化による渦電流Ｉは、図３１に示すような向きとなる。したがって、電極軸ＥＡＸと測定管軸ＰＡＸとを含む平面内において、磁場Ｂａの変化によって発生する、流速と無関係な電極間起電力Ｅは、図３１に示すような向きとなる。この向きをマイナス方向とする。 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 in 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 shown in 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.

このとき、電極間起電力Ｅは、次式に示すように向きを考えた磁場の時間微分−ｄＢ１／ｄｔに比例係数ｒｋをかけ、位相θ１をθ１＋θ００で置き換えたものとなる（ｒｋ、θ００は、被測定流体の導電率及び誘電率と電極２ａ，２ｂの配置を含む測定管１の構造に関係する）。
Ｅ＝ｒｋ・ω０・ｂ１・ｓｉｎ（ω０・ｔ−θ１−θ００） ・・・（５）
そして、式（５）を変形すると次式となる。
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） At this time, the inter-electrode electromotive force E is obtained by multiplying the time derivative -dB1 / dt of the magnetic field considering the direction by the proportional coefficient rk and replacing the phase θ1 with θ1 + θ00 as shown in the following equation (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)

ここで、式（６）をω０・ｔを基準として複素座標平面に写像すると、実軸成分Ｅｘ、虚軸成分Ｅｙは次式となる。
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） 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)

さらに、式（７）、式（８）に示したＥｘ，Ｅｙを次式に示す複素ベクトルＥｃに変換する。
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） 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)

複素座標に変換された式（９）の電極間起電力Ｅｃは、磁場の時間変化のみに起因し、流速とは無関係な電極間起電力となる。式（９）のｒｋ・ω０・ｂ１・ｅｘｐ｛ｊ・（π／２＋θ１＋θ００）｝は、長さがｒｋ・ω０・ｂ１、実軸からの角度がπ／２＋θ１＋θ００の複素ベクトルである。
また、前述の比例係数ｒｋ及び角度θ００は、次の複素ベクトルｋｃで表すことができる。
ｋｃ＝ｒｋ・ｃｏｓ（θ００）＋ｊ・ｒｋ・ｓｉｎ（θ００）
＝ｒｋ・ｅｘｐ（ｊ・θ００） ・・・（１０）
式（１０）において、ｒｋはベクトルｋｃの大きさ、θ００は実軸に対するベクトルｋｃの角度である。 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 that is independent of 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.
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.

次に、被測定流体の流速に起因する電極間起電力について説明する。被測定流体の流速の大きさがＶ（Ｖ≠０）の場合、発生する渦電流には、流速０のときの渦電流Ｉに加えて、被測定流体の流速ベクトルｖに起因する成分ｖ×Ｂａが発生するため、流速ベクトルｖと磁場Ｂａによる渦電流Ｉｖは、図３２に示すような向きとなる。したがって、流速ベクトルｖと磁場Ｂａによって発生する電極間起電力Ｅｖは時間変化によって発生する電極間起電力Ｅと逆向きとなり、Ｅｖの方向をプラス方向とする。   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 due to 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.

このとき、流速に起因する電極間起電力Ｅｖは、次式に示すように、磁場Ｂ１に比例係数ｒｋｖをかけ、位相θ１をθ１＋θ０１で置き換えたものとなる（ｒｋｖ、θ０１は、流速の大きさＶと被測定流体の導電率及び誘電率と電極２ａ，２ｂの配置を含む測定管１の構造に関係する）。
Ｅｖ＝ｒｋｖ・｛ｂ１・ｃｏｓ（ω０・ｔ−θ１−θ０１）｝ ・・・（１１）
式（１１）を変形すると次式となる。
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） 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)

ここで、式（１２）をω０・ｔを基準として複素座標平面に写像すると、実軸成分Ｅｖｘ、虚軸成分Ｅｖｙは次式となる。
Ｅｖｘ＝ｒｋｖ・ｂ１・｛ｃｏｓ（θ１＋θ０１）｝ ・・・（１３）
Ｅｖｙ＝ｒｋｖ・ｂ１・｛ｓｉｎ（θ１＋θ０１）｝ ・・・（１４）
さらに、式（１３）、式（１４）に示したＥｖｘ，Ｅｖｙを次式に示す複素ベクトルＥｖｃに変換する。
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） 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)

複素座標に変換された式（１５）の電極間起電力Ｅｖｃは、被測定流体の流速に起因する電極間起電力となる。式（１５）のｒｋｖ・ｂ１・ｅｘｐ｛ｊ・（θ１＋θ０１）｝は、長さがｒｋｖ・ｂ１、実軸からの角度がθ１＋θ０１の複素ベクトルである。
また、前述の比例係数ｒｋｖ及び角度θ０１は、次の複素ベクトルｋｖｃで表すことができる。
ｋｖｃ＝ｒｋｖ・ｃｏｓ（θ０１）＋ｊ・ｒｋｖ・ｓｉｎ（θ０１）
＝ｒｋｖ・ｅｘｐ（ｊ・θ０１） ・・・（１６）
式（１６）においてｒｋｖはベクトルｋｖｃの大きさ、θ０１は実軸に対するベクトルｋｖｃの角度である。ここで、ｒｋｖは、前記比例係数ｒｋ（式（１０）参照）に流速の大きさＶと比例係数γをかけたものに相当する。すなわち、次式が成立する。
ｒｋｖ＝γ・ｒｋ・Ｖ ・・・（１７） The inter-electrode electromotive force Evc of the equation (15) converted into the complex coordinates becomes the inter-electrode 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.
Further, 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)

磁場の時間変化に起因する電極間起電力Ｅｃと流体の流速に起因する電極間起電力Ｅｖｃとを合わせた全体の電極間起電力Ｅａｃは、式（１５）に式（１７）を代入した式と、式（９）とを足すことにより、次式で表される。
Ｅａｃ＝ｒｋ・ω０・ｂ１・ｅｘｐ｛ｊ・（π／２＋θ１＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ１・ｅｘｐ｛ｊ・（θ１＋θ０１）｝ ・・・（１８） 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)

式（１８）から分かるように、電極間起電力Ｅａｃは、ｒｋ・ω０・ｂ１・ｅｘｐ｛ｊ・（π／２＋θ１＋θ００）｝とγ・ｒｋ・Ｖ・ｂ１・ｅｘｐ｛ｊ・（θ１＋θ０１）｝の２個の複素ベクトルにより記述される。複素ベクトルｒｋ・ω０・ｂ１・ｅｘｐ｛ｊ・（π／２＋θ１＋θ００）｝は後述する∂Ａ／∂ｔ成分であり、複素ベクトルγ・ｒｋ・Ｖ・ｂ１・ｅｘｐ｛ｊ・（θ１＋θ０１）｝は後述するｖ×Ｂ成分である。この２個の複素ベクトルを合成した合成ベクトルの長さが出力（電極間起電力Ｅａｃ）の振幅を表し、この合成ベクトルの角度φが入力（励磁電流）の位相ω０・ｔに対する電極間起電力Ｅａｃの位相差（位相遅れ）を表す。
なお、流量は流速に測定管の断面積をかけたものとなるため、通常、初期状態での校正において流速と流量は一対一の関係となり、流速を求めることと流量を求めることは同等に扱えるので、以下（流量を求めるために）流速を求める方式として説明を進める。 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). 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 determination of the flow rate and the determination of the flow rate can be handled equally. Therefore, the description will be given below as a method for obtaining the flow velocity (in order to obtain the flow rate).

特許文献１の電磁流量計は、上記のような理論を背景に、スパンのシフトに影響されないパラメータ（非対称励磁パラメータ）を抽出し、これに基づき流量を出力することで、スパンのシフトの問題を解決している。
ここで、図３３を用いてスパンのシフトについて説明する。被測定流体の流速が変化していないにもかかわらず、電磁流量計によって計測される流速の大きさＶが変化したとすると、この出力変動の要因としてスパンのシフトが考えられる。 The electromagnetic flow meter of Patent Document 1 extracts the parameter (asymmetric excitation parameter) that is not affected by the span shift, and outputs the flow rate based on this parameter, thereby solving the problem of the span shift. It has been solved.
Here, the shift of the span 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 the span can be considered as a factor of this output fluctuation.

例えば、初期状態において被測定流体の流速が０のときに電磁流量計の出力が０（ｖ）となり、流速が１（ｍ／ｓｅｃ）のときに出力が１（ｖ）となるように校正したとする。ここでの電磁流量計の出力は、流速の大きさＶを表す電圧である。このような校正により、被測定流体の流速が１（ｍ／ｓｅｃ）であれば、電磁流量計の出力は当然１（ｖ）になるはずである。ところが、ある時間ｔ１が経過したところで、被測定流体の流速が同じく１（ｍ／ｓｅｃ）であるにもかかわらず、電磁流量計の出力が１．２（ｖ）になることがある。この出力変動の要因として考えられるのが、スパンのシフトである。スパンのシフトという現象は、例えば電磁流量計の周囲温度の変化などにより、励磁コイルを流れる励磁電流値が一定値を維持できなくなるなどの原因により発生する。   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 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 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, for example, due to a change in the ambient temperature of the electromagnetic flowmeter, which makes it impossible to maintain a constant value of the excitation current flowing through the excitation coil.

特許文献１の電磁流量計は、スパンのシフトを補正することにより正確な流量計測を実現するものであるが、流量計測の精度に影響を与える他の要因として、出力の０点のシフトがある。ここで、図３４を用いて出力の０点のシフトについて説明しておく。被測定流体の流速が変化していないにもかかわらず、電磁流量計によって計測される流速の大きさＶが変化したとすると、この出力変動の要因として０点のシフトが考えられる。
例えば、初期状態において被測定流体の流量が０のときに電磁流量計の出力が０（ｖ）となり、流速が１（ｍ／ｓｅｃ）のときに出力が１（ｖ）となるように校正したとする。ここでの電磁流量計の出力は、流速の大きさＶを表す電圧である。このような校正により、被測定流体の流速が１（ｍ／ｓｅｃ）であれば、電磁流量計の出力は当然１（ｖ）になるはずである。ところが、ある時間ｔ１が経過したところで、被測定流体の流速が同じく１（ｍ／ｓｅｃ）であるにもかかわらず、電磁流量計の出力が１．５（ｖ）になり、さらに流速を０に戻しても０．５（ｖ）が出力され、０にならないことがある。この出力変動の要因として考えられるのが、０点のシフトである。０点のシフトという現象は、例えば電磁流量計の周囲温度の変化などにより、磁場の変化によって発生する電圧が変動し、キャンセルできなくなることから生じる。 The electromagnetic flow meter of Patent Document 1 realizes accurate flow measurement by correcting a span shift, but another factor affecting the accuracy of flow measurement 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 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 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.

励磁コイルに供給する励磁電流に正弦波を用いる正弦波励磁方式の電磁流量計には、商用周波数ノイズの影響を受けやすいという欠点があるが、この欠点は励磁電流の周波数を高くした高周波励磁方式によって解決することができる（例えば、非特許文献１参照）。また、高周波励磁方式には、電気化学ノイズやスパイクノイズといった１／ｆノイズに強いという利点があり、さらに応答性（流量変化に対して流量信号を素早く追従させる特性）を向上させることができるという利点がある。正弦波励磁方式の電磁流量計では、常に磁場が変化しており、この磁場の変化によって発生する電極間起電力の成分の影響をなくすために、電極軸を境とする測定管の前後で磁場が対称に分布するような構造となっている。しかし、実際には電極や取り出し線の位置ずれ、コイルから発生する磁場の対称性のずれなどにより、磁場の時間変化によって発生する成分の影響を受ける。そこで、正弦波励磁方式の電磁流量計では、磁場の時間変化によって発生する成分の影響を校正時にオフセットとして取り除いているが、磁場のシフトや磁場の分布の変化等により影響をうけ、電磁流量計の出力の０点がシフトしてしまうことが避けられない。また、正弦波励磁方式の電磁流量計では、位相検波により磁場の変化による成分をキャンセルするようにしているが、この位相検波が安定しないため、出力の０点の安定性が悪いという欠点があった。   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.

一方、励磁コイルに供給する励磁電流に矩形波を用いる矩形波励磁方式の電磁流量計の場合、磁場の変化がなくなったところで、電極間起電力を検出するという手法をとっているため、出力の０点の安定性が正弦波励磁方式に比べて優れている（例えば、非特許文献１参照）。しかし、矩形波励磁方式の電磁流量計では、励磁電流が高周波になると、励磁コイルのインピーダンスや、励磁電流の応答性、磁場の応答性、励磁コイルのコアや測定管での過電流損失といった影響を無視できなくなり、矩形波励磁を維持すること（すなわち、磁場の変化がないところで電極間起電力を検出すること）が難しくなり、出力の０点の安定性を確保できなくなる。結果として、矩形波励磁方式の電磁流量計の場合、高周波励磁が難しく、流量変化に対する応答性の向上や１／ｆノイズの除去を実現できないという問題点があった。   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.

また、正弦波励磁方式と矩形波励磁方式のいずれにおいても、被測定流体を流したままでは０点がシフトしたかどうかを確認することができないので、被測定流体を止めて流量を０にした上で、出力の０点がシフトしたかどうかを確認し、設定している０点のオフセットを修正する作業が必要となる。   In addition, in both the sine wave excitation method and the rectangular wave excitation method, it is impossible to confirm whether or not the zero point is shifted while the fluid to be measured is flowing, so the fluid to be measured is stopped and the flow rate is set to zero. In the above, it is necessary to check whether or not the output zero point has shifted, and to correct the set zero offset.

なお、出願人は、本明細書に記載した先行技術文献情報で特定される先行技術文献以外には、本発明に関連する先行技術文献を出願時までに発見するには至らなかった。
ＷＯ ０３／０２７６１４ 社団法人日本計量機器工業連合会編，「計装エンジニアのための流量計測 ＡｔｏＺ」，工業技術社，１９９５年，ｐ．１４３−１６０ 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 Industry Association, “Flow Measurement AtoZ for Instrumentation Engineers”, Kogyo Kogyosha, 1995, p. 143-160

まず、電磁流量計のスパン補正の問題を説明するために必要な物理現象について説明しておく。変化する磁場中を物体が移動する場合、電磁誘導によって２種類の電界、(a) 磁場の時間変化によって発生する電界Ｅ(i)＝∂Ａ／∂ｔ 、(b) 磁場中を物体が動くことにより発生する電界Ｅ(v)＝ｖ×Ｂ が発生する。ｖ×ＢはｖとＢの外積を示し、∂Ａ／∂ｔはＡの時間による偏微分を示す。ｖ、Ｂ、Ａはそれぞれ下記に対応しており、３次元（ｘ、ｙ、ｚ）に方向をもつベクトルである（ｖ：流速、Ｂ：磁束密度、Ａ：ベクトルポテンシャル（磁束密度とはＢ＝ｒｏｔＡの関係がある））。ただし、ここでの３次元ベクトルは複素平面上のベクトルとは意味が異なる。この２種類の電界によって、電位分布が流体中に発生し、この電位は電極によって検出することができる。
特許文献１の電磁流量計では、基本的な理論展開においては実軸に対するベクトルｋｃの角度θ００、実軸に対するベクトルｋｖｃの角度θ０１を考慮しているが、スパンのシフトの問題を解決できる電磁流量計の制約条件として、θ００＝θ０１＝０を前提においている。すなわち、上記前提が成立するように電磁流量計の条件を整えることが制約条件になる。なお、θ１は初期位相であり、励磁電流と電極間起電力に共通の位相部分である。ゆえに、従来技術および本発明のように、励磁電流と電極間起電力の位相差のみを考える場合は、理解を容易にするためθ１＝０とする。 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 (i) = ∂A / ∂t generated by temporal change of the magnetic field; (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, it is assumed that θ00 = θ01 = 0. 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.

前記制約条件が流量計測に与える影響について、図３５を用いて複素ベクトルの考え方で説明する。図３５において、Ｒｅは実軸、Ｉｍは虚軸である。まず、磁場の時間変化のみに依存し、被測定流体の流速に依存しない電極間起電力Ｅｃを∂Ａ／∂ｔ成分と呼び、この∂Ａ／∂ｔ成分をベクトルＶａで表すと共に、被測定流体の流速に依存する電極間起電力Ｅｖｃをｖ×Ｂ成分と呼び、このｖ×Ｂ成分をベクトルＶｂで表す。前述のスパンとは、この被測定流体の流速に依存するｖ×Ｂ成分の流速の大きさＶにかかる係数である。なお、θ００，θ０１の前述の定義を言い換えると、θ００は虚軸に対するベクトルＶａの角度、θ０１は実軸に対するベクトルＶｂの角度である。   The influence of the constraint conditions on the flow rate measurement will be described using the concept of complex vectors with reference to FIG. In FIG. 35, 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.

図３０に示した電磁流量計の構成において、θ００＝θ０１＝０ということは、ベクトルＶａが虚軸Ｉｍ上に存在し、ベクトルＶｂが実軸Ｒｅ上に存在することを意味する。すなわち、ベクトルＶａとＶｂは直交する位置関係にある。このように、特許文献１の電磁流量計は、∂Ａ／∂ｔ成分のベクトルＶａとｖ×Ｂ成分のベクトルＶｂが直交することを前提としている。   In the configuration of the electromagnetic flow meter shown in FIG. 30, 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 to each other.

しかしながら、現実の電磁流量計において、上記前提は必ずしも常に成立するとは限らない。その理由は、ミクロ的には∂Ａ／∂ｔ成分のベクトルＶａとｖ×Ｂ成分のベクトルＶｂの直交性は保証されるが、マクロ的に見ると、被測定流体に印加される磁場が理想的な分布になっていないため、電極で検出されるマクロ的な∂Ａ／∂ｔ成分のベクトルＶａとｖ×Ｂ成分のベクトルＶｂが若干のゆがみを含むと考えなければならないからである。したがって、ベクトルＶａとＶｂは直交しないし、θ００≠０、θ０１≠０、θ００≠θ０１と考えなければならない。   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.

以上の説明から明らかなように、高精度の流量計測を指向する場合には、ベクトルＶａとＶｂの直交性を精密に考慮しなければならないが、特許文献１の電磁流量計では、ベクトルＶａとＶｂの直交性を前提としているので、直交性に誤差が生じる場合には、正確なスパン補正や流量計測ができない可能性があった。   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.

次に、電磁流量計の０補正の問題について説明すると、特許文献１の電磁流量計では、出力の０点のシフトを考慮しておらず、０点の誤差を補正することができないという問題点があった。特許文献１の電磁流量計で０点のシフトによる流量計測誤差が生じることは、式（１８）において∂Ａ／∂ｔ成分が変動すると、流速の大きさＶが０であっても、電極間起電力Ｅａｃが０にならないことから明らかである。
一方、非特許文献１に記載された電磁流量計では、校正時に０点の誤差を補正することができる。しかし、正弦波励磁方式の電磁流量計では、校正した後に０点がシフトしてしまうことがあり、０点の安定性を確保することができないという問題点があった。また、矩形波励磁方式の電磁流量計においても、高周波励磁において０点の安定性を確保することができないという問題点があった。
さらに、特許文献１および非特許文献１に記載されたいずれの電磁流量計においても、被測定流体を流したままの状態では出力の０点の誤差を補正することができないという問題点があった。 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. .

本発明は、上記課題を解決するためになされたもので、正確なスパン補正を自動的に行うことができ、かつ高周波励磁においても出力の０点の安定性を確保することができ、被測定流体の流量を０にすることなく０点の誤差を補正することができる電磁流量計を提供することを目的とする。   The present invention has been made to solve the above-described problems, and can automatically perform accurate span correction, and can ensure the stability of the output zero point even in high-frequency excitation, and can be measured. An object of the present invention is to provide an electromagnetic flow meter capable of correcting an error at zero point without reducing the flow rate of fluid.

本発明の電磁流量計は、被測定流体が流れる測定管と、この測定管に配設され、前記流体に印加される磁場と前記流体の流れとによって生じた起電力を検出する電極と、この電極を含む、前記測定管の軸方向と垂直な第１の平面に対して非対称かつ時間変化する磁場を前記流体に印加する励磁部と、前記電極で検出される、前記流体の流速とは無関係な∂Ａ／∂ｔ成分の起電力と前記流体の流速に起因するｖ×Ｂ成分の起電力との合成起電力から、前記∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出する０点補正部と、前記合成起電力から、前記∂Ａ／∂ｔ成分と同一又は異なる∂Ａ／∂ｔ成分を抽出し、この抽出した∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するスパン補正部と、前記変動要因を除去したｖ×Ｂ成分から前記流体の流量を算出する流量出力部とを備えるものである。
また、本発明の電磁流量計の１構成例において、前記０点補正部は、前記電極で検出される合成起電力から前記∂Ａ／∂ｔ成分を抽出して、前記合成起電力の中から、前記抽出した∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、前記スパン補正部は、前記抽出された∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するものである。 An electromagnetic flowmeter of 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, and a first plane perpendicular to the axial direction of the measuring tube, and is independent of the fluid velocity detected by the electrode The v × B component is extracted by removing the ∂A / ∂t component from the combined electromotive force of the ∂A / ∂t component electromotive force and the v × B component electromotive force resulting from the fluid flow velocity. The ∂A / ∂t component, which is the same as or different from the ∂A / ∂t component, is extracted from the zero point correction unit and the combined electromotive force, and is extracted based on the extracted ∂A / ∂t component. Factor of variation of span, which is a coefficient for the magnitude V of the flow velocity of v × B component Span correction unit that removes, but and a flow rate output unit for calculating the flow rate of the fluid from the v × B component obtained by removing the variation factor.
Further, in one configuration example of the electromagnetic flowmeter of the present invention, the zero point correction unit extracts the ∂A / 成分 t component from the combined electromotive force detected by the electrode, and from the combined electromotive force, The v × B component is extracted by removing the extracted ∂A / ∂t component, and the span correction unit is configured to extract the extracted v × B based on the extracted ∂A / ∂t component. This removes the variation factor of the span, which is a coefficient related to the magnitude V of the flow velocity of the component.

また、本発明の電磁流量計の１構成例において、前記励磁部は、複数の励磁周波数を同時又は交互に与える磁場を前記流体に印加し、前記０点補正部は、前記電極で検出される合成起電力のうち、同時又は交互に得られる複数の周波数成分の振幅と位相を求めることにより前記∂Ａ／∂ｔ成分を抽出するものである。
また、本発明の電磁流量計の１構成例（第１の実施の形態）において、前記励磁部は、前記電極を含む、前記測定管の軸方向と垂直な第１の平面からオフセットを設けて離れた位置に配設された励磁コイルと、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給する電源部とからなり、前記０点補正部は、前記電極で検出される合成起電力のうち前記第１の周波数と第２の周波数の２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて前記２つの周波数成分の起電力差を前記∂Ａ／∂ｔ成分として抽出し、前記電極で検出される合成起電力のうち前記第１の周波数の成分又は前記第２の周波数の成分の中から、前記抽出した∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出するものである。
また、本発明の電磁流量計の１構成例において、前記０点補正部は、前記電極で検出される合成起電力から第１の∂Ａ／∂ｔ成分を抽出して、前記合成起電力の中から、前記抽出した第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、前記スパン補正部は、前記合成起電力から第２の∂Ａ／∂ｔ成分を抽出し、この抽出した第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するものである。 Further, in one configuration example of the electromagnetic flowmeter of the present invention, the excitation unit applies a magnetic field that simultaneously or alternately applies a plurality of excitation frequencies to the fluid, and the zero point correction unit is detected by the electrode. Of the combined electromotive force, the ∂A / ∂t component is extracted by obtaining the amplitude and phase of a plurality of frequency components obtained simultaneously or alternately.
Further, in one configuration example (first embodiment) of the electromagnetic flowmeter of the present invention, the excitation unit is provided with an offset from a first plane perpendicular to the axial direction of the measurement tube, including the electrodes. An excitation coil disposed at a distant position, and a power supply unit that supplies the excitation coil with an excitation current that simultaneously or alternately applies two excitation frequencies different in the first frequency and the second frequency. The point correction unit obtains the amplitude and phase of two frequency components of the first frequency and the second frequency of the combined electromotive force detected by the electrode, and the two frequencies based on these amplitudes and phases The component electromotive force difference is extracted as the ∂A / ∂t component, and the extracted component from the first frequency component or the second frequency component of the combined electromotive force detected by the electrode is extracted. By removing ∂A / ∂t component And it extracts the serial the v × B component.
Further, in one configuration example of the electromagnetic flowmeter of the present invention, the zero point correction unit extracts a first ∂A / ∂t component from the combined electromotive force detected by the electrode, and The v × B component is extracted by removing the extracted first ∂A / ∂t component from the inside, and the span correction unit extracts the second ∂A / ∂t component from the combined electromotive force Then, based on the extracted second ∂A / ∂t component, the variation factor of the span, which is a coefficient related to the magnitude V of the flow velocity of the extracted v × B component, is removed.

また、本発明の電磁流量計の１構成例において、前記励磁部は、前記電極を含む、前記測定管の軸方向と垂直な第１の平面から第１のオフセットを設けて離れた位置に配設された第１の励磁コイルと、前記第１の平面から第２のオフセットを設けて離れた位置に、前記第１の平面を挟んで前記第１の励磁コイルと対向するように配設された第２の励磁コイルと、前記第１の励磁コイルに供給する励磁電流と第２の励磁コイルに供給する励磁電流の位相差を切り替えながら、複数の励磁周波数を同時又は交互に与える励磁電流を前記第１の励磁コイルと第２の励磁コイルに供給する電源部とからなり、前記０点補正部は、前記第１の励磁コイルにより発生する第１の磁場と前記第２の励磁コイルにより発生する第２の磁場との位相差が第１の値である第１の励磁状態において、前記電極で検出される合成起電力のうち、同時又は交互に得られる複数の周波数成分の振幅と位相を求めることにより前記第１の∂Ａ／∂ｔ成分を抽出し、前記スパン補正部は、前記第１の磁場と第２の磁場との位相差が前記第１の励磁状態と異なる第２の励磁状態において、前記電極で検出される合成起電力のうち、同時又は交互に得られる複数の周波数成分の振幅と位相を求めることにより前記第２の∂Ａ／∂ｔ成分を抽出するものである。
また、本発明の電磁流量計の１構成例（第２の実施の形態）において、前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記第１の励磁コイルと第２の励磁コイルに供給し、前記０点補正部は、前記第１の励磁状態において、前記電極で検出される合成起電力のうち前記第１の周波数と第２の周波数の２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて前記２つの周波数成分の起電力差を前記第１の∂Ａ／∂ｔ成分として抽出し、前記電極で検出される合成起電力のうち前記第１の周波数の成分又は前記第２の周波数の成分の中から、前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、前記スパン補正部は、前記第２の励磁状態において、前記電極で検出される合成起電力のうち前記２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて前記２つの周波数成分の起電力差を前記第２の∂Ａ／∂ｔ成分として抽出し、この抽出した第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するものである。 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 for applying a plurality of excitation frequencies simultaneously or alternately 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. The first excitation coil and a power supply unit that supplies the second excitation coil. The zero point correction unit is generated by the first magnetic field generated by the first excitation coil and the second excitation coil. The phase difference with the second magnetic field is the first value In a first excitation state, the first ∂A / 求 め る t component is extracted by obtaining the amplitude and phase of a plurality of frequency components obtained simultaneously or alternately from the composite electromotive force detected by the electrode. In the second excitation state in which the phase difference between the first magnetic field and the second magnetic field is different from the first excitation state, the span correction unit includes: The second ∂A / ∂t component is extracted by obtaining the amplitude and phase of a plurality of frequency components obtained simultaneously or alternately.
Further, in one configuration example (second embodiment) of the electromagnetic flow meter of the present invention, the power supply section provides an excitation current that simultaneously or alternately provides two excitation frequencies different in the first frequency and the second frequency. Are supplied to the first excitation coil and the second excitation coil, and the zero point correction unit is configured to output the first frequency and the first frequency of the combined electromotive force detected by the electrode in the first excitation state. The amplitude and phase of two frequency components of two frequencies are obtained, and the electromotive force difference between the two frequency components is extracted as the first ∂A / ∂t component based on these amplitudes and phases. The v × B component is extracted by removing the first ∂A / ∂t component from the first frequency component or the second frequency component of the detected composite electromotive force, In the second excitation state, the span correction unit is An amplitude and a phase of the two frequency components of the combined electromotive force detected by the recording electrode are obtained, and an electromotive force difference between the two frequency components is calculated based on the amplitude and the phase by the second ∂A / ∂t. This is extracted as a component, and based on the extracted second ∂A / ∂t component, the variation factor of the span, which is a coefficient related to the magnitude V of the flow velocity of the extracted v × B component, is removed. .

また、本発明の電磁流量計の１構成例において、前記励磁部は、前記電極を含む、前記測定管の軸方向と垂直な第１の平面から第１のオフセットを設けて離れた位置に配設された第１の励磁コイルと、前記第１の平面から第２のオフセットを設けて離れた位置に、前記第１の平面を挟んで前記第１の励磁コイルと対向するように配設された第２の励磁コイルと、前記第１の励磁コイルに供給する励磁電流と第２の励磁コイルに供給する励磁電流の位相差を切り替えながら、複数の励磁周波数を同時又は交互に与える励磁電流を前記第１の励磁コイルと第２の励磁コイルに供給する電源部とからなり、前記０点補正部は、前記第１の励磁コイルにより発生する第１の磁場と前記第２の励磁コイルにより発生する第２の磁場との位相差が第１の値である第１の励磁状態において、前記電極で検出される合成起電力のうち、同時又は交互に得られる複数の周波数成分の振幅と位相を求めることにより前記第１の∂Ａ／∂ｔ成分を抽出し、前記スパン補正部は、前記第１の磁場と第２の磁場との位相差が前記第１の励磁状態と異なる第２の励磁状態において、前記電極で検出される合成起電力のうち１つの周波数成分の振幅と位相を求めることにより前記第２の∂Ａ／∂ｔ成分を抽出するものである。
また、本発明の電磁流量計の１構成例（第３の実施の形態）において、前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記第１の励磁コイルと第２の励磁コイルに供給し、前記０点補正部は、前記第１の励磁状態において、前記電極で検出される合成起電力のうち前記第１の周波数と第２の周波数の２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて前記２つの周波数成分の起電力差を前記第１の∂Ａ／∂ｔ成分として抽出し、前記電極で検出される合成起電力のうち前記第１の周波数の成分又は前記第２の周波数の成分の中から、前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、前記スパン補正部は、前記第２の励磁状態において、前記電極で検出される合成起電力のうち前記第１の周波数の成分又は前記第２の周波数の成分の振幅と位相を求め、この振幅と位相に基づいて前記第１の周波数の成分又は前記第２の周波数の成分の起電力を前記第２の∂Ａ／∂ｔ成分として抽出し、この抽出した第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するものである。 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 for applying a plurality of excitation frequencies simultaneously or alternately 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. The first excitation coil and a power supply unit that supplies the second excitation coil. The zero point correction unit is generated by the first magnetic field generated by the first excitation coil and the second excitation coil. The phase difference with the second magnetic field is the first value In a first excitation state, the first ∂A / 求 め る t component is extracted by obtaining the amplitude and phase of a plurality of frequency components obtained simultaneously or alternately from the composite electromotive force detected by the electrode. The span correction unit may include one of the combined electromotive forces detected by the electrodes in a second excitation state in which a phase difference between the first magnetic field and the second magnetic field is different from the first excitation state. The second ∂A / ∂t component is extracted by obtaining the amplitude and phase of two frequency components.
Further, in one configuration example (third embodiment) of the electromagnetic flowmeter of the present invention, the power supply section provides an excitation current that simultaneously or alternately provides two excitation frequencies having different first and second frequencies. Are supplied to the first excitation coil and the second excitation coil, and the zero point correction unit is configured to output the first frequency and the first frequency of the combined electromotive force detected by the electrode in the first excitation state. The amplitude and phase of two frequency components of two frequencies are obtained, and the electromotive force difference between the two frequency components is extracted as the first ∂A / ∂t component based on these amplitudes and phases. The v × B component is extracted by removing the first ∂A / ∂t component from the first frequency component or the second frequency component of the detected composite electromotive force, In the second excitation state, the span correction unit is An amplitude and a phase of the first frequency component or the second frequency component of the synthetic electromotive force detected by the recording electrode are obtained, and the first frequency component or the first frequency is obtained based on the amplitude and phase. 2 is extracted as the second ∂A / ∂t component, and based on the extracted second ∂A / 基 づ い t component, the flow velocity of the extracted v × B component is extracted. This is to remove a span variation factor which is a coefficient related to the size V.

また、本発明の電磁流量計の１構成例において、前記励磁部は、前記流体に磁場を印加する励磁コイルと、複数の励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給する電源部とからなり、前記電極は、前記励磁コイルの軸を含む、前記測定管の軸方向と垂直な第２の平面から第１のオフセットを設けて離れた位置に配設された第１の電極と、前記第２の平面から第２のオフセットを設けて離れた位置に、前記第２の平面を挟んで前記第１の電極と対向するように配設された第２の電極とからなり、前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力和を複数の周波数成分について同時又は交互に求め、複数の起電力和から前記第１の∂Ａ／∂ｔ成分を抽出し、前記スパン補正部は、前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力差を複数の周波数成分について同時又は交互に求め、複数の起電力差から前記第２の∂Ａ／∂ｔ成分を抽出するものである。
また、本発明の電磁流量計の１構成例（第４の実施の形態）において、前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給し、前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力和、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力和を求め、これら２つの起電力和の差分を前記第１の∂Ａ／∂ｔ成分として抽出し、前記第１の周波数の起電力和又は前記第２の周波数の起電力和の中から前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、前記スパン補正部は、前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力差、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力差を求め、これら２つの起電力差の差分を前記第２の∂Ａ／∂ｔ成分として抽出し、この第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するものである。 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 source that supplies an excitation current that simultaneously or alternately provides a plurality of excitation frequencies to the excitation coil. 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 exciting coil. And a second electrode disposed to face the first electrode across the second plane at a position away from the second plane by providing a second offset, The zero point correction unit obtains an amplitude and a phase for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitudes thereof. And the first combined electromotive force and the second combined electromotive force based on the phase The sum of electromotive forces of the same frequency component is obtained simultaneously or alternately for a plurality of frequency components, and the first ∂A / ∂t component is extracted from the plurality of electromotive force sums. An electromotive force difference between the same frequency components of the electromotive force and the second combined electromotive force is obtained simultaneously or alternately for a plurality of frequency components, and the second ∂A / ∂t component is extracted from the plurality of electromotive force differences. is there.
Further, in one configuration example (fourth embodiment) of the electromagnetic flow meter of the present invention, the power supply section provides an excitation current that simultaneously or alternately provides two excitation frequencies having different first and second frequencies. Is supplied to the exciting coil, and the zero point correction unit has an amplitude for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode. And the phase, and based on these amplitudes and phases, the electromotive force sum of the first frequency component of the first combined electromotive force and the first frequency component of the second combined electromotive force, and A sum of electromotive forces of a second frequency component of the first combined electromotive force and a second frequency component of the second combined electromotive force is obtained, and a difference between the two electromotive force sums is calculated as the first power. A / ∂t component is extracted and the sum of electromotive forces of the first frequency or the second frequency The v × B component is extracted by removing the first ∂A / ∂t component from the power sum, and the span correction unit includes the first frequency component of the first combined electromotive force and the component An electromotive force difference between the second combined electromotive force and a first frequency component, and a second frequency component of the first combined electromotive force and a second frequency component of the second combined electromotive force. And the difference between these two electromotive force differences is extracted as the second ∂A / 、 t component, and the extracted v × based on the second ∂A / ∂t component This removes a span variation factor, which is a coefficient related to the magnitude V of the flow velocity of the B component.

また、本発明の電磁流量計の１構成例において、前記励磁部は、前記流体に磁場を印加する励磁コイルと、複数の励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給する電源部とからなり、前記電極は、前記励磁コイルの軸を含む、前記測定管の軸方向と垂直な第２の平面から第１のオフセットを設けて離れた位置に配設された第１の電極と、前記第２の平面から第２のオフセットを設けて離れた位置に、前記第２の平面を挟んで前記第１の電極と対向するように配設された第２の電極とからなり、前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力差を複数の周波数成分について同時又は交互に求め、複数の起電力差から前記第１の∂Ａ／∂ｔ成分を抽出し、前記スパン補正部は、前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力和を複数の周波数成分について同時又は交互に求め、複数の起電力和から前記第２の∂Ａ／∂ｔ成分を抽出するものである。
また、本発明の電磁流量計の１構成例（第４の実施の形態）において、前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給し、前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力差、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力差を求め、これら２つの起電力差の差分を前記第１の∂Ａ／∂ｔ成分として抽出し、前記第１の周波数の起電力差又は前記第２の周波数の起電力差の中から前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、前記スパン補正部は、前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力和、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力和を求め、これら２つの起電力和の差分を前記第２の∂Ａ／∂ｔ成分として抽出し、この第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するものである。 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 source that supplies an excitation current that simultaneously or alternately provides a plurality of excitation frequencies to the excitation coil. 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 exciting coil. And a second electrode disposed to face the first electrode across the second plane at a position away from the second plane by providing a second offset, The zero point correction unit obtains an amplitude and a phase for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitudes thereof. And the first combined electromotive force and the second combined electromotive force based on the phase An electromotive force difference of the same frequency component is simultaneously or alternately obtained for a plurality of frequency components, the first ∂A / ∂t component is extracted from the plurality of electromotive force differences, and the span correction unit is configured to perform the first synthesis. An electromotive force sum of the same frequency component of the electromotive force and the second combined electromotive force is obtained simultaneously or alternately for a plurality of frequency components, and the second ∂A / ∂t component is extracted from the plurality of electromotive force sums. is there.
Further, in one configuration example (fourth embodiment) of the electromagnetic flow meter of the present invention, the power supply section provides an excitation current that simultaneously or alternately provides two excitation frequencies having different first and second frequencies. Is supplied to the exciting coil, and the zero point correction unit has an amplitude for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode. And the phase, and the electromotive force difference between the first frequency component of the first combined electromotive force and the first frequency component of the second combined electromotive force based on the amplitude and phase, and An electromotive force difference between a second frequency component of the first combined electromotive force and a second frequency component of the second combined electromotive force is obtained, and a difference between the two electromotive force differences is calculated as the first power. Extracted as A / ∂t component, the electromotive force difference of the first frequency or the second frequency The v × B component is extracted by removing the first ∂A / ∂t component from the power difference, and the span correction unit includes the first frequency component of the first combined electromotive force and the An electromotive force sum of the second combined electromotive force and a first frequency component; and a second frequency component of the first combined electromotive force and a second frequency component of the second combined electromotive force; And the difference between these two electromotive force sums is extracted as the second ∂A / 基 づ い t component, and based on the second ∂A / ∂t component, the extracted v × This removes a span variation factor, which is a coefficient related to the magnitude V of the flow velocity of the B component.

また、本発明の電磁流量計の１構成例において、前記励磁部は、前記流体に磁場を印加する励磁コイルと、複数の励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給する電源部とからなり、前記電極は、前記励磁コイルの軸を含む、前記測定管の軸方向と垂直な第２の平面から第１のオフセットを設けて離れた位置に配設された第１の電極と、前記第２の平面から第２のオフセットを設けて離れた位置に、前記第２の平面を挟んで前記第１の電極と対向するように配設された第２の電極とからなり、前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力和を複数の周波数成分について同時又は交互に求め、複数の起電力和から前記第１の∂Ａ／∂ｔ成分を抽出し、前記スパン補正部は、前記第１の合成起電力と第２の合成起電力の１つの周波数成分の起電力差から前記第２の∂Ａ／∂ｔ成分を抽出するものである。   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 source that supplies an excitation current that simultaneously or alternately provides a plurality of excitation frequencies to the excitation coil. 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 exciting coil. And a second electrode disposed to face the first electrode across the second plane at a position away from the second plane by providing a second offset, The zero point correction unit obtains an amplitude and a phase for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitudes thereof. And the first combined electromotive force based on the phase The sum of electromotive forces of the same frequency component is obtained simultaneously or alternately for a plurality of frequency components, and the first ∂A / ∂t component is extracted from the plurality of electromotive force sums. The second ∂A / ∂t component is extracted from the electromotive force difference between one frequency component of the electromotive force and the second combined electromotive force.

また、本発明の電磁流量計の１構成例（第５の実施の形態）において、前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給し、前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力和、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力和を求め、これら２つの起電力和の差分を前記第１の∂Ａ／∂ｔ成分として抽出し、前記第１の周波数の起電力和又は前記第２の周波数の起電力和の中から前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、前記スパン補正部は、前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力差、又は前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力差を前記第２の∂Ａ／∂ｔ成分として抽出し、この第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するものである。   Further, in one configuration example (fifth embodiment) of the electromagnetic flowmeter of the present invention, the power supply section provides an excitation current that simultaneously or alternately provides two excitation frequencies having different first and second frequencies. Is supplied to the exciting coil, and the zero point correction unit has an amplitude for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode. And the phase, and based on these amplitudes and phases, the electromotive force sum of the first frequency component of the first combined electromotive force and the first frequency component of the second combined electromotive force, and A sum of electromotive forces of a second frequency component of the first combined electromotive force and a second frequency component of the second combined electromotive force is obtained, and a difference between the two electromotive force sums is calculated as the first power. A / ∂t component is extracted and the sum of electromotive forces of the first frequency or the second frequency The v × B component is extracted by removing the first ∂A / ∂t component from the power sum, and the span correction unit includes the first frequency component of the first combined electromotive force and the component An electromotive force difference with a first frequency component of the second combined electromotive force, or a second frequency component of the first combined electromotive force and a second frequency component of the second combined electromotive force Is extracted as the second ∂A / ∂t component, and based on the second ∂A / ∂t component, the coefficient applied to the flow velocity magnitude V of the extracted v × B component This is to remove the span fluctuation factor.

本発明によれば、電極で検出される、流体の流速とは無関係な∂Ａ／∂ｔ成分の起電力と流体の流速に起因するｖ×Ｂ成分の起電力との合成起電力から、∂Ａ／∂ｔ成分を取り除くことによりｖ×Ｂ成分を抽出し、電極で検出される合成起電力から、前記∂Ａ／∂ｔ成分と同一又は異なる∂Ａ／∂ｔ成分を抽出し、この抽出した∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去し、変動要因を除去したｖ×Ｂ成分から流体の流量を算出するようにしたので、正確なスパン補正を自動的に行うことができ、かつ被測定流体の流量を０にすることなく電磁流量計の出力の０点を補正することができ、高周波励磁においても０点の安定性を確保することができる。その結果、本発明では、高精度の流量計測を行うことができる。   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 v × B component electromotive force caused by the fluid flow velocity, ∂ The v × B component is extracted by removing the A / ∂t component, and the same or different ∂A / ∂t component as the ∂A / ∂t component is extracted from the combined electromotive force detected by the electrode, and this extraction is performed. Based on the obtained ∂A / ∂t component, the variation factor of the span, which is a coefficient related to the magnitude V of the flow velocity of the extracted v × B component, is removed, and the fluid is removed from the v × B component from which the variation factor is removed. Since the flow rate is calculated, accurate span correction can be automatically performed, and the zero point of the output of the electromagnetic flow meter can be corrected without reducing the flow rate of the fluid to be measured. The stability of 0 point can be ensured also in the excitation. As a result, in the present invention, highly accurate flow rate measurement can be performed.

本発明は、電磁流量計の電極で検出される電極間起電力から、∂Ａ／∂ｔ成分のベクトルＶａとｖ×Ｂ成分のベクトルＶｂとの合成ベクトルＶａ＋Ｖｂを求めたとき、ベクトルＶａは磁場の時間変化のみに依存し、被測定流体の流速の大きさＶに無関係なベクトルであり、ベクトルＶｂは被測定流体の流速の大きさＶに比例して大きさが変化するベクトルであることに着目している。   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 the electromotive force detected by the electrodes of the electromagnetic flowmeter, 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.

励磁周波数を０にすれば、合成ベクトルＶａ＋ＶｂからベクトルＶｂのみが取り出せることになるが、低周波領域での出力に対するノイズの影響が大きく現実的ではない。そこで、本発明では、合成ベクトルＶａ＋Ｖｂの中から０点の変動要因となる第１の∂Ａ／∂ｔ成分を抽出して、この第１の∂Ａ／∂ｔ成分を合成ベクトルＶａ＋Ｖｂから引くことにより、ｖ×Ｂ成分のみを抽出するようにしている。ｖ×Ｂ成分を０にすることなく（流量を０にすることなく）、また∂Ａ／∂ｔ成分を０にすることなく（励磁周波数を０にすることなく）、ｖ×Ｂ成分のみを取り出せることが重要である。   If the excitation frequency is set to 0, only the vector Vb can be extracted from the combined vector Va + Vb. However, the influence of noise on the output in the low frequency region is large and not realistic. Therefore, in the present invention, the first ∂A / ∂t component, which is a variation factor of 0 point, is extracted from the combined vector Va + Vb, and the first ∂A / ∂t component is subtracted from the combined vector Va + Vb. Thus, only the v × B component is extracted. 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 obtained. It is important to be able to take it out.

次に、本発明では、抽出したｖ×Ｂ成分に含まれるスパン変動要因を消去することが可能な第２の∂Ａ／∂ｔ成分を抽出して、ｖ×Ｂ成分を第２の∂Ａ／∂ｔ成分により正規化してスパン変動要因を除去し、スパン変動要因を除去したｖ×Ｂ成分に基づき、被測定流体の流量を算出するようにしている。第２の∂Ａ／∂ｔ成分を抽出することにより、第２の∂Ａ／∂ｔ成分とｖ×Ｂ成分とが直交するか否かに関係なく、第２の∂Ａ／∂ｔ成分とｖ×Ｂ成分を別々のベクトルとして扱えることが重要である。なお、第２の∂Ａ／∂ｔ成分は、第１の∂Ａ／∂ｔ成分と同じ場合もある。   Next, in the present invention, the second ∂A / ∂t component that can eliminate the span variation factor included in the extracted v × B component is extracted, and the v × B component is converted into the second ∂A. Normalization is performed using the / t component to remove the span variation factor, and the flow rate of the fluid to be measured is calculated based on the v × B component from which the span variation factor has been removed. By extracting the second ∂A / ∂t component, the second ∂A / ∂t component and whether or not the second ∂A / 成分 t component and the v × B component are orthogonal to each other It is important to be able to treat the v × B component as separate vectors. The second ∂A / ∂t component may be the same as the first ∂A / ∂t component.

以上により、本発明では、ｖ×Ｂ成分のスパンを補正することができ、０点の変動要因とスパンの変動要因がともに除去された出力を得ることができる。以下、０点とスパンを実際に補正するための本発明の基本原理について説明する。   As described above, according to the present invention, the span of the v × B component can be corrected, and an output from which both the zero-point variation factor and the span variation factor are removed can be obtained. Hereinafter, the basic principle of the present invention for actually correcting the zero point and the span will be described.

［第１の基本原理］
本発明の第１の基本原理に基づく電磁流量計は、電極で検出される合成ベクトルから∂Ａ／∂ｔ成分を抽出し、この∂Ａ／∂ｔ成分を合成ベクトルの中から取り除くことによりｖ×Ｂ成分のみを抽出し、抽出した∂Ａ／∂ｔ成分に基づいてｖ×Ｂ成分の流速の大きさＶにかかる係数（スパン）の変動要因を除去し、スパン変動要因を除去したｖ×Ｂ成分から流体の流量を算出するものである。この第１の基本原理に基づく電磁流量計の構成は、図３０に示した従来の電磁流量計と同様であるので、図３０の符号を用いて第１の基本原理を説明する。 [First basic principle]
The electromagnetic flow meter based on the first basic principle of the present invention extracts the ∂A / ∂t component from the combined vector detected by the electrode, and removes this ∂A / ∂t component from the combined vector. Extracting only the B component, removing the coefficient (span) variation factor for the flow velocity V of the v × B component based on the extracted ∂A / ∂t component, and removing the span variation factor The fluid flow rate is calculated from the B component. Since the configuration of the electromagnetic flowmeter based on the first basic principle is the same as that of the conventional electromagnetic flowmeter shown in FIG. 30, the first basic principle will be described using the reference numerals in FIG.

図３０の電磁流量計で説明した式（１８）の右辺第１項は励磁コイル３から発生する磁場の変化に起因する∂Ａ／∂ｔ成分、右辺第２項は励磁コイル３から発生する磁場と流速に起因するｖ×Ｂ成分となる。この合成ベクトルにおけるｖ×Ｂ成分の流速Ｖに係る係数の変動部分と∂Ａ／∂ｔ成分のω０に係る係数の変動部分が等しく、合成ベクトルから取り出した１つの∂Ａ／∂ｔ成分を用いて、０補正とスパン補正を行う方式が使用できる。この場合に適用できる原理を以下説明する。   The first term on the right side of the equation (18) described in the electromagnetic flow meter of FIG. 30 is the ∂A / ∂t component resulting from the change in the magnetic field generated from the excitation coil 3, and the second term on the right side is the magnetic field generated from the excitation coil 3. And v × B component due to the flow velocity. In this synthesized vector, the coefficient fluctuation part related to the flow velocity V of the v × B component is equal to the coefficient fluctuation part related to ω0 of the ∂A / ∂t component, and one ∂A / ∂t component extracted from the composite vector is used. Thus, a method of performing zero correction and span correction can be used. The principle applicable in this case will be described below.

励磁コイル３に角周波数ω０の励磁電流を供給した場合に電極２ａ，２ｂで検出される電極間起電力は、以下の∂Ａ／∂ｔ成分のベクトルＶａ１０とｖ×Ｂ成分のベクトルＶｂ１０の合成ベクトルＶａ１０＋Ｖｂ１０に相当する。
Ｖａ１０＝ｒａ・ｅｘｐ（ｊ・θａ）・Ｃ１・ω０ ・・・（１９）
Ｖｂ１０＝ｒｂ・ｅｘｐ（ｊ・θｂ）・Ｃ１・Ｖ ・・・（２０）
図１にベクトルＶａ１０とベクトルＶｂ１０と合成ベクトルＶａ１０＋Ｖｂ１０とを示す。 The inter-electrode electromotive force detected by the electrodes 2a and 2b when the exciting current of the angular frequency ω0 is supplied to the exciting coil 3 is a combination of the following vector A10 of the ∂A / ∂t component and the vector Vb10 of the v × B component. It corresponds to the vector Va10 + Vb10.
Va10 = ra · exp (j · θa) · C1 · ω0 (19)
Vb10 = rb · exp (j · θb) · C1 · V (20)
FIG. 1 shows a vector Va10, a vector Vb10, and a combined vector Va10 + Vb10.

ここで、∂Ａ／∂ｔ成分のベクトルＶａ１０は、磁場の変化により発生する起電力なので、励磁周波数ω０に比例する大きさになる。このベクトルＶａ１０の大きさの既知の比例定数部分をｒａ、ベクトルＶａ１０の既知の方向をθａとすると、Ｃ１が磁場のシフトなどの「変化する要素」として与えられる。   Here, the vector Va10 of the ベ ク ト ル A / 起 t component is an electromotive force generated by a change in the magnetic field, and thus has a magnitude proportional to the excitation frequency ω0. Assuming that the known proportional constant portion of the magnitude of the vector Va10 is ra and the known direction of the vector Va10 is θa, C1 is given as a “changing element” such as a magnetic field shift.

また、ｖ×Ｂ成分のベクトルＶｂ１０は、測定管中の流体の移動により発生する起電力なので、流速の大きさＶに比例する大きさになる。このベクトルＶｂ１０の大きさの既知の比例定数部分をｒｂ、ベクトルＶｂ１０の既知の方向をθｂとすると、Ｃ１が磁場のシフトなどの「変化する要素」として与えられる。したがって、∂Ａ／∂ｔ成分のベクトルＶａ１０におけるＣ１とｖ×Ｂ成分のベクトルＶｂ１０におけるＣ１は、同一の要素になる。流速の大きさＶが０の時は、ベクトルＶａ１０が変動することにより、合成ベクトルの大きさが変動する（すなわち、０点が変動する）。   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. Assuming that the known proportional constant part of the magnitude of the vector Vb10 is rb and the known direction of the vector Vb10 is θb, C1 is given as a “changing element” such as a magnetic field shift. Therefore, C1 in the vector Va10 of ∂A / ∂t component and C1 in the vector Vb10 of v × B component are the same element. When the magnitude V of the flow velocity is 0, the magnitude of the combined vector varies (that is, the zero point varies) due to the variation of the vector Va10.

図２は、０補正及びスパン補正の対象となる合成ベクトルから∂Ａ／∂ｔ成分のベクトルＶａ１０を抽出する処理を複素ベクトル表現した図である。電極２ａ，２ｂで検出される合成ベクトルから∂Ａ／∂ｔ成分を抽出する方法としては、複数の励磁周波数による磁場を被測定流体に印加し、電極間起電力に含まれる複数の周波数成分の出力差を利用して∂Ａ／∂ｔ成分を抽出する方法を用いる。電極間起電力から直接求めることができる複素ベクトルは合成ベクトルＶａ１０＋Ｖｂ１０であり、ベクトルＶａ１０，Ｖｂ１０が直接的に計測できるわけではない。そこで、∂Ａ／∂ｔ成分の大きさは励磁周波数ωに比例し、ｖ×Ｂ成分は励磁周波数ωに依存しないことに着眼する。具体的には、ある角周波数ω０で励磁したときの合成ベクトルと別の角周波数ω２で励磁したときの合成ベクトルとの差を求める。この差は、∂Ａ／∂ｔ成分の大きさの変化分だけを与えるベクトルになるので、この変化分から∂Ａ／∂ｔ成分を抽出することができる。   FIG. 2 is a complex vector representation of the process of extracting the vector Va10 of the ∂A / ∂t component from the combined vector to be subjected to 0 correction and span correction. As a method of extracting the ∂A / ∂t component from the combined vector detected by the electrodes 2a and 2b, 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 obtained. A method of extracting the ∂A / ∂t component using the output difference is used. The complex vector that can be directly obtained from the inter-electrode electromotive force is the combined vector Va10 + Vb10, and the vectors Va10 and Vb10 cannot be directly measured. Therefore, it is noted that the magnitude of the ∂A / ∂t component is proportional to the excitation frequency ω, and the v × B component does not depend on the excitation frequency ω. Specifically, the difference between the combined vector when excited at a certain angular frequency ω0 and the 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 ∂A / ∂t component, the ∂A / ∂t component can be extracted from this change.

励磁角周波数をω２としたときのｖ×Ｂ成分のベクトルは式（２０）に示したベクトルＶｂ１０と同じである。一方、励磁角周波数をω２としたときの∂Ａ／∂ｔ成分のベクトルＶａ１２は、式（１９）においてω０をω２で置き換えたものとなり、次式のようになる。
Ｖａ１２＝ｒａ・ｅｘｐ（ｊ・θａ）・Ｃ１・ω２ ・・・（２１） The vector of the v × B component when the excitation angular frequency is ω2 is the same as the vector Vb10 shown in Expression (20). On the other hand, the vector Va12 of the ∂A / ∂t component when the excitation angular frequency is ω2 is obtained by replacing ω0 with ω2 in the equation (19), and is represented by the following equation.
Va12 = ra · exp (j · θa) · C1 · ω2 (21)

電極間起電力に含まれる角周波数ω０の成分（合成ベクトルＶａ１０＋Ｖｂ１０）と角周波数ω２の成分（合成ベクトルＶａ１２＋Ｖｂ１０）との差分を求めると、ｖ×Ｂ成分がキャンセルされ、求めた差分をω０／（ω０−ω２）倍したものはベクトルＶａ１０と同じになる。よって、合成ベクトルＶａ１０＋Ｖｂ１０中の∂Ａ／∂ｔ成分のベクトルＶａ１０を異なる周波数成分の出力差を利用することにより抽出することができる。   When the difference between the component of the angular frequency ω0 (synthetic vector Va10 + Vb10) and the component of the angular frequency ω2 (synthetic vector Va12 + Vb10) included in the inter-electrode electromotive force is obtained, the v × B component is canceled and the obtained difference is ω0 / ( The product multiplied by [omega] 0- [omega] 2) is the same as the vector Va10. Therefore, the vector Va10 of ∂A / ∂t component in the combined vector Va10 + Vb10 can be extracted by using the output difference of different frequency components.

図３は、合成ベクトル中のｖ×Ｂ成分のベクトルＶｂ１０を抽出する処理を複素ベクトル表現した図である。合成ベクトルＶａ１０＋Ｖｂ１０からベクトルＶａ１０を引くことにより、式（２０）に示したｖ×Ｂ成分のベクトルＶｂ１０を抽出することができる。式（２０）より、ｖ×Ｂ成分のベクトルＶｂ１０には、角周波数に関連する項（０点変動要因）が含まれていないことが分かる。   FIG. 3 is a diagram representing the process of extracting the vector Vb10 of the v × B component in the composite vector as a complex vector. By subtracting the vector Va10 from the combined vector Va10 + Vb10, the vector Vb10 of the v × B component shown in Expression (20) can be extracted. From equation (20), it can be seen that the v × B component vector Vb10 does not include a term related to the angular frequency (factor of zero point variation).

抽出したｖ×Ｂ成分のベクトルＶｂ１０と∂Ａ／∂ｔ成分のベクトルＶａ１０の変動要因はどちらもＣ１なので、∂Ａ／∂ｔ成分のベクトルＶａ１０でｖ×Ｂ成分のベクトルＶｂ１０を正規化すれば、ｖ×Ｂ成分のベクトルＶｂ１０のスパン変動要因が消去できる。   Since both of the fluctuation factors of the extracted v × B component vector Vb10 and the ∂A / ∂t component vector Va10 are C1, if the v × B component vector Vb10 is normalized by the ∂A / ∂t component vector Va10, , The span variation factor of the vector Vb10 of the v × B component can be eliminated.

図４は、ｖ×Ｂ成分のベクトルＶｂ１０を∂Ａ／∂ｔ成分のベクトルＶａ１０により正規化する処理を複素ベクトル表現した図である。抽出した∂Ａ／∂ｔ成分のベクトルＶａ１０により、ｖ×Ｂ成分のベクトルＶｂ１０を正規化する。正規化したｖ×Ｂ成分をω０倍した正規化ｖ×Ｂ成分をＶｎｂ１０とすると、Ｖｎｂ１０は式（２２）で表される。
Ｖｎｂ１０＝（Ｖｂ１０／Ｖａ１０）・ω０
＝（ｒｂ／ｒａ）・ｅｘｐ｛ｊ・（θｂ−θａ）｝・Ｖ ・・・（２２） FIG. 4 is a diagram representing a process of normalizing the v × B component vector Vb10 with the vector Va10 of ∂A / ∂t component in a complex vector representation. The v × B component vector Vb10 is normalized by the extracted ∂A / ∂t component vector Va10. Assuming that a normalized v × B component obtained by multiplying the normalized v × B component by ω0 is Vnb10, Vnb10 is expressed by Expression (22).
Vnb10 = (Vb10 / Va10) · ω0
= (Rb / ra) · exp {j · (θb−θa)} · V (22)

なお、正規化したｖ×Ｂ成分をω０倍する理由は、流速の大きさＶにかかる係数（スパン）からω０を取り除くためである。式（２２）によれば、正規化ベクトルＶｎｂ１０のＶにかかる係数から変動要因Ｃ１が消去され、スパンが補正されていることが分かる。式（２２）より、被測定流体の流速の大きさＶを以下のように算出することができる。
Ｖ＝｜Ｖｎｂ１０／［（ｒｂ／ｒａ）・ｅｘｐ｛ｊ・（θｂ−θａ）｝］｜
＝｜Ｖｎｂ１０｜／（ｒｂ／ｒａ） ・・・（２３） The reason why the normalized v × B component is multiplied by ω0 is to remove ω0 from the coefficient (span) related to the magnitude V of the flow velocity. According to Expression (22), it can be seen that the variation factor C1 is eliminated from the coefficient applied to V of the normalized vector Vnb10, and the span is corrected. From equation (22), the magnitude V of the flow velocity of the fluid to be measured can be calculated as follows.
V = | Vnb10 / [(rb / ra) · exp {j · (θb−θa)}] |
= | Vnb10 | / (rb / ra) (23)

［第２の基本原理］
次に、本発明の第２の基本原理について説明する。本発明の第２の基本原理に基づく電磁流量計は、電極で検出される合成ベクトルから第１の∂Ａ／∂ｔ成分を抽出し、この第１の∂Ａ／∂ｔ成分を合成ベクトルの中から取り除くことによりｖ×Ｂ成分のみを抽出し、次に合成ベクトルから第２の∂Ａ／∂ｔ成分を抽出し、抽出した第２の∂Ａ／∂ｔ成分に基づいてｖ×Ｂ成分の流速の大きさＶにかかる係数（スパン）の変動要因を除去し、スパン変動要因を除去したｖ×Ｂ成分から流体の流量を算出するものである。 [Second basic principle]
Next, the second basic principle of the present invention will be described. The electromagnetic flow meter based on the second basic principle of the present invention extracts the first ∂A / ∂t component from the combined vector detected by the electrodes, and uses the first ∂A / ∂t component as the combined vector. Only the v × B component is extracted by removing from the inside, then the second ∂A / ∂t component is extracted from the combined vector, and the v × B component is based on the extracted second ∂A / ∂t component The coefficient (span) variation factor related to the magnitude V of the flow velocity is removed, and the fluid flow rate is calculated from the v × B component from which the span variation factor is removed.

まず、第２の基本原理に基づく電磁流量計のうち、２個の励磁コイルと１対の電極とを有する電磁流量計の原理を図５を用いて説明する。図５の電磁流量計は、測定管１と、電極２ａ，２ｂと、測定管軸ＰＡＸの方向と直交する、電極２ａ，２ｂを含む平面ＰＬＮを測定管１の境としたとき、この平面ＰＬＮを境とする測定管１の前後で非対称な、時間変化する磁場を被測定流体に印加する第１の励磁コイル３ａ、第２の励磁コイル３ｂとを有する。第１の励磁コイル３ａは、平面ＰＬＮから例えば下流側にオフセット距離ｄ１だけ離れた位置に配設される。第２の励磁コイル３ｂは、平面ＰＬＮから例えば上流側にオフセット距離ｄ２だけ離れた位置に、平面ＰＬＮを挟んで第１の励磁コイル３ａと対向するように配設される。   First, the principle of an electromagnetic flowmeter having two excitation coils and a pair of electrodes among the electromagnetic flowmeters based on the second basic principle will be described with reference to FIG. When the plane PLN including the electrodes 2a and 2b perpendicular to the direction of the measurement tube 1, the electrodes 2a and 2b, and the measurement tube axis PAX is used as the boundary of the measurement tube 1, the electromagnetic flow meter of FIG. 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.

第２の励磁コイル３ｂを平面ＰＬＮを挟んで第１の励磁コイル３ａと対向するように配設した場合、電極２ａ，２ｂで検出される電極間起電力のうち、第１の励磁コイル３ａから発生する磁場および流体の流速に起因するｖ×Ｂ成分と、第２の励磁コイル３ｂから発生する磁場および流体の流速に起因するｖ×Ｂ成分とは同じ方向になる。一方、電極間起電力のうち、第１の励磁コイル３ａから発生する磁場の変化に起因する∂Ａ／∂ｔ成分と、第２の励磁コイル３ｂから発生する磁場の変化に起因する∂Ａ／∂ｔ成分とは逆向きになる。そのため、第１の励磁コイル３ａから発生する磁場の変化に起因する∂Ａ／∂ｔ成分と、第１の励磁コイル３ａから発生する磁場および流体の流速に起因するｖ×Ｂ成分と、第２の励磁コイル３ｂから発生する磁場の変化に起因する∂Ａ／∂ｔ成分と、第２の励磁コイル３ｂから発生する磁場および流体の流速に起因するｖ×Ｂ成分とを合わせた全ての合成ベクトルにおけるｖ×Ｂ成分の変動要因と∂Ａ／∂ｔ成分の変動要因は、等しくならないことを考慮して補正を行う必要がある。   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.

ここで、第１の励磁コイル３ａから発生する磁場Ｂｂのうち、電極２ａ，２ｂ間を結ぶ電極軸ＥＡＸ上において電極軸ＥＡＸおよび測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ２と、第２の励磁コイル３ｂから発生する磁場Ｂｃのうち、電極軸ＥＡＸ上において電極軸ＥＡＸおよび測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ３は、以下のように与えられるものとする。
Ｂ２＝ｂ２・ｃｏｓ（ω０・ｔ−θ２） ・・・（２４）
Ｂ３＝ｂ３・ｃｏｓ（ω０・ｔ−θ３） ・・・（２５）
式（２４）、式（２５）において、ｂ２，ｂ３はそれぞれ磁束密度Ｂ２，Ｂ３の振幅、ω０は角周波数、θ２は磁束密度Ｂ２とω０・ｔとの位相差（位相遅れ）、θ３は磁束密度Ｂ３とω０・ｔとの位相差である。以下、磁束密度Ｂ２を磁場Ｂ２とし、磁束密度Ｂ３を磁場Ｂ３とする。 Here, 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 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) (24)
B3 = b3 · cos (ω0 · t−θ3) (25)
In the equations (24) and (25), 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 a magnetic field B2, and the magnetic flux density B3 is defined as a magnetic field B3.

被測定流体の流速が０の場合、発生する渦電流は、磁場の変化に起因する成分のみとなり、磁場Ｂｂの変化による渦電流Ｉ１、磁場Ｂｃの変化による渦電流Ｉ２は、図６に示すような向きとなる。したがって、電極軸ＥＡＸと測定管軸ＰＡＸとを含む平面内において、磁場Ｂｂの変化によって発生する、流速と無関係な電極間起電力Ｅ１と、磁場Ｂｃの変化によって発生する、流速と無関係な電極間起電力Ｅ２は、図６に示すように互いに逆向きとなる。   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. Accordingly, in the plane including the electrode axis EAX and the measurement tube axis PAX, the inter-electrode electromotive force E1 generated by the change of the magnetic field Bb and unrelated to the flow velocity and the electrode unrelated to the flow velocity generated by the change of the magnetic field Bc. The electromotive forces E2 are opposite to each other as shown in FIG.

被測定流体の流速がＶ（Ｖ≠０）の場合、発生する渦電流には、流速０のときの渦電流Ｉ１，Ｉ２に加えて、被測定流体の流速ベクトルｖに起因する成分ｖ×Ｂｂ，ｖ×Ｂｃが発生するため、流速ベクトルｖと磁場Ｂｂによる渦電流Ｉｖ１、流速ベクトルｖと磁場Ｂｃによる渦電流Ｉｖ２は、図７に示すような向きとなる。したがって、流速ベクトルｖと磁場Ｂｂによって発生する電極間起電力Ｅｖ１、流速ベクトルｖと磁場Ｂｃによって発生する電極間起電力Ｅｖ２は、同じ向きとなる。   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.

図６、図７で説明した電極間起電力の向きを考慮すると、磁場の時間変化に起因する電極間起電力と被測定流体の流速に起因する電極間起電力とを合わせた全体の電極間起電力を複素ベクトルであらわした起電力Ｅａｃ２は、式（１０）、式（１６）、式（１７）を用いれば、式（１８）に対応して次式で表される。
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）｝ ・・・（２６） In consideration of the direction of the inter-electrode electromotive force described in FIGS. 6 and 7, the inter-electrode electromotive force due to the time change of the magnetic field and the inter-electrode electromotive force due to the flow velocity of the fluid under measurement are combined. 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)} (26)

ここで、ω０・ｔに対する磁場Ｂ２の位相遅れθ２とω０・ｔに対する磁場Ｂ３の位相遅れθ３との関係がθ３＝θ２＋Δθ３で、虚軸に対する∂Ａ／∂ｔ成分の角度θ００と実軸に対するｖ×Ｂ成分の角度θ０１との関係がθ０１＝θ００＋Δθ０１である状態を第１の励磁状態とし、この第１の励磁状態における電極間起電力Ｅａｃ２をＥａｃ２０とすると、電極間起電力Ｅａｃ２０は次式のようになる。
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 ・・・（２７） 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 (27)

また、磁場Ｂ２と磁場Ｂ３との位相差が第１の励磁状態から一定値πだけ変化し（θ３＝π＋θ２＋Δθ３）、かつθ０１＝θ００＋Δθ０１である状態を第２の励磁状態とし、この第２の励磁状態における電極間起電力Ｅａｃ２をＥａｃ２Ｒとしたときの電極間起電力Ｅａｃ２Ｒは式（２７）より次式のようになる。
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 ・・・（２８） 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 Equation (27).
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 (28)

式（２６）の右辺第１項は第１の励磁コイル３ａから発生する磁場の変化に起因する∂Ａ／∂ｔ成分、右辺第２項は第１の励磁コイル３ａから発生する磁場と流体の流速に起因するｖ×Ｂ成分、右辺第３項は第２の励磁コイル３ｂから発生する磁場の変化に起因する∂Ａ／∂ｔ成分、右辺第４項は第２の励磁コイル３ｂから発生する磁場と流体の流速に起因するｖ×Ｂ成分となる。   The first term on the right side of Equation (26) 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.

また、式（２７）の右辺第１項と式（２８）の右辺第１項とを合わせたものが、第１の励磁コイル３ａから発生する磁場の変化に起因する∂Ａ／∂ｔ成分と第２の励磁コイル３ｂから発生する磁場の変化に起因する∂Ａ／∂ｔ成分とを合わせた全ての∂Ａ／∂ｔ成分、式（２７）の右辺第２項と式（２８）の右辺第２項とを合わせたものが、第１の励磁コイル３ａから発生する磁場および流体の流速に起因するｖ×Ｂ成分と第２の励磁コイル３ｂから発生する磁場および流体の流速に起因するｖ×Ｂ成分とを合わせた全てのｖ×Ｂ成分となる。   The combination of the first term on the right side of Equation (27) and the first term on the right side of Equation (28) 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 exciting coil 3b, the second term on the right side of equation (27) and the right side of equation (28) 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.

式（２７）において、全てのｖ×Ｂ成分の流速の大きさＶに係る係数の変動要因と、全ての∂Ａ／∂ｔ成分の角周波数ω０に係る係数の変動要因とが一致しないことから分かるように、図５の電磁流量計の構成では、合成ベクトルから取り出した１つの∂Ａ／∂ｔ成分を用いて０補正とスパン補正とを行う前述の第１の基本原理が使用できない。そこで、コイル間の位相差を第１の励磁状態での位相差プラスπとすると、式（２７）における全てのｖ×Ｂ成分の流速Ｖに係る係数の変動要因と式（２８）における全ての∂Ａ／∂ｔ成分のω０に係る係数の変動要因とが等しくなり、この第２の励磁状態の∂Ａ／∂ｔ成分を取り出せば、補正が可能になる。この場合に適用できる原理を以下説明する。   In Expression (27), the coefficient variation factors related to the magnitude V of the flow velocity 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, the configuration of the electromagnetic flow meter of FIG. 5 cannot use the first basic principle described above that performs 0 correction and span correction 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 flow velocity V of all v × B components in equation (27) and all the factors in equation (28). The variation factor of the coefficient related to ω0 of the ∂A / ∂t component becomes equal, and if the 補正 A / ∂t component in the second excitation state is extracted, the correction can be performed. The principle applicable in this case will be described below.

第１の励磁コイル３ａのみに角周波数ω０の励磁電流を供給した場合に電極２ａ，２ｂで検出される電極間起電力は、第１の基本原理で既述したように、式（１９）に示す∂Ａ／∂ｔ成分のベクトルＶａ１０と式（２０）に示すｖ×Ｂ成分のベクトルＶｂ１０の合成ベクトルＶａ１０＋Ｖｂ１０に相当する。図８に、ベクトルＶａ１０とベクトルＶｂ１０と合成ベクトルＶａ１０＋Ｖｂ１０とを示す。   When the excitation current having the 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 equation (19) as described in the first basic principle. This corresponds to a combined vector Va10 + Vb10 of a vector Va10 of ∂A / ∂t component shown and a vector Vb10 of v × B component shown in equation (20). FIG. 8 shows a vector Va10, a vector Vb10, and a combined vector Va10 + Vb10.

一方、第２の励磁コイル３ｂのみに角周波数ω０の励磁電流を供給した場合に電極２ａ，２ｂで検出される電極間起電力は、以下の∂Ａ／∂ｔ成分のベクトルＶａ２０とｖ×Ｂ成分のベクトルＶｂ２０の合成ベクトルＶａ２０＋Ｖｂ２０に相当する。
Ｖａ２０＝−ｒａ・ｅｘｐ（ｊ・θａ）・Ｃ２・ω０ ・・・（２９）
Ｖｂ２０＝ ｒｂ・ｅｘｐ（ｊ・θｂ）・Ｃ２・Ｖ ・・・（３０）
図９に、ベクトルＶａ２０とベクトルＶｂ２０と合成ベクトルＶａ２０＋Ｖｂ２０とを示す。 On the other hand, when an excitation current having an angular frequency ω0 is supplied only to the second excitation coil 3b, the inter-electrode electromotive force detected by the electrodes 2a and 2b is the following vector Va20 and v × B of ∂A / ∂t components: This corresponds to the combined vector Va20 + Vb20 of the component vector Vb20.
Va20 = −ra · exp (j · θa) · C2 · ω0 (29)
Vb20 = rb · exp (j · θb) · C2 · V (30)
FIG. 9 shows a vector Va20, a vector Vb20, and a combined vector Va20 + Vb20.

ここで、∂Ａ／∂ｔ成分のベクトルＶａ２０の大きさの比例定数部分をｒａ、ベクトルＶａ２０の既知の方向をθａとすると、Ｃ２が磁場のシフトなどの「変化する要素」として与えられる。また、ｖ×Ｂ成分のベクトルＶｂ２０の大きさの既知の比例定数部分をｒｂ、ベクトルＶｂ２０の既知の方向をθｂとすると、Ｃ２が磁場のシフトなどの「変化する要素」として与えられる。したがって、∂Ａ／∂ｔ成分のベクトルＶａ２０におけるＣ２とｖ×Ｂ成分のベクトルＶｂ２０におけるＣ２は、同一の要素になる。   Here, if the proportional constant portion of the magnitude of the vector Va20 of the ∂A / ∂t component is ra and the known direction of the vector Va20 is θa, C2 is given as a “changing element” such as a magnetic field shift. Further, assuming that the known proportional constant part of the size of the vector Vb20 of the v × B component is rb and the known direction of the vector Vb20 is θb, C2 is given as a “changing element” such as a magnetic field shift. Therefore, C2 in the vector Va20 of ∂A / ∂t component and C2 in the vector Vb20 of v × B component are the same element.

第１の励磁コイル３ａから発生する磁場の変化に起因する∂Ａ／∂ｔ成分（図８）と第２の励磁コイル３ｂから発生する磁場の変化に起因する∂Ａ／∂ｔ成分（図９）とが逆方向を向いていることに注意すれば、励磁コイル３ａと３ｂの両方に角周波数ω０の励磁電流を供給した場合の電極間起電力は、以下の∂Ａ／∂ｔ成分のベクトルＶａｓ０とｖ×Ｂ成分のベクトルＶｂｓ０の合成ベクトルＶａｓ０＋Ｖｂｓ０に相当することが分かる。
Ｖａｓ０＝Ｖａ１０＋Ｖａ２０
＝ｒａ・ｅｘｐ（ｊ・θａ）・（Ｃ１−Ｃ２）・ω０ ・・・（３１）
Ｖｂｓ０＝Ｖｂ１０＋Ｖｂ２０
＝ｒｂ・ｅｘｐ（ｊ・θｂ）・（Ｃ１＋Ｃ２）・Ｖ ・・・（３２） ∂A / ∂t component (FIG. 8) resulting from the change of the magnetic field generated from the first excitation coil 3a (FIG. 8) and ∂A / ∂t component (FIG. 9) resulting from the change of the magnetic field generated from the second excitation coil 3b. 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) · (C1-C2) · ω0 (31)
Vbs0 = Vb10 + Vb20
= Rb · exp (j · θb) · (C1 + C2) · V (32)

図１０に、ベクトルＶａｓ０とベクトルＶｂｓ０と合成ベクトルＶａｓ０＋Ｖｂｓ０とを示す。式（３２）に示すベクトルＶｂｓ０の流速の大きさＶにかかる係数の中で（Ｃ１＋Ｃ２）が、スパン変動要因として与えられる。また、流速の大きさＶが０の時は、ベクトルＶａｓ０が変動することにより、合成ベクトルの大きさが変動する（すなわち、０点が変動する）。   FIG. 10 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 (32), (C1 + C2) is given as a span variation factor. In addition, when the magnitude V of the flow velocity is 0, the magnitude of the combined vector varies (that is, the zero point varies) due to the variation of the vector Vas0.

図１１は、０補正及びスパン補正の対象となる合成ベクトルから第１の∂Ａ／∂ｔ成分を抽出する処理を複素ベクトル表現した図である。合成ベクトルから∂Ａ／∂ｔ成分を抽出する方法としては、複数の励磁周波数による磁場を被測定流体に印加し、電極間起電力に含まれる複数の周波数成分の出力差を利用して∂Ａ／∂ｔ成分を抽出する方法を用いる。第１の基本原理と同様に、電極間起電力から直接求めることができる複素ベクトルは合成ベクトルＶａｓ０＋Ｖｂｓ０であり、ベクトルＶａｓ０，Ｖｂｓ０が直接的に計測できるわけではない。そこで、∂Ａ／∂ｔ成分の大きさは励磁周波数ωに比例し、ｖ×Ｂ成分は励磁周波数ωに依存しないことに着眼する。具体的には、ある角周波数ω０で励磁したときの合成ベクトルと別の角周波数ω２で励磁したときの合成ベクトルとの差を求める。この差は、∂Ａ／∂ｔ成分の大きさの変化分だけを与えるベクトルになるので、この変化分から∂Ａ／∂ｔ成分を抽出することができる。   FIG. 11 is a complex vector representation of the process of extracting the first ∂A / ∂t component from the combined vector to be subjected to 0 correction and span correction. As a method of extracting the ∂A / ∂t component from the combined vector, a magnetic field having a plurality of excitation frequencies is applied to the fluid to be measured, and 出力 A is obtained by using the output difference of the plurality of frequency components included in the inter-electrode electromotive force. A method for extracting the ∂t component is used. Similar to the first basic principle, the complex vector that can be directly obtained from the electromotive force between the electrodes is the combined vector Vas0 + Vbs0, and the vectors Vas0 and Vbs0 cannot be directly measured. Therefore, it is noted that the magnitude of the ∂A / ∂t component is proportional to the excitation frequency ω, and the v × B component does not depend on the excitation frequency ω. Specifically, the difference between the combined vector when excited at a certain angular frequency ω0 and the 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 ∂A / ∂t component, the ∂A / ∂t component can be extracted from this change.

励磁角周波数をω２としたときのｖ×Ｂ成分のベクトルは式（３２）に示したベクトルＶｂｓ０と同じである。一方、励磁角周波数をω２としたときの∂Ａ／∂ｔ成分のベクトルＶａｓ２は、式（３１）においてω０をω２で置き換えたものとなり、次式のようになる。
Ｖａｓ２＝ｒａ・ｅｘｐ（ｊ・θａ）・（Ｃ１−Ｃ２）・ω２ ・・・（３３） The vector of v × B component when the excitation angular frequency is ω2 is the same as the vector Vbs0 shown in Expression (32). On the other hand, the vector Vas2 of the ∂A / ∂t component when the excitation angular frequency is ω2 is obtained by replacing ω0 with ω2 in the equation (31), and is represented by the following equation.
Vas2 = ra · exp (j · θa) · (C1-C2) · ω2 (33)

電極間起電力に含まれる角周波数ω０の成分（合成ベクトルＶａｓ０＋Ｖｂｓ０）と角周波数ω２の成分（合成ベクトルＶａｓ２＋Ｖｂｓ０）との差分を求めると、ｖ×Ｂ成分がキャンセルされ、求めた差分をω０／（ω０−ω２）倍したものはベクトルＶａｓ０と同じになる。よって、合成ベクトルＶａｓ０＋Ｖｂｓ０中の∂Ａ／∂ｔ成分のベクトルＶａｓ０を異なる周波数成分の出力差を利用することにより抽出することができる。ここで、抽出した∂Ａ／∂ｔ成分を第１の∂Ａ／∂ｔ成分とする。   When the difference between the component of the angular frequency ω0 (synthetic vector Vas0 + Vbs0) and the component of the angular frequency ω2 (synthetic vector Vas2 + Vbs0) included in the inter-electrode electromotive force is obtained, the v × B component is canceled, and the obtained difference is ω0 / ( The product multiplied by ω0−ω2) is the same as the vector Vas0. Therefore, the vector Vas0 of ∂A / ∂t component in the combined vector Vas0 + Vbs0 can be extracted by using the output difference of different frequency components. Here, let the extracted ∂A / ∂t component be the first ∂A / ∂t component.

図１２は、合成ベクトルＶａｓ０＋Ｖｂｓ０からｖ×Ｂ成分のベクトルＶｂｓ０を抽出する処理を複素ベクトル表現した図である。合成ベクトルＶａｓ０＋Ｖｂｓ０から第１の∂Ａ／∂ｔ成分のベクトルＶａｓ０を引くことにより、式（３２）に示したｖ×Ｂ成分のベクトルＶｂｓ０を抽出することができる。式（３２）より、ｖ×Ｂ成分のベクトルＶｂｓ０には、角周波数ω０，ω２に関連する項（０点変動要因）が含まれていないことが分かる。   FIG. 12 is a diagram in which the process of extracting the vector Vbs0 of the v × B component from the combined vector Vas0 + Vbs0 is expressed as a complex vector. By subtracting the vector Vas0 of the first ∂A / ∂t component from the combined vector Vas0 + Vbs0, the vector Vbs0 of the v × B component shown in Expression (32) can be extracted. From the equation (32), it can be seen that the vector Vbs0 of the v × B component does not include a term (zero point variation factor) related to the angular frequencies ω0 and ω2.

合成ベクトルＶａｓ０＋Ｖｂｓ０中の∂Ａ／∂ｔ成分のベクトルＶａｓ０におけるスパン変動要因（Ｃ１−Ｃ２）とｖ×Ｂ成分のベクトルＶｂｓ０におけるスパン変動要因（Ｃ１＋Ｃ２）とは異なる値となる。したがって、第１の∂Ａ／∂ｔ成分によりｖ×Ｂ成分の正規化を行っても次式の通り、スパン変動要因（Ｃ１−Ｃ２）／（Ｃ１＋Ｃ２）が残り、スパン変動要因を除去することはできない。
Ｖｂｓ０／Ｖａｓ０＝（ｒｂ／ｒａ）・ｅｘｐ｛ｊ・（θｂ−θａ）｝
・｛（Ｃ１−Ｃ２）／（Ｃ１＋Ｃ２）｝・（Ｖ／ω）
・・・（３４） The span variation factor (C1-C2) in the vector Vas0 of the ∂A / ∂t component in the combined vector Vas0 + Vbs0 and the span variation factor (C1 + C2) in the vector Vbs0 of the v × B component are different values. Therefore, even if the v × B component is normalized by the first ∂A / ∂t component, the span variation factor (C1-C2) / (C1 + C2) remains as shown in the following equation, and the span variation factor is removed. I can't.
Vbs0 / Vas0 = (rb / ra) · exp {j · (θb−θa)}
・ {(C1-C2) / (C1 + C2)} (V / ω)
... (34)

そのため、ｖ×Ｂ成分の変動要因と同じスパン変動要因（Ｃ１＋Ｃ２）を含む第２の∂Ａ／∂ｔ成分を抽出する必要がある。このような第２の∂Ａ／∂ｔ成分を抽出するために、第１の励磁コイル３ａから発生する磁場と第２の励磁コイル３ｂから発生する磁場との位相差がΔθ３である第１の励磁状態から位相差がΔθ３＋πである第２の励磁状態に変化させると、スパン変動要因Ｃ２が反転することを利用する。つまり、第１の励磁状態に対して位相差を＋π変化させた第２の励磁状態の位相条件で第２の励磁コイル３ｂのみを角周波数ω０で励磁した場合に電極２ａ，２ｂで検出される合成ベクトルは、第１の励磁状態で検出した合成ベクトル（図９）に対して反転し、以下の∂Ａ／∂ｔ成分のベクトルＶａ２０Ｒとｖ×Ｂ成分のベクトルＶｂ２０Ｒの合成ベクトルＶａ２０Ｒ＋Ｖｂ２０Ｒに相当する。
Ｖａ２０Ｒ＝ｒａ・ｅｘｐ（ｊ・θａ）・Ｃ２・ω０ ・・・（３５）
Ｖｂ２０Ｒ＝−ｒｂ・ｅｘｐ（ｊ・θｂ）・Ｃ２・Ｖ ・・・（３６）
図１３に、ベクトルＶａ２０ＲとベクトルＶｂ２０Ｒと合成ベクトルＶａ２０Ｒ＋Ｖｂ２０Ｒとを示す。 Therefore, it is necessary to extract the second ∂A / ∂t component including the same span variation factor (C1 + C2) as the variation factor of the v × B component. In order to extract such a second ∂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 the span variation factor C2 is reversed 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. 9) detected in the first excitation state, and corresponds to a combined vector Va20R + Vb20R of the following vector A20 / Vt component Va20R and v × B component vector Vb20R. .
Va20R = ra · exp (j · θa) · C2 · ω0 (35)
Vb20R = −rb · exp (j · θb) · C2 · V (36)
FIG. 13 shows a vector Va20R, a vector Vb20R, and a combined vector Va20R + Vb20R.

角周波数ω０の第１の励磁電流を第１の励磁コイル３ａに供給し、第１の励磁電流との位相差がΔθ３＋πで角周波数がω０の第２の励磁電流を第２の励磁コイル３ｂに供給した場合の電極間起電力は、以下の∂Ａ／∂ｔ成分のベクトルＶａｓ０Ｒとｖ×Ｂ成分のベクトルＶｂｓ０Ｒの合成ベクトルＶａｓ０Ｒ＋Ｖｂｓ０Ｒに相当する。
Ｖａｓ０Ｒ＝Ｖａ１０＋Ｖａ２０Ｒ
＝ｒａ・ｅｘｐ（ｊ・θａ）・（Ｃ１＋Ｃ２）・ω０ ・・・（３７）
Ｖｂｓ０Ｒ＝Ｖｂ１０＋Ｖｂ２０Ｒ
＝ｒｂ・ｅｘｐ（ｊ・θｂ）・（Ｃ１−Ｃ２）・Ｖ ・・・（３８）
図１４に、ベクトルＶａｓ０ＲとベクトルＶｂｓ０Ｒと合成ベクトルＶａｓ０Ｒ＋Ｖｂｓ０Ｒとを示す。 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) · (C1 + C2) · ω0 (37)
Vbs0R = Vb10 + Vb20R
= Rb · exp (j · θb) · (C1-C2) · V (38)
FIG. 14 shows a vector Vas0R, a vector Vbs0R, and a combined vector Vas0R + Vbs0R.

∂Ａ／∂ｔ成分のベクトルＶａｓ０Ｒにおけるスパン変動要因は、前述のｖ×Ｂ成分のベクトルＶｂｓ０のスパン変動要因（Ｃ１＋Ｃ２）と等しい。したがって、第２の∂Ａ／∂ｔ成分としてＶａｓ０Ｒを抽出すれば、ベクトルＶｂｓ０の正規化が可能になる。第２の∂Ａ／∂ｔ成分のベクトルＶａｓ０Ｒを抽出する方法としては、以下の２つの方法がある。第１の抽出方法は、第１の∂Ａ／∂ｔ成分を抽出する際にも使用した方法、すなわち複数の励磁周波数による磁場を被測定流体に印加し、電極間起電力に含まれる複数の周波数成分の出力差を利用して∂Ａ／∂ｔ成分を抽出する方法である。第２の抽出方法は、Ｖａｓ０Ｒ≫Ｖｂｓ０Ｒと近似できる場合に、Ｖｂｓ０Ｒ≒０として、近似的に第２の∂Ａ／∂ｔ成分のベクトルＶａｓ０Ｒを抽出する方法である。   The span variation factor in the vector Vas0R of the ∂A / ∂t component is equal to the span variation factor (C1 + C2) of the vector Vbs0 of the v × B component. Therefore, if Vas0R is extracted as the second ∂A / ∂t component, the vector Vbs0 can be normalized. There are the following two methods for extracting the second ∂A / ∂t component vector Vas0R. The first extraction method is a method that is also used when extracting the first ∂A / ∂t component, that is, a magnetic field having a plurality of excitation frequencies is applied to the fluid to be measured, and a plurality of electromotive forces included in the interelectrode electromotive force are included. This is a method of extracting the ∂A / ∂t component using the output difference of the frequency components. The second extraction method is a method of approximately extracting the second ∂A / ∂t component vector Vas0R as Vbs0R≈0 when it can be approximated as Vas0R >> Vbs0R.

図１５は、第１の抽出方法により合成ベクトルＶａｓ０Ｒ＋Ｖｂｓ０Ｒから第２の∂Ａ／∂ｔ成分を抽出する処理を複素ベクトル表現した図である。励磁角周波数をω２としたときのｖ×Ｂ成分のベクトルは式（３８）に示したベクトルＶｂｓ０Ｒと同じである。一方、励磁角周波数をω２としたときの∂Ａ／∂ｔ成分のベクトルＶａｓ２Ｒは、式（３７）においてω０をω２で置き換えたものとなり、次式のようになる。
Ｖａｓ２Ｒ＝ｒａ・ｅｘｐ（ｊ・θａ）・（Ｃ１＋Ｃ２）・ω２ ・・・（３９） FIG. 15 is a diagram representing complex vector representation of the process of extracting the second ∂A / ∂t component from the combined vector Vas0R + Vbs0R by the first extraction method. The vector of the v × B component when the excitation angular frequency is ω2 is the same as the vector Vbs0R shown in Expression (38). On the other hand, the vector Vas2R of the ∂A / ∂t component when the excitation angular frequency is ω2 is obtained by replacing ω0 with ω2 in equation (37), and is expressed by the following equation.
Vas2R = ra · exp (j · θa) · (C1 + C2) · ω2 (39)

第２の励磁状態で検出した電極間起電力に含まれる角周波数ω０の成分（合成ベクトルＶａｓ０Ｒ＋Ｖｂｓ０Ｒ）と角周波数ω２の成分（合成ベクトルＶａｓ２Ｒ＋Ｖｂｓ０Ｒ）との差分を求めると、ｖ×Ｂ成分がキャンセルされ、求めた差分をω０／（ω０−ω２）倍したものはベクトルＶａｓ０Ｒと同じになる。よって、合成ベクトルＶａｓ０Ｒ＋Ｖｂｓ０Ｒから第２の∂Ａ／∂ｔ成分のベクトルＶａｓ０Ｒを異なる周波数成分の出力差を利用することにより抽出することができる。   When the difference between the angular frequency ω0 component (synthetic vector Vas0R + Vbs0R) and the angular frequency ω2 component (synthetic vector Vas2R + Vbs0R) included in the interelectrode electromotive force detected in the second excitation state is obtained, the v × B component is canceled. The difference obtained by multiplying the obtained difference by ω0 / (ω0−ω2) is the same as the vector Vas0R. Therefore, the vector Vas0R of the second ∂A / ∂t component can be extracted from the combined vector Vas0R + Vbs0R by using the output difference of different frequency components.

図１６は、ｖ×Ｂ成分のベクトルＶｂｓ０を第２の∂Ａ／∂ｔ成分のベクトルＶａｓ０Ｒにより正規化する処理を複素ベクトル表現した図である。抽出した第２の∂Ａ／∂ｔ成分のベクトルＶａｓ０Ｒにより、ｖ×Ｂ成分のベクトルＶｂｓ０を正規化する。正規化したｖ×Ｂ成分をω０倍した正規化ｖ×Ｂ成分をＶｎｂｓ０とすると、Ｖｎｂｓ０は次式で表される。
Ｖｎｂｓ０＝｛Ｖｂｓ０／Ｖａｓ０Ｒ｝・ω０
＝（ｒｂ／ｒａ）・ｅｘｐ｛ｊ・（θｂ−θａ）｝・Ｖ ・・・（４０） FIG. 16 is a diagram in which the process of normalizing the v × B component vector Vbs0 with the second ∂A / ∂t component vector Vas0R is expressed as a complex vector. The v × B component vector Vbs0 is normalized by the extracted second ∂A / ∂t component vector Vas0R. Assuming that a normalized v × B component obtained by multiplying the normalized v × B component by ω0 is Vnbs0, Vnbs0 is expressed by the following equation.
Vnbs0 = {Vbs0 / Vas0R} · ω0
= (Rb / ra) · exp {j · (θb−θa)} · V (40)

なお、正規化したｖ×Ｂ成分をω０倍する理由は、流速の大きさＶにかかる係数（スパン）からω０を取り除くためである。式（４０）によれば、正規化ｖ×Ｂ成分Ｖｎｂｓ０のＶにかかる係数から変動要因（Ｃ１＋Ｃ２）が消去され、スパンが補正されていることが分かる。式（４０）より、被測定流体の流速の大きさＶを以下のように算出することができる。
Ｖ＝｜Ｖｎｂｓ０／［（ｒｂ／ｒａ）・ｅｘｐ｛ｊ・（θｂ−θａ）｝］｜
＝｜Ｖｎｂｓ０｜／（ｒｂ／ｒａ） ・・・（４１） The reason why the normalized v × B component is multiplied by ω0 is to remove ω0 from the coefficient (span) related to the magnitude V of the flow velocity. According to the equation (40), it can be seen that the variation factor (C1 + C2) is eliminated from the coefficient applied to V of the normalized v × B component Vnbs0, and the span is corrected. From equation (40), 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) (41)

次に、第２の基本原理に基づく電磁流量計のうち、１個の励磁コイルと２対の電極とを有する電磁流量計の原理を図１７を用いて説明する。図１７の電磁流量計は、測定管１と、被測定流体に印加される磁場および測定管軸ＰＡＸの双方と直交し、かつ被測定流体と接触するように測定管１に対向配置され、前記磁場と被測定流体の流れとによって生じた起電力を検出する第１の電極２ａ，２ｂおよび第２の電極２ｃ，２ｄと、測定管軸ＰＡＸと直交する、第１の電極２ａ，２ｂを含む平面をＰＬＮ１、測定管軸ＰＡＸと直交する、第２の電極２ｃ，２ｄを含む平面をＰＬＮ２としたとき、平面ＰＬＮ１を境とする測定管１の前後で非対称な、時間変化する磁場を被測定流体に印加すると同時に、平面ＰＬＮ２を境とする測定管１の前後で非対称な、時間変化する磁場を被測定流体に印加する励磁コイル３とを有する。   Next, the principle of an electromagnetic flowmeter having one excitation coil and two pairs of electrodes among the electromagnetic flowmeters based on the second basic principle will be described with reference to FIG. The electromagnetic flow meter of FIG. 17 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.

第１の電極２ａ，２ｂは、励磁コイル３の軸を含む、測定管軸ＰＡＸの方向と垂直な平面ＰＬＮ３から例えば上流側にオフセット距離ｄ３だけ離れた位置に配設される。第２の電極２ｃ，２ｄは、平面ＰＬＮ３から例えば下流側にオフセット距離ｄ４だけ離れた位置に配設され、平面ＰＬＮ３を挟んで第１の電極２ａ，２ｂと対向するように配設される。   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 to face the first electrodes 2a and 2b across the plane PLN3.

第２の電極２ｃ，２ｄを平面ＰＬＮ３を挟んで第１の電極２ａ，２ｂと対向するように配設した場合、第１の電極２ａ，２ｂで検出される電極間起電力のうち、励磁コイル３から発生する磁場および流体の流速に起因するｖ×Ｂ成分と、第２の電極２ｃ，２ｄで検出される電極間起電力のうち、励磁コイル３から発生する磁場および流体の流速に起因するｖ×Ｂ成分とは、同じ方向になる。一方、第１の電極２ａ，２ｂで検出される電極間起電力のうち、励磁コイル３から発生する磁場の変化に起因する∂Ａ／∂ｔ成分と、第２の電極２ｃ，２ｄで検出される電極間起電力のうち、励磁コイル３から発生する磁場の変化に起因する∂Ａ／∂ｔ成分とは逆向きになる。そのため、第１の電極２ａ，２ｂで検出される∂Ａ／∂ｔ成分およびｖ×Ｂ成分と、第２の電極２ｃ，２ｄで検出される∂Ａ／∂ｔ成分およびｖ×Ｂ成分とを合わせた全ての合成ベクトルにおけるｖ×Ｂ成分の変動要因と∂Ａ／∂ｔ成分の変動要因は、等しくならないことを考慮して補正を行う必要がある。   When the second electrodes 2c and 2d are disposed so as to face the first electrodes 2a and 2b across the plane PLN3, the excitation 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, out of the inter-electrode electromotive force detected by the first electrodes 2a and 2b, the ∂A / ∂t component caused by the change of 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.

ここで、励磁コイル３から発生する磁場Ｂｄのうち、電極２ａ，２ｂ間を結ぶ電極軸ＥＡＸ１上において電極軸ＥＡＸ１および測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ４と、励磁コイル３から発生する磁場Ｂｄのうち、電極２ｃ，２ｄ間を結ぶ電極軸ＥＡＸ２上において電極軸ＥＡＸ２および測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ５は、以下のように与えられるものとする。
Ｂ４＝ｂ４・ｃｏｓ（ω０・ｔ−θ４） ・・・（４２）
Ｂ５＝ｂ５・ｃｏｓ（ω０・ｔ−θ５） ・・・（４３） Here, 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 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) (42)
B5 = b5 · cos (ω0 · t−θ5) (43)

但し、Ｂ４、Ｂ５は１つの励磁コイル３から発生しているので、ｂ４とｂ５、θ４とθ５は互いに関係があり、独立変数ではない。式（４２）、式（４３）において、ｂ４，ｂ５はそれぞれ磁束密度Ｂ４，Ｂ５の振幅、ω０は角周波数、θ４は磁束密度Ｂ４とω０・ｔとの位相差（位相遅れ）、θ５は磁束密度Ｂ５とω０・ｔとの位相差である。以下、磁束密度Ｂ４を磁場Ｂ４とし、磁束密度Ｂ５を磁場Ｂ５とする。   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 (42) and (43), 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.

被測定流体の流速が０の場合、発生する渦電流は、磁場の変化に起因する成分のみとなり、磁場Ｂｄの変化による渦電流Ｉは、図１８に示すような向きとなる。したがって、電極軸ＥＡＸ１と測定管軸ＰＡＸとを含む平面内において磁場Ｂｄの変化によって発生する電極２ａ，２ｂ間の、流速と無関係な起電力Ｅ１と、電極軸ＥＡＸ２と測定管軸ＰＡＸとを含む平面内において磁場Ｂｄの変化によって発生する電極２ｃ，２ｄ間の、流速と無関係な起電力Ｅ２とは、図１８に示すように互いに逆向きとなる。   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 Bd has a direction as shown in FIG. Accordingly, 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, the electrode axis EAX2, and the measurement tube axis PAX is 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. 18 as shown in FIG.

被測定流体の流速がＶ（Ｖ≠０）の場合、発生する渦電流には、流速０のときの渦電流Ｉに加えて、被測定流体の流速ベクトルｖに起因する成分ｖ×Ｂｄが発生するため、流速ベクトルｖと磁場Ｂｄによる渦電流Ｉｖは、図１９に示すような向きとなる。したがって、流速ベクトルｖと磁場Ｂｄによって発生する電極２ａ，２ｂの起電力Ｅｖ１と、流速ベクトルｖと磁場Ｂｄによって発生する電極２ｃ，２ｄ間の起電力Ｅｖ２とは、同じ向きとなる。   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.

図１８、図１９で説明した電極間起電力の向きを考慮すると、磁場の時間変化に起因する電極間起電力を複素ベクトルに変換した起電力と被測定流体の流速に起因する電極間起電力を複素ベクトルに変換した起電力とを合わせた、電極２ａ，２ｂ間の第１の電極間起電力Ｅａｃ３１は、式（１０）、式（１６）、式（１７）を用いれば、式（１８）に対応して次式で表される。
Ｅａｃ３１＝ｒｋ・ω０・ｂ４・ｅｘｐ｛ｊ・（π／２＋θ４＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ４・ｅｘｐ｛ｊ・（θ４＋θ０１）｝ ・・・（４４） In consideration of the direction of the interelectrode electromotive force described in FIGS. 18 and 19, the electromotive force generated 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 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 expressed by the following equation.
Eac31 = rk · ω0 · b4 · exp {j · (π / 2 + θ4 + θ00)}
+ Γ · rk · V · b4 · exp {j · (θ4 + θ01)} (44)

また、磁場の時間変化に起因する電極間起電力を複素ベクトルに変換した起電力と被測定流体の流速に起因する電極間起電力を複素ベクトルに変換した起電力とを合わせた、電極２ｃ，２ｄ間の第２の電極間起電力Ｅａｃ３２は、式（１０）、式（１６）、式（１７）を用いれば、式（１８）に対応して次式で表される。
Ｅａｃ３２＝ｒｋ・ω０・ｂ５・ｅｘｐ｛ｊ・（−π／２＋θ５＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ５・ｅｘｐ｛ｊ・（θ５＋θ０１）｝ ・・・（４５） 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)} (45)

ここで、ω０・ｔに対する磁場Ｂ４の位相遅れθ４とω０・ｔに対する磁場Ｂ５の位相遅れθ５との関係をθ５＝θ４＋Δθ５とし、虚軸に対する∂Ａ／∂ｔ成分の角度θ００と実軸に対するｖ×Ｂ成分の角度θ０１との関係をθ０１＝θ００＋Δθ０１とする。式（４４）にθ５＝θ４＋Δθ５、θ０１＝θ００＋Δθ０１を代入したときの第１の電極間起電力Ｅａｃ３１と式（４５）にθ５＝θ４＋Δθ５、θ０１＝θ００＋Δθ０１を代入したときの第２の電極間起電力Ｅａｃ３２との和をＥａｃ３ｓとすれば、起電力和Ｅａｃ３ｓは次式で表される。
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 ・・・（４６） 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 xB component is θ01 = θ00 + Δθ01. The first inter-electrode electromotive force Eac31 when θ5 = θ4 + Δθ5 and θ01 = θ00 + Δθ01 are substituted into Equation (44) and the second inter-electrode electromotive force when θ5 = θ4 + Δθ5 and θ01 = θ00 + Δθ01 are substituted into Equation (45) 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 (46)

また、式（４４）にθ５＝θ４＋Δθ５、θ０１＝θ００＋Δθ０１を代入したときの第１の電極間起電力Ｅａｃ３１と式（４５）にθ５＝θ４＋Δθ５、θ０１＝θ００＋Δθ０１を代入したときの第２の電極間起電力Ｅａｃ３２との差をＥａｃ３ｄとすれば、起電力差Ｅａｃ３ｄは次式で表される。
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 ・・・（４７） Further, the first inter-electrode electromotive force Eac31 when θ5 = θ4 + Δθ5 and θ01 = θ00 + Δθ01 are substituted into the equation (44) and the second electrode interval when θ5 = θ4 + Δθ5 and θ01 = θ00 + Δθ01 are substituted into the equation (45). 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 (47)

式（４４）の右辺第１項は第１の電極２ａ，２ｂで検出される∂Ａ／∂ｔ成分、式（４４）の右辺第２項は第１の電極２ａ，２ｂで検出されるｖ×Ｂ成分となる。式（４５）の右辺第１項は第２の電極２ｃ，２ｄで検出される∂Ａ／∂ｔ成分、式（４５）の右辺第２項は第２の電極２ｃ，２ｄで検出されるｖ×Ｂ成分となる。
式（４６）の右辺第１項は起電力和Ｅａｃ３ｓの中の∂Ａ／∂ｔ成分、式（４６）の右辺第２項は起電力和Ｅａｃ３ｓの中のｖ×Ｂ成分となる。式（４７）の右辺第１項は起電力差Ｅａｃ３ｄの中の∂Ａ／∂ｔ成分、式（４７）の右辺第２項は起電力差Ｅａｃ３ｄの中のｖ×Ｂ成分となる。 The first term on the right side of Equation (44) is the ∂A / ∂t component detected by the first electrodes 2a and 2b, and the second term on the right side of Equation (44) is v detected by the first electrodes 2a and 2b. × B component. The first term on the right side of Equation (45) is the ∂A / ∂t component detected by the second electrodes 2c and 2d, and the second term on the right side of Equation (45) is v detected by the second electrodes 2c and 2d. × B component.
The first term on the right side of Equation (46) is the ∂A / ∂t component in the electromotive force sum Eac3s, and the second term on the right side of Equation (46) is the v × B component in the electromotive force sum Eac3s. The first term on the right side of Equation (47) is the ∂A / ∂t component in the electromotive force difference Eac3d, and the second term on the right side of Equation (47) is the v × B component in the electromotive force difference Eac3d.

式（４６）において、起電力和Ｅａｃ３ｓの中のｖ×Ｂ成分の流速の大きさＶに係る係数の変動要因と、起電力和Ｅａｃ３ｓの中の∂Ａ／∂ｔ成分の角周波数ω０に係る係数の変動要因とが一致しないことから分かるように、図１７の電磁流量計の構成では、合成ベクトルから取り出した１つの∂Ａ／∂ｔ成分を用いて０補正とスパン補正とを行う前述の第１の基本原理が使用できない。   In Expression (46), the coefficient variation factor related 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, the configuration of the electromagnetic flow meter of FIG. 17 performs the zero correction and the span correction using one ∂A / ∂t component extracted from the combined vector. The first basic principle cannot be used.

そこで、式（４６）に示した起電力和Ｅａｃ３ｓの中のｖ×Ｂ成分の流速の大きさＶに係る係数の変動要因と、式（４７）に示した起電力差Ｅａｃ３ｄの中の∂Ａ／∂ｔ成分の角周波数ω０に係る係数の変動要因とが等しくなることを利用して、起電力差Ｅａｃ３ｄの中の∂Ａ／∂ｔ成分を取り出せば、０補正とスパン補正が可能になり、図５の電磁流量計と同じ原理を補正に適用できる。   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 (46) and ∂A in the electromotive force difference Eac3d shown in Expression (47). Using the fact that the variation factor of the coefficient related to the angular frequency ω0 of the / ∂t component becomes equal, if the ∂A / ∂t component in the electromotive force difference Eac3d is extracted, 0 correction and span correction can be performed. The same principle as the electromagnetic flow meter of FIG. 5 can be applied to the correction.

図５の電磁流量計の場合で説明した原理の内容を図１７の電磁流量計に対応させるには、第１の励磁コイル３ａから発生する磁場の影響に起因する起電力を第１の電極２ａ，２ｂで検出される起電力Ｅａｃ３１に置き換え、第２の励磁コイル３ｂから発生する磁場の影響に起因する起電力を第２の電極２ｃ，２ｄで検出される起電力Ｅａｃ３２に置き換え、第１の励磁状態で検出される起電力を起電力和Ｅａｃ３ｓに置き換え、第２の励磁状態で検出される起電力を起電力差Ｅａｃ３ｄに置き換えればよい。   In order to make the content of the principle explained in the case of the electromagnetic flow meter of FIG. 5 correspond to the electromagnetic flow meter of FIG. 17, the electromotive force due to the influence of the magnetic field generated from the first exciting coil 3a is changed to the first electrode 2a. The electromotive force Eac31 detected by the second excitation coil 3b 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 is replaced by the first electromotive force Eac31. The electromotive force detected in the excitation state may be replaced with the electromotive force sum Eac3s, and the electromotive force detected in the second excitation state may be replaced with the electromotive force difference Eac3d.

［第１の実施の形態］
次に、本発明の第１の実施の形態について説明する。本実施の形態は、前述の第１の基本原理を用いるものである。本実施の形態の電磁流量計は１個の励磁コイルと１対の電極とを有するものであり、信号処理系を除く構成は図３０に示した従来の電磁流量計と同様であるので、図３０の符号を用いて本実施の形態の原理を説明する。 [First Embodiment]
Next, a first embodiment of the present invention will be described. This embodiment uses the first basic principle described above. The electromagnetic flow meter of the present embodiment has one exciting coil and a pair of electrodes, and the configuration excluding the signal processing system is the same as that of the conventional electromagnetic flow meter shown in FIG. The principle of the present embodiment will be described using reference numeral 30.

図３０において、励磁コイル３から発生する磁場のうち、電極２ａ，２ｂ間を結ぶ電極軸ＥＡＸ上において電極軸ＥＡＸおよび測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ６は、以下のように与えられるものとする。
Ｂ６＝ｂ６・ｃｏｓ（ω０・ｔ−θ６）＋ｂ６・ｃｏｓ（ω２・ｔ−θ６）
・・・（４８）
式（４８）において、ω０，ω２は異なる角周波数、ｂ６は磁束密度Ｂ６の角周波数ω０の成分の振幅および角周波数ω２の成分の振幅、θ６は角周波数ω０の成分とω０・ｔとの位相差（位相遅れ）および角周波数ω２の成分とω２・ｔとの位相差である。以下、磁束密度Ｂ６を磁場Ｂ６とする。 In FIG. 30, the magnetic field component (magnetic flux density) B6 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX connecting the electrodes 2a and 2b out of the magnetic field generated from the exciting coil 3 is Shall be given as follows.
B6 = b6 · cos (ω0 · t−θ6) + b6 · cos (ω2 · t−θ6)
... (48)
In equation (48), 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 θ6 is the order of the angular frequency ω0 component and ω0 · t. This is the phase difference (phase delay) and the phase difference between the component of the angular frequency ω2 and ω2 · t. Hereinafter, the magnetic flux density B6 is referred to as a magnetic field B6.

このとき、磁場の時間変化に起因する電極間起電力を複素ベクトルに変換した起電力と流体の流速に起因する電極間起電力を複素ベクトルに変換した起電力とを合わせた全体の電極間起電力のうち、角周波数ω０の成分の起電力をＥ１０ｃとすると、電極間起電力Ｅ１０ｃは式（１８）と同様の次式で表される。
Ｅ１０ｃ＝ｒｋ・ω０・ｂ６・ｅｘｐ｛ｊ・（π／２＋θ６＋θ００）｝
＋γ・ｒｋ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ０１）｝ ・・・（４９） At this time, the entire inter-electrode electromotive force obtained by combining the electromotive force obtained by converting the inter-electrode electromotive force caused by the temporal change of the magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force caused by the fluid flow velocity into the complex vector. If the electromotive force of the component of the angular frequency ω0 in the electric power is E10c, the interelectrode electromotive force E10c is expressed by the following equation similar to the equation (18).
E10c = rk · ω0 · b6 · exp {j · (π / 2 + θ6 + θ00)}
+ Γ · rk · b6 · exp {j · (θ6 + θ01)} (49)

また、磁場の時間変化に起因する電極間起電力を複素ベクトルに変換した起電力と流体の流速に起因する電極間起電力を複素ベクトルに変換した起電力とを合わせた全体の電極間起電力のうち、角周波数ω２の成分の起電力をＥ１２ｃとすると、電極間起電力Ｅ１２ｃは式（１８）と同様の次式で表される。
Ｅ１２ｃ＝ｒｋ・ω２・ｂ６・ｅｘｐ｛ｊ・（π／２＋θ６＋θ００）｝
＋γ・ｒｋ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ０１）｝ ・・・（５０） Also, the total inter-electrode electromotive force that combines the 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 fluid flow velocity into the complex vector. Among them, when the electromotive force of the component of the angular frequency ω2 is E12c, the interelectrode electromotive force E12c is expressed by the following equation similar to the equation (18).
E12c = rk · ω2 · b6 · exp {j · (π / 2 + θ6 + θ00)}
+ Γ · rk · b6 · exp {j · (θ6 + θ01)} (50)

ここで、虚軸に対する∂Ａ／∂ｔ成分の角度θ００と実軸に対するｖ×Ｂ成分の角度θ０１との関係をθ０１＝θ００＋Δθ０１とし、式（４９）にθ０１＝θ００＋Δθ０１を代入したときの電極間起電力Ｅ１０ｃをＥ１０とすると、Ｅ１０は次式で表される。
Ｅ１０＝ｒｋ・ω０・ｂ６・ｅｘｐ｛ｊ・（π／２＋θ６＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ００＋Δθ０１）｝
＝ｒｋ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ００）｝
・｛ω０・ｅｘｐ（ｊ・π／２）＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）｝
・・・（５１） Here, 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 between the electrodes when θ01 = θ00 + Δθ01 is substituted into Equation (49) When the electromotive force E10c is E10, E10 is expressed by the following equation.
E10 = rk · ω0 · b6 · exp {j · (π / 2 + θ6 + θ00)}
+ Γ · rk · V · b6 · exp {j · (θ6 + θ00 + Δθ01)}
= Rk · b6 · exp {j · (θ6 + θ00)}
{Ω0 · exp (j · π / 2) + γ · V · exp (j · Δθ01)}
... (51)

同様に、式（５０）にθ０１＝θ００＋Δθ０１を代入したときの電極間起電力Ｅ１２ｃをＥ１２とすると、Ｅ１２は次式で表される。
Ｅ１２＝ｒｋ・ω２・ｂ６・ｅｘｐ｛ｊ・（π／２＋θ６＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ００＋Δθ０１）｝
＝ｒｋ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ００）｝
・｛ω２・ｅｘｐ（ｊ・π／２）＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）｝
・・・（５２） Similarly, when the inter-electrode electromotive force E12c when E01 = θ00 + Δθ01 is substituted into the equation (50) is E12, E12 is expressed by the following equation.
E12 = rk · ω2 · b6 · exp {j · (π / 2 + θ6 + θ00)}
+ Γ · rk · V · b6 · exp {j · (θ6 + θ00 + Δθ01)}
= Rk · b6 · exp {j · (θ6 + θ00)}
{Ω2 · exp (j · π / 2) + γ · V · exp (j · Δθ01)}
... (52)

電極間起電力Ｅ１０とＥ１２との差をとり、求めた差分をω０／（ω０−ω２）倍した結果をＥｄＡ１１とすれば、次式が成立する。この起電力差ＥｄＡ１１は、第１の基本原理の∂Ａ／∂ｔ成分に相当する。
ＥｄＡ１１＝（Ｅ１０−Ｅ１２）・ω０／（ω０−ω２）
＝ｒｋ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ００）｝
・｛ω０・ｅｘｐ（ｊ・π／２）＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）
−ω２・ｅｘｐ（ｊ・π／２）−γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）｝
・ω０／（ω０−ω２）
＝［ｒｋ・ｂ６・ｅｘｐ｛ｊ・（π／２＋θ６＋θ００）｝］・ω０
・・・（５３） Taking the difference between the inter-electrode electromotive forces E10 and E12 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA11, the following equation is established. This electromotive force difference EdA11 corresponds to the ∂A / ∂t component of the first basic principle.
EdA11 = (E10−E12) · ω0 / (ω0−ω2)
= Rk · b6 · exp {j · (θ6 + θ00)}
・ {Ω0 ・ exp (j ・ π / 2) + γ ・ V ・ exp (j ・ Δθ01)
−ω2 · exp (j · π / 2) −γ · V · exp (j · Δθ01)}
・ Ω0 / (ω0−ω2)
= [Rk · b6 · exp {j · (π / 2 + θ6 + θ00)}] · ω0
... (53)

式（５３）に示す起電力差ＥｄＡ１１は、流速の大きさＶに関係しないので、∂Ａ／∂ｔによって発生する成分のみとなる。この起電力差起電力差ＥｄＡ１１を用いて電極間起電力Ｅ１０（合成ベクトルＶａ１０＋Ｖｂ１０）からｖ×Ｂ成分を取り出す。なお、起電力差ＥｄＡ１１は、正確には電極間起電力Ｅ１０とＥ１２との起電力差をω０／（ω０−ω２）倍したものであるが、ω０／（ω０−ω２）倍した理由は、式の展開を容易にするためである。   Since the electromotive force difference EdA11 shown in the equation (53) is not related to the magnitude V of the flow velocity, it becomes only the component generated by ∂A / ∂t. Using this electromotive force difference electromotive force difference EdA11, a v × B component is extracted from the interelectrode electromotive force E10 (combined vector Va10 + Vb10). The electromotive force difference EdA11 is precisely the electromotive force difference between the interelectrode electromotive forces E10 and E12 multiplied by ω0 / (ω0−ω2). The reason why the electromotive force difference EdA11 is multiplied by ω0 / (ω0−ω2) is This is to facilitate the expansion of the formula.

式（５１）に示す電極間起電力Ｅ１０から式（５３）に示す起電力差ＥｄＡ１１を引いたときに得られるｖ×Ｂ成分をＥｖＢ１０とすると、ｖ×Ｂ成分ＥｖＢ１０は次式で表される。
ＥｖＢ１０＝Ｅ１０−ＥｄＡ１１
＝ｒｋ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ００）｝
・｛ω０・ｅｘｐ（ｊ・π／２）＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）｝
−［ｒｋ・ｂ６・ｅｘｐ｛ｊ・（π／２＋θ６＋θ００）｝］・ω０
＝［γ・ｒｋ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ００＋Δθ０１）｝］・Ｖ
・・・（５４） When the v × B component obtained by subtracting the electromotive force difference EdA11 shown in equation (53) from the interelectrode electromotive force E10 shown in equation (51) is EvB10, the v × B component EvB10 is expressed by the following equation. .
EvB10 = E10-EdA11
= Rk · b6 · exp {j · (θ6 + θ00)}
{Ω0 · exp (j · π / 2) + γ · V · exp (j · Δθ01)}
− [Rk · b6 · exp {j · (π / 2 + θ6 + θ00)}] · ω0
= [Γ · rk · b6 · exp {j · (θ6 + θ00 + Δθ01)}] · V
... (54)

ｖ×Ｂ成分ＥｖＢ１０は角周波数ω０，ω２に関係しない。流速の大きさＶが０のときｖ×Ｂ成分ＥｖＢ１０も０となることから分かるように、ｖ×Ｂ成分ＥｖＢ１０より、０点が補正された出力を得ることができる。式（５４）によれば、流速の大きさＶにかかる係数の大きさと方向は、複素ベクトル［γ・ｒｋ・ｂ６・ｅｘｐ｛ｊ・（θ６＋θ００＋Δθ０１）｝］で表される。   The v × B component EvB10 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvB10 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the zero point is corrected can be obtained from the v × B component EvB10. According to the equation (54), the magnitude and direction of the coefficient relating to the magnitude V of the flow velocity are represented by a complex vector [γ · rk · b6 · exp {j · (θ6 + θ00 + Δθ01)}].

次に、ｖ×Ｂ成分ＥｖＢ１０の流速の大きさＶにかかる係数（スパン）の変動要因を除去するために、∂Ａ／∂ｔ成分を用いてｖ×Ｂ成分を正規化する。式（５４）のｖ×Ｂ成分ＥｖＢ１０を式（５３）の起電力差ＥｄＡ１１で正規化し、ω０倍した結果をＥｖＢｎ１とすれば、正規化起電力ＥｖＢｎ１は次式で表される。
ＥｖＢｎ１＝ＥｖＢ１０／ＥｄＡ１１・ω０
＝［γ・ｒｋ・ｂ１・ｅｘｐ｛ｊ・（θ１＋θ００＋Δθ０１）｝・Ｖ］
／［ｒｋ・ｂ１・ｅｘｐ｛ｊ・（π／２＋θ１＋θ００）｝・ω０］
・ω０
＝［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］・Ｖ ・・・（５５） Next, in order to remove the factor of variation of the coefficient (span) related to the flow velocity magnitude V of the v × B component EvB10, the v × B component is normalized using the ∂A / ∂t component. When the v × B component EvB10 of the equation (54) is normalized by the electromotive force difference EdA11 of the equation (53) and multiplied by ω0 is EvBn1, the normalized electromotive force EvBn1 is expressed by the following equation.
EvBn1 = EvB10 / EdA11 · ω0
= [Γ · rk · b1 · exp {j · (θ1 + θ00 + Δθ01)} · V]
/ [Rk · b1 · exp {j · (π / 2 + θ1 + θ00)} · ω0]
・ Ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (55)

式（５５）ではｖ×Ｂにより発生する成分が正規化されスパンの変動要因が除去されている。流速の大きさＶにかかる複素係数は、γの大きさ、−π／２＋Δθ０１の実軸からの角度をもつ。係数γおよび角度Δθ０１は校正等により予め求めることができる定数であり、正規化起電力ＥｖＢｎ１は被測定流体の流速が変化しないかぎり一定となる。したがって、０補正の過程において抽出した∂Ａ／∂ｔの成分をもちいてｖ×Ｂ成分の正規化を行うことにより、０点の補正に加えて、磁場のシフトや位相変化による誤差を自動的に補正するスパン補正を実現することができる。   In the equation (55), the component generated by v × B is normalized to remove the span variation factor. 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 normalized electromotive force EvBn1 is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by normalizing the v × B component using the component ∂A / ∂t extracted during the zero correction process, in addition to the zero point correction, errors due to magnetic field shifts and phase changes are automatically detected. It is possible to realize a span correction to be corrected.

式（５５）より、流速の大きさＶは次式のように表される。
Ｖ＝｜（ＥｖＢｎ１）／［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］｜
＝｜（ＥｖＢｎ１）｜／γ ・・・（５６） From the equation (55), the magnitude V of the flow velocity is expressed as the following equation.
V = | (EvBn1) / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | (EvBn1) | / γ (56)

なお、第１の基本原理で用いた定数および変数と、本実施の形態の定数および変数との対応関係は以下の表１のとおりである。本実施の形態は、表１から明らかなように、前述の第１の基本原理を具体的に実現する１つの例である。   Table 1 below shows the correspondence between the constants and variables used in the first basic principle and the constants and variables of the present embodiment. As is clear from Table 1, this embodiment is one example that specifically realizes the first basic principle described above.

Figure 0004555023
Figure 0004555023

次に、本実施の形態の電磁流量計の具体的な構成とその動作について説明する。図２０は本実施の形態の電磁流量計の構成を示すブロック図であり、図３０と同一の構成には同一の符号を付してある。本実施の形態の電磁流量計は、測定管１と、電極２ａ，２ｂと、電極２ａ，２ｂを含む、測定管軸ＰＡＸの方向と垂直な平面ＰＬＮから軸方向にオフセット距離ｄだけ離れた位置に配設された励磁コイル３と、励磁コイル３に励磁電流を供給する電源部４と、信号変換部５と、信号変換部５によってスパンの変動要因が除去されたｖ×Ｂ成分から被測定流体の流量を算出する流量出力部６とを有する。   Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. FIG. 20 is a block diagram showing the configuration of the electromagnetic flowmeter of the present embodiment. The same components as those in FIG. 30 are given the same reference numerals. The electromagnetic flow meter of the present embodiment is a position that is offset from the plane PLN perpendicular to the direction of the measurement tube axis PAX, including the measurement tube 1, the electrodes 2a and 2b, and the electrodes 2a and 2b, by an offset distance d in the axial direction. Excitation coil 3 disposed in the power supply unit 4, a power supply unit 4 for supplying an excitation current to the excitation coil 3, a signal conversion unit 5, and the v × B component from which the variation factor of the span has been removed by the signal conversion unit 5 And a flow rate output unit 6 for calculating the flow rate of the fluid.

励磁コイル３と電源部４とは、平面ＰＬＮに対して非対称、かつ時間変化する磁場を被測定流体に印加する励磁部となる。
信号変換部５は、電極２ａ，２ｂで検出される合成起電力のうち第１の角周波数ω０と第２の角周波数ω２の２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて２つの周波数成分の起電力差を∂Ａ／∂ｔ成分として抽出し、合成起電力のうち第１の角周波数ω０の成分又は第２の角周波数ω２の成分の中から、抽出した∂Ａ／∂ｔ成分を取り除くことによりｖ×Ｂ成分を抽出する０点補正部５１と、抽出された∂Ａ／∂ｔ成分に基づいて、ｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するスパン補正部５２とから構成される。 The excitation coil 3 and the power supply unit 4 serve as an excitation unit that applies 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 two frequency components of the first angular frequency ω0 and the second angular frequency ω2 in the combined electromotive force detected by the electrodes 2a and 2b, and uses these amplitudes and phases as the amplitude and phase. Based on this, an electromotive force difference between the two frequency components is extracted as ∂A / ∂t component, and the extracted の 中 is extracted from the component of the first angular frequency ω0 or the component of the second angular frequency ω2 of the combined electromotive force. A zero point correction unit 51 that extracts the v × B component by removing the A / ∂t component, and a coefficient related to the magnitude V of the flow velocity of the v × B component based on the extracted ∂A / ∂t component. It comprises a span correction unit 52 that removes a variation factor of a certain span.

電源部４は、第１の角周波数ω０の正弦波成分と第２の角周波数ω２の正弦波成分とを含む励磁電流を励磁コイル３に供給する。このとき、励磁電流における角周波数ω０の成分と角周波数ω２の成分の振幅は同一である。   The power supply unit 4 supplies an excitation current including a sine wave component having a first angular frequency ω 0 and a sine wave component having a second angular frequency ω 2 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.

図２１は信号変換部５と流量出力部６の動作を示すフローチャートである。まず、信号変換部５の０点補正部５１は、電極２ａと２ｂ間の起電力のうち角周波数ω０の成分の起電力Ｅ１０の振幅ｒ１０を求めると共に、実軸と電極間起電力Ｅ１０との位相差φ１０を図示しない位相検波器により求める。また、０点補正部５１は、電極２ａと２ｂ間の起電力のうち角周波数ω２の成分の起電力Ｅ１２の振幅ｒ１２を求めると共に、実軸と電極間起電力Ｅ１２との位相差φ１２を位相検波器により求める（図２１ステップ１０１）。電極間起電力Ｅ１０，Ｅ１２は、バンドパスフィルタによっても周波数分離することができるが、実際にはコムフィルタとよばれる櫛形のデジタルフィルタを使用すれば、２つの角周波数ω０，ω２の成分に簡単に分離することができる。   FIG. 21 is a flowchart showing the operations of the signal conversion unit 5 and the flow rate output unit 6. First, the zero point 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, and calculates the real axis and the interelectrode electromotive force E10. The phase difference φ10 is obtained by a phase detector (not shown). The zero point 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 phase difference φ12 between the real axis and the interelectrode electromotive force E12 is phase-shifted. It calculates | requires with a detector (FIG. 21 step 101). The inter-electrode electromotive forces E10 and E12 can be frequency-separated also by a band-pass filter, but in practice, if a comb-shaped digital filter called a comb filter is used, it can be easily divided into two angular frequency components ω0 and ω2. Can be separated.

続いて、０点補正部５１は、電極間起電力Ｅ１０の実軸成分Ｅ１０ｘと虚軸成分Ｅ１０ｙ、および電極間起電力Ｅ１２の実軸成分Ｅ１２ｘと虚軸成分Ｅ１２ｙを次式のように算出する（ステップ１０２）。
Ｅ１０ｘ＝ｒ１０・ｃｏｓ（φ１０） ・・・（５７）
Ｅ１０ｙ＝ｒ１０・ｓｉｎ（φ１０） ・・・（５８）
Ｅ１２ｘ＝ｒ１２・ｃｏｓ（φ１２） ・・・（５９）
Ｅ１２ｙ＝ｒ１２・ｓｉｎ（φ１２） ・・・（６０） Subsequently, the zero point correction unit 51 calculates the real axis component E10x and the imaginary axis component E10y of the interelectrode electromotive force E10, and the real axis component E12x and the imaginary axis component E12y of the interelectrode electromotive force E12 as in the following equations. (Step 102).
E10x = r10 · cos (φ10) (57)
E10y = r10 · sin (φ10) (58)
E12x = r12 · cos (φ12) (59)
E12y = r12 · sin (φ12) (60)

式（５７）〜式（６０）の算出後、０点補正部５１は、電極間起電力Ｅ１０とＥ１２との起電力差ＥｄＡ１１の大きさを求める（ステップ１０３）。このステップ１０３の処理は、∂Ａ／∂ｔ成分を求めることに対応する処理であり、式（５３）の算出に相当する処理である。信号変換部５は、起電力差ＥｄＡ１１の実軸成分ＥｄＡ１１ｘと虚軸成分ＥｄＡ１１ｙを次式のように算出する。
ＥｄＡ１１ｘ＝（Ｅ１０ｘ−Ｅ１２ｘ）・ω０／（ω０−ω２） ・・・（６１）
ＥｄＡ１１ｙ＝（Ｅ１０ｙ−Ｅ１２ｙ）・ω０／（ω０−ω２） ・・・（６２） After calculating the equations (57) to (60), the zero point correction unit 51 obtains the magnitude of the electromotive force difference EdA11 between the electrode electromotive forces E10 and E12 (step 103). The process of step 103 is a process corresponding to obtaining the ∂A / ∂t component, and is a process corresponding to the calculation of Expression (53). The signal converter 5 calculates the real axis component EdA11x and the imaginary axis component EdA11y of the electromotive force difference EdA11 as in the following equation.
EdA11x = (E10x−E12x) · ω0 / (ω0−ω2) (61)
EdA11y = (E10y−E12y) · ω0 / (ω0−ω2) (62)

０点補正部５１は、電極間起電力Ｅ１０から起電力差ＥｄＡ１１を取り除き、ｖ×Ｂ成分ＥｖＢ１０の大きさを求める（ステップ１０４）。このステップ１０４の処理は、式（５４）の算出に相当する処理である。０点補正部５１は、ｖ×Ｂ成分ＥｖＢ１０の大きさ｜ＥｖＢ１０｜を次式のように算出する。
｜ＥｖＢ１０｜＝｛（Ｅ１０ｘ−ＥｄＡ１１ｘ）2
＋（Ｅ１０ｙ−ＥｄＡ１１ｙ）2｝1/2 ・・・（６３） The zero point correction unit 51 removes the electromotive force difference EdA11 from the interelectrode electromotive force E10, and obtains the magnitude of the v × B component EvB10 (step 104). The process of step 104 is a process corresponding to the calculation of equation (54). The zero point correction unit 51 calculates the magnitude | EvB10 | of the v × B component EvB10 as follows.
| EvB10 | = {(E10x−EdA11x) 2
+ (E10y-EdA11y) 2 } 1/2 (63)

次に、信号変換部５のスパン補正部５２は、ｖ×Ｂ成分ＥｖＢ１０を起電力差ＥｄＡ１１で正規化した正規化起電力ＥｖＢｎ１の大きさを求める（ステップ１０５）。このステップ１０５の処理は、式（５５）の算出に相当する処理である。スパン補正部５２は、正規化起電力ＥｖＢｎ１の大きさ｜ＥｖＢｎ１｜を次式のように算出する。
｜ＥｖＢｎ１｜＝（｜ＥｖＢ１０｜／｜ＥｄＡ１１｜）・ω０ ・・・（６４） Next, the span correction unit 52 of the signal conversion unit 5 obtains the magnitude of the normalized electromotive force EvBn1 obtained by normalizing the v × B component EvB10 with the electromotive force difference EdA11 (step 105). The process of step 105 is a process corresponding to the calculation of Expression (55). The span correction unit 52 calculates the magnitude | EvBn1 | of the normalized electromotive force EvBn1 as the following equation.
| EvBn1 | = (| EvB10 | / | EdA11 |) · ω0 (64)

流量出力部６は、被測定流体の流速の大きさＶを次式のように算出する（ステップ１０６）。このステップ１０６の処理は、式（５６）の算出に相当する処理である。
Ｖ＝｜ＥｖＢｎ１｜／γ ・・・（６５）
なお、比例係数γは、校正等により予め求めることができる定数である。信号変換部５と流量出力部６とは、以上のようなステップ１０１〜１０６の処理を例えばオペレータによって計測終了が指示されるまで（ステップ１０７においてＹＥＳ）、一定周期毎に行う。 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 106). The process of step 106 is a process corresponding to the calculation of Expression (56).
V = | EvBn1 | / γ (65)
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 106 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 107).

以上のように、本実施の形態では、励磁コイル３から大きさが等しくかつ周波数が異なる２つの成分を含む磁場を被測定流体に印加し、電極２ａと２ｂ間の起電力のうち角周波数ω０の成分の起電力Ｅ１０と角周波数ω２の成分の起電力Ｅ１２とから起電力差ＥｄＡ１１（∂Ａ／∂ｔ成分）を抽出し、この∂Ａ／∂ｔ成分を電極間起電力Ｅ１０（合成ベクトルＶａ１０＋Ｖｂ１０）の中から取り除くことによりｖ×Ｂ成分を抽出し、∂Ａ／∂ｔ成分を用いてｖ×Ｂ成分の流速の大きさＶにかかるスパンを正規化して、スパン変動要素を消去するようにしたので、正確なスパン補正を自動的に行うことができ、かつ被測定流体の流量を０にすることなく電磁流量計の出力の０点を補正することができ、高周波励磁においても０点の安定性を確保することができる。   As described above, in the present embodiment, a magnetic field including two components having the same magnitude and different frequencies from the exciting coil 3 is applied to the fluid to be measured, and the angular frequency ω0 of the electromotive force between the electrodes 2a and 2b. The electromotive force difference EdA11 (∂A / ∂t component) is extracted from the electromotive force E10 of the component and the electromotive force E12 of the component of the angular frequency ω2, and this ∂A / ∂t component is extracted from the inter-electrode electromotive force E10 (synthesis vector). The v × B component is extracted by removing it from Va10 + Vb10), and the span of the flow velocity V of the v × B component is normalized using the ∂A / ∂t component to eliminate the span variation element Therefore, 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. Ensure the stability of It is possible.

なお、本実施の形態では、角周波数ω０の成分の起電力Ｅ１０を０補正およびスパン補正の対象としたが、角周波数ω２の成分の起電力Ｅ１２を０補正およびスパン補正の対象としてもよい。この場合は、次式のように電極間起電力Ｅ１２からＥ１０を引いて起電力差ＥｄＡ１１（∂Ａ／∂ｔ成分）を求める。
ＥｄＡ１１＝（Ｅ１２−Ｅ１０）・ω２／（ω２−ω０） ・・・（６６） 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 EdA11 (∂A / ∂t component) is obtained by subtracting E10 from the interelectrode electromotive force E12 as in the following equation.
EdA11 = (E12−E10) · ω2 / (ω2−ω0) (66)

そして、電極間起電力Ｅ１２から起電力差ＥｄＡ１１を引くことによりｖ×Ｂ成分ＥｖＢ１２を抽出し、次式のように起電力差ＥｄＡ１１を用いてｖ×Ｂ成分ＥｖＢ１２の流速の大きさＶにかかるスパンを正規化すればよい。その他の処理は電極間起電力Ｅ１０を０補正およびスパン補正の対象とする場合と同じである。
｜ＥｖＢｎ１｜＝｜（ＥｖＢ１２／ＥｄＡ１１）・ω２｜ ・・・（６７） Then, the v × B component EvB12 is extracted by subtracting the electromotive force difference EdA11 from the interelectrode electromotive force E12, and the flow velocity magnitude V of the v × B component EvB12 is applied using the electromotive force difference EdA11 as in the following equation. What is necessary is just to normalize a span. The other processes are the same as the case where the interelectrode electromotive force E10 is subjected to 0 correction and span correction.
| EvBn1 | = | (EvB12 / EdA11) · ω2 | (67)

また、本実施の形態では、複数の励磁周波数ω０，ω２で同時に励磁する例を示したが、単一の励磁周波数ω０又はω２で励磁を行い、励磁周波数をω０とω２で交互に切り替えながら励磁をした場合でも同じ効果を得ることができる。   In this embodiment, an example is shown in which excitation is performed simultaneously with a plurality of excitation frequencies ω0 and ω2, but excitation is performed with a single excitation frequency ω0 or ω2, and excitation is performed while alternately switching the excitation frequency between ω0 and ω2. The same effect can be obtained even when

［第２の実施の形態］
次に、本発明の第２の実施の形態について説明する。本実施の形態は、第１の実施の形態の電磁流量計に対して励磁コイルを１個追加したものであり、前述の第２の基本原理を用いるものである。本実施の形態の電磁流量計は２個の励磁コイルと１対の電極とを有するものであり、信号処理系を除く構成は図５に示した電磁流量計と同様であるので、図５の符号を用いて本実施の形態の原理を説明する。新たに追加する第２の励磁コイルを既存の第１の励磁コイルと同じ側に追加した場合には、第１の実施の形態の冗長な構成となる。したがって、第２の励磁コイルは、電極を含む平面を挟んで第１の励磁コイルと異なる側に配設する必要がある。 [Second Embodiment]
Next, a second embodiment of the present invention will be described. In the present embodiment, one excitation coil is added to the electromagnetic flow meter of the first embodiment, and the second basic principle described above is used. 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. When a second exciting coil to be newly added is added to the same side as the existing first exciting coil, the redundant configuration of the first embodiment is obtained. Therefore, the second exciting coil needs to be arranged on a different side from the first exciting coil across the plane including the electrodes.

第１の励磁コイル３ａから発生する磁場Ｂｂのうち、電極２ａ，２ｂ間を結ぶ電極軸ＥＡＸ上において電極軸ＥＡＸおよび測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ７と、第２の励磁コイル３ｂから発生する磁場Ｂｃのうち、電極軸ＥＡＸ上において電極軸ＥＡＸおよび測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ８は、以下のように与えられるものとする。
Ｂ７＝ｂ７・ｃｏｓ（ω０・ｔ−θ７）＋ｂ７・ｃｏｓ（ω２・ｔ−θ７）
・・・（６８）
Ｂ８＝ｂ８・ｃｏｓ（ω０・ｔ−θ８）＋ｂ８・ｃｏｓ（ω２・ｔ−θ８）
・・・（６９） Of the magnetic field Bb generated from the first exciting coil 3a, 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 connecting the electrodes 2a and 2b, Of the magnetic field Bc generated from the exciting coil 3b, the magnetic field component (magnetic flux density) B8 orthogonal to both the electrode axis EAX and the measurement tube axis PAX on the electrode axis EAX is given as follows.
B7 = b7 · cos (ω0 · t−θ7) + b7 · cos (ω2 · t−θ7)
... (68)
B8 = b8 · cos (ω0 · t−θ8) + b8 · cos (ω2 · t−θ8)
... (69)

式（６８）、式（６９）において、ω０，ω２は異なる角周波数、ｂ７は磁束密度Ｂ７の角周波数ω０の成分の振幅および角周波数ω２の成分の振幅、ｂ８は磁束密度Ｂ８の角周波数ω０の成分の振幅および角周波数ω２の成分の振幅、θ７は磁束密度Ｂ７の角周波数ω０の成分とω０・ｔとの位相差（位相遅れ）および角周波数ω２の成分とω２・ｔとの位相差、θ８は磁束密度Ｂ８の角周波数ω０の成分とω０・ｔとの位相差および角周波数ω２の成分とω２・ｔとの位相差である。以下、磁束密度Ｂ７を磁場Ｂ７とし、磁束密度Ｂ８を磁場Ｂ８とする。   In equations (68) and (69), ω0 and ω2 are different angular frequencies, b7 is the amplitude of the component of angular frequency ω0 and the amplitude of the component of angular frequency ω2 of magnetic flux density B7, and b8 is the angular frequency ω0 of magnetic flux density B8. And θ7 is the phase difference (phase lag) 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. , Θ8 is the phase difference between the angular frequency ω0 component of the magnetic flux density B8 and ω0 · t, and the phase difference between the angular frequency ω2 component and ω2 · t. Hereinafter, the magnetic flux density B7 is referred to as a magnetic field B7, and the magnetic flux density B8 is referred to as a magnetic field B8.

被測定流体の流速が０の場合、発生する渦電流は、磁場の変化に起因する成分のみとなり、磁場Ｂｂの変化による渦電流Ｉ１、磁場Ｂｃの変化による渦電流Ｉ２は、図６に示すような向きとなる。したがって、電極軸ＥＡＸと測定管軸ＰＡＸとを含む平面内において、磁場Ｂｂの変化によって発生する、流速と無関係な電極間起電力Ｅ１と、磁場Ｂｃの変化によって発生する、流速と無関係な電極間起電力Ｅ２は、図６に示すように互いに逆向きとなる。   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. Accordingly, in the plane including the electrode axis EAX and the measurement tube axis PAX, the inter-electrode electromotive force E1 generated by the change of the magnetic field Bb and unrelated to the flow velocity and the electrode unrelated to the flow velocity generated by the change of the magnetic field Bc. The electromotive forces E2 are opposite to each other as shown in FIG.

被測定流体の流速がＶ（Ｖ≠０）の場合、発生する渦電流には、流速０のときの渦電流Ｉ１，Ｉ２に加えて、被測定流体の流速ベクトルｖに起因する成分ｖ×Ｂｂ，ｖ×Ｂｃが発生するため、流速ベクトルｖと磁場Ｂｂによる渦電流Ｉｖ１、流速ベクトルｖと磁場Ｂｃによる渦電流Ｉｖ２は、図７に示すような向きとなる。したがって、流速ベクトルｖと磁場Ｂｂによって発生する電極間起電力Ｅｖ１、流速ベクトルｖと磁場Ｂｃによって発生する電極間起電力Ｅｖ２は、同じ向きとなる。   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.

図６、図７で説明した電極間起電力の向きを考慮すると、磁場の時間変化に起因する電極間起電力を複素ベクトルに変換した起電力と被測定流体の流速に起因する電極間起電力を複素ベクトルに変換した起電力とを合わせた全体の電極間起電力のうち、角周波数ω０の成分の起電力をＥ２０ｃとすると、電極間起電力Ｅ２０ｃは式（２６）と同様の次式で表される。
Ｅ２０ｃ＝ｒｋ・ω０・ｂ７・ｅｘｐ｛ｊ・（π／２＋θ７＋θ００）｝
＋ｒｋ・ω０・ｂ８・ｅｘｐ｛ｊ・（−π／２＋θ８＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ７・ｅｘｐ｛ｊ・（θ７＋θ０１）｝
＋γ・ｒｋ・Ｖ・ｂ８・ｅｘｐ｛ｊ・（θ８＋θ０１）｝ ・・・（７０） In consideration of the direction of the electromotive force between the electrodes explained in FIGS. 6 and 7, 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. If the electromotive force of the component of the angular frequency ω0 is E20c among the total inter-electrode electromotive force combined with the electromotive force converted into a complex vector, the interelectrode electromotive force E20c is the following equation similar to Equation (26). expressed.
E20c = rk · ω0 · b7 · exp {j · (π / 2 + θ7 + θ00)}
+ Rk · ω0 · b8 · exp {j · (−π / 2 + θ8 + θ00)}
+ Γ · rk · V · b7 · exp {j · (θ7 + θ01)}
+ Γ · rk · V · b8 · exp {j · (θ8 + θ01)} (70)

また、磁場の時間変化に起因する電極間起電力を複素ベクトルに変換した起電力と被測定流体の流速に起因する電極間起電力を複素ベクトルに変換した起電力とを合わせた全体の電極間起電力のうち、角周波数ω２の成分の起電力をＥ２２ｃとすると、電極間起電力Ｅ２２ｃは式（２６）と同様の次式で表される。
Ｅ２２ｃ＝ｒｋ・ω２・ｂ７・ｅｘｐ｛ｊ・（π／２＋θ７＋θ００）｝
＋ｒｋ・ω２・ｂ８・ｅｘｐ｛ｊ・（−π／２＋θ８＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ７・ｅｘｐ｛ｊ・（θ７＋θ０１）｝
＋γ・ｒｋ・Ｖ・ｂ８・ｅｘｐ｛ｊ・（θ８＋θ０１）｝ ・・・（７１） 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 If the electromotive force of the component of the angular frequency ω2 in the electromotive force is E22c, the interelectrode electromotive force E22c is expressed by the following equation similar to Equation (26).
E22c = rk · ω2 · b7 · exp {j · (π / 2 + θ7 + θ00)}
+ Rk · ω2 · b8 · exp {j · (−π / 2 + θ8 + θ00)}
+ Γ · rk · V · b7 · exp {j · (θ7 + θ01)}
+ Γ · rk · V · b8 · exp {j · (θ8 + θ01)} (71)

ここで、ω０・ｔ，ω２・ｔに対する磁場Ｂ７の位相遅れθ７とω０・ｔ，ω２・ｔに対する磁場Ｂ８の位相遅れθ８との関係がθ８＝θ７＋Δθ８で、虚軸に対する∂Ａ／∂ｔ成分の角度θ００と実軸に対するｖ×Ｂ成分の角度θ０１との関係がθ０１＝θ００＋Δθ０１である状態を第１の励磁状態とし、この第１の励磁状態における電極間起電力Ｅ２０ｃをＥ２０とすると、電極間起電力Ｅ２０は次式のようになる。
Ｅ２０＝ｒｋ・ω０・ｂ７・ｅｘｐ｛ｊ・（π／２＋θ７＋θ００）｝
＋ｒｋ・ω０・ｂ８・ｅｘｐ｛ｊ・（−π／２＋θ７＋Δθ８＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ７・ｅｘｐ｛ｊ・（θ７＋θ００＋Δθ０１）｝
＋γ・ｒｋ・Ｖ・ｂ８・ｅｘｐ｛ｊ・（θ７＋Δθ８＋θ００＋Δθ０１）｝
＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］
・・・（７２） Here, the relationship between the phase delay θ7 of the magnetic field B7 with respect to ω0 · t and ω2 · t and the phase delay θ8 of the magnetic field B8 with respect to ω0 · t and ω2 · t is θ8 = θ7 + Δθ8, and ∂A / ∂t component with respect to the imaginary axis When the relationship between the angle θ00 of the first axis and the angle θ01 of the v × B component with respect to the real axis is θ01 = θ00 + Δθ01 is the first excitation state, and the inter-electrode electromotive force E20c in the first excitation state is E20, The inter-electromotive force E20 is expressed by the following equation.
E20 = rk · ω0 · b7 · exp {j · (π / 2 + θ7 + θ00)}
+ Rk · ω0 · b8 · exp {j · (−π / 2 + θ7 + Δθ8 + θ00)}
+ Γ · rk · V · b7 · exp {j · (θ7 + θ00 + Δθ01)}
+ Γ · rk · V · b8 · exp {j · (θ7 + Δθ8 + θ00 + Δθ01)}
= Rk · exp {j · (θ7 + θ00)}
[Ω0 · exp (j · π / 2) · {b7−b8 · exp (j · Δθ8)}
+ Γ · V · exp (j · Δθ01) · {b7 + b8 · exp (j · Δθ8)}]
... (72)

また、θ８＝θ７＋Δθ８、θ０１＝θ００＋Δθ０１である第１の励磁状態における電極間起電力Ｅ２２ｃをＥ２２とすると、電極間起電力Ｅ２２は次式のようになる。
Ｅ２２＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・［ω２・ｅｘｐ（ｊ・π／２）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］
・・・（７３） Further, when the interelectrode electromotive force E22c in the first excitation state where θ8 = θ7 + Δθ8 and θ01 = θ00 + Δθ01 is E22, the interelectrode electromotive force E22 is expressed by the following equation.
E22 = rk · exp {j · (θ7 + θ00)}
[Ω2 · exp (j · π / 2) · {b7−b8 · exp (j · Δθ8)}
+ Γ · V · exp (j · Δθ01) · {b7 + b8 · exp (j · Δθ8)}]
... (73)

また、磁場Ｂ７と磁場Ｂ８との位相差が第１の励磁状態から一定値πだけ変化し（θ８＝π＋θ７＋Δθ８）、かつθ０１＝θ００＋Δθ０１である状態を第２の励磁状態とし、この第２の励磁状態における電極間起電力Ｅ２０ｃをＥ２π０とすると、電極間起電力Ｅ２π０は式（７２）より次式のようになる。
Ｅ２π０＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）
・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝］ ・・・（７４） In addition, a state in which the phase difference between the magnetic field B7 and the magnetic field B8 changes by a constant value π from the first excitation state (θ8 = π + θ7 + Δθ8) and θ01 = θ00 + Δθ01 is set as the second excitation state. When the inter-electrode electromotive force E20c in the state is E2π0, the inter-electrode electromotive force E2π0 is expressed by the following equation from the equation (72).
E2π0 = rk · exp {j · (θ7 + θ00)}
[Ω0 · exp (j · π / 2) · {b7 + b8 · exp (j · Δθ8)}
+ Γ · V · exp (j · Δθ01)
{B7−b8 · exp (j · Δθ8)}] (74)

また、θ８＝π＋θ７＋Δθ８、θ０１＝θ００＋Δθ０１である第２の励磁状態における電極間起電力Ｅ２２ｃをＥ２π２とすると、電極間起電力Ｅ２π２は式（７３）より次式のようになる。
Ｅ２π２＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・［ω２・ｅｘｐ（ｊ・π／２）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）
・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝］ ・・・（７５） When the interelectrode electromotive force E22c in the second excitation state where θ8 = π + θ7 + Δθ8 and θ01 = θ00 + Δθ01 is E2π2, the interelectrode electromotive force E2π2 is expressed by the following equation from Equation (73).
E2π2 = rk · exp {j · (θ7 + θ00)}
[Ω2 · exp (j · π / 2) · {b7 + b8 · exp (j · Δθ8)}
+ Γ · V · exp (j · Δθ01)
{B7−b8 · exp (j · Δθ8)}] (75)

ここで、測定管軸ＰＡＸと直交する、電極２ａ，２ｂを含む平面ＰＬＮから第１の励磁コイル３ａまでの距離ｄ１と平面ＰＬＮから第２の励磁コイル３ｂまでの距離ｄ２とが略等しいとすると（ｄ１≒ｄ２）、ｂ７≒ｂ８、Δθ８≒０になる。この場合、式（７２）、式（７３）、式（７４）、式（７５）は以下のようになる。
Ｅ２０≒ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・｛２・ｂ７・γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）｝ ・・・（７６）
Ｅ２２≒ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・｛２・ｂ７・γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）｝ ・・・（７７）
Ｅ２π０≒ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・｛２・ｂ７・ω０・ｅｘｐ（ｊ・π／２）｝ ・・・（７８）
Ｅ２π２≒ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・｛２・ｂ７・ω２・ｅｘｐ（ｊ・π／２）｝ ・・・（７９） Here, it is assumed that the distance d1 from the plane PLN including the electrodes 2a and 2b and the first excitation coil 3a perpendicular to the measurement tube axis PAX and the distance d2 from the plane PLN to the second excitation coil 3b are substantially equal. (D1≈d2), b7≈b8, and Δθ8≈0. In this case, Expression (72), Expression (73), Expression (74), and Expression (75) are as follows.
E20≈rk · exp {j · (θ7 + θ00)}
{2 · b7 · γ · V · exp (j · Δθ01)} (76)
E22≈rk · exp {j · (θ7 + θ00)}
{2 · b7 · γ · V · exp (j · Δθ01)} (77)
E2π0≈rk · exp {j · (θ7 + θ00)}
{2 · b7 · ω0 · exp (j · π / 2)} (78)
E2π2≈rk · exp {j · (θ7 + θ00)}
{2 · b7 · ω2 · exp (j · π / 2)} (79)

すなわち、電極間起電力Ｅ２０，Ｅ２２はほぼｖ×Ｂ成分の起電力のみとなり、電極間起電力Ｅ２π０，Ｅ２π２はほぼ∂Ａ／∂ｔ成分の起電力のみとなるので、∂Ａ／∂ｔ成分の抽出やｖ×Ｂ成分の抽出、および正規化や０補正演算の際の演算誤差を小さくすることができる。この点が、本実施の形態と第１の実施の形態の技術的な意義における相違点である。ただし、以後の理論展開もｂ７≠ｂ８、Δθ８≠０として進める。   That is, the inter-electrode electromotive forces E20 and E22 are substantially only the electromotive force of the v × B component, and the inter-electrode electromotive forces E2π0 and E2π2 are substantially only the electromotive force of the ∂A / ∂t component. , V × B component extraction, normalization, and zero correction calculation errors can be reduced. This is the difference in technical significance between the present embodiment and the first embodiment. However, the subsequent theoretical development proceeds as b7 ≠ b8 and Δθ8 ≠ 0.

電極間起電力Ｅ２０とＥ２２との差をとり、求めた差分をω０／（ω０−ω２）倍した結果を起電力差ＥｄＡ２１とすれば、次式が成立する。ここで、起電力差ＥｄＡ２１は第２の基本原理の第１の∂Ａ／∂ｔ成分に相当する。
ＥｄＡ２１＝（Ｅ２０−Ｅ２２）・ω０／（ω０−ω２）
＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝
−ω２・ｅｘｐ（ｊ・π／２）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝
−γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］
・ω０／（ω０−ω２）
＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝
・・・（８０） Taking the difference between the electromotive forces E20 and E22 between the electrodes and multiplying the obtained difference by ω0 / (ω0−ω2) as the electromotive force difference EdA21, the following equation is established. Here, the electromotive force difference EdA21 corresponds to the first ∂A / ∂t component of the second basic principle.
EdA21 = (E20−E22) · ω0 / (ω0−ω2)
= Rk · exp {j · (θ7 + θ00)}
[Ω0 · exp (j · π / 2) · {b7−b8 · exp (j · Δθ8)}
+ Γ · V · exp (j · Δθ01) · {b7 + b8 · exp (j · Δθ8)}
−ω2 · exp (j · π / 2) · {b7−b8 · exp (j · Δθ8)}
−γ · V · exp (j · Δθ01) · {b7 + b8 · exp (j · Δθ8)}]
・ Ω0 / (ω0−ω2)
= Rk · exp {j · (θ7 + θ00)}
.Omega.0.exp (j.pi / 2). {B7-b8.exp (j..DELTA..theta.8)}
... (80)

式（８０）に示す起電力差ＥｄＡ２１は、流速の大きさＶに関係しないので、∂Ａ／∂ｔによって発生する成分のみとなる。この起電力差ＥｄＡ２１を用いて電極間起電力Ｅ２０（合成ベクトルＶａｓ０＋Ｖｂｓ０）からｖ×Ｂ成分を取り出す。なお、起電力差ＥｄＡ２１は、正確には電極間起電力Ｅ２０とＥ２２との起電力差をω０／（ω０−ω２）倍したものであるが、ω０／（ω０−ω２）倍した理由は、式の展開を容易にするためである。   Since the electromotive force difference EdA21 shown in the equation (80) is not related to the magnitude V of the flow velocity, it becomes only the component generated by ∂A / ∂t. Using this electromotive force difference EdA21, a v × B component is extracted from the interelectrode electromotive force E20 (combined vector Vas0 + Vbs0). Note that the electromotive force difference EdA21 is precisely the electromotive force difference between the electrode electromotive forces E20 and E22 multiplied by ω0 / (ω0−ω2), but the reason for the multiplication by ω0 / (ω0−ω2) is as follows. This is to facilitate the expansion of the formula.

式（７２）に示す電極間起電力Ｅ２０から式（８０）に示す起電力差ＥｄＡ２１を引いたときに得られるｖ×Ｂ成分をＥｖＢ２０とすると、ｖ×Ｂ成分ＥｖＢ２０は次式で表される。
ＥｖＢ２０＝Ｅ２０−ＥｄＡ２１
＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］
−ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝
＝［γ・ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００＋Δθ０１）｝
・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］・Ｖ ・・・（８１） When the v × B component obtained by subtracting the electromotive force difference EdA21 shown in the equation (80) from the interelectrode electromotive force E20 shown in the equation (72) is EvB20, the v × B component EvB20 is expressed by the following equation. .
EvB20 = E20−EdA21
= Rk · exp {j · (θ7 + θ00)}
[Ω0 · exp (j · π / 2) · {b7−b8 · exp (j · Δθ8)}
+ Γ · V · exp (j · Δθ01) · {b7 + b8 · exp (j · Δθ8)}]
−rk · exp {j · (θ7 + θ00)}
.Omega.0.exp (j.pi / 2). {B7-b8.exp (j..DELTA..theta.8)}
= [Γ · rk · exp {j · (θ7 + θ00 + Δθ01)}
{B7 + b8 · exp (j · Δθ8)}] · V (81)

ｖ×Ｂ成分ＥｖＢ２０は角周波数ω０，ω２に関係しない。流速の大きさＶが０のときｖ×Ｂ成分ＥｖＢ２０も０となることから分かるように、ｖ×Ｂ成分ＥｖＢ２０より、０点が補正された出力を得ることができる。式（８１）によれば、流速の大きさＶにかかる係数の大きさと方向は、複素ベクトル［γ・ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００＋Δθ０１）｝・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］で表される。   The v × B component EvB20 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvB20 becomes 0 when the magnitude V of the flow velocity is 0, an output in which the zero point is corrected can be obtained from the v × B component EvB20. According to the equation (81), the magnitude and direction of the coefficient relating to the magnitude V of the flow velocity are complex vectors [γ · rk · exp {j · (θ7 + θ00 + Δθ01)} · {b7 + b8 · exp (j · Δθ8)}]. expressed.

次に、ｖ×Ｂ成分ＥｖＢ２０の流速の大きさＶにかかる係数（スパン）の変動要因を除去するために、このスパンの変動要因と同じ変動要因を持つ第２の∂Ａ／∂ｔ成分を抽出する。このときの抽出方法としては第２の基本原理で説明した第１の抽出方法を用いる。電極間起電力Ｅ２π０とＥ２π２との差をとり、求めた差分をω０／（ω０−ω２）倍した結果を起電力差ＥｄＡ２２とすれば、次式が成立する。ここで、起電力差ＥｄＡ２２は第２の基本原理の第２の∂Ａ／∂ｔ成分に相当する。
ＥｄＡ２２＝（Ｅ２π０−Ｅ２π２）・ω０／（ω０−ω２）
＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝
−ω２・ｅｘｐ（ｊ・π／２）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝
−γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝］
・ω０／（ω０−ω２）
＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝
・・・（８２） Next, in order to remove the variation factor of the coefficient (span) related to the flow velocity magnitude V of the v × B component EvB20, the second ∂A / ∂t component having the same variation factor as this span variation factor is obtained. Extract. As the extraction method at this time, the first extraction method described in the second basic principle is used. Taking the difference between the electromotive forces E2π0 and E2π2 between the electrodes, and multiplying the obtained difference by ω0 / (ω0−ω2) is the electromotive force difference EdA22, the following equation is established. Here, the electromotive force difference EdA22 corresponds to the second ∂A / ∂t component of the second basic principle.
EdA22 = (E2π0−E2π2) · ω0 / (ω0−ω2)
= Rk · exp {j · (θ7 + θ00)}
[Ω0 · exp (j · π / 2) · {b7 + b8 · exp (j · Δθ8)}
+ Γ · V · exp (j · Δθ01) · {b7−b8 · exp (j · Δθ8)}
−ω2 · exp (j · π / 2) · {b7 + b8 · exp (j · Δθ8)}
−γ · V · exp (j · Δθ01) · {b7−b8 · exp (j · Δθ8)}]
・ Ω0 / (ω0−ω2)
= Rk · exp {j · (θ7 + θ00)}
.Omega.0.exp (j.pi / 2). {B7 + b8.exp (j..DELTA..theta.8)}
... (82)

起電力差ＥｄＡ２２は、流速の大きさＶに関係しないので、∂Ａ／∂ｔにより発生する成分のみとなる。この起電力差ＥｄＡ２２を用いてｖ×Ｂ成分ＥｖＢ２０の流速の大きさＶにかかる係数（スパン）を正規化する。なお、起電力差ＥｄＡ２２は、正確には電極間起電力Ｅ２π０とＥ２π２との起電力差をω０／（ω０−ω２）倍したものであるが、ω０／（ω０−ω２）倍した理由は、式の展開を容易にするためである。   Since the electromotive force difference EdA22 is not related to the magnitude V of the flow velocity, only the component generated by ∂A / ∂t is present. Using this electromotive force difference EdA22, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component EvB20 is normalized. The electromotive force difference EdA22 is precisely the difference between the electromotive forces E2π0 and E2π2 between the electrodes, which is multiplied by ω0 / (ω0−ω2). The reason for the multiplication by ω0 / (ω0−ω2) is as follows: This is to facilitate the expansion of the formula.

式（８１）のｖ×Ｂ成分ＥｖＢ２０を式（８２）の起電力差ＥｄＡ２２で正規化し、ω０倍した結果をＥｖＢｎ２とすれば、正規化起電力ＥｖＢｎ２は次式で表される。
ＥｖＢｎ２＝（ＥｖＢ２０／ＥｄＡ２２）・ω０
＝［γ・ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００＋Δθ０１）｝
・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］・Ｖ
／［ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］・ω０
＝［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］・Ｖ ・・・（８３） If the v × B component EvB20 in the equation (81) is normalized by the electromotive force difference EdA22 in the equation (82) and multiplied by ω0 is EvBn2, the normalized electromotive force EvBn2 is expressed by the following equation.
EvBn2 = (EvB20 / EdA22) · ω0
= [Γ · rk · exp {j · (θ7 + θ00 + Δθ01)}
{B7 + b8 · exp (j · Δθ8)}] · V
/ [Rk · exp {j · (θ7 + θ00)}
Ω0 · exp (j · π / 2) · {b7 + b8 · exp (j · Δθ8)}] · ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (83)

式（８３）ではｖ×Ｂにより発生する成分が正規化されスパンの変動要因が除去されている。流速の大きさＶにかかる複素係数は、γの大きさ、−π／２＋Δθ０１の実軸からの角度をもつ。係数γおよび角度Δθ０１は校正等により予め求めることができる定数であり、正規化起電力ＥｖＢｎ２は被測定流体の流速が変化しないかぎり一定となる。したがって、抽出した第２の∂Ａ／∂ｔの成分をもちいてｖ×Ｂ成分の正規化を行うことにより、０点の補正に加えて、磁場のシフトや位相変化による誤差を自動的に補正するスパン補正を実現することができる。   In the equation (83), the component generated by v × B is normalized to eliminate the span variation factor. 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 normalized electromotive force EvBn2 is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by normalizing the v × B component using the extracted second ∂A / ∂t component, in addition to the zero point correction, errors due to magnetic field shift and phase change are automatically corrected. Span correction can be realized.

式（８３）より、流速の大きさＶは次式のように表される。
Ｖ＝｜ＥｖＢｎ２／［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］｜
＝｜ＥｖＢｎ２｜／γ ・・・（８４） From the equation (83), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn2 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn2 | / γ (84)

なお、第２の基本原理で用いた定数および変数と、本実施の形態の定数および変数との対応関係は以下の表２のとおりである。本実施の形態は、表２から明らかなように、前述の第２の基本原理を具体的に実現する１つの例である。   The correspondence relationship between the constants and variables used in the second 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 an example that specifically realizes the second basic principle described above.

Figure 0004555023
Figure 0004555023

次に、本実施の形態の電磁流量計の具体的な構成とその動作について説明する。図２２は本実施の形態の電磁流量計の構成を示すブロック図であり、図５と同一の構成には同一の符号を付してある。本実施の形態の電磁流量計は、測定管１と、電極２ａ，２ｂと、第１、第２の励磁コイル３ａ，３ｂと、第１、第２の励磁コイル３ａ，３ｂに励磁電流を供給する電源部４ａと、信号変換部５ａと、信号変換部５ａによってスパンの変動要因が除去されたｖ×Ｂ成分から被測定流体の流量を算出する流量出力部６ａとを有する。   Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. FIG. 22 is a block diagram showing the configuration of the electromagnetic flowmeter of the present embodiment. 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. A power supply unit 4a, a signal conversion unit 5a, and a flow rate output unit 6a that calculates the flow rate of the fluid to be measured from the v × B component from which the variation factor of the span has been removed by the signal conversion unit 5a.

第１、第２の励磁コイル３ａ，３ｂと電源部４ａとは、平面ＰＬＮに対して非対称、かつ時間変化する磁場を被測定流体に印加する励磁部となる。
信号変換部５ａは、第１の励磁状態において、電極２ａ，２ｂで検出される合成起電力のうち第１の角周波数ω０と第２の角周波数ω２の２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて２つの周波数成分の起電力差を第１の∂Ａ／∂ｔ成分として抽出し、合成起電力のうち第１の角周波数ω０の成分又は第２の角周波数ω２の成分の中から、第１の∂Ａ／∂ｔ成分を取り除くことによりｖ×Ｂ成分を抽出する０点補正部５１ａと、第２の励磁状態において、電極２ａ，２ｂで検出される合成起電力のうち２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて２つの周波数成分の起電力差を第２の∂Ａ／∂ｔ成分として抽出し、この抽出した第２の∂Ａ／∂ｔ成分に基づいて、ｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するスパン補正部５２ａとから構成される。 The first and second exciting coils 3a and 3b and the power supply unit 4a serve as an exciting unit that applies 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 5a obtains the amplitude and phase of two frequency components of the first angular frequency ω0 and the second angular frequency ω2 in the combined electromotive force detected by the electrodes 2a and 2b in the first excitation state. The electromotive force difference between the two frequency components is extracted as the first ∂A / ∂t component based on these amplitudes and phases, and the component of the first angular frequency ω0 or the second angular frequency of the combined electromotive force is extracted. A zero point correction unit 51a that extracts the v × B component by removing the first ∂A / ∂t component from the ω2 component, and the combination detected by the electrodes 2a and 2b in the second excitation state The amplitude and phase of two frequency components of the electromotive force are obtained, and the electromotive force difference between the two frequency components is extracted as the second ∂A / ∂t component based on these amplitudes and phases. Based on the ∂A / ∂t component, the magnitude of the flow velocity V × B component V Composed of a span correction unit 52a for removing variation factor of the span is such factor.

本実施の形態では、前述のとおり、平面ＰＬＮから第１の励磁コイル３ａまでの距離ｄ１と平面ＰＬＮから第２の励磁コイル３ｂまでの距離ｄ２とが略等しいとする。
電源部４ａは、第１の角周波数ω０の正弦波成分と第２の角周波数ω２の正弦波成分とを含む第１の励磁電流を第１の励磁コイル３ａに供給すると同時に、第１の励磁電流との位相差がΔθ８で、第１の角周波数ω０の正弦波成分と第２の角周波数ω２の正弦波成分とを含む第２の励磁電流を第２の励磁コイル３ｂに供給する第１の励磁状態をＴ１秒継続し、この第１の励磁状態に対して第１の励磁電流と第２の励磁電流との位相差をΔθ８＋πに変更した第２の励磁状態をＴ２秒継続することをＴ秒周期で繰り返す。すなわち、Ｔ＝Ｔ１＋Ｔ２である。 In the present embodiment, as described above, it is assumed that the distance d1 from the plane PLN to the first excitation coil 3a and the distance d2 from the plane PLN to the second excitation coil 3b are substantially equal.
The power supply unit 4a supplies the first excitation current including the sine wave component having the first angular frequency ω0 and the sine wave component having the second angular frequency ω2 to the first excitation coil 3a, and at the same time, the first excitation current is supplied. A first excitation current having a phase difference of Δθ8 and including a sine wave component of the first angular frequency ω0 and a sine wave component of the second angular frequency ω2 is supplied to the second excitation coil 3b. The excitation state 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 Δθ8 + π with respect to the first excitation state is continued for T2 seconds. Repeats every T seconds. That is, T = T1 + T2.

図２３は信号変換部５ａと流量出力部６ａの動作を示すフローチャートである。まず、信号変換部５ａの０点補正部５１ａは、第１の励磁状態において、電極２ａと２ｂ間の起電力のうち角周波数ω０の成分の起電力Ｅ２０の振幅ｒ２０を求めると共に、実軸と電極間起電力Ｅ２０との位相差φ２０を図示しない位相検波器により求める。また、０点補正部５１ａは、第１の励磁状態において、電極２ａと２ｂ間の起電力のうち角周波数ω２の成分の起電力Ｅ２２の振幅ｒ２２を求めると共に、実軸と電極間起電力Ｅ２２との位相差φ２２を位相検波器により求める（図２３ステップ２０１）。   FIG. 23 is a flowchart showing the operation of the signal conversion unit 5a and the flow rate output unit 6a. First, the zero point correction unit 51a of the signal conversion unit 5a 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, A phase difference φ20 from the interelectrode electromotive force E20 is obtained by a phase detector (not shown). In addition, in the first excitation state, the zero point correction unit 51a 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 real axis and the interelectrode electromotive force E22. Is obtained by a phase detector (step 201 in FIG. 23).

続いて、０点補正部５１ａは、第２の励磁状態において、電極２ａと２ｂ間の起電力のうち角周波数ω０の成分の起電力Ｅ２π０の振幅ｒ２π０を求めると共に、実軸と電極間起電力Ｅ２π０との位相差φ２π０を位相検波器により求める。また、０点補正部５１ａは、第２の励磁状態において、電極２ａと２ｂ間の起電力のうち角周波数ω２の成分の起電力Ｅ２π２の振幅ｒ２π２を求めると共に、実軸と電極間起電力Ｅ２π２との位相差φ２π２を図示しない位相検波器により求める（ステップ２０２）。   Subsequently, in the second excitation state, the zero point correction unit 51a 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 between the real axis and the electrodes. A phase difference φ2π0 with respect to E2π0 is obtained by a phase detector. In addition, in the second excitation state, the zero point correction unit 51a 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 also generates the electromotive force E2π2 between the real axis and the electrode. Is obtained by a phase detector (not shown) (step 202).

次に、０点補正部５１ａは、電極間起電力Ｅ２０の実軸成分Ｅ２０ｘと虚軸成分Ｅ２０ｙ、および電極間起電力Ｅ２２の実軸成分Ｅ２２ｘと虚軸成分Ｅ２２ｙを次式のように算出する（ステップ２０３）。
Ｅ２０ｘ＝ｒ２０・ｃｏｓ（φ２０） ・・・（８５）
Ｅ２０ｙ＝ｒ２０・ｓｉｎ（φ２０） ・・・（８６）
Ｅ２２ｘ＝ｒ２２・ｃｏｓ（φ２２） ・・・（８７）
Ｅ２２ｙ＝ｒ２２・ｓｉｎ（φ２２） ・・・（８８） Next, the zero point correction unit 51a calculates the real axis component E20x and the imaginary axis component E20y of the interelectrode electromotive force E20, and the real axis component E22x and the imaginary axis component E22y of the interelectrode electromotive force E22 as follows. (Step 203).
E20x = r20 · cos (φ20) (85)
E20y = r20 · sin (φ20) (86)
E22x = r22 · cos (φ22) (87)
E22y = r22 · sin (φ22) (88)

式（８５）〜式（８８）の算出後、０点補正部５１ａは、電極間起電力Ｅ２０とＥ２２との起電力差ＥｄＡ２１の大きさを求める（ステップ２０４）。このステップ２０４の処理は、第１の∂Ａ／∂ｔ成分を求めることに対応する処理であり、式（８０）の算出に相当する処理である。０点補正部５１ａは、起電力差ＥｄＡ２１の実軸成分ＥｄＡ２１ｘと虚軸成分ＥｄＡ２１ｙを次式のように算出する。
ＥｄＡ２１ｘ＝（Ｅ２０ｘ−Ｅ２２ｘ）・ω０／（ω０−ω２） ・・・（８９）
ＥｄＡ２１ｙ＝（Ｅ２０ｙ−Ｅ２２ｙ）・ω０／（ω０−ω２） ・・・（９０） After calculating the equations (85) to (88), the zero point correction unit 51a calculates the magnitude of the electromotive force difference EdA21 between the electrode electromotive forces E20 and E22 (step 204). The process of step 204 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of Expression (80). The zero point correction unit 51a calculates the real axis component EdA21x and the imaginary axis component EdA21y of the electromotive force difference EdA21 as follows.
EdA21x = (E20x−E22x) · ω0 / (ω0−ω2) (89)
EdA21y = (E20y−E22y) · ω0 / (ω0−ω2) (90)

０点補正部５１ａは、電極間起電力Ｅ２０から起電力差ＥｄＡ２１を取り除き、ｖ×Ｂ成分ＥｖＢ２０の大きさを求める（ステップ２０５）。このステップ２０５の処理は、式（８１）の算出に相当する処理である。０点補正部５１ａは、ｖ×Ｂ成分ＥｖＢ２０の大きさ｜ＥｖＢ２０｜を次式のように算出する。
｜ＥｖＢ２０｜＝｛（Ｅ２０ｘ−ＥｄＡ２１ｘ）2
＋（Ｅ２０ｙ−ＥｄＡ２１ｙ）2｝1/2 ・・・（９１） The zero point correction unit 51a removes the electromotive force difference EdA21 from the interelectrode electromotive force E20, and obtains the magnitude of the v × B component EvB20 (step 205). The process of step 205 is a process corresponding to the calculation of equation (81). The zero point correction unit 51a calculates the magnitude | EvB20 | of the v × B component EvB20 as the following equation.
| EvB20 | = {(E20x−EdA21x) 2
+ (E20y-EdA21y) 2 } 1/2 (91)

次に、信号変換部５ａのスパン補正部５２ａは、電極間起電力Ｅ２π０の実軸成分Ｅ２π０ｘと虚軸成分Ｅ２π０ｙ、および電極間起電力Ｅ２π２の実軸成分Ｅ２π２ｘと虚軸成分Ｅ２π２ｙを次式のように算出する（ステップ２０６）。
Ｅ２π０ｘ＝ｒ２π０・ｃｏｓ（φ２π０） ・・・（９２）
Ｅ２π０ｙ＝ｒ２π０・ｓｉｎ（φ２π０） ・・・（９３）
Ｅ２π２ｘ＝ｒ２π２・ｃｏｓ（φ２π２） ・・・（９４）
Ｅ２π２ｙ＝ｒ２π２・ｓｉｎ（φ２π２） ・・・（９５） Next, the span correction unit 52a of the signal conversion unit 5a calculates the real axis component E2π0x and the imaginary axis component E2π0y of the interelectrode electromotive force E2π0 and the real axis component E2π2x and the imaginary axis component E2π2y of the interelectrode electromotive force E2π2 as (Step 206).
E2π0x = r2π0 · cos (φ2π0) (92)
E2π0y = r2π0 · sin (φ2π0) (93)
E2π2x = r2π2 · cos (φ2π2) (94)
E2π2y = r2π2 · sin (φ2π2) (95)

式（９２）〜式（９５）の算出後、スパン補正部５２ａは、電極間起電力Ｅ２π０とＥ２π２との起電力差ＥｄＡ２２の大きさを求める（ステップ２０７）。このステップ２０７の処理は、第２の∂Ａ／∂ｔ成分を求めることに対応する処理であり、式（８２）の算出に相当する処理である。スパン補正部５２ａは、起電力差ＥｄＡ２２の大きさ｜ＥｄＡ２２｜を次式のように算出する。
｜ＥｄＡ２２｜＝｛（Ｅ２π０ｘ−Ｅ２π２ｘ）2
＋（Ｅ２π０ｙ−Ｅ２π２ｙ）2｝1/2・ω０／（ω０−ω２）
・・・（９６） After calculating the equations (92) to (95), the span correction unit 52a obtains the magnitude of the electromotive force difference EdA22 between the electrode electromotive forces E2π0 and E2π2 (step 207). The process in step 207 is a process corresponding to obtaining the second ∂A / ∂t component, and is a process corresponding to the calculation of the equation (82). The span correction unit 52a calculates the magnitude | EdA22 | of the electromotive force difference EdA22 as the following equation.
| EdA22 | = {(E2π0x−E2π2x) 2
+ (E2π0y−E2π2y) 2 } 1/2 · ω0 / (ω0−ω2)
... (96)

続いて、スパン補正部５２ａは、ｖ×Ｂ成分ＥｖＢ２０を起電力差ＥｄＡ２２で正規化した正規化起電力ＥｖＢｎ２の大きさを求める（ステップ２０８）。このステップ２０８の処理は、式（８３）の算出に相当する処理である。スパン補正部５２ａは、正規化起電力ＥｖＢｎ２の大きさ｜ＥｖＢｎ２｜を次式のように算出する。
｜ＥｖＢｎ２｜＝（｜ＥｖＢ２０｜／｜ＥｄＡ２２｜）・ω０ ・・・（９７） Subsequently, the span correction unit 52a obtains the magnitude of the normalized electromotive force EvBn2 obtained by normalizing the v × B component EvB20 with the electromotive force difference EdA22 (step 208). The process of step 208 is a process corresponding to the calculation of equation (83). The span correction unit 52a calculates the magnitude | EvBn2 | of the normalized electromotive force EvBn2 as the following equation.
| EvBn2 | = (| EvB20 | / | EdA22 |) · ω0 (97)

流量出力部６ａは、被測定流体の流速の大きさＶを次式のように算出する（ステップ２０９）。このステップ２０９の処理は、式（８４）の算出に相当する処理である。
Ｖ＝｜ＥｖＢｎ２｜／γ ・・・（９８）
なお、比例係数γは、校正等により予め求めることができる定数である。信号変換部５ａと流量出力部６ａとは、以上のようなステップ２０１〜２０９の処理を例えばオペレータによって計測終了が指示されるまで（ステップ２１０においてＹＥＳ）、一定周期毎に行う。なお、ステップ２０２〜２０９の処理は第２の励磁状態において行われる。 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 209). The process of step 209 is a process corresponding to the calculation of equation (84).
V = | EvBn2 | / γ (98)
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 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.

以上のように、本実施の形態では、周波数が異なる２つの成分を含む磁場Ｂ７を第１の励磁コイル３ａから被測定流体に印加すると同時に、磁場Ｂ７との位相差がΔθ８（第１の値）で、周波数が異なる２つの成分を含む磁場Ｂ８を第２の励磁コイル３ｂから被測定流体に印加する第１の励磁状態において、角周波数ω０の成分の起電力Ｅ２０と角周波数ω２の成分の起電力Ｅ２２とを求め、電極間起電力Ｅ２０とＥ２２とから起電力差ＥｄＡ２１（第１の∂Ａ／∂ｔ成分）を抽出し、この第１の∂Ａ／∂ｔ成分を電極間起電力Ｅ２０（合成ベクトルＶａｓ０＋Ｖｂｓ０）の中から取り除くことによりｖ×Ｂ成分を抽出し、磁場Ｂ７と磁場Ｂ８との位相差を第１の励磁状態から一定値πだけ変化させた第２の励磁状態において、角周波数ω０の成分の起電力Ｅ２π０と角周波数ω２の成分の起電力Ｅ２π２とを求め、電極間起電力Ｅ２π０とＥ２π２とから起電力差ＥｄＡ２２（第２の∂Ａ／∂ｔ成分）を抽出し、この第２の∂Ａ／∂ｔ成分を用いてｖ×Ｂ成分の流速の大きさＶにかかるスパンを正規化して、スパン変動要素を消去するようにしたので、正確なスパン補正を自動的に行うことができ、かつ被測定流体の流量を０にすることなく電磁流量計の出力の０点を補正することができ、高周波励磁においても０点の安定性を確保することができる。   As described above, in the present embodiment, the magnetic field B7 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 B7 is Δθ8 (first value). ), In the first excitation state in which the magnetic field B8 including two components having different frequencies is applied from the second excitation coil 3b to the fluid to be measured, the electromotive force E20 of the component of the angular frequency ω0 and the component of the component of the angular frequency ω2 An electromotive force E22 is obtained, an electromotive force difference EdA21 (first ∂A / ∂t component) is extracted from the interelectrode electromotive forces E20 and E22, and the first ∂A / ∂t component is extracted from the interelectrode electromotive force. In the second excitation state in which the v × B component is extracted by removing it from E20 (synthetic vector Vas0 + Vbs0), and the phase difference between the magnetic field B7 and the magnetic field B8 is changed from the first excitation state by a constant value π. Formation of angular frequency ω0 The electromotive force E2π0 and the electromotive force E2π2 of the component of the angular frequency ω2 are obtained, and the electromotive force difference EdA22 (second ∂A / 抽出 t component) is extracted from the interelectrode electromotive forces E2π0 and E2π2, and this second Since the span of the v × B component flow velocity magnitude V is normalized using ∂A / ∂t components and the span variation factor is eliminated, accurate span correction can be performed automatically. In addition, 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.

また、本実施の形態では、電極２ａ，２ｂを含む平面ＰＬＮから第１の励磁コイル３ａまでの距離ｄ１と平面ＰＬＮから第２の励磁コイル３ｂまでの距離ｄ２とを調整することにより、電極間起電力Ｅ２０，Ｅ２２がほぼｖ×Ｂ成分の起電力のみとなり、電極間起電力Ｅ２π０，Ｅ２π２がほぼ∂Ａ／∂ｔ成分の起電力のみとなるようにすることができる。これにより、本実施の形態では、ｖ×Ｂ成分および∂Ａ／∂ｔ成分をより効果的に抽出することが可能であり、第１の実施の形態に比べて演算誤差を小さくすることが可能である。   In the present embodiment, the distance d1 from the plane PLN including the electrodes 2a and 2b to the first excitation coil 3a and the distance d2 from the plane PLN to the second excitation coil 3b are adjusted to adjust the distance between the electrodes. The electromotive forces E20 and E22 can be substantially only the electromotive force of the v × B component, and the inter-electrode electromotive forces E2π0 and E2π2 can be only the electromotive force of the ∂A / ∂t component. Thereby, in this embodiment, it is possible to extract the v × B component and the ∂A / ∂t component more effectively, and the calculation error can be reduced as compared with the first embodiment. It is.

なお、本実施の形態では、角周波数ω０の成分の起電力Ｅ２０を０補正およびスパン補正の対象としたが、角周波数ω２の成分の起電力Ｅ２２を０補正およびスパン補正の対象としてもよい。この場合は、次式のように電極間起電力Ｅ２２からＥ２０を引いて起電力差ＥｄＡ２１（第１の∂Ａ／∂ｔ成分）を求める。
ＥｄＡ２１＝（Ｅ２２−Ｅ２０）・ω２／（ω２−ω０） ・・・（９９）
そして、電極間起電力Ｅ２２から起電力差ＥｄＡ２１を引くことによりｖ×Ｂ成分ＥｖＢ２２を抽出する。 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 EdA21 (first ∂A / ∂t component) is obtained by subtracting E20 from the interelectrode electromotive force E22 as in the following equation.
EdA21 = (E22−E20) · ω2 / (ω2−ω0) (99)
Then, the v × B component EvB22 is extracted by subtracting the electromotive force difference EdA21 from the interelectrode electromotive force E22.

さらに、次式のように電極間起電力Ｅ２π２からＥ２π０を引いて起電力差ＥｄＡ２２（第２の∂Ａ／∂ｔ成分）を求める。
ＥｄＡ２２＝（Ｅ２π２−Ｅ２π０）・ω２／（ω２−ω０） ・・・（１００）
そして、次式のように起電力差ＥｄＡ２２を用いてｖ×Ｂ成分ＥｖＢ２２の流速の大きさＶにかかるスパンを正規化すればよい。その他の処理は電極間起電力Ｅ２０を０補正およびスパン補正の対象とする場合と同じである。
｜ＥｖＢｎ２｜＝｜（ＥｖＢ２２／ＥｄＡ２２）・ω２｜ ・・・（１０１） Further, the electromotive force difference EdA22 (second ∂A / ∂t component) is obtained by subtracting E2π0 from the interelectrode electromotive force E2π2 as in the following equation.
EdA22 = (E2π2-E2π0) · ω2 / (ω2-ω0) (100)
And the span concerning the magnitude | size V of the flow velocity of vxB component EvB22 should just be normalized using the electromotive force difference EdA22 like following Formula. The other processes are the same as the case where the interelectrode electromotive force E20 is the target of zero correction and span correction.
| EvBn2 | = | (EvB22 / EdA22) · ω2 | (101)

また、本実施の形態では、複数の励磁周波数ω０，ω２で同時に励磁する例を示したが、単一の励磁周波数ω０又はω２で励磁を行い、励磁周波数をω０とω２で交互に切り替えながら励磁をした場合でも同じ効果を得ることができる。   In this embodiment, an example is shown in which excitation is performed simultaneously with a plurality of excitation frequencies ω0 and ω2, but excitation is performed with a single excitation frequency ω0 or ω2, and excitation is performed while alternately switching the excitation frequency between ω0 and ω2. The same effect can be obtained even when

［第３の実施の形態］
次に、本発明の第３の実施の形態について説明する。本実施の形態は、前述の第２の基本原理を用いるものである。本実施の形態の電磁流量計は２個の励磁コイルと１対の電極とを有するものであり、信号処理系を除く構成は図５に示した電磁流量計と同様であるので、図５の符号を用いて本実施の形態の原理を説明する。 [Third Embodiment]
Next, a third embodiment of the present invention will be described. This embodiment uses the second basic principle described above. 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.

式（８１）で示したｖ×Ｂ成分ＥｖＢ２０の流速の大きさＶにかかる係数（スパン）の変動要因を除去するために、このスパンの変動要因と同じ変動要因を持つ第２の∂Ａ／∂ｔ成分を抽出する。このときの抽出方法としては第２の基本原理で説明した第２の抽出方法を用いる。   In order to remove the variation factor of the coefficient (span) related to the magnitude V of the flow velocity of the v × B component EvB20 represented by the equation (81), the second ∂A / ∂t component is extracted. As the extraction method at this time, the second extraction method described in the second basic principle is used.

初期状態（校正時の状態）において、第１の励磁コイル３ａから発生する磁場Ｂ７と第２の励磁コイル３ｂから発生する磁場Ｂ８を等しく設定しておくと、その後の磁場Ｂ７とＢ８との差は小さくなり、次式の条件が成り立つ。
｜ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｜≫｜ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｜
・・・（１０２） If the magnetic field B7 generated from the first excitation coil 3a and the magnetic field B8 generated from the second excitation coil 3b are set equal in the initial state (state at the time of calibration), the difference between the subsequent magnetic fields B7 and B8 Becomes smaller and the following condition is satisfied.
| B7 + b8 · exp (j · Δθ8) | >> | b7−b8 · exp (j · Δθ8) |
... (102)

また、通常ω０＞γ・Ｖが成り立つことから、式（１０２）の条件を考慮すると、式（７４）において次式の条件が成り立つ。
｜ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝｜
≫｜γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ７−ｂ８・ｅｘｐ（ｊ・Δθ８）｝｜
・・・（１０３） In addition, since ω0> γ · V is normally satisfied, when the condition of the equation (102) is considered, the following equation is satisfied in the equation (74).
| Ω0 · exp (j · π / 2) · {b7 + b8 · exp (j · Δθ8)} |
»| Γ · V · exp (j · Δθ01) · {b7-b8 · exp (j · Δθ8)} |
... (103)

式（１０３）の条件を用いて、電極間起電力Ｅ２π０を近似した電極間起電力ＥｄＡ３２は次式のように表される。ここで、起電力ＥｄＡ３２は第２の基本原理の第２の∂Ａ／∂ｔ成分に相当する。
ＥｄＡ３２≒Ｅ２π０ ・・・（１０４）
ＥｄＡ３２＝ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝
・・・（１０５） The interelectrode electromotive force EdA32 that approximates the interelectrode electromotive force E2π0 using the condition of the equation (103) is expressed as the following equation. Here, the electromotive force EdA32 corresponds to the second ∂A / ∂t component of the second basic principle.
EdA32≈E2π0 (104)
EdA32 = rk · exp {j · (θ7 + θ00)}
.Omega.0.exp (j.pi / 2). {B7 + b8.exp (j..DELTA..theta.8)}
... (105)

電極間起電力ＥｄＡ３２は、流速の大きさＶに関係しないので、∂Ａ／∂ｔにより発生する成分のみとなる。この電極間起電力ＥｄＡ３２を用いて、ｖ×Ｂ成分ＥｖＢ２０の流速の大きさＶにかかる係数（スパン）を正規化する。式（８１）のｖ×Ｂ成分ＥｖＢ２０を式（１０５）の電極間起電力ＥｄＡ３２で正規化し、ω０倍したものをＥｖＢｎ３とすれば、正規化起電力ＥｖＢｎ３は次式で表される。
ＥｖＢｎ３＝（ＥｖＢ２０／ＥｄＡ３２）・ω０
＝［γ・ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００＋Δθ０１）｝
・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］・Ｖ
／［ｒｋ・ｅｘｐ｛ｊ・（θ７＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ７＋ｂ８・ｅｘｐ（ｊ・Δθ８）｝］・ω０
＝［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］・Ｖ ・・・（１０６） Since the interelectrode electromotive force EdA32 is not related to the magnitude V of the flow velocity, it is only a component generated by ∂A / ∂t. The interelectrode electromotive force EdA32 is used to normalize the coefficient (span) applied to the flow velocity magnitude V of the v × B component EvB20. If the v × B component EvB20 of the equation (81) is normalized by the interelectrode electromotive force EdA32 of the equation (105) and multiplied by ω0 is EvBn3, the normalized electromotive force EvBn3 is expressed by the following equation.
EvBn3 = (EvB20 / EdA32) · ω0
= [Γ · rk · exp {j · (θ7 + θ00 + Δθ01)}
{B7 + b8 · exp (j · Δθ8)}] · V
/ [Rk · exp {j · (θ7 + θ00)}
Ω0 · exp (j · π / 2) · {b7 + b8 · exp (j · Δθ8)}] · ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (106)

式（１０６）ではｖ×Ｂにより発生する成分が正規化されスパンの変動要因が除去されている。流速の大きさＶにかかる複素係数は、γの大きさ、−π／２＋Δθ０１の実軸からの角度をもつ。係数γおよび角度Δθ０１は校正等により予め求めることができる定数であり、正規化起電力ＥｖＢｎ３は被測定流体の流速が変化しないかぎり一定となる。したがって、抽出した第２の∂Ａ／∂ｔの成分をもちいてｖ×Ｂ成分の正規化を行うことにより、０点の補正に加えて、磁場のシフトや位相変化による誤差を自動的に補正するスパン補正を実現することができる。   In the equation (106), the component generated by v × B is normalized to remove the span variation factor. 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 normalized electromotive force EvBn3 is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by normalizing the v × B component using the extracted second ∂A / ∂t component, in addition to the zero point correction, errors due to magnetic field shift and phase change are automatically corrected. Span correction can be realized.

式（１０６）より、流速の大きさＶは次式のように表される。
Ｖ＝｜ＥｖＢｎ３／［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］｜
＝｜ＥｖＢｎ３｜／γ ・・・（１０７） From the equation (106), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn3 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn3 | / γ (107)

なお、第２の基本原理で用いた定数および変数と、本実施の形態の定数および変数との対応関係は以下の表３のとおりである。本実施の形態は、表３から明らかなように、前述の第２の基本原理を具体的に実現する１つの例である。   The correspondence relationship between the constants and variables used in the second basic principle and the constants and variables of the present embodiment is as shown in Table 3 below. As is apparent from Table 3, this embodiment is one example that specifically realizes the second basic principle described above.

Figure 0004555023
Figure 0004555023

次に、本実施の形態の電磁流量計の具体的な構成とその動作について説明する。本実施の形態の電磁流量計の構成は第２の実施の形態と同様であるので、図２２の符号を用いて説明する。本実施の形態の電磁流量計は、測定管１と、電極２ａ，２ｂと、第１、第２の励磁コイル３ａ，３ｂと、第１、第２の励磁コイル３ａ，３ｂに励磁電流を供給する電源部４ａと、信号変換部５ａと、流量出力部６ａとを有する。   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 second embodiment, description will be made using the reference numerals 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 4a, signal conversion unit 5a, and flow rate output unit 6a.

信号変換部５ａは、第１の励磁状態において、電極２ａ，２ｂで検出される合成起電力のうち第１の角周波数ω０と第２の角周波数ω２の２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて２つの周波数成分の起電力差を第１の∂Ａ／∂ｔ成分として抽出し、合成起電力のうち第１の角周波数ω０の成分又は第２の角周波数ω２の成分の中から、第１の∂Ａ／∂ｔ成分を取り除くことによりｖ×Ｂ成分を抽出する０点補正部５１ａと、第２の励磁状態において、電極２ａ，２ｂで検出される合成起電力のうち第１の角周波数ω０の成分又は第２の角周波数ω２の成分の振幅と位相を求め、この振幅と位相に基づいて第１の角周波数ω０の成分又は第２の角周波数ω２の成分の起電力を第２の∂Ａ／∂ｔ成分として抽出し、この抽出した第２の∂Ａ／∂ｔ成分に基づいて、ｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するスパン補正部５２ａとから構成される。   The signal conversion unit 5a obtains the amplitude and phase of two frequency components of the first angular frequency ω0 and the second angular frequency ω2 in the combined electromotive force detected by the electrodes 2a and 2b in the first excitation state. The electromotive force difference between the two frequency components is extracted as the first ∂A / ∂t component based on these amplitudes and phases, and the component of the first angular frequency ω0 or the second angular frequency of the combined electromotive force is extracted. A zero point correction unit 51a that extracts the v × B component by removing the first ∂A / ∂t component from the ω2 component, and the combination detected by the electrodes 2a and 2b in the second excitation state The amplitude and phase of the component of the first angular frequency ω0 or the component of the second angular frequency ω2 of the electromotive force are obtained, and the component of the first angular frequency ω0 or the second angular frequency ω2 is obtained based on the amplitude and phase. Is extracted as the second ∂A / ∂t component, and this extraction Was based on the second ∂A / ∂t component, v composed of a span correction unit 52a for removing variation factor of the span is a coefficient according to the magnitude V of the flow velocity of × B component.

電源部４ａの動作は第２の実施の形態と同じである。図２４は本実施の形態の信号変換部５ａと流量出力部６ａの動作を示すフローチャートである。まず、図２４のステップ３０１の処理は図２３のステップ２０１と同じである。続いて、信号変換部５ａの０点補正部５１ａは、第２の励磁状態において、電極２ａと２ｂ間の起電力のうち角周波数ω０の成分の起電力Ｅ２π０の振幅ｒ２π０を求めると共に、実軸と電極間起電力Ｅ２π０との位相差φ２π０を位相検波器により求める（ステップ３０２）。図２４のステップ３０３〜３０５の処理は、それぞれステップ２０３〜２０５と同じである。   The operation of the power supply unit 4a is the same as that of the second embodiment. FIG. 24 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 processing in step 301 in FIG. 24 is the same as that in step 201 in FIG. Subsequently, the zero point correction unit 51a of the signal conversion unit 5a 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 in the second excitation state, and the real axis And a phase detector φ2π0 is obtained by a phase detector (step 302). The processing in steps 303 to 305 in FIG. 24 is the same as that in steps 203 to 205, respectively.

次に、信号変換部５ａのスパン補正部５２ａは、電極間起電力Ｅ２π０を近似した起電力ＥｄＡ３２の大きさを求める（ステップ３０６）。このステップ３０６の処理は、第２の∂Ａ／∂ｔ成分を求めることに対応する処理であり、式（１０５）の算出に相当する処理である。スパン補正部５２ａは、電極間起電力Ｅ２π０を近似した起電力ＥｄＡ３２の大きさ｜ＥｄＡ３２｜を次式のように算出する。
｜ＥｄＡ３２｜＝ｒ２π０ ・・・（１０８） Next, the span correction unit 52a of the signal conversion unit 5a obtains the magnitude of the electromotive force EdA32 that approximates the interelectrode electromotive force E2π0 (step 306). The process of step 306 is a process corresponding to obtaining the second ∂A / ∂t component, and is a process corresponding to the calculation of equation (105). The span correction unit 52a calculates the magnitude | EdA32 | of the electromotive force EdA32 that approximates the interelectrode electromotive force E2π0 as the following equation.
| EdA32 | = r2π0 (108)

続いて、スパン補正部５２ａは、ｖ×Ｂ成分ＥｖＢ２０を電極間起電力ＥｄＡ３２で正規化した正規化起電力ＥｖＢｎ３の大きさを求める（ステップ３０７）。このステップ３０７の処理は、式（１０６）の算出に相当する処理である。スパン補正部５２ａは、正規化起電力ＥｖＢｎ３の大きさ｜ＥｖＢｎ３｜を次式のように算出する。
｜ＥｖＢｎ３｜＝（｜ＥｖＢ２０｜／｜ＥｄＡ３２｜）・ω０ ・・・（１０９） Subsequently, the span correction unit 52a obtains the magnitude of the normalized electromotive force EvBn3 obtained by normalizing the v × B component EvB20 with the interelectrode electromotive force EdA32 (step 307). The process of step 307 is a process corresponding to the calculation of equation (106). The span correction unit 52a calculates the magnitude | EvBn3 | of the normalized electromotive force EvBn3 as follows.
| EvBn3 | = (| EvB20 | / | EdA32 |) · ω0 (109)

流量出力部６ａは、被測定流体の流速の大きさＶを次式のように算出する（ステップ３０８）。このステップ３０８の処理は、式（１０７）の算出に相当する処理である。
Ｖ＝｜ＥｖＢｎ３｜／γ ・・・（１１０）
なお、比例係数γは、校正等により予め求めることができる定数である。信号変換部５ａと流量出力部６ａとは、以上のようなステップ３０１〜３０８の処理を例えばオペレータによって計測終了が指示されるまで（ステップ３０９においてＹＥＳ）、一定周期毎に行う。なお、ステップ３０２〜３０８の処理は第２の励磁状態において行われる。 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 308). The process of step 308 is a process corresponding to the calculation of equation (107).
V = | EvBn3 | / γ (110)
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 301 to 308 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 309). Note that the processing in steps 302 to 308 is performed in the second excitation state.

以上のように、本実施の形態では、第１の励磁コイル３ａから発生する磁場Ｂ７と第２の励磁コイル３ｂから発生する磁場Ｂ８とが等しくなるように設定しておくと、電極間起電力Ｅ２π０が近似的に第２の∂Ａ／∂ｔ成分として抽出できることに着眼し、第２の実施の形態と同様にｖ×Ｂ成分を抽出した後、近似的に抽出した第２の∂Ａ／∂ｔ成分を用いてｖ×Ｂ成分の流速の大きさＶにかかるスパンを正規化して、スパン変動要素を消去するようにしたので、正確なスパン補正を自動的に行うことができ、かつ被測定流体の流量を０にすることなく電磁流量計の出力の０点を補正することができ、高周波励磁においても０点の安定性を確保することができる。また、本実施の形態では、角周波数ω０の起電力Ｅ２０から抽出したｖ×Ｂ成分を同じ角周波数ω０の起電力Ｅ２π０から抽出した第２の∂Ａ／∂ｔ成分を用いて正規化するので、第２の実施の形態に比べて周波数による誤差の影響を少なくすることができる。   As described above, in the present embodiment, when the magnetic field B7 generated from the first excitation coil 3a is set to be equal to the magnetic field B8 generated from the second excitation coil 3b, the inter-electrode electromotive force is set. Focusing on the fact that E2π0 can be approximately extracted as the second ∂A / ∂t component, after extracting the v × B component as in the second embodiment, the second ∂A / Since the span for the magnitude V of the flow velocity of the v × B component is normalized using the ∂t component to eliminate the span variation element, accurate span correction can be automatically performed and The zero point of the output of the electromagnetic flow meter can be corrected without setting the flow rate of the measurement fluid to zero, and the stability of the zero point can be ensured even in high frequency excitation. In the present embodiment, the v × B component extracted from the electromotive force E20 having the angular frequency ω0 is normalized using the second ∂A / ∂t component extracted from the electromotive force E2π0 having the same angular frequency ω0. Compared with the second embodiment, the influence of the error due to the frequency can be reduced.

なお、本実施の形態では、角周波数ω０の成分の起電力Ｅ２０を０補正およびスパン補正の対象としたが、角周波数ω２の成分の起電力Ｅ２２を０補正およびスパン補正の対象としてもよい。この場合は、第２の励磁状態において電極間起電力Ｅ２π０を求める代わりに、Ｅ２π２を求める。そして、次式のように電極間起電力Ｅ２２からＥ２０を引いて起電力差ＥｄＡ２１（第１の∂Ａ／∂ｔ成分）を求める。
ＥｄＡ２１＝（Ｅ２２−Ｅ２０）・ω２／（ω２−ω０） ・・・（１１１）
そして、電極間起電力Ｅ２２から起電力差ＥｄＡ２１を引くことによりｖ×Ｂ成分ＥｖＢ２２を抽出する。 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, instead of obtaining the interelectrode electromotive force E2π0 in the second excitation state, E2π2 is obtained. Then, the electromotive force difference EdA21 (first ∂A / ∂t component) is obtained by subtracting E20 from the interelectrode electromotive force E22 as in the following equation.
EdA21 = (E22−E20) · ω2 / (ω2−ω0) (111)
Then, the v × B component EvB22 is extracted by subtracting the electromotive force difference EdA21 from the interelectrode electromotive force E22.

さらに、次式のように電極間起電力Ｅ２π２を近似した起電力ＥｄＡ３２（第２の∂Ａ／∂ｔ成分）を求める。
ＥｄＡ３２≒Ｅ２π２ ・・・（１１２）
そして、次式のように電極間起電力ＥｄＡ３２を用いてｖ×Ｂ成分ＥｖＢ２２の流速の大きさＶにかかるスパンを正規化すればよい。その他の処理は電極間起電力Ｅ２０を０補正およびスパン補正の対象とする場合と同じである。
｜ＥｖＢｎ３｜＝｜（ＥｖＢ２２／ＥｄＡ３２）・ω２｜ ・・・（１１３） Further, an electromotive force EdA32 (second ∂A / ∂t component) that approximates the interelectrode electromotive force E2π2 is obtained as in the following equation.
EdA32≈E2π2 (112)
And the span concerning the magnitude | size V of the flow velocity of vxB component EvB22 should just be normalized using the electromotive force EdA32 between electrodes like following Formula. The other processes are the same as the case where the interelectrode electromotive force E20 is the target of zero correction and span correction.
| EvBn3 | = | (EvB22 / EdA32) · ω2 | (113)

また、本実施の形態では、複数の励磁周波数ω０，ω２で同時に励磁する例を示したが、単一の励磁周波数ω０又はω２で励磁を行い、励磁周波数をω０とω２で交互に切り替えながら励磁をした場合でも同じ効果を得ることができる。   In this embodiment, an example is shown in which excitation is performed simultaneously with a plurality of excitation frequencies ω0 and ω2, but excitation is performed with a single excitation frequency ω0 or ω2, and excitation is performed while alternately switching the excitation frequency between ω0 and ω2. The same effect can be obtained even when

［第４の実施の形態］
次に、本発明の第４の実施の形態について説明する。本実施の形態は、第１の実施の形態の電磁流量計に対して電極を１個追加したものであり、前述の第２の基本原理を用いるものである。本実施の形態の電磁流量計は１個の励磁コイルと２対の電極とを有するものであり、信号処理系を除く構成は図１７に示した電磁流量計と同様であるので、図１７の符号を用いて本実施の形態の原理を説明する。新たに追加する第２の電極を既存の第１の電極と同じ側に追加した場合には、第１の実施の形態の冗長な構成となる。したがって、第２の電極は、励磁コイルを挟んで第１の電極と異なる側に配設する必要がある。 [Fourth Embodiment]
Next, a fourth embodiment of the present invention will be described. In the present embodiment, one electrode is added to the electromagnetic flow meter of the first embodiment, and the second basic principle described above is used. 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.

励磁コイル３から発生する磁場Ｂｄのうち、電極２ａ，２ｂ間を結ぶ電極軸ＥＡＸ１上において電極軸ＥＡＸ１および測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ９と、励磁コイル３から発生する磁場Ｂｄのうち、電極２ｃ，２ｄ間を結ぶ電極軸ＥＡＸ２上において電極軸ＥＡＸ２および測定管軸ＰＡＸの双方と直交する磁場成分（磁束密度）Ｂ１０は、以下のように与えられるものとする。
Ｂ９＝ｂ９・ｃｏｓ（ω０・ｔ−θ９）＋ｂ９・ｃｏｓ（ω２・ｔ−θ９）
・・・（１１４）
Ｂ１０＝ｂ１０・ｃｏｓ（ω０・ｔ−θ１０）＋ｂ１０・ｃｏｓ（ω２・ｔ−θ１０）
・・・（１１５） Of the magnetic field Bd generated from the exciting coil 3, the magnetic field component (magnetic flux density) B9 orthogonal to both the electrode axis EAX1 and the measuring tube axis PAX on the electrode axis EAX1 connecting the electrodes 2a and 2b, and generated from the exciting coil 3 The magnetic field component (magnetic flux density) B10 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.
B9 = b9 · cos (ω0 · t−θ9) + b9 · cos (ω2 · t−θ9)
... (114)
B10 = b10 · cos (ω0 · t−θ10) + b10 · cos (ω2 · t−θ10)
... (115)

但し、Ｂ９、Ｂ１０は１つの励磁コイル３から発生しているので、ｂ９とｂ１０、θ９とθ１０は互いに関係があり、独立変数ではない。式（１１４）、式（１１５）において、ω０，ω２は異なる角周波数、ｂ９は磁束密度Ｂ９の角周波数ω０の成分の振幅および角周波数ω２の成分の振幅、ｂ１０は磁束密度Ｂ１０の角周波数ω０の成分の振幅および角周波数ω２の成分の振幅、θ９は磁束密度Ｂ９の角周波数ω０の成分とω０・ｔとの位相差（位相遅れ）および角周波数ω２の成分とω２・ｔとの位相差、θ１０は磁束密度Ｂ１０の角周波数ω０の成分とω０・ｔとの位相差および角周波数ω２の成分とω２・ｔとの位相差である。以下、磁束密度Ｂ９を磁場Ｂ９とし、磁束密度Ｂ１０を磁場Ｂ１０とする。   However, since B9 and B10 are generated from one exciting coil 3, b9 and b10 and θ9 and θ10 are related to each other and are not independent variables. In Expressions (114) and (115), ω0 and ω2 are different angular frequencies, b9 is the amplitude of the angular frequency ω0 component and the amplitude of the angular frequency ω2 component of the magnetic flux density B9, and b10 is the angular frequency ω0 of the magnetic flux density B10. And θ9 is the phase difference (phase lag) between the angular frequency ω0 component of the magnetic flux density B9 and ω0 · t, and the phase difference between the angular frequency ω2 component and ω2 · t. , Θ10 is the phase difference between the angular frequency ω0 component of the magnetic flux density B10 and ω0 · t, and the phase difference between the angular frequency ω2 component and ω2 · t. Hereinafter, the magnetic flux density B9 is referred to as a magnetic field B9, and the magnetic flux density B10 is referred to as a magnetic field B10.

被測定流体の流量が０の場合、発生する渦電流は、磁場の変化に起因する成分のみとなり、磁場Ｂｄの変化による渦電流Ｉは、図１８に示すような向きとなる。したがって、電極軸ＥＡＸ１と測定管軸ＰＡＸとを含む平面内において、磁場Ｂｄの変化によって発生する、流速と無関係な第１の電極間起電力Ｅ１と、電極軸ＥＡＸ２と測定管軸ＰＡＸとを含む平面内において、磁場Ｂｄの変化によって発生する、流速と無関係な第２の電極間起電力Ｅ２は、図１８に示すように互いに逆向きとなる   When the flow rate 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 Bd has a direction as shown in FIG. Accordingly, in the plane including the electrode axis EAX1 and the measurement tube axis PAX, the first interelectrode electromotive force E1 which is generated by the change of the magnetic field Bd and is independent of the flow velocity, the electrode axis EAX2, and the measurement tube axis PAX is included. In the plane, the second inter-electrode electromotive force E2 generated by the change of the magnetic field Bd and irrelevant to the flow velocity is opposite to each other as shown in FIG.

被測定流体の流速の大きさがＶ（Ｖ≠０）の場合、発生する渦電流には、流速０のときの渦電流Ｉに加えて、被測定流体の流速ベクトルｖに起因する成分ｖ×Ｂｄが発生するため、流速ベクトルｖと磁場Ｂｄによる渦電流Ｉｖは、図１９に示すような向きとなる。したがって、流速ベクトルｖと磁場Ｂｄによって発生する第１の電極間起電力Ｅｖ１、流速ベクトルｖと磁場Ｂｄによって発生する第２の電極間起電力Ｅｖ２は、同じ向きとなる。   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 Bd is generated, the eddy current Iv due to the flow velocity vector v and the magnetic field Bd is oriented as shown in FIG. Therefore, the first interelectrode electromotive force Ev1 generated by the flow velocity vector v and the magnetic field Bd, and the second interelectrode electromotive force Ev2 generated by the flow velocity vector v and the magnetic field Bd are in the same direction.

図１８、図１９で説明した電極間起電力の向きを考慮すると、磁場の時間変化に起因する電極間起電力を複素ベクトルに変換した起電力と被測定流体の流速に起因する電極間起電力を複素ベクトルに変換した起電力とを合わせた、電極２ａ，２ｂ間の第１の電極間起電力のうち、角周波数ω０の成分の起電力Ｅ４１０ｃは式（４４）と同様の次式で表される。
Ｅ４１０ｃ＝ｒｋ・ω０・ｂ９・ｅｘｐ｛ｊ・（π／２＋θ９＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ９・ｅｘｐ｛ｊ・（θ９＋θ０１）｝ ・・（１１６） In consideration of the direction of the interelectrode electromotive force described in FIGS. 18 and 19, the electromotive force generated 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 first inter-electrode electromotive force between the electrodes 2a and 2b, the electromotive force E410c of the component of the angular frequency ω0 is expressed by the following equation similar to the equation (44). Is done.
E410c = rk · ω0 · b9 · exp {j · (π / 2 + θ9 + θ00)}
+ Γ · rk · V · b9 · exp {j · (θ9 + θ01)} (116)

また、電極２ａ，２ｂ間の第１の電極間起電力のうち、角周波数ω２の成分の起電力Ｅ４１２ｃは式（４４）と同様の次式で表される。
Ｅ４１２ｃ＝ｒｋ・ω２・ｂ９・ｅｘｐ｛ｊ・（π／２＋θ９＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ９・ｅｘｐ｛ｊ・（θ９＋θ０１）｝ ・・（１１７） Of the first interelectrode electromotive force between the electrodes 2a and 2b, the electromotive force E412c of the component of the angular frequency ω2 is expressed by the following equation similar to the equation (44).
E412c = rk · ω2 · b9 · exp {j · (π / 2 + θ9 + θ00)}
+ Γ · rk · V · b9 · exp {j · (θ9 + θ01)} (117)

同様に、図１８、図１９で説明した電極間起電力の向きを考慮すると、磁場の時間変化に起因する電極間起電力を複素ベクトルに変換した起電力と被測定流体の流速に起因する電極間起電力を複素ベクトルに変換した起電力とを合わせた、電極２ｃ，２ｄ間の第２の電極間起電力のうち、角周波数ω０の成分の起電力Ｅ４２０ｃは式（４５）と同様の次式で表される。
Ｅ４２０ｃ＝ｒｋ・ω０・ｂ１０・ｅｘｐ｛ｊ・（−π／２＋θ１０＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ１０・ｅｘｐ｛ｊ・（θ１０＋θ０１）｝
・・・（１１８） Similarly, in consideration of the direction of the electromotive force between the electrodes described in FIGS. 18 and 19, the electromotive force obtained by converting the interelectrode electromotive force caused by the time change of the magnetic field into a complex vector and the electrode caused by the flow velocity of the fluid to be measured. Of the second inter-electrode electromotive force between the electrodes 2c and 2d, which is combined with the electromotive force obtained by converting the inter-electromotive force into a complex vector, the electromotive force E420c of the component of the angular frequency ω0 is the same as the equation (45). It is expressed by an expression.
E420c = rk · ω0 · b10 · exp {j · (−π / 2 + θ10 + θ00)}
+ Γ · rk · V · b10 · exp {j · (θ10 + θ01)}
... (118)

また、電極２ｃ，２ｄ間の第２の電極間起電力のうち、角周波数ω２の成分の起電力Ｅ４２２ｃは式（４５）と同様の次式で表される。
Ｅ４２２ｃ＝ｒｋ・ω２・ｂ１０・ｅｘｐ｛ｊ・（−π／２＋θ１０＋θ００）｝
＋γ・ｒｋ・Ｖ・ｂ１０・ｅｘｐ｛ｊ・（θ１０＋θ０１）｝
・・・（１１９） Of the second interelectrode electromotive force between the electrodes 2c and 2d, the electromotive force E422c of the component of the angular frequency ω2 is expressed by the following equation similar to the equation (45).
E422c = rk · ω2 · b10 · exp {j · (−π / 2 + θ10 + θ00)}
+ Γ · rk · V · b10 · exp {j · (θ10 + θ01)}
... (119)

ここで、ω０・ｔ，ω２・ｔに対する磁場Ｂ９の位相遅れθ９とω０・ｔ，ω２・ｔに対する磁場Ｂ１０の位相遅れθ１０との関係をθ１０＝θ９＋Δθ１０とし、虚軸に対する∂Ａ／∂ｔ成分の角度θ００と実軸に対するｖ×Ｂ成分の角度θ０１との関係をθ０１＝θ００＋Δθ０１とする。式（１１６）にθ１０＝θ９＋Δθ１０、θ０１＝θ００＋Δθ０１を代入したときの第１の電極間起電力Ｅ４１０ｃと式（１１８）にθ１０＝θ９＋Δθ１０、θ０１＝θ００＋Δθ０１を代入したときの第２の電極間起電力Ｅ４２０ｃとの和をＥ４ｓ０とすれば、起電力和Ｅ４ｓ０は次式で表される。
Ｅ４ｓ０＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）
・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）
・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］ ・・・（１２０） Here, the relationship between the phase delay θ9 of the magnetic field B9 with respect to ω0 · t and ω2 · t and the phase delay θ10 of the magnetic field B10 with respect to ω0 · t and ω2 · t is θ10 = θ9 + Δθ10, and ∂A / ∂t component with respect to the imaginary axis And θ01 = θ00 + Δθ01 between the angle θ00 and the angle θ01 of the v × B component with respect to the real axis. The first inter-electrode electromotive force E410c when θ10 = θ9 + Δθ10 and θ01 = θ00 + Δθ01 are substituted into equation (116), and the second inter-electrode electromotive force when θ10 = θ9 + Δθ10 and θ01 = θ00 + Δθ01 are substituted into equation (118) If the sum with E420c is E4s0, the electromotive force sum E4s0 is expressed by the following equation.
E4s0 = rk · exp {j · (θ9 + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B9-b10 · exp (j · Δθ10)}
+ Γ · V · exp (j · Δθ01)
{B9 + b10 · exp (j · Δθ10)}] (120)

また、式（１１７）にθ１０＝θ９＋Δθ１０、θ０１＝θ００＋Δθ０１を代入したときの第１の電極間起電力Ｅ４１２ｃと式（１１９）にθ１０＝θ９＋Δθ１０、θ０１＝θ００＋Δθ０１を代入したときの第２の電極間起電力Ｅ４２２ｃとの和をＥ４ｓ２とすれば、起電力和Ｅ４ｓ２は次式で表される。
Ｅ４ｓ２＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・［ω２・ｅｘｐ（ｊ・π／２）
・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）
・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］ ・・・（１２１） Further, the first inter-electrode electromotive force E412c when θ10 = θ9 + Δθ10 and θ01 = θ00 + Δθ01 are substituted into the equation (117), and the second electrode interval when θ10 = θ9 + Δθ10 and θ01 = θ00 + Δθ01 are substituted into the equation (119). If the sum of the electromotive force E422c and E4s2 is E4s2, the electromotive force sum E4s2 is expressed by the following equation.
E4s2 = rk · exp {j · (θ9 + θ00)}
・ [Ω2 ・ exp (j ・ π / 2)
{B9-b10 · exp (j · Δθ10)}
+ Γ · V · exp (j · Δθ01)
{B9 + b10 · exp (j · Δθ10)}] (121)

また、式（１１６）にθ１０＝θ９＋Δθ１０、θ０１＝θ００＋Δθ０１を代入したときの第１の電極間起電力Ｅ４１０ｃと式（１１８）にθ１０＝θ９＋Δθ１０、θ０１＝θ００＋Δθ０１を代入したときの第２の電極間起電力Ｅ４２０ｃとの差をＥ４ｄ０とすれば、起電力差Ｅ４ｄ０は次式で表される。
Ｅ４ｄ０＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）
・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）
・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］ ・・・（１２２） Also, the first inter-electrode electromotive force E410c when θ10 = θ9 + Δθ10 and θ01 = θ00 + Δθ01 are substituted into the equation (116), and the second interelectrode between when θ10 = θ9 + Δθ10 and θ01 = θ00 + Δθ01 are substituted into the equation (118). If the difference from the electromotive force E420c is E4d0, the electromotive force difference E4d0 is expressed by the following equation.
E4d0 = rk · exp {j · (θ9 + θ00)}
・ [Ω0 ・ exp (j ・ π / 2)
{B9 + b10 · exp (j · Δθ10)}
+ Γ · V · exp (j · Δθ01)
{B9-b10 · exp (j · Δθ10)}] (122)

また、式（１１７）にθ１０＝θ９＋Δθ１０、θ０１＝θ００＋Δθ０１を代入したときの第１の電極間起電力Ｅ４１２ｃと式（１１９）にθ１０＝θ９＋Δθ１０、θ０１＝θ００＋Δθ０１を代入したときの第２の電極間起電力Ｅ４２２ｃとの差をＥ４ｄ２とすれば、起電力差Ｅ４ｄ２は次式で表される。
Ｅ４ｄ２＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・［ω２・ｅｘｐ（ｊ・π／２）
・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）
・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］ ・・・（１２３） Further, the first inter-electrode electromotive force E412c when θ10 = θ9 + Δθ10 and θ01 = θ00 + Δθ01 are substituted into the equation (117), and the second electrode interval when θ10 = θ9 + Δθ10 and θ01 = θ00 + Δθ01 are substituted into the equation (119). If the difference from the electromotive force E422c is E4d2, the electromotive force difference E4d2 is expressed by the following equation.
E4d2 = rk · exp {j · (θ9 + θ00)}
・ [Ω2 ・ exp (j ・ π / 2)
{B9 + b10 · exp (j · Δθ10)}
+ Γ · V · exp (j · Δθ01)
{B9-b10 · exp (j · Δθ10)}] (123)

ここで、励磁コイル３の軸を含む平面ＰＬＮ３から電極２ａ，２ｂ間を結ぶ電極軸ＥＡＸ１までの距離ｄ３と平面ＰＬＮ３から電極２ｃ，２ｄ間を結ぶ電極軸ＥＡＸ２までの距離ｄ４とが略等しいとすると（ｄ３≒ｄ４）、ｂ９≒ｂ１０、Δθ１０≒０になる。この場合、式（１２０）、式（１２１）、式（１２２）、式（１２３）は以下のようになる。
Ｅ４ｓ０≒ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・｛２・ｂ９・γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）｝ ・・・（１２４）
Ｅ４ｓ２≒ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・｛２・ｂ９・γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）｝ ・・・（１２５）
Ｅ４ｄ０≒ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・｛２・ｂ９・ω０・ｅｘｐ（ｊ・π／２）｝ ・・・（１２６）
Ｅ４ｄ２≒ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・｛２・ｂ９・ω２・ｅｘｐ（ｊ・π／２）｝ ・・・（１２７） Here, a distance d3 from the plane PLN3 including the axis of the exciting coil 3 to the electrode axis EAX1 connecting the electrodes 2a and 2b and a distance d4 from the plane PLN3 to the electrode axis EAX2 connecting the electrodes 2c and 2d are substantially equal. Then (d3≈d4), b9≈b10, and Δθ10≈0. In this case, Formula (120), Formula (121), Formula (122), and Formula (123) are as follows.
E4s0≈rk · exp {j · (θ9 + θ00)}
{2 · b9 · γ · V · exp (j · Δθ01)} (124)
E4s2≈rk · exp {j · (θ9 + θ00)}
{2 · b9 · γ · V · exp (j · Δθ01)} (125)
E4d0≈rk · exp {j · (θ9 + θ00)}
{2 · b9 · ω0 · exp (j · π / 2)} (126)
E4d2≈rk · exp {j · (θ9 + θ00)}
{2 · b9 · ω2 · exp (j · π / 2)} (127)

すなわち、起電力和Ｅ４ｓ０，Ｅ４ｓ２はほぼｖ×Ｂ成分の起電力のみとなり、起電力差Ｅ４ｄ０，Ｅ４ｄ２はほぼ∂Ａ／∂ｔ成分の起電力のみとなるので、∂Ａ／∂ｔ成分の抽出やｖ×Ｂ成分の抽出、および正規化や０補正演算の際の演算誤差を小さくすることができる。この点が、本実施の形態と第１の実施の形態の技術的な意義における相違点である。ただし、以後の理論展開もｂ９≠ｂ１０、Δθ１０≠０として進める。   That is, the electromotive force sums E4s0 and E4s2 are substantially only the electromotive force of the v × B component, and the electromotive force differences E4d0 and E4d2 are substantially only the electromotive force of the ∂A / ∂t component. And v.times.B component extraction, and normalization and zero correction calculation errors can be reduced. This is the difference in technical significance between the present embodiment and the first embodiment. However, the subsequent theoretical development proceeds as b9 ≠ b10 and Δθ10 ≠ 0.

起電力和Ｅ４ｓ０とＥ４ｓ２との差をとり、求めた差分をω０／（ω０−ω２）倍した結果をＥｄＡ４１とすれば、次式が成立する。ここで、差分ＥｄＡ４１は第２の基本原理における第１の∂Ａ／∂ｔ成分に相当する。
ＥｄＡ４１＝（Ｅ４ｓ０−Ｅ４ｓ２）・ω０／（ω０−ω２）
＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
−ω２・ｅｘｐ（ｊ・π／２）・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
−γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］
・ω０／（ω０−ω２）
＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
・・・（１２８） Taking the difference between the electromotive force sums E4s0 and E4s2 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA41, the following equation is established. Here, the difference EdA41 corresponds to the first ∂A / ∂t component in the second basic principle.
EdA41 = (E4s0−E4s2) · ω0 / (ω0−ω2)
= Rk · exp {j · (θ9 + θ00)}
[Ω0 · exp (j · π / 2) · {b9−b10 · exp (j · Δθ10)}
+ Γ · V · exp (j · Δθ01) · {b9 + b10 · exp (j · Δθ10)}
−ω2 · exp (j · π / 2) · {b9−b10 · exp (j · Δθ10)}
−γ · V · exp (j · Δθ01) · {b9 + b10 · exp (j · Δθ10)}]
・ Ω0 / (ω0−ω2)
= Rk · exp {j · (θ9 + θ00)}
.Omega.0.exp (j.pi / 2). {B9-b10.exp (j..DELTA..theta.10)}
... (128)

式（１２８）に示す差分ＥｄＡ４１は、流速の大きさＶに関係しないので、∂Ａ／∂ｔによって発生する成分のみとなる。この差分ＥｄＡ４１を用いて起電力和Ｅ４ｓ０（合成ベクトルＶａｓ０＋Ｖｂｓ０）からｖ×Ｂ成分を取り出す。なお、差分ＥｄＡ４１は、正確には起電力和Ｅ４ｓ０とＥ４ｓ２との差分をω０／（ω０−ω２）倍したものであるが、ω０／（ω０−ω２）倍した理由は、式の展開を容易にするためである。   Since the difference EdA41 shown in the equation (128) is not related to the magnitude V of the flow velocity, it becomes only the component generated by ∂A / ∂t. Using this difference EdA41, a v × B component is extracted from the electromotive force sum E4s0 (combined vector Vas0 + Vbs0). The difference EdA41 is precisely the difference between the electromotive force sums E4s0 and E4s2 multiplied by ω0 / (ω0−ω2), but the reason for the multiplication by ω0 / (ω0−ω2) is that the expression can be easily expanded. It is to make it.

式（１２０）に示す起電力和Ｅ４ｓ０から式（１２８）に示す差分ＥｄＡ４１を引いたときに得られるｖ×Ｂ成分をＥｖＢ４０とすると、ｖ×Ｂ成分ＥｖＢ４０は次式で表される。
ＥｖＢ４０＝Ｅ４ｓ０−ＥｄＡ４１
＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］
−ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
＝［γ・ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００＋Δθ０１）｝
・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］・Ｖ ・・・（１２９） When the v × B component obtained by subtracting the difference EdA41 shown in the equation (128) from the electromotive force sum E4s0 shown in the equation (120) is EvB40, the v × B component EvB40 is expressed by the following equation.
EvB40 = E4s0-EdA41
= Rk · exp {j · (θ9 + θ00)}
[Ω0 · exp (j · π / 2) · {b9−b10 · exp (j · Δθ10)}
+ Γ · V · exp (j · Δθ01) · {b9 + b10 · exp (j · Δθ10)}]
−rk · exp {j · (θ9 + θ00)}
.Omega.0.exp (j.pi / 2). {B9-b10.exp (j..DELTA..theta.10)}
= [Γ · rk · exp {j · (θ9 + θ00 + Δθ01)}
{B9 + b10 · exp (j · Δθ10)}] · V (129)

ｖ×Ｂ成分ＥｖＢ４０は角周波数ω０，ω２に関係しない。流速の大きさＶが０のときｖ×Ｂ成分ＥｖＢ４０も０となることから分かるように、ｖ×Ｂ成分ＥｖＢ４０より、０点が補正された出力を得ることができる。式（１２９）によれば、流速の大きさＶにかかる係数の大きさと方向は、複素ベクトル［γ・ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００＋Δθ０１）｝・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］で表される。   The v × B component EvB40 is not related to the angular frequencies ω0 and ω2. As can be seen from the fact that the v × B component EvB40 becomes 0 when the magnitude V of the flow velocity is 0, an output with zero point corrected can be obtained from the v × B component EvB40. According to the equation (129), the magnitude and direction of the coefficient relating to the flow velocity magnitude V are complex vectors [γ · rk · exp {j · (θ9 + θ00 + Δθ01)} · {b9 + b10 · exp (j · Δθ10)}]. expressed.

次に、ｖ×Ｂ成分ＥｖＢ４０の流速の大きさＶにかかる係数（スパン）の変動要因を除去するために、このスパンの変動要因と同じ変動要因を持つ第２の∂Ａ／∂ｔ成分を抽出する。このときの抽出方法としては第２の基本原理で説明した第１の抽出方法を用いる。起電力差Ｅ４ｄ０と起電力差Ｅ４ｄ２との差をとり、求めた差分をω０／（ω０−ω２）倍した結果をＥｄＡ４２とすれば、次式が成立する。ここで、差分ＥｄＡ４２は第２の基本原理における第２の∂Ａ／∂ｔ成分に相当する。
ＥｄＡ４２＝（Ｅ４ｄ０−Ｅ４ｄ２）・ω０／（ω０−ω２）
＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・［ω０・ｅｘｐ（ｊ・π／２）・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
＋γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
−ω２・ｅｘｐ（ｊ・π／２）・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
−γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］
・ω０／（ω０−ω２）
＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝
・・・（１３０） Next, in order to remove the variation factor of the coefficient (span) related to the flow velocity magnitude V of the v × B component EvB40, the second ∂A / ∂t component having the same variation factor as this span variation factor is obtained. Extract. As the extraction method at this time, the first extraction method described in the second basic principle is used. Taking the difference between the electromotive force difference E4d0 and the electromotive force difference E4d2 and multiplying the obtained difference by ω0 / (ω0−ω2) as EdA42, the following equation is established. Here, the difference EdA42 corresponds to the second ∂A / ∂t component in the second basic principle.
EdA42 = (E4d0−E4d2) · ω0 / (ω0−ω2)
= Rk · exp {j · (θ9 + θ00)}
[Ω0 · exp (j · π / 2) · {b9 + b10 · exp (j · Δθ10)}
+ Γ · V · exp (j · Δθ01) · {b9−b10 · exp (j · Δθ10)}
−ω2 · exp (j · π / 2) · {b9 + b10 · exp (j · Δθ10)}
−γ · V · exp (j · Δθ01) · {b9−b10 · exp (j · Δθ10)}]
・ Ω0 / (ω0−ω2)
= Rk · exp {j · (θ9 + θ00)}
.Omega.0.exp (j.pi / 2). {B9 + b10.exp (j..DELTA..theta.10)}
... (130)

差分ＥｄＡ４２は、流速の大きさＶに関係しないので、∂Ａ／∂ｔにより発生する成分のみとなる。この差分ＥｄＡ４２を用いてｖ×Ｂ成分ＥｖＢ４０の流速の大きさＶにかかる係数（スパン）を正規化する。なお、差分ＥｄＡ４２は、正確には起電力差Ｅ４ｄ０とＥ４ｄ２との差分をω０／（ω０−ω２）倍したものであるが、ω０／（ω０−ω２）倍した理由は、式の展開を容易にするためである。   Since the difference EdA42 is not related to the magnitude V of the flow velocity, only the component generated by ∂A / ∂t. Using this difference EdA42, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component EvB40 is normalized. The difference EdA42 is precisely the difference between the electromotive force differences E4d0 and E4d2 multiplied by ω0 / (ω0−ω2). The reason for the multiplication by ω0 / (ω0−ω2) is that the expression can be easily expanded. It is to make it.

式（１２９）のｖ×Ｂ成分ＥｖＢ４０を式（１３０）の差分ＥｄＡ４２で正規化し、ω０倍した結果をＥｖＢｎ４とすれば、正規化起電力ＥｖＢｎ４は次式で表される。
ＥｖＢｎ４＝（ＥｖＢ４０／ＥｄＡ４２）・ω０
＝［γ・ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００＋Δθ０１）｝
・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］・Ｖ
／［ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］
・ω０
＝［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］・Ｖ ・・・（１３１） When the v × B component EvB40 of the equation (129) is normalized by the difference EdA42 of the equation (130) and multiplied by ω0 is EvBn4, the normalized electromotive force EvBn4 is expressed by the following equation.
EvBn4 = (EvB40 / EdA42) · ω0
= [Γ · rk · exp {j · (θ9 + θ00 + Δθ01)}
{B9 + b10 · exp (j · Δθ10)}] · V
/ [Rk · exp {j · (θ9 + θ00)}
.Omega.0.exp (j.pi / 2). {B9 + b10.exp (j..DELTA..theta.10)}]
・ Ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (131)

式（１３１）ではｖ×Ｂにより発生する成分が正規化されスパンの変動要因が除去されている。流速の大きさＶにかかる複素係数は、γの大きさ、−π／２＋Δθ０１の実軸からの角度をもつ。係数γおよび角度Δθ０１は校正等により予め求めることができる定数であり、正規化起電力ＥｖＢｎ４は被測定流体の流速が変化しないかぎり一定となる。したがって、抽出した第２の∂Ａ／∂ｔの成分をもちいてｖ×Ｂ成分の正規化を行うことにより、０点の補正に加えて、磁場のシフトや位相変化による誤差を自動的に補正するスパン補正を実現することができる。   In the equation (131), the component generated by v × B is normalized to eliminate the span variation factor. 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 normalized electromotive force EvBn4 is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by normalizing the v × B component using the extracted second ∂A / ∂t component, in addition to the zero point correction, errors due to magnetic field shift and phase change are automatically corrected. Span correction can be realized.

式（１３１）より、流速の大きさＶは次式のように表される。
Ｖ＝｜ＥｖＢｎ４／［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］｜
＝｜ＥｖＢｎ４｜／γ ・・・（１３２） From the equation (131), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn4 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn4 | / γ (132)

なお、第２の基本原理で用いた定数および変数と、本実施の形態の定数および変数との対応関係は以下の表４のとおりである。本実施の形態は、表４から明らかなように、前述の第２の基本原理を具体的に実現する１つの例である。   The correspondence relationship between the constants and variables used in the second basic principle and the constants and variables of the present embodiment is as shown in Table 4 below. As is clear from Table 4, this embodiment is an example that specifically realizes the second basic principle described above.

Figure 0004555023
Figure 0004555023

次に、本実施の形態の電磁流量計の具体的な構成とその動作について説明する。図２５は本実施の形態の電磁流量計の構成を示すブロック図であり、図１７と同一の構成には同一の符号を付してある。本実施の形態の電磁流量計は、測定管１と、第１の電極２ａ，２ｂと、第２の電極２ｃ，２ｄと、励磁コイル３と、電源部４ｂと、信号変換部５ｂと、信号変換部５ｂによってスパンの変動要因が除去されたｖ×Ｂ成分から被測定流体の流量を算出する流量出力部６ｂとを有している。   Next, a specific configuration and operation of the electromagnetic flow meter of the present embodiment will be described. FIG. 25 is a block diagram showing the configuration of the electromagnetic flowmeter of the present embodiment. The same components as those in FIG. The electromagnetic flowmeter 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 4b, a signal conversion unit 5b, a signal A flow rate output unit 6b that calculates the flow rate of the fluid to be measured from the v × B component from which the span variation factor has been removed by the conversion unit 5b.

信号変換部５ｂは、電極２ａ，２ｂで検出される第１の合成起電力と電極２ｃ，２ｄで検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて第１の合成起電力の第１の角周波数ω０の成分と第２の合成起電力の第１の角周波数ω０の成分との起電力和、および第１の合成起電力の第２の角周波数ω２の成分と第２の合成起電力の第２の角周波数ω２の成分との起電力和を求め、これら２つの起電力和の差分を第１の∂Ａ／∂ｔ成分として抽出し、第１の角周波数ω０の起電力和又は第２の角周波数ω２の起電力和の中から第１の∂Ａ／∂ｔ成分を取り除くことによりｖ×Ｂ成分を抽出する０点補正部５１ｂと、第１の合成起電力の第１の角周波数ω０の成分と第２の合成起電力の第１の角周波数ω０の成分との起電力差、および第１の合成起電力の第２の角周波数ω２の成分と第２の合成起電力の第２の角周波数ω２の成分との起電力差を求め、これら２つの起電力差の差分を第２の∂Ａ／∂ｔ成分として抽出し、この第２の∂Ａ／∂ｔ成分に基づいて、ｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するスパン補正部５２ｂとから構成される。   The signal conversion unit 5b obtains the amplitude and phase for each of the first combined electromotive force detected by the electrodes 2a and 2b and the second combined electromotive force detected by the electrodes 2c and 2d, and the amplitude and phase are obtained. Based on the sum of the electromotive forces of the component of the first angular frequency ω0 of the first combined electromotive force and the component of the first angular frequency ω0 of the second combined electromotive force, and the second of the first combined electromotive force The sum of electromotive forces of the component of the angular frequency ω2 and the component of the second combined electromotive force at the second angular frequency ω2 is obtained, and the difference between the two electromotive force sums is extracted as the first ∂A / ∂t component. The 0-point correction unit 51b for extracting the v × B component by removing the first ∂A / ∂t component from the electromotive force sum of the first angular frequency ω0 or the electromotive force sum of the second angular frequency ω2. And a component of the first angular frequency ω0 of the first combined electromotive force and a component of the first angular frequency ω0 of the second combined electromotive force. And the difference in electromotive force between the component at the second angular frequency ω2 of the first combined electromotive force and the component at the second angular frequency ω2 of the second combined electromotive force. The difference of the difference is extracted as the second ∂A / ∂t component, and based on the second ∂A / ∂t component, the variation factor of the span, which is a coefficient applied to the flow velocity magnitude V of the v × B component It is comprised from the span correction | amendment part 52b which removes.

本実施の形態では、前述のとおり、励磁コイル３の軸を含む平面ＰＬＮ３から電極２ａ，２ｂ間を結ぶ電極軸ＥＡＸ１までの距離ｄ３と平面ＰＬＮ３から電極２ｃ，２ｄ間を結ぶ電極軸ＥＡＸ２までの距離ｄ４とが略等しいとする。
電源部４ｂは、第１の角周波数ω０の正弦波成分と第２の角周波数ω２の正弦波成分とを含む励磁電流を励磁コイル３に供給する。このとき、励磁電流における角周波数ω０の成分と角周波数ω２の成分の振幅は同一である。 In the present embodiment, as described above, the distance d3 from the plane PLN3 including the axis of the exciting coil 3 to the electrode axis EAX1 connecting the electrodes 2a and 2b and the electrode axis EAX2 connecting the plane PLN3 to the electrodes 2c and 2d. Assume that the distance d4 is substantially equal.
The power supply unit 4b supplies an excitation current including a sine wave component having the first angular frequency ω0 and a sine wave component having the second 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.

図２６は信号変換部５ｂと流量出力部６ｂの動作を示すフローチャートである。まず、信号変換部５ｂの０点補正部５１ｂは、第１の電極間起電力の角周波数ω０の成分Ｅ４１０ｃと第２の電極間起電力の角周波数ω０の成分Ｅ４２０ｃとの和Ｅ４ｓ０の振幅ｒ４ｓ０を求めると共に、実軸と起電力和Ｅ４ｓ０との位相差φ４ｓ０を図示しない位相検波器により求める。また、０点補正部５１ｂは、第１の電極間起電力の角周波数ω２の成分Ｅ４１２ｃと第２の電極間起電力の角周波数ω２の成分Ｅ４２２ｃとの和Ｅ４ｓ２の振幅ｒ４ｓ２を求めると共に、実軸と起電力和Ｅ４ｓ２との位相差φ４ｓ２を位相検波器により求める。また、０点補正部５１ｂは、第１の電極間起電力の角周波数ω０の成分Ｅ４１０ｃと第２の電極間起電力の角周波数ω０の成分Ｅ４２０ｃとの差Ｅ４ｄ０の振幅ｒ４ｄ０を求めると共に、実軸と起電力差Ｅ４ｄ０との位相差φ４ｄ０を位相検波器により求める。さらに、０点補正部５１ｂは、第１の電極間起電力の角周波数ω２の成分Ｅ４１２ｃと第２の電極間起電力の角周波数ω２の成分Ｅ４２２ｃとの差Ｅ４ｄ２の振幅ｒ４ｄ２を求めると共に、実軸と起電力差Ｅ４ｄ２との位相差φ４ｄ２を位相検波器により求める（図２６ステップ４０１）。電極間起電力Ｅ４１０ｃ，Ｅ４２０，Ｅ４１２ｃ，Ｅ４２２ｃは、バンドパスフィルタやコムフィルタによって周波数分離することができる。   FIG. 26 is a flowchart showing the operation of the signal conversion unit 5b and the flow rate output unit 6b. First, the zero point correction unit 51b of the signal conversion unit 5b has an amplitude r4s0 of the sum E4s0 of the component E410c of the angular frequency ω0 of the first interelectrode electromotive force and the component E420c of the angular frequency ω0 of the second interelectrode electromotive force. And a phase difference φ4s0 between the real axis and the electromotive force sum E4s0 is obtained by a phase detector (not shown). The zero point correction unit 51b obtains the amplitude r4s2 of the sum E4s2 of the component E412c of the angular frequency ω2 of the first inter-electrode electromotive force and the component E422c of the angular frequency ω2 of the second inter-electrode electromotive force, and A phase difference φ4s2 between the axis and the electromotive force sum E4s2 is obtained by a phase detector. The zero point correction unit 51b obtains the amplitude r4d0 of the difference E4d0 between the component E410c of the angular frequency ω0 of the first inter-electrode electromotive force and the component E420c of the angular frequency ω0 of the second inter-electrode electromotive force. A phase difference φ4d0 between the shaft and the electromotive force difference E4d0 is obtained by a phase detector. Further, the zero point correction unit 51b obtains the amplitude r4d2 of the difference E4d2 between the component E412c of the angular frequency ω2 of the first interelectrode electromotive force and the component E422c of the angular frequency ω2 of the second interelectrode electromotive force, and A phase difference φ4d2 between the shaft and the electromotive force difference E4d2 is obtained by a phase detector (step 401 in FIG. 26). The inter-electrode electromotive forces E410c, E420, E412c, and E422c can be frequency-separated by a bandpass filter or a comb filter.

続いて、０点補正部５１ｂは、起電力和Ｅ４ｓ０の実軸成分Ｅ４ｓ０ｘと虚軸成分Ｅ４ｓ０ｙ、および起電力和Ｅ４ｓ２の実軸成分Ｅ４ｓ２ｘと虚軸成分Ｅ４ｓ２ｙを次式のように算出する（ステップ４０２）。
Ｅ４ｓ０ｘ＝ｒ４ｓ０・ｃｏｓ（φ４ｓ０） ・・・（１３３）
Ｅ４ｓ０ｙ＝ｒ４ｓ０・ｓｉｎ（φ４ｓ０） ・・・（１３４）
Ｅ４ｓ２ｘ＝ｒ４ｓ２・ｃｏｓ（φ４ｓ２） ・・・（１３５）
Ｅ４ｓ２ｙ＝ｒ４ｓ２・ｓｉｎ（φ４ｓ２） ・・・（１３６） Subsequently, the zero point correction unit 51b calculates the real axis component E4s0x and the imaginary axis component E4s0y of the electromotive force sum E4s0 and the real axis component E4s2x and the imaginary axis component E4s2y of the electromotive force sum E4s2 as follows (step) 402).
E4s0x = r4s0 · cos (φ4s0) (133)
E4s0y = r4s0 · sin (φ4s0) (134)
E4s2x = r4s2 · cos (φ4s2) (135)
E4s2y = r4s2 · sin (φ4s2) (136)

式（１３３）〜式（１３６）の算出後、０点補正部５１ｂは、起電力和Ｅ４ｓ０とＥ４ｓ２との差分ＥｄＡ４１の大きさを求める（ステップ４０３）。このステップ４０３の処理は、第１の∂Ａ／∂ｔ成分を求めることに対応する処理であり、式（１２８）の算出に相当する処理である。０点補正部５１ｂは、差分ＥｄＡ４１の実軸成分ＥｄＡ４１ｘと虚軸成分ＥｄＡ４１ｙを次式のように算出する。
ＥｄＡ４１ｘ＝（Ｅ４ｓ０ｘ−Ｅ４ｓ２ｘ）・ω０／（ω０−ω２） ・・（１３７）
ＥｄＡ４１ｙ＝（Ｅ４ｓ０ｙ−Ｅ４ｓ２ｙ）・ω０／（ω０−ω２） ・・（１３８） After calculating Equations (133) to (136), the zero point correction unit 51b obtains the magnitude of the difference EdA41 between the electromotive force sums E4s0 and E4s2 (Step 403). The process of step 403 is a process corresponding to obtaining the first ∂A / ∂t component, and is a process corresponding to the calculation of Expression (128). The zero point correction unit 51b calculates the real axis component EdA41x and the imaginary axis component EdA41y of the difference EdA41 as in the following equation.
EdA41x = (E4s0x−E4s2x) · ω0 / (ω0−ω2) (137)
EdA41y = (E4s0y−E4s2y) · ω0 / (ω0−ω2) (138)

０点補正部５１ｂは、起電力和Ｅ４ｓ０から差分ＥｄＡ４１を取り除き、ｖ×Ｂ成分ＥｖＢ４０の大きさを求める（ステップ４０４）。このステップ４０４の処理は、式（１２９）の算出に相当する処理である。０点補正部５１ｂは、ｖ×Ｂ成分ＥｖＢ４０の大きさ｜ＥｖＢ４０｜を次式のように算出する。
｜ＥｖＢ４０｜＝｛（Ｅ４ｓ０ｘ−ＥｄＡ４１ｘ）2
＋（Ｅ４ｓ０ｙ−ＥｄＡ４１ｙ）2｝1/2 ・・・（１３９） The zero point correction unit 51b removes the difference EdA41 from the electromotive force sum E4s0 and obtains the magnitude of the v × B component EvB40 (step 404). The process of step 404 is a process corresponding to the calculation of equation (129). The zero point correction unit 51b calculates the magnitude | EvB40 | of the v × B component EvB40 as the following equation.
| EvB40 | = {(E4s0x−EdA41x) 2
+ (E4s0y-EdA41y) 2 } 1/2 (139)

次に、信号変換部５ｂのスパン補正部５２ｂは、起電力差Ｅ４ｄ０の実軸成分Ｅ４ｄ０ｘと虚軸成分Ｅ４ｄ０ｙ、および起電力差Ｅ４ｄ２の実軸成分Ｅ４ｄ２ｘと虚軸成分Ｅ４ｄ２ｙを次式のように算出する（ステップ４０５）。
Ｅ４ｄ０ｘ＝ｒ４ｄ０・ｃｏｓ（φ４ｄ０） ・・・（１４０）
Ｅ４ｄ０ｙ＝ｒ４ｄ０・ｓｉｎ（φ４ｄ０） ・・・（１４１）
Ｅ４ｄ２ｘ＝ｒ４ｄ２・ｃｏｓ（φ４ｄ２） ・・・（１４２）
Ｅ４ｄ２ｙ＝ｒ４ｄ２・ｓｉｎ（φ４ｄ２） ・・・（１４３） Next, the span correction unit 52b of the signal conversion unit 5b calculates the real axis component E4d0x and the imaginary axis component E4d0y of the electromotive force difference E4d0 and the real axis component E4d2x and the imaginary axis component E4d2y of the electromotive force difference E4d2 as Calculate (step 405).
E4d0x = r4d0 · cos (φ4d0) (140)
E4d0y = r4d0 · sin (φ4d0) (141)
E4d2x = r4d2 · cos (φ4d2) (142)
E4d2y = r4d2 · sin (φ4d2) (143)

式（１４０）〜式（１４３）の算出後、スパン補正部５２ｂは、起電力差Ｅ４ｄ０とＥ４ｄ２との差分ＥｄＡ４２の大きさを求める（ステップ４０６）。このステップ４０６の処理は、第２の∂Ａ／∂ｔ成分を求めることに対応する処理であり、式（１３０）の算出に相当する処理である。スパン補正部５２ｂは、差分ＥｄＡ４２の大きさ｜ＥｄＡ４２｜を次式のように算出する。
｜ＥｄＡ４２｜＝｛（Ｅ４ｄ０ｘ−Ｅ４ｄ２ｘ）2
＋（Ｅ４ｄ０ｙ−Ｅ４ｄ２ｙ）2｝1/2・ω０／（ω０−ω２）
・・・（１４４） After calculating the equations (140) to (143), the span correction unit 52b obtains the magnitude of the difference EdA42 between the electromotive force differences E4d0 and E4d2 (step 406). The process of step 406 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 52b calculates the magnitude | EdA42 | of the difference EdA42 as follows.
| EdA42 | = {(E4d0x−E4d2x) 2
+ (E4d0y−E4d2y) 2 } 1/2 · ω0 / (ω0−ω2)
... (144)

続いて、スパン補正部５２ｂは、ｖ×Ｂ成分ＥｖＢ４０を差分ＥｄＡ４２で正規化した正規化起電力ＥｖＢｎ４の大きさを求める（ステップ４０７）。このステップ４０７の処理は、式（１３１）の算出に相当する処理である。スパン補正部５２ｂは、正規化起電力ＥｖＢｎ４の大きさ｜ＥｖＢｎ４｜を次式のように算出する。
｜ＥｖＢｎ４｜＝（｜ＥｖＢ４０｜／｜ＥｄＡ４２｜）・ω０ ・・・（１４５） Subsequently, the span correction unit 52b obtains the magnitude of the normalized electromotive force EvBn4 obtained by normalizing the v × B component EvB40 with the difference EdA42 (step 407). The process of step 407 is a process corresponding to the calculation of equation (131). The span correction unit 52b calculates the magnitude | EvBn4 | of the normalized electromotive force EvBn4 as the following equation.
| EvBn4 | = (| EvB40 | / | EdA42 |) · ω0 (145)

流量出力部６ｂは、被測定流体の流速の大きさＶを次式のように算出する（ステップ４０８）。このステップ４０８の処理は、式（１３２）の算出に相当する処理である。
Ｖ＝｜ＥｖＢｎ４｜／γ ・・・（１４６）
なお、比例係数γは、校正等により予め求めることができる定数である。信号変換部５ｂと流量出力部６ｂとは、以上のようなステップ４０１〜４０８の処理を例えばオペレータによって計測終了が指示されるまで（ステップ４０９においてＹＥＳ）、一定周期毎に行う。 The flow rate output unit 6b calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 408). The process of step 408 is a process corresponding to the calculation of Expression (132).
V = | EvBn4 | / γ (146)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5b and the flow rate output unit 6b perform the processing in steps 401 to 408 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 409).

以上のように、本実施の形態では、励磁コイル３から大きさが等しくかつ周波数が異なる２つの成分を含む磁場を被測定流体に印加し、第１の電極間起電力の角周波数ω０の成分Ｅ４１０ｃと第２の電極間起電力の角周波数ω０の成分Ｅ４２０ｃとの和Ｅ４ｓ０、および第１の電極間起電力の角周波数ω２の成分Ｅ４１２ｃと第２の電極間起電力の角周波数ω２の成分Ｅ４２２ｃとの和Ｅ４ｓ２を求め、起電力和Ｅ４ｓ０とＥ４ｓ２とから差分ＥｄＡ４１（第１の∂Ａ／∂ｔ成分）を抽出し、この第１の∂Ａ／∂ｔ成分を起電力和Ｅ４ｓ０（合成ベクトルＶａｓ０＋Ｖｂｓ０）の中から取り除くことによりｖ×Ｂ成分を抽出し、また起電力Ｅ４１０ｃとＥ４２０ｃとの差Ｅ４ｄ０、および起電力Ｅ４１２ｃとＥ４２２ｃとの差Ｅ４ｄ２を求め、起電力差Ｅ４ｄ０とＥ４ｄ２とから差分ＥｄＡ４２（第２の∂Ａ／∂ｔ成分）を抽出し、この第２の∂Ａ／∂ｔ成分を用いてｖ×Ｂ成分の流速の大きさＶにかかるスパンを正規化して、スパン変動要素を消去するようにしたので、正確なスパン補正を自動的に行うことができ、かつ被測定流体の流量を０にすることなく電磁流量計の出力の０点を補正することができ、高周波励磁においても０点の安定性を確保することができる。   As described above, in the present embodiment, a magnetic field including two components having the same magnitude and different frequencies from the exciting coil 3 is applied to the fluid to be measured, and the component of the first inter-electrode electromotive force at the angular frequency ω0. The sum E4s0 of the component E420c and the component E420c of the angular frequency ω0 of the second inter-electrode electromotive force, and the component of the angular frequency ω2 of the angular frequency ω2 of the first inter-electrode electromotive force and the component of the angular frequency ω2 of the second inter-electrode electromotive force A sum E4s2 with E422c is obtained, a difference EdA41 (first ∂A / ∂t component) is extracted from the electromotive force sums E4s0 and E4s2, and this first ∂A / ∂t component is extracted as an electromotive force sum E4s0 (combined) The v × B component is extracted by removing from the vector Vas0 + Vbs0), and the difference E4d0 between the electromotive forces E410c and E420c and the difference E4d2 between the electromotive forces E412c and E422c are obtained. A difference EdA42 (second ∂A / ∂t component) is extracted from the power differences E4d0 and E4d2, and the span of the flow velocity V of the v × B component is obtained using the second ∂A / ∂t component. Since the span variation factor is eliminated, accurate span correction can be automatically performed, and the zero point of the output of the electromagnetic flowmeter can be reduced without reducing the flow rate of the fluid to be measured. Correction can be made, and stability at zero point can be secured even in high-frequency excitation.

また、本実施の形態では、励磁コイル３の軸を含む平面ＰＬＮ３から第１の電極２ａ，２ｂまでの距離ｄ３と平面ＰＬＮ３から第２の電極２ｃ，２ｄまでの距離ｄ４とを調整することにより、起電力和Ｅ４ｓ０，Ｅ４ｓ２がほぼｖ×Ｂ成分の起電力のみとなり、起電力差Ｅ４ｄ０，Ｅ４ｄ２がほぼ∂Ａ／∂ｔ成分の起電力のみとなるようにすることができる。これにより、本実施の形態では、ｖ×Ｂ成分および∂Ａ／∂ｔ成分をより効果的に抽出することが可能であり、第１の実施の形態に比べて演算誤差を小さくすることが可能である。   In the present embodiment, the distance d3 from the plane PLN3 including the axis of the exciting coil 3 to the first electrodes 2a and 2b and the distance d4 from the plane PLN3 to the second electrodes 2c and 2d are adjusted. Thus, the electromotive force sums E4s0 and E4s2 can be almost only the electromotive force of the v × B component, and the electromotive force differences E4d0 and E4d2 can be almost only the electromotive force of the ∂A / ∂t component. Thereby, in this embodiment, it is possible to extract the v × B component and the ∂A / ∂t component more effectively, and the calculation error can be reduced as compared with the first embodiment. It is.

なお、本実施の形態では、角周波数ω０の成分の起電力和Ｅ４ｓ０を０補正およびスパン補正の対象としたが、角周波数ω２の成分の起電力和Ｅ４ｓ２を０補正およびスパン補正の対象としてもよい。この場合は、次式のように起電力和Ｅ４ｓ２からＥ４ｓ０を引いて差分ＥｄＡ４１（第１の∂Ａ／∂ｔ成分）を求める。
ＥｄＡ４１＝（Ｅ４ｓ２−Ｅ４ｓ０）・ω２／（ω２−ω０） ・・・（１４７）
そして、起電力和Ｅ４ｓ２から差分ＥｄＡ４１を引くことによりｖ×Ｂ成分ＥｖＢ４２を抽出する。 In the present embodiment, the electromotive force sum E4s0 of the component of the angular frequency ω0 is set as a target for zero correction and span correction, but the electromotive force sum E4s2 of the component of the angular frequency ω2 is also set as a target of zero correction and span correction. Good. In this case, the difference EdA41 (first ∂A / ∂t component) is obtained by subtracting E4s0 from the electromotive force sum E4s2 as in the following equation.
EdA41 = (E4s2-E4s0) · ω2 / (ω2-ω0) (147)
Then, the v × B component EvB42 is extracted by subtracting the difference EdA41 from the electromotive force sum E4s2.

さらに、次式のように起電力差Ｅ４ｄ２からＥ４ｄ０を引いて差分ＥｄＡ４２（第２の∂Ａ／∂ｔ成分）を求める。
ＥｄＡ４２＝（Ｅ４ｄ２−Ｅ４ｄ０）・ω２／（ω２−ω０） ・・・（１４８）
そして、次式のように差分ＥｄＡ４２を用いてｖ×Ｂ成分ＥｖＢ４２の流速の大きさＶにかかるスパンを正規化すればよい。その他の処理は起電力和Ｅ４ｓ０を０補正およびスパン補正の対象とする場合と同じである。
｜ＥｖＢｎ４｜＝｜（ＥｖＢ４２／ＥｄＡ４２）・ω２｜ ・・・（１４９） Further, the difference EdA42 (second ∂A / ∂t component) is obtained by subtracting E4d0 from the electromotive force difference E4d2 as in the following equation.
EdA42 = (E4d2-E4d0) · ω2 / (ω2-ω0) (148)
And the span concerning the magnitude | size V of the flow velocity of vxB component EvB42 should just be normalized using difference EdA42 like following Formula. The other processes are the same as those in the case where the electromotive force sum E4s0 is the target of 0 correction and span correction.
| EvBn4 | = | (EvB42 / EdA42) · ω2 | (149)

また、本実施の形態では、起電力和Ｅ４ｓ０又はＥ４ｓ２を０補正およびスパン補正の対象としたが、起電力差Ｅ４ｄ０を０補正およびスパン補正の対象としてもよい。この場合は、起電力差Ｅ４ｄ０からＥ４ｄ２を引いて第１の∂Ａ／∂ｔ成分を抽出し、起電力差Ｅ４ｄ０から第１の∂Ａ／∂ｔ成分を引くことによりｖ×Ｂ成分を抽出し、起電力和Ｅ４ｓ０からＥ４ｓ２を引いて第２の∂Ａ／∂ｔ成分を抽出し、この第２の∂Ａ／∂ｔ成分を用いてｖ×Ｂ成分を正規化すればよい。   Further, in the present embodiment, the electromotive force sum E4s0 or E4s2 is the target of 0 correction and span correction, but the electromotive force difference E4d0 may be the target of 0 correction and span correction. In this case, the first ∂A / ∂t component is extracted by subtracting E4d2 from the electromotive force difference E4d0, and the v × B component is extracted by subtracting the first ∂A / ∂t component from the electromotive force difference E4d0. Then, the second ∂A / ∂t component is extracted by subtracting E4s2 from the electromotive force sum E4s0, and the v × B component may be normalized using the second ∂A / ∂t component.

同様に、起電力差Ｅ４ｄ２を０補正およびスパン補正の対象とする場合には、起電力差Ｅ４ｄ２からＥ４ｄ０を引いて第１の∂Ａ／∂ｔ成分を抽出し、起電力差Ｅ４ｄ２から第１の∂Ａ／∂ｔ成分を引くことによりｖ×Ｂ成分を抽出し、起電力和Ｅ４ｓ２からＥ４ｓ０を引いて第２の∂Ａ／∂ｔ成分を抽出し、この第２の∂Ａ／∂ｔ成分を用いてｖ×Ｂ成分を正規化すればよい。   Similarly, when the electromotive force difference E4d2 is to be subjected to 0 correction and span correction, the first ∂A / ∂t component is extracted by subtracting E4d0 from the electromotive force difference E4d2, and the first electromotive force difference E4d2 is extracted from the first electromotive force difference E4d2. The v × B component is extracted by subtracting the ∂A / ∂t component of the signal, the E4s0 is subtracted from the electromotive force sum E4s2, and the second ∂A / ∂t component is extracted. What is necessary is just to normalize a vxB component using a component.

また、本実施の形態では、複数の励磁周波数ω０，ω２で同時に励磁する例を示したが、単一の励磁周波数ω０又はω２で励磁を行い、励磁周波数をω０とω２で交互に切り替えながら励磁をした場合でも同じ効果を得ることができる。   In this embodiment, an example is shown in which excitation is performed simultaneously with a plurality of excitation frequencies ω0 and ω2, but excitation is performed with a single excitation frequency ω0 or ω2, and excitation is performed while alternately switching the excitation frequency between ω0 and ω2. The same effect can be obtained even when

［第５の実施の形態］
次に、本発明の第５の実施の形態について説明する。本実施の形態は、前述の第２の基本原理を用いるものである。本実施の形態の電磁流量計は１個の励磁コイルと２対の電極とを有するものであり、信号処理系を除く構成は図１７に示した電磁流量計と同様であるので、図１７の符号を用いて本実施の形態の原理を説明する。 [Fifth Embodiment]
Next, a fifth embodiment of the present invention will be described. This embodiment uses the second basic principle described above. 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.

式（１２９）で示したｖ×Ｂ成分ＥｖＢ４０の流速の大きさＶにかかる係数（スパン）の変動要因を除去するために、このスパンの変動要因と同じ変動要因を持つ第２の∂Ａ／∂ｔ成分を抽出する。このときの抽出方法としては第２の基本原理で説明した第２の抽出方法を用いる。   In order to remove the variation factor of the coefficient (span) related to the magnitude V of the flow velocity of the v × B component EvB40 expressed by the equation (129), the second ∂A / ∂t component is extracted. As the extraction method at this time, the second extraction method described in the second basic principle is used.

初期状態（校正時の状態）において、励磁コイル３から発生する磁場Ｂ９、磁場Ｂ１０を等しく調整しておくと、その後の磁場Ｂ９とＢ１０との差は小さくなり、次式の条件が成り立つ。
｜ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｜
≫｜ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｜ ・・・（１５０） If the magnetic fields B9 and B10 generated from the exciting coil 3 are adjusted to be equal in the initial state (the state at the time of calibration), the difference between the subsequent magnetic fields B9 and B10 becomes small, and the following condition is satisfied.
| B9 + b10 · exp (j · Δθ10) |
>> | b9-b10 · exp (j · Δθ10) | (150)

また、通常ω０＞γ・Ｖが成り立つことから、式（１５０）の条件を考慮すると、式（１２２）において次式の条件が成り立つ。
｜ω０・ｅｘｐ（ｊ・π／２）・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝｜
≫｜γ・Ｖ・ｅｘｐ（ｊ・Δθ０１）
・｛ｂ９−ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝｜ ・・・（１５１） In addition, since ω0> γ · V is normally satisfied, when the condition of the expression (150) is considered, the condition of the following expression is satisfied in the expression (122).
| Ω0 · exp (j · π / 2) · {b9 + b10 · exp (j · Δθ10)} |
≫ ｜ γ ・ V ・ exp (j ・ Δθ01)
{B9-b10 · exp (j · Δθ10)} | (151)

式（１５１）の条件を用いて、起電力差Ｅ４ｄ０を近似した起電力差ＥｄＡ５２は次式のように表される。ここで、起電力差ＥｄＡ５２は第２の基本原理における第２の∂Ａ／∂ｔ成分に相当する。
ＥｄＡ５２≒Ｅ２ｄ０ ・・・（１５２）
ＥｄＡ５２＝ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）
・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝ ・・・（１５３） The electromotive force difference EdA52 that approximates the electromotive force difference E4d0 using the condition of the equation (151) is expressed as the following equation. Here, the electromotive force difference EdA52 corresponds to the second ∂A / ∂t component in the second basic principle.
EdA52≈E2d0 (152)
EdA52 = rk · exp {j · (θ9 + θ00)}
・ Ω0 ・ exp (j ・ π / 2)
{B9 + b10 · exp (j · Δθ10)} (153)

起電力差ＥｄＡ５２は、流速の大きさＶに関係しないので、∂Ａ／∂ｔにより発生する成分のみとなる。この起電力差ＥｄＡ５２を用いて、ｖ×Ｂ成分ＥｖＢ４０の流速の大きさＶにかかる係数（スパン）を正規化する。式（１２９）のｖ×Ｂ成分ＥｖＢ４０を式（１５３）の起電力差ＥｄＡ５２で正規化し、ω０倍したものをＥｖＢｎ５とすれば、正規化起電力ＥｖＢｎ５は次式で表される。
ＥｖＢｎ５＝（ＥｖＢ４０／ＥｄＡ５２）・ω０
＝［γ・ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００＋Δθ０１）｝
・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］・Ｖ
／［ｒｋ・ｅｘｐ｛ｊ・（θ９＋θ００）｝
・ω０・ｅｘｐ（ｊ・π／２）・｛ｂ９＋ｂ１０・ｅｘｐ（ｊ・Δθ１０）｝］
・ω０
＝［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］・Ｖ ・・・（１５４） Since the electromotive force difference EdA52 is not related to the magnitude V of the flow velocity, it is only a component generated by ∂A / ∂t. Using this electromotive force difference EdA52, the coefficient (span) applied to the magnitude V of the flow velocity of the v × B component EvB40 is normalized. If the v × B component EvB40 of the equation (129) is normalized by the electromotive force difference EdA52 of the equation (153) and multiplied by ω0 is EvBn5, the normalized electromotive force EvBn5 is expressed by the following equation.
EvBn5 = (EvB40 / EdA52) · ω0
= [Γ · rk · exp {j · (θ9 + θ00 + Δθ01)}
{B9 + b10 · exp (j · Δθ10)}] · V
/ [Rk · exp {j · (θ9 + θ00)}
.Omega.0.exp (j.pi / 2). {B9 + b10.exp (j..DELTA..theta.10)}]
・ Ω0
= [Γ · exp {j · (−π / 2 + Δθ01)}] · V (154)

式（１５４）ではｖ×Ｂにより発生する成分が正規化されスパンの変動要因が除去されている。流速の大きさＶにかかる複素係数は、γの大きさ、−π／２＋Δθ０１の実軸からの角度をもつ。係数γおよび角度Δθ０１は校正等により予め求めることができる定数であり、正規化起電力ＥｖＢｎ５は被測定流体の流速が変化しないかぎり一定となる。したがって、抽出した第２の∂Ａ／∂ｔの成分をもちいてｖ×Ｂ成分の正規化を行うことにより、０点の補正に加えて、磁場のシフトや位相変化による誤差を自動的に補正するスパン補正を実現することができる。   In the equation (154), the component generated by v × B is normalized to remove the span variation factor. 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 normalized electromotive force EvBn5 is constant as long as the flow velocity of the fluid to be measured does not change. Therefore, by normalizing the v × B component using the extracted second ∂A / ∂t component, in addition to the zero point correction, errors due to magnetic field shift and phase change are automatically corrected. Span correction can be realized.

式（１５４）より、流速の大きさＶは次式のように表される。
Ｖ＝｜ＥｖＢｎ５／［γ・ｅｘｐ｛ｊ・（−π／２＋Δθ０１）｝］｜
＝｜ＥｖＢｎ５｜／γ ・・・（１５５） From the equation (154), the magnitude V of the flow velocity is expressed as the following equation.
V = | EvBn5 / [γ · exp {j · (−π / 2 + Δθ01)}] |
= | EvBn5 | / γ (155)

なお、第２の基本原理で用いた定数および変数と、本実施の形態の定数および変数との対応関係は以下の表５のとおりである。本実施の形態は、表５から明らかなように、前述の第２の基本原理を具体的に実現する１つの例である。   The correspondence relationship between the constants and variables used in the second basic principle and the constants and variables of the present embodiment is as shown in Table 5 below. As is apparent from Table 5, this embodiment is an example that specifically realizes the second basic principle described above.

Figure 0004555023
Figure 0004555023

次に、本実施の形態の電磁流量計の具体的な構成とその動作について説明する。本実施の形態の電磁流量計の構成は第４の実施の形態と同様であるので、図２５の符号を用いて説明する。本実施の形態の電磁流量計は、測定管１と、第１の電極２ａ，２ｂと、第２の電極２ｃ，２ｄと、励磁コイル３と、電源部４ｂと、信号変換部５ｂと、流量出力部６ｂとを有している。   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 fourth embodiment, description will be made using the reference numerals in FIG. 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 4b, a signal conversion unit 5b, a flow rate. And an output unit 6b.

信号変換部５ｂは、電極２ａ，２ｂで検出される第１の合成起電力と電極２ｃ，２ｄで検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて第１の合成起電力の第１の角周波数ω０の成分と第２の合成起電力の第１の角周波数ω０の成分との起電力和、および第１の合成起電力の第２の角周波数ω２の成分と第２の合成起電力の第２の角周波数ω２の成分との起電力和を求め、これら２つの起電力和の差分を第１の∂Ａ／∂ｔ成分として抽出し、第１の角周波数ω０の起電力和又は第２の角周波数ω２の起電力和の中から第１の∂Ａ／∂ｔ成分を取り除くことによりｖ×Ｂ成分を抽出する０点補正部５１ｂと、第１の合成起電力の第１の角周波数ω０の成分と第２の合成起電力の第１の角周波数ω０の成分との起電力差、又は第１の合成起電力の第２の角周波数ω２の成分と第２の合成起電力の第２の角周波数ω２の成分との起電力差を第２の∂Ａ／∂ｔ成分として抽出し、この第２の∂Ａ／∂ｔ成分に基づいて、ｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するスパン補正部５２ｂとから構成される。   The signal conversion unit 5b obtains the amplitude and phase for each of the first combined electromotive force detected by the electrodes 2a and 2b and the second combined electromotive force detected by the electrodes 2c and 2d, and the amplitude and phase are obtained. Based on the sum of the electromotive forces of the component of the first angular frequency ω0 of the first combined electromotive force and the component of the first angular frequency ω0 of the second combined electromotive force, and the second of the first combined electromotive force The sum of electromotive forces of the component of the angular frequency ω2 and the component of the second combined electromotive force at the second angular frequency ω2 is obtained, and the difference between the two electromotive force sums is extracted as the first ∂A / ∂t component. The 0-point correction unit 51b that extracts the v × B component by removing the first ∂A / ∂t component from the electromotive force sum of the first angular frequency ω0 or the electromotive force sum of the second angular frequency ω2. And a first angular frequency ω0 component of the first combined electromotive force and a first angular frequency ω0 component of the second combined electromotive force. Or the difference in electromotive force between the second angular frequency ω2 component of the first combined electromotive force and the second angular frequency ω2 component of the second combined electromotive force. A span correction unit 52b that extracts the t variation component and removes the variation factor of the span, which is a coefficient related to the magnitude V of the flow velocity of the v × B component, based on the second ∂A / ∂t component. The

電源部４ｂの動作は第４の実施の形態と同じである。図２７は本実施の形態の信号変換部５ｂと流量出力部６ｂの動作を示すフローチャートである。まず、信号変換部５ｂの０点補正部５１ｂは、起電力和Ｅ４ｓ０の振幅ｒ４ｓ０を求めると共に、実軸と起電力和Ｅ４ｓ０との位相差φ４ｓ０を図示しない位相検波器により求める。また、０点補正部５１ｂは、起電力和Ｅ４ｓ２の振幅ｒ４ｓ２を求めると共に、実軸と起電力和Ｅ４ｓ２との位相差φ４ｓ２を位相検波器により求める。さらに、０点補正部５１ｂは、起電力差Ｅ４ｄ０の振幅ｒ４ｄ０を求めると共に、実軸と起電力差Ｅ４ｄ０との位相差φ４ｄ０を位相検波器により求める（図２７ステップ５０１）。図２７のステップ５０２〜５０４の処理は、図２６のステップ４０２〜４０４と同じである。   The operation of the power supply unit 4b is the same as that of the fourth embodiment. FIG. 27 is a flowchart showing the operation of the signal conversion unit 5b and the flow rate output unit 6b of the present embodiment. First, the zero point correction unit 51b of the signal conversion unit 5b obtains the amplitude r4s0 of the electromotive force sum E4s0 and obtains the phase difference φ4s0 between the real axis and the electromotive force sum E4s0 by a phase detector (not shown). Further, the zero point correction unit 51b obtains the amplitude r4s2 of the electromotive force sum E4s2, and obtains the phase difference φ4s2 between the real axis and the electromotive force sum E4s2 by the phase detector. Further, the zero point correction unit 51b obtains the amplitude r4d0 of the electromotive force difference E4d0 and obtains the phase difference φ4d0 between the real axis and the electromotive force difference E4d0 using a phase detector (step 501 in FIG. 27). The processing in steps 502 to 504 in FIG. 27 is the same as that in steps 402 to 404 in FIG.

次に、信号変換部５ｂのスパン補正部５２ｂは、起電力差Ｅ４ｄ０を近似した起電力差ＥｄＡ５２の大きさを求める（ステップ５０５）。このステップ５０５の処理は、第２の∂Ａ／∂ｔ成分を求めることに対応する処理であり、式（１５３）の算出に相当する処理である。スパン補正部５２ｂは、起電力差ＥｄＡ５２の大きさ｜ＥｄＡ５２｜を次式のように算出する。
｜ＥｄＡ５２｜＝ｒ２ｄ０ ・・・（１５６） Next, the span correction unit 52b of the signal conversion unit 5b obtains the magnitude of the electromotive force difference EdA52 that approximates the electromotive force difference E4d0 (step 505). The process of step 505 is a process corresponding to obtaining the second ∂A / ∂t component, and is a process corresponding to the calculation of Expression (153). The span correction unit 52b calculates the magnitude | EdA52 | of the electromotive force difference EdA52 as the following equation.
| EdA52 | = r2d0 (156)

続いて、スパン補正部５２ｂは、ｖ×Ｂ成分ＥｖＢ４０を起電力差ＥｄＡ５２で正規化した正規化起電力ＥｖＢｎ５の大きさを求める（ステップ５０６）。このステップ５０６の処理は、式（１５４）の算出に相当する処理である。スパン補正部５２ｂは、正規化起電力ＥｖＢｎ５の大きさ｜ＥｖＢｎ５｜を次式のように算出する。
｜ＥｖＢｎ５｜＝（｜ＥｖＢ４０｜／｜ＥｄＡ５２｜）・ω０ ・・・（１５７） Subsequently, the span correction unit 52b obtains the magnitude of the normalized electromotive force EvBn5 obtained by normalizing the v × B component EvB40 with the electromotive force difference EdA52 (step 506). The process of step 506 is a process corresponding to the calculation of equation (154). The span correction unit 52b calculates the magnitude | EvBn5 | of the normalized electromotive force EvBn5 as follows.
| EvBn5 | = (| EvB40 | / | EdA52 |) · ω0 (157)

流量出力部６ｂは、被測定流体の流速の大きさＶを次式のように算出する（ステップ５０７）。このステップ５０７の処理は、式（１５５）の算出に相当する処理である。
Ｖ＝｜ＥｖＢｎ５｜／γ ・・・（１５８）
なお、比例係数γは、校正等により予め求めることができる定数である。信号変換部５ｂと流量出力部６ｂとは、以上のようなステップ５０１〜５０７の処理を例えばオペレータによって計測終了が指示されるまで（ステップ５０８においてＹＥＳ）、一定周期毎に行う。 The flow rate output unit 6b calculates the magnitude V of the flow velocity of the fluid to be measured as in the following equation (step 507). The process of step 507 is a process corresponding to the calculation of Expression (155).
V = | EvBn5 | / γ (158)
The proportionality coefficient γ is a constant that can be obtained in advance by calibration or the like. The signal conversion unit 5b and the flow rate output unit 6b perform the processing in steps 501 to 507 as described above at regular intervals until, for example, the operator instructs the end of measurement (YES in step 508).

以上のように、本実施の形態では、励磁コイル３から発生する磁場Ｂ９とＢ１０とが等しくなるように調整しておくと、起電力差Ｅ４ｄ０が近似的に第２の∂Ａ／∂ｔ成分として抽出できることに着眼し、第４の実施の形態と同様にｖ×Ｂ成分を抽出した後、近似的に抽出した第２の∂Ａ／∂ｔ成分を用いてｖ×Ｂ成分の流速の大きさＶにかかるスパンを正規化して、スパン変動要素を消去するようにしたので、正確なスパン補正を自動的に行うことができ、かつ被測定流体の流量を０にすることなく電磁流量計の出力の０点を補正することができ、高周波励磁においても０点の安定性を確保することができる。また、本実施の形態では、角周波数ω０の起電力和Ｅ４ｓ０から抽出したｖ×Ｂ成分を同じ角周波数ω０の起電力差Ｅ４ｄ０から抽出した第２の∂Ａ／∂ｔ成分を用いて正規化するので、第４の実施の形態に比べて周波数による誤差の影響が少なくなる。   As described above, in this embodiment, when the magnetic fields B9 and B10 generated from the exciting coil 3 are adjusted to be equal, the electromotive force difference E4d0 is approximately the second ∂A / ∂t component. As in the fourth embodiment, the v × B component is extracted, and then the velocity of the v × B component is increased using the approximately extracted second ∂A / ∂t component. Since the span fluctuation factor is eliminated by normalizing the span over the V, accurate span correction can be automatically performed, and the flow rate of the electromagnetic flowmeter 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 this embodiment, the v × B component extracted from the electromotive force sum E4s0 of the angular frequency ω0 is normalized using the second ∂A / ∂t component extracted from the electromotive force difference E4d0 of the same angular frequency ω0. Therefore, the influence of the error due to the frequency is reduced as compared with the fourth embodiment.

なお、本実施の形態では、角周波数ω０の成分の起電力和Ｅ４ｓ０を０補正およびスパン補正の対象としたが、角周波数ω２の成分の起電力和Ｅ４ｓ２を０補正およびスパン補正の対象としてもよい。この場合は、起電力差Ｅ４ｄ０を求める代わりに、Ｅ４ｄ２を求める。そして、次式のように起電力和Ｅ４ｓ２からＥ４ｓ０を引いて差分ＥｄＡ４１（第１の∂Ａ／∂ｔ成分）を求める。
ＥｄＡ４１＝（Ｅ４ｓ２−Ｅ４ｓ０）・ω２／（ω２−ω０） ・・・（１５９）
そして、起電力和Ｅ４ｓ２から差分ＥｄＡ４１を引くことによりｖ×Ｂ成分ＥｖＢ４２を抽出する。 In the present embodiment, the electromotive force sum E4s0 of the component of the angular frequency ω0 is set as a target for zero correction and span correction, but the electromotive force sum E4s2 of the component of the angular frequency ω2 is also set as a target of zero correction and span correction. Good. In this case, instead of obtaining the electromotive force difference E4d0, E4d2 is obtained. Then, the difference EdA41 (first ∂A / ∂t component) is obtained by subtracting E4s0 from the electromotive force sum E4s2 as in the following equation.
EdA41 = (E4s2-E4s0) · ω2 / (ω2-ω0) (159)
Then, the v × B component EvB42 is extracted by subtracting the difference EdA41 from the electromotive force sum E4s2.

さらに、次式のように起電力差Ｅ４ｄ２を近似した起電力差ＥｄＡ５２（第２の∂Ａ／∂ｔ成分）を求める。
ＥｄＡ５２≒Ｅ４ｄ２ ・・・（１６０）
そして、次式のように起電力差ＥｄＡ５２を用いてｖ×Ｂ成分ＥｖＢ４２の流速の大きさＶにかかるスパンを正規化すればよい。その他の処理は起電力和Ｅ４ｓ０を０補正およびスパン補正の対象とする場合と同じである。
｜ＥｖＢｎ５｜＝｜（ＥｖＢ４２／ＥｄＡ５２）・ω２｜ ・・・（１６１） Further, an electromotive force difference EdA52 (second ∂A / ∂t component) that approximates the electromotive force difference E4d2 is obtained as in the following equation.
EdA52≈E4d2 (160)
And the span concerning the magnitude | size V of the flow velocity of vxB component EvB42 should just be normalized using the electromotive force difference EdA52 like following Formula. The other processes are the same as those in the case where the electromotive force sum E4s0 is the target of 0 correction and span correction.
| EvBn5 | = | (EvB42 / EdA52) · ω2 | (161)

また、本実施の形態では、複数の励磁周波数ω０，ω２で同時に励磁する例を示したが、単一の励磁周波数ω０又はω２で励磁を行い、励磁周波数をω０とω２で交互に切り替えながら励磁をした場合でも同じ効果を得ることができる。   In this embodiment, an example is shown in which excitation is performed simultaneously with a plurality of excitation frequencies ω0 and ω2, but excitation is performed with a single excitation frequency ω0 or ω2, and excitation is performed while alternately switching the excitation frequency between ω0 and ω2. The same effect can be obtained even when

なお、第１の実施の形態〜第５の実施の形態では、励磁電流に正弦波を用いる正弦波励磁方式を採用しているが、矩形波の場合正弦波の組み合わせと考えることができるので、励磁電流に矩形波を用いる矩形波励磁方式を採用してもよい。
また、第１の実施の形態〜第５の実施の形態で使用する電極２ａ，２ｂ，２ｃ，２ｄとしては、図２８に示すように、測定管１の内壁から露出して被測定流体に接触する形式の電極でもよいし、図２９に示すように、被測定流体と接触しない容量結合式の電極でもよい。容量結合式の場合、電極２ａ，２ｂ，２ｃ，２ｄは、測定管１の内壁に形成されるセラミックやテフロン（登録商標）等からなるライニング１０によって被覆される。 In the first to fifth embodiments, a sine wave excitation method using a sine wave as an excitation current is adopted. However, 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. 28, the electrodes 2a, 2b, 2c, and 2d used in the first to fifth embodiments are exposed from the inner wall of the measuring tube 1 and come into contact with the fluid to be measured. 29, 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.

また、第１の実施の形態〜第５の実施の形態では、第１の電極として１対の電極２ａ，２ｂを使用し、第２の電極として１対の電極２ｃ，２ｄを使用しているが、これに限るものではなく、第１の電極と第２の電極をそれぞれ１個ずつにしてもよい。電極が１個だけの場合には、被測定流体の電位を接地電位にするための接地リングや接地電極が測定管１に設けられており、１個の電極に生じた起電力（接地電位との電位差）を信号変換部５，５ａ，５ｂで検出すればよい。電極軸は、１対の電極を使用する場合はこの１対の電極間を結ぶ直線である。一方、電極が１個だけの場合、この１個の実電極を含む平面ＰＬＮ上において、測定管軸ＰＡＸを挟んで実電極と対向する位置に仮想の電極を配置したと仮定したとき、実電極と仮想の電極とを結ぶ直線が電極軸となる。   In the first to fifth 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.

本発明は、測定管内を流れる被測定流体の流量計測に適用することができる。   The present invention can be applied to flow measurement of a fluid to be measured flowing in a measurement tube.

本発明の第１の基本原理に基づく電磁流量計における∂Ａ／∂ｔ成分のベクトルとｖ×Ｂ成分のベクトルと合成ベクトルとを示す図である。It is a figure which shows the vector of (A) / (t) component, the vector of vxB component, and a synthetic | combination vector in the electromagnetic flowmeter based on the 1st basic principle of this invention. 本発明の第１の基本原理に基づく電磁流量計において電極で検出される合成ベクトルから∂Ａ／∂ｔ成分を抽出する処理を複素ベクトル表現した図である。It is the figure which expressed complex vector expression about the processing which extracts ∂A / ∂t component from the synthetic vector detected by the electrode in the electromagnetic flow meter based on the 1st basic principle of the present invention. 本発明の第１の基本原理に基づく電磁流量計において電極で検出される合成ベクトルからｖ×Ｂ成分を抽出する処理を複素ベクトル表現した図である。It is the figure which expressed complex vector expression about the processing which extracts the vxB ingredient from the synthetic vector detected with an electrode in the electromagnetic flow meter based on the 1st basic principle of the present invention. 本発明の第１の基本原理に基づく電磁流量計においてｖ×Ｂ成分を∂Ａ／∂ｔ成分により正規化する処理を複素ベクトル表現した図である。It is the figure which expressed complex vector expression about the processing which normalizes vxB ingredient by ∂A / ∂t component in the electromagnetic flow meter based on the 1st basic principle of the present invention. 本発明の第２の基本原理に基づく電磁流量計のうち２個の励磁コイルと１対の電極とを有する電磁流量計の原理を説明するためのブロック図である。It is a block diagram for demonstrating the principle of the electromagnetic flowmeter which has two excitation coils and a pair of electrodes among the electromagnetic flowmeters based on the 2nd basic principle of this invention. 図５の電磁流量計において被測定流体の流量が０の場合の渦電流及び電極間起電力を示す図である。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. 図５の電磁流量計において被測定流体の流量が０でない場合の渦電流及び電極間起電力を示す図である。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. 図５の電磁流量計において第１の励磁コイルのみで励磁した場合の∂Ａ／∂ｔ成分のベクトルとｖ×Ｂ成分のベクトルと合成ベクトルとを示す図である。FIG. 6 is a diagram illustrating a vector of ∂A / ∂t component, a vector of v × B component, and a combined vector when excited by only the first excitation coil in the electromagnetic flow meter of FIG. 5. 図５の電磁流量計において第２の励磁コイルのみで励磁した場合の∂Ａ／∂ｔ成分のベクトルとｖ×Ｂ成分のベクトルと合成ベクトルとを示す図である。FIG. 6 is a diagram illustrating a vector of ∂A / ∂t component, a vector of v × B component, and a combined vector when excitation is performed with only the second excitation coil in the electromagnetic flow meter of FIG. 5. 図５の電磁流量計において２つの励磁コイルで励磁した場合の∂Ａ／∂ｔ成分のベクトルとｖ×Ｂ成分のベクトルと合成ベクトルとを示す図である。FIG. 6 is a diagram illustrating a vector of ∂A / ∂t component, a vector of v × B component, and a combined vector when excited by two excitation coils in the electromagnetic flow meter of FIG. 5. 図５の電磁流量計において電極で検出される合成ベクトルから第１の∂Ａ／∂ｔ成分を抽出する処理を複素ベクトル表現した図である。FIG. 6 is a diagram representing a process of extracting a first ∂A / ∂t component from a combined vector detected by an electrode in the electromagnetic flow meter of FIG. 5 in a complex vector representation. 図５の電磁流量計において電極で検出される合成ベクトルからｖ×Ｂ成分を抽出する処理を複素ベクトル表現した図である。It is the figure which expressed the complex vector expression about the process which extracts a vxB component from the synthetic | combination vector detected with an electrode in the electromagnetic flowmeter of FIG. 図５の電磁流量計において第２の励磁状態で第２の励磁コイルのみで励磁した場合の∂Ａ／∂ｔ成分のベクトルとｖ×Ｂ成分のベクトルと合成ベクトルとを示す図である。FIG. 6 is a diagram illustrating a vector of ∂A / ∂t component, a vector of v × B component, and a combined vector when the electromagnetic flowmeter of FIG. 5 is excited by only the second excitation coil in the second excitation state. 図５の電磁流量計において第２の励磁状態で２つの励磁コイルを励磁した場合の∂Ａ／∂ｔ成分のベクトルとｖ×Ｂ成分のベクトルと合成ベクトルとを示す図である。FIG. 6 is a diagram showing a vector of ∂A / 成分 t component, a vector of v × B component, and a combined vector when two exciting coils are excited in the second excitation state in the electromagnetic flow meter of FIG. 5. 図５の電磁流量計において電極で検出される合成ベクトルから第２の∂Ａ／∂ｔ成分を抽出する処理を複素ベクトル表現した図である。FIG. 6 is a diagram representing a process of extracting a second ∂A / ∂t component from a combined vector detected by an electrode in the electromagnetic flow meter of FIG. 5 in a complex vector representation. 図５の電磁流量計においてｖ×Ｂ成分を第２の∂Ａ／∂ｔ成分により正規化する処理を複素ベクトル表現した図である。FIG. 6 is a diagram representing a complex vector representation of a process of normalizing a v × B component with a second ∂A / ∂t component in the electromagnetic flow meter of FIG. 5. 本発明の第２の基本原理に基づく電磁流量計のうち１個の励磁コイルと２対の電極とを有する電磁流量計の原理を説明するためのブロック図である。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 2nd basic principle of this invention. 図１７の電磁流量計において被測定流体の流量が０の場合の渦電流及び電極間起電力を示す図である。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. 図１７の電磁流量計において被測定流体の流量が０でない場合の渦電流及び電極間起電力を示す図である。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. 本発明の第１の実施の形態の電磁流量計の構成を示すブロック図である。It is a block diagram which shows the structure of the electromagnetic flowmeter of the 1st Embodiment of this invention. 本発明の第１の実施の形態における信号変換部と流量出力部の動作を示すフローチャートである。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. 本発明の第２の実施の形態の電磁流量計の構成を示すブロック図である。It is a block diagram which shows the structure of the electromagnetic flowmeter of the 2nd Embodiment of this invention. 本発明の第２の実施の形態における信号変換部と流量出力部の動作を示すフローチャートである。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. 本発明の第３の実施の形態における信号変換部と流量出力部の動作を示すフローチャートである。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. 本発明の第４の実施の形態の電磁流量計の構成を示すブロック図である。It is a block diagram which shows the structure of the electromagnetic flowmeter of the 4th Embodiment of this invention. 本発明の第４の実施の形態における信号変換部と流量出力部の動作を示すフローチャートである。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. 本発明の第５の実施の形態における信号変換部と流量出力部の動作を示すフローチャートである。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. 本発明の電磁流量計で用いる電極の１例を示す断面図である。It is sectional drawing which shows one example of the electrode used with the electromagnetic flowmeter of this invention. 本発明の電磁流量計で用いる電極の他の例を示す断面図である。It is sectional drawing which shows the other example of the electrode used with the electromagnetic flowmeter of this invention. 従来の電磁流量計の原理を説明するためのブロック図である。It is a block diagram for demonstrating the principle of the conventional electromagnetic flowmeter. 従来の電磁流量計において被測定流体の流量が０の場合の渦電流及び電極間起電力を示す図である。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. 従来の電磁流量計において被測定流体の流量が０でない場合の渦電流及び電極間起電力を示す図である。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. 電磁流量計におけるスパンのシフトを説明するための図である。It is a figure for demonstrating the shift of the span in an electromagnetic flowmeter. 電磁流量計における０点のシフトを説明するための図である。It is a figure for demonstrating the zero point shift in an electromagnetic flowmeter. 従来の電磁流量計の問題点を説明するための図である。It is a figure for demonstrating the problem of the conventional electromagnetic flowmeter.

符号の説明Explanation of symbols

１…測定管、２ａ、２ｂ、２ｃ、２ｄ…電極、３、３ａ、３ｂ…励磁コイル、４、４ａ、４ｂ…電源部、５、５ａ、５ｂ…信号変換部、６、６ａ、６ｂ…流量出力部、５１、５１ａ、５１ｂ…０点補正部、５２、５２ａ、５２ｂ…スパン補正部。
DESCRIPTION OF SYMBOLS 1 ... Measuring tube, 2a, 2b, 2c, 2d ... Electrode, 3, 3a, 3b ... Excitation coil, 4, 4a, 4b ... Power supply part, 5, 5a, 5b ... Signal conversion part, 6, 6a, 6b ... Flow rate Output unit 51, 51a, 51b ... 0 point correction unit, 52, 52a, 52b ... Span correction unit.

Claims (15)

被測定流体が流れる測定管と、
この測定管に配設され、前記流体に印加される磁場と前記流体の流れとによって生じた起電力を検出する電極と、
この電極を含む、前記測定管の軸方向と垂直な第１の平面に対して非対称かつ時間変化する磁場を前記流体に印加する励磁部と、
前記電極で検出される、前記流体の流速とは無関係な∂Ａ／∂ｔ成分の起電力と前記流体の流速に起因するｖ×Ｂ成分の起電力との合成起電力から、前記∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出する０点補正部と、
前記合成起電力から、前記∂Ａ／∂ｔ成分と同一又は異なる∂Ａ／∂ｔ成分を抽出し、この抽出した∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去するスパン補正部と、
前記変動要因を除去したｖ×Ｂ成分から前記流体の流量を算出する流量出力部とを備えることを特徴とする電磁流量計。 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 exciting 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 electromotive force of the ∂A / ∂t component that is detected by the electrode and independent of the fluid flow velocity and the v × B component electromotive force caused by the fluid flow velocity, the 流速 A / A zero point correction unit that extracts the v × B component by removing the ∂t component;
From the combined electromotive force, a ∂A / ∂t component that is the same as or different from the ∂A / ∂t component is extracted, and based on the extracted ∂A / ∂t component, the flow velocity of the extracted v × B component A span correction unit for removing a variation factor of the span, which is a coefficient related to the magnitude V of
An electromagnetic flowmeter comprising: a flow rate output unit that calculates a flow rate of the fluid from a v × B component from which the variation factor is removed. 請求項１記載の電磁流量計において、
前記０点補正部は、前記電極で検出される合成起電力から前記∂Ａ／∂ｔ成分を抽出して、前記合成起電力の中から、前記抽出した∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、
前記スパン補正部は、前記抽出された∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去することを特徴とする電磁流量計。 The electromagnetic flowmeter according to claim 1,
The zero point correction unit extracts the ∂A / ∂t component from the combined electromotive force detected by the electrode, and removes the extracted ∂A / ∂t component from the combined electromotive force. Extracting the v × B component;
The span correction unit removes a variation factor of the span, which is a coefficient related to the magnitude V of the flow velocity of the extracted v × B component, based on the extracted ∂A / ∂t component. Electromagnetic flow meter to do. 請求項２記載の電磁流量計において、
前記励磁部は、複数の励磁周波数を同時又は交互に与える磁場を前記流体に印加し、
前記０点補正部は、前記電極で検出される合成起電力のうち、同時又は交互に得られる複数の周波数成分の振幅と位相を求めることにより前記∂Ａ／∂ｔ成分を抽出することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 2,
The excitation unit applies a magnetic field that gives a plurality of excitation frequencies simultaneously or alternately to the fluid,
The zero point correction unit extracts the ∂A / ∂t component by obtaining the amplitude and phase of a plurality of frequency components obtained simultaneously or alternately from the composite electromotive force detected by the electrode. Electromagnetic flow meter. 請求項３記載の電磁流量計において、
前記励磁部は、前記電極を含む、前記測定管の軸方向と垂直な第１の平面からオフセットを設けて離れた位置に配設された励磁コイルと、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給する電源部とからなり、
前記０点補正部は、前記電極で検出される合成起電力のうち前記第１の周波数と第２の周波数の２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて前記２つの周波数成分の起電力差を前記∂Ａ／∂ｔ成分として抽出し、前記電極で検出される合成起電力のうち前記第１の周波数の成分又は前記第２の周波数の成分の中から、前記抽出した∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 3, wherein
The excitation unit includes an excitation coil disposed at a position apart from the first plane perpendicular to the axial direction of the measurement tube, including the electrodes, and a first frequency and a second frequency. A power supply unit that supplies the exciting coil with exciting currents that simultaneously or alternately provide two different exciting frequencies;
The zero point correction unit obtains the amplitude and phase of two frequency components of the first frequency and the second frequency in the combined electromotive force detected by the electrode, and based on the amplitude and phase, the 2 points The difference in electromotive force of two frequency components is extracted as the ∂A / ∂t component, and the component of the first frequency or the component of the second frequency in the combined electromotive force detected by the electrode An electromagnetic flowmeter, wherein the v × B component is extracted by removing the extracted ∂A / ∂t component. 請求項１記載の電磁流量計において、
前記０点補正部は、前記電極で検出される合成起電力から第１の∂Ａ／∂ｔ成分を抽出して、前記合成起電力の中から、前記抽出した第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、
前記スパン補正部は、前記合成起電力から第２の∂Ａ／∂ｔ成分を抽出し、この抽出した第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去することを特徴とする電磁流量計。 The electromagnetic flowmeter according to claim 1,
The zero point correction unit extracts a first ∂A / ∂t component from the combined electromotive force detected by the electrode, and extracts the extracted first ∂A / ∂t from the combined electromotive force. Extracting the v × B component by removing the component;
The span correction unit extracts a second ∂A / ∂t component from the combined electromotive force, and based on the extracted second ∂A / ∂t component, the flow velocity of the extracted v × B component An electromagnetic flow meter characterized by removing a variation factor of a span, which is a coefficient related to the magnitude V of the. 請求項５記載の電磁流量計において、
前記励磁部は、前記電極を含む、前記測定管の軸方向と垂直な第１の平面から第１のオフセットを設けて離れた位置に配設された第１の励磁コイルと、前記第１の平面から第２のオフセットを設けて離れた位置に、前記第１の平面を挟んで前記第１の励磁コイルと対向するように配設された第２の励磁コイルと、前記第１の励磁コイルに供給する励磁電流と第２の励磁コイルに供給する励磁電流の位相差を切り替えながら、複数の励磁周波数を同時又は交互に与える励磁電流を前記第１の励磁コイルと第２の励磁コイルに供給する電源部とからなり、
前記０点補正部は、前記第１の励磁コイルにより発生する第１の磁場と前記第２の励磁コイルにより発生する第２の磁場との位相差が第１の値である第１の励磁状態において、前記電極で検出される合成起電力のうち、同時又は交互に得られる複数の周波数成分の振幅と位相を求めることにより前記第１の∂Ａ／∂ｔ成分を抽出し、
前記スパン補正部は、前記第１の磁場と第２の磁場との位相差が前記第１の励磁状態と異なる第２の励磁状態において、前記電極で検出される合成起電力のうち、同時又は交互に得られる複数の周波数成分の振幅と位相を求めることにより前記第２の∂Ａ／∂ｔ成分を抽出することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 5, wherein
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 The excitation current that supplies a plurality of excitation frequencies simultaneously or alternately is supplied to the first excitation coil and the second excitation coil while switching the phase difference between the excitation current supplied to the second excitation coil and the excitation current supplied to the second excitation coil. Power supply
The zero point correction unit is a first excitation state in which 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 value. And extracting the first ∂A / ∂t component by obtaining the amplitude and phase of a plurality of frequency components obtained simultaneously or alternately from the synthetic electromotive force detected by the electrode,
In the second excitation state in which the phase difference between the first magnetic field and the second magnetic field is different from the first excitation state, the span correction unit may simultaneously or among the combined electromotive forces detected by the electrodes An electromagnetic flowmeter characterized in that the second ∂A / ∂t component is extracted by obtaining the amplitude and phase of a plurality of frequency components obtained alternately. 請求項６記載の電磁流量計において、
前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記第１の励磁コイルと第２の励磁コイルに供給し、
前記０点補正部は、前記第１の励磁状態において、前記電極で検出される合成起電力のうち前記第１の周波数と第２の周波数の２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて前記２つの周波数成分の起電力差を前記第１の∂Ａ／∂ｔ成分として抽出し、前記電極で検出される合成起電力のうち前記第１の周波数の成分又は前記第２の周波数の成分の中から、前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、
前記スパン補正部は、前記第２の励磁状態において、前記電極で検出される合成起電力のうち前記２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて前記２つの周波数成分の起電力差を前記第２の∂Ａ／∂ｔ成分として抽出し、この抽出した第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 6, wherein
The power supply unit supplies an excitation current that simultaneously or alternately provides two excitation frequencies having different first and second frequencies to the first excitation coil and the second excitation coil,
The zero point correction unit obtains the amplitude and phase of two frequency components of the first frequency and the second frequency in the combined electromotive force detected by the electrode in the first excitation state, The electromotive force difference between the two frequency components is extracted as the first ∂A / ∂t component based on the amplitude and phase, and the first frequency component or the component of the combined electromotive force detected by the electrode The v × B component is extracted by removing the first ∂A / ∂t component from the second frequency component,
The span correction unit obtains the amplitude and phase of the two frequency components of the combined electromotive force detected by the electrode in the second excitation state, and the two frequency components based on the amplitude and phase. Is extracted as the second ∂A / ∂t component, and on the basis of the extracted second ∂A / ∂t component, the flow velocity V of the extracted v × B component is obtained. An electromagnetic flow meter characterized by removing a variation factor of a span which is such a coefficient. 請求項５記載の電磁流量計において、
前記励磁部は、前記電極を含む、前記測定管の軸方向と垂直な第１の平面から第１のオフセットを設けて離れた位置に配設された第１の励磁コイルと、前記第１の平面から第２のオフセットを設けて離れた位置に、前記第１の平面を挟んで前記第１の励磁コイルと対向するように配設された第２の励磁コイルと、前記第１の励磁コイルに供給する励磁電流と第２の励磁コイルに供給する励磁電流の位相差を切り替えながら、複数の励磁周波数を同時又は交互に与える励磁電流を前記第１の励磁コイルと第２の励磁コイルに供給する電源部とからなり、
前記０点補正部は、前記第１の励磁コイルにより発生する第１の磁場と前記第２の励磁コイルにより発生する第２の磁場との位相差が第１の値である第１の励磁状態において、前記電極で検出される合成起電力のうち、同時又は交互に得られる複数の周波数成分の振幅と位相を求めることにより前記第１の∂Ａ／∂ｔ成分を抽出し、
前記スパン補正部は、前記第１の磁場と第２の磁場との位相差が前記第１の励磁状態と異なる第２の励磁状態において、前記電極で検出される合成起電力のうち１つの周波数成分の振幅と位相を求めることにより前記第２の∂Ａ／∂ｔ成分を抽出することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 5, wherein
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 The excitation current that supplies a plurality of excitation frequencies simultaneously or alternately is supplied to the first excitation coil and the second excitation coil while switching the phase difference between the excitation current supplied to the second excitation coil and the excitation current supplied to the second excitation coil. Power supply
The zero point correction unit is a first excitation state in which 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 value. And extracting the first ∂A / ∂t component by obtaining the amplitude and phase of a plurality of frequency components obtained simultaneously or alternately from the synthetic electromotive force detected by the electrode,
The span correction unit has one frequency of the combined electromotive force detected by the electrode in a second excitation state in which a phase difference between the first magnetic field and the second magnetic field is different from the first excitation state. 2. The electromagnetic flowmeter according to claim 1, wherein the second ∂A / ∂t component is extracted by obtaining an amplitude and a phase of the component. 請求項８記載の電磁流量計において、
前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記第１の励磁コイルと第２の励磁コイルに供給し、
前記０点補正部は、前記第１の励磁状態において、前記電極で検出される合成起電力のうち前記第１の周波数と第２の周波数の２つの周波数成分の振幅と位相を求め、これらの振幅と位相に基づいて前記２つの周波数成分の起電力差を前記第１の∂Ａ／∂ｔ成分として抽出し、前記電極で検出される合成起電力のうち前記第１の周波数の成分又は前記第２の周波数の成分の中から、前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、
前記スパン補正部は、前記第２の励磁状態において、前記電極で検出される合成起電力のうち前記第１の周波数の成分又は前記第２の周波数の成分の振幅と位相を求め、この振幅と位相に基づいて前記第１の周波数の成分又は前記第２の周波数の成分の起電力を前記第２の∂Ａ／∂ｔ成分として抽出し、この抽出した第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 8,
The power supply unit supplies an excitation current that simultaneously or alternately provides two excitation frequencies having different first and second frequencies to the first excitation coil and the second excitation coil,
The zero point correction unit obtains the amplitude and phase of two frequency components of the first frequency and the second frequency in the combined electromotive force detected by the electrode in the first excitation state, The electromotive force difference between the two frequency components is extracted as the first ∂A / ∂t component based on the amplitude and phase, and the first frequency component or the component of the combined electromotive force detected by the electrode The v × B component is extracted by removing the first ∂A / ∂t component from the second frequency component,
The span correction unit obtains the amplitude and phase of the first frequency component or the second frequency component of the combined electromotive force detected by the electrode in the second excitation state, and calculates the amplitude and Based on the phase, an electromotive force of the first frequency component or the second frequency component is extracted as the second ∂A / 位相 t component, and the extracted second ∂A / ∂t component is extracted. An electromagnetic flow meter characterized in that, based on the extracted v × B component, the variation factor of the span, which is a coefficient related to the magnitude V of the flow velocity, is removed. 請求項５記載の電磁流量計において、
前記励磁部は、前記流体に磁場を印加する励磁コイルと、複数の励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給する電源部とからなり、
前記電極は、前記励磁コイルの軸を含む、前記測定管の軸方向と垂直な第２の平面から第１のオフセットを設けて離れた位置に配設された第１の電極と、前記第２の平面から第２のオフセットを設けて離れた位置に、前記第２の平面を挟んで前記第１の電極と対向するように配設された第２の電極とからなり、
前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力和を複数の周波数成分について同時又は交互に求め、複数の起電力和から前記第１の∂Ａ／∂ｔ成分を抽出し、
前記スパン補正部は、前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力差を複数の周波数成分について同時又は交互に求め、複数の起電力差から前記第２の∂Ａ／∂ｔ成分を抽出することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 5, wherein
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 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. A second electrode disposed to face the first electrode across the second plane at a position away from the plane by providing a second offset,
The zero point correction unit obtains an amplitude and a phase for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitudes thereof. And sum of electromotive forces of the same frequency components of the first composite electromotive force and the second composite electromotive force for a plurality of frequency components based on the phase and the phase. A / ∂t component is extracted,
The span correction unit obtains an electromotive force difference of the same frequency component of the first combined electromotive force and the second combined electromotive force simultaneously or alternately for a plurality of frequency components, and calculates the second electromotive force difference from the plurality of electromotive force differences. An electromagnetic flowmeter that extracts ∂A / ∂t components. 請求項１０記載の電磁流量計において、
前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給し、
前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力和、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力和を求め、これら２つの起電力和の差分を前記第１の∂Ａ／∂ｔ成分として抽出し、前記第１の周波数の起電力和又は前記第２の周波数の起電力和の中から前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、
前記スパン補正部は、前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力差、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力差を求め、これら２つの起電力差の差分を前記第２の∂Ａ／∂ｔ成分として抽出し、この第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 10, wherein
The power supply unit supplies an excitation current that gives two excitation frequencies different in first frequency and second frequency simultaneously or alternately to the excitation coil,
The zero point correction unit obtains an amplitude and a phase for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitudes thereof. And the first electromotive force sum of the first frequency component of the first combined electromotive force and the first frequency component of the second combined electromotive force based on the phase and the phase of the first combined electromotive force, 2 to obtain the sum of electromotive forces of the second frequency component and the second frequency component of the second combined electromotive force, and extract the difference between the two electromotive force sums as the first ∂A / ∂t component. The v × B component is extracted by removing the first ∂A / ∂t component from the electromotive force sum of the first frequency or the electromotive force sum of the second frequency,
The span correction unit includes an electromotive force difference between a first frequency component of the first combined electromotive force and a first frequency component of the second combined electromotive force, and the first combined electromotive force. An electromotive force difference between a second frequency component and a second frequency component of the second combined electromotive force is obtained, and a difference between the two electromotive force differences is extracted as the second ∂A / ∂t component. Then, based on the second ∂A / ∂t component, a span variation factor, which is a coefficient applied to the magnitude V of the flow velocity of the extracted v × B component, is removed. . 請求項５記載の電磁流量計において、
前記励磁部は、前記流体に磁場を印加する励磁コイルと、複数の励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給する電源部とからなり、
前記電極は、前記励磁コイルの軸を含む、前記測定管の軸方向と垂直な第２の平面から第１のオフセットを設けて離れた位置に配設された第１の電極と、前記第２の平面から第２のオフセットを設けて離れた位置に、前記第２の平面を挟んで前記第１の電極と対向するように配設された第２の電極とからなり、
前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力差を複数の周波数成分について同時又は交互に求め、複数の起電力差から前記第１の∂Ａ／∂ｔ成分を抽出し、
前記スパン補正部は、前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力和を複数の周波数成分について同時又は交互に求め、複数の起電力和から前記第２の∂Ａ／∂ｔ成分を抽出することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 5, wherein
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 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. A second electrode disposed to face the first electrode across the second plane at a position away from the plane by providing a second offset,
The zero point correction unit obtains an amplitude and a phase for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitudes thereof. Based on the phase and the phase, an electromotive force difference between the same frequency components of the first combined electromotive force and the second combined electromotive force is obtained simultaneously or alternately for a plurality of frequency components, and the first power is calculated from the plurality of electromotive force differences. A / ∂t component is extracted,
The span correction unit obtains the electromotive force sum of the same frequency component of the first combined electromotive force and the second combined electromotive force simultaneously or alternately for a plurality of frequency components, and calculates the second electromotive force from the plurality of electromotive force sums. An electromagnetic flowmeter that extracts ∂A / ∂t components. 請求項１２記載の電磁流量計において、
前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給し、
前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力差、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力差を求め、これら２つの起電力差の差分を前記第１の∂Ａ／∂ｔ成分として抽出し、前記第１の周波数の起電力差又は前記第２の周波数の起電力差の中から前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、
前記スパン補正部は、前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力和、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力和を求め、これら２つの起電力和の差分を前記第２の∂Ａ／∂ｔ成分として抽出し、この第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 12,
The power supply unit supplies an excitation current that gives two excitation frequencies different in first frequency and second frequency simultaneously or alternately to the excitation coil,
The zero point correction unit obtains an amplitude and a phase for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitudes thereof. And the phase difference between the first frequency component of the first combined electromotive force and the first frequency component of the second combined electromotive force, and the first combined electromotive force The difference between the two frequency components and the second frequency component of the second combined electromotive force is obtained, and the difference between the two electromotive force differences is extracted as the first ∂A / ∂t component. The v × B component is extracted by removing the first ∂A / ∂t component from the electromotive force difference of the first frequency or the electromotive force difference of the second frequency,
The span correction unit includes an electromotive force sum of a first frequency component of the first combined electromotive force and a first frequency component of the second combined electromotive force, and the first combined electromotive force. A sum of electromotive forces of a second frequency component and a second frequency component of the second combined electromotive force is obtained, and a difference between the two electromotive force sums is extracted as the second ∂A / ∂t component. Then, based on the second ∂A / ∂t component, a span variation factor, which is a coefficient applied to the magnitude V of the flow velocity of the extracted v × B component, is removed. . 請求項５記載の電磁流量計において、
前記励磁部は、前記流体に磁場を印加する励磁コイルと、複数の励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給する電源部とからなり、
前記電極は、前記励磁コイルの軸を含む、前記測定管の軸方向と垂直な第２の平面から第１のオフセットを設けて離れた位置に配設された第１の電極と、前記第２の平面から第２のオフセットを設けて離れた位置に、前記第２の平面を挟んで前記第１の電極と対向するように配設された第２の電極とからなり、
前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力と第２の合成起電力の同一周波数成分の起電力和を複数の周波数成分について同時又は交互に求め、複数の起電力和から前記第１の∂Ａ／∂ｔ成分を抽出し、
前記スパン補正部は、前記第１の合成起電力と第２の合成起電力の１つの周波数成分の起電力差から前記第２の∂Ａ／∂ｔ成分を抽出することを特徴とする電磁流量計。 The electromagnetic flow meter according to claim 5, wherein
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 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. A second electrode disposed to face the first electrode across the second plane at a position away from the plane by providing a second offset,
The zero point correction unit obtains an amplitude and a phase for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitudes thereof. And sum of electromotive forces of the same frequency components of the first composite electromotive force and the second composite electromotive force for a plurality of frequency components based on the phase and the phase. A / ∂t component is extracted,
The span correction unit extracts the second ∂A / ∂t component from an electromotive force difference between one frequency component of the first combined electromotive force and the second combined electromotive force. Total. 請求項１４記載の電磁流量計において、
前記電源部は、第１の周波数と第２の周波数の異なる２つの励磁周波数を同時又は交互に与える励磁電流を前記励磁コイルに供給し、
前記０点補正部は、前記第１の電極で検出される第１の合成起電力と前記第２の電極で検出される第２の合成起電力の各々について振幅と位相を求め、これらの振幅と位相に基づいて前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力和、および前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力和を求め、これら２つの起電力和の差分を前記第１の∂Ａ／∂ｔ成分として抽出し、前記第１の周波数の起電力和又は前記第２の周波数の起電力和の中から前記第１の∂Ａ／∂ｔ成分を取り除くことにより前記ｖ×Ｂ成分を抽出し、
前記スパン補正部は、前記第１の合成起電力の第１の周波数の成分と前記第２の合成起電力の第１の周波数の成分との起電力差、又は前記第１の合成起電力の第２の周波数の成分と前記第２の合成起電力の第２の周波数の成分との起電力差を前記第２の∂Ａ／∂ｔ成分として抽出し、この第２の∂Ａ／∂ｔ成分に基づいて、前記抽出されたｖ×Ｂ成分の流速の大きさＶにかかる係数であるスパンの変動要因を除去することを特徴とする電磁流量計。
The electromagnetic flow meter according to claim 14, wherein
The power supply unit supplies an excitation current that gives two excitation frequencies different in first frequency and second frequency simultaneously or alternately to the excitation coil,
The zero point correction unit obtains an amplitude and a phase for each of the first combined electromotive force detected by the first electrode and the second combined electromotive force detected by the second electrode, and the amplitudes thereof. And the first electromotive force sum of the first frequency component of the first combined electromotive force and the first frequency component of the second combined electromotive force based on the phase and the phase of the first combined electromotive force, 2 to obtain the sum of electromotive forces of the second frequency component and the second frequency component of the second combined electromotive force, and extract the difference between the two electromotive force sums as the first ∂A / ∂t component. The v × B component is extracted by removing the first ∂A / ∂t component from the electromotive force sum of the first frequency or the electromotive force sum of the second frequency,
The span correction unit includes an electromotive force difference between a first frequency component of the first combined electromotive force and a first frequency component of the second combined electromotive force, or the first combined electromotive force. The electromotive force difference between the second frequency component and the second frequency component of the second combined electromotive force is extracted as the second ∂A / ∂t component, and this second ∂A / ∂t An electromagnetic flowmeter characterized in that, based on a component, a span variation factor, which is a coefficient related to the magnitude V of the flow velocity of the extracted v × B component, is removed.
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JPH05501916A (en) * 1989-09-26 1993-04-08 ザ　フォックスボロ　カンパニー Electromagnetic flowmeters and related improvements
WO2003027614A1 (en) * 2001-09-20 2003-04-03 Yamatake Corporation Electromagnetic flowmeter
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JPH05501916A (en) * 1989-09-26 1993-04-08 ザ　フォックスボロ　カンパニー Electromagnetic flowmeters and related improvements
WO2003027614A1 (en) * 2001-09-20 2003-04-03 Yamatake Corporation Electromagnetic flowmeter
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