Coriolis mass flowmeter
The Coriolis mass flowmeter enhances sensitivity by employing a rotationally symmetrical measurement tube with rotational vibration and a single sensor to detect displacement, addressing geometric constraints and improving sensitivity and noise reduction.
Patent Information
- Application Number
- JP2023097340
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2023-06-13
- Publication Date
- 2024-12-25
AI Technical Summary
Conventional Coriolis mass flowmeters face challenges in increasing measurement sensitivity due to geometric restrictions and trade-offs between phase difference magnitude and signal strength, making it difficult to enhance sensitivity.
A Coriolis mass flowmeter design with a measurement tube having both ends fixed and rotationally symmetrical about the center, utilizing exciters that induce rotational vibration, and a sensor to detect displacement, velocity, or acceleration proportional to the amplitude of this vibration, along with a calculation unit to determine mass flow rate.
The design allows for increased measurement sensitivity by enhancing rotational vibration, enabling higher sensitivity in mass flow rate detection and reducing noise from multiple sensors, while being less susceptible to external vibrations.
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Figure 2024178860000001_ABST
Abstract
Description
[Technical field]
[0001] The present invention relates to a Coriolis mass flowmeter. [Background technology]
[0002] Coriolis mass flowmeters are known as flowmeters that measure the flow rate of a fluid flowing through a measuring pipe. Fig. 6 is an explanatory diagram for explaining the configuration and operation of a conventional Coriolis mass flowmeter.
[0003] 6, measuring tube 101, through which the fluid to be measured flows, has a U-shape that is rotationally symmetrical by 180° about the Z-axis (for example, the vertical direction). Both ends of measuring tube 101, through which the fluid flows in and out, are fixed on the X-axis.
[0004] In measuring pipe 101, a sensor 102 for detecting (velocity) displacement is installed in the pipe section on the inlet side of the fluid. Furthermore, a sensor 103 for detecting (velocity) displacement is installed in the pipe section on the outlet side at the same height (Z coordinate) as sensor 102. These sensors 102 and 103 detect the (velocity) displacement of measuring pipe 101 at the installation positions at the same height (Z coordinate).
[0005] An exciter 104 is installed in the center (on the Z axis) of the measurement tube 101 as an excitation device that excites the measurement tube 101. The operation of the exciter 104 is controlled by a converter 111, and it applies a harmonic excitation force 105 in the Y direction. The exciter 104 resonates in a vibration mode (flexure mode) that deflects the measurement tube 101 in the Y direction by the harmonic excitation force 105 in the Y direction, as shown by the dotted line in the figure.
[0006] Since the vibration amplitude generated in the measurement tube 101 is minute, the amplitude of the measurement tube 101 due to the harmonic excitation force 105 of the exciter 104 can be regarded as a rotational vibration around the X-axis of the measurement tube 101. In addition, when the measurement tube 101 is used as a reference, the X-axis is a rotating coordinate system that rotates and vibrates at the resonance frequency of the measurement tube 101.
[0007] Here, when looking at the measurement tube 101 along the flow of the fluid in the measurement tube 101, the area from the inlet to the first bend is called the inlet side, and the area from the last bend to the outlet is called the outlet side. Flow velocity vector 106 of the fluid on the inlet side is a vector in the positive Z-axis direction. Also, flow velocity vector 107 of the fluid on the outlet side is an inverse vector to flow velocity vector 106 (vector in the negative Z-axis direction).
[0008] Because flow velocity vectors 106, 107 in the Z-axis direction are perpendicular to the axis vector (X-axis direction) in the rotating coordinate system, a Coriolis force is generated by the fluid in the Y-direction. Specifically, a Coriolis force 108 acting in the positive Y-direction is generated on the inlet side, and a Coriolis force 109 acting in the negative Y-direction is generated on the outlet side. These Coriolis forces 108, 109 are proportional to the mass flow rate of the fluid.
[0009] The diagram on the right side of the arrow in Fig. 6 shows Coriolis force 108 acting on the inlet side and Coriolis force 109 acting on the outlet side. Since the magnitudes of Coriolis forces 108 and 109 are equal, Coriolis forces 108 and 109 become torsional vibration 110 that rotates measuring tube 101 around the Z axis. Therefore, measuring tube 101 is not only subjected to vibration motion in the flexure mode, but also torsional vibration 110 around the Z axis. The amplitude (torsion angle) of the vibration component in this torsional vibration 110 is proportional to the Coriolis force.
[0010] At this time, the (velocity) displacement detected by the sensors 102 and 103 is basically a vibration in a bending mode, but the torsional vibration 110 is superimposed on each of them in opposite phases. Therefore, a slight phase difference occurs in the vibration waveforms detected by the sensors 102 and 103. This phase difference originates from the torsional vibration 110 and is proportional to the torsion angle.
[0011] Converter 111 detects the above phase difference by processing the signals received from sensors 102 and 103. Furthermore, converter 111 uses the proportional relationship between the above phase difference, torsion angle, Coriolis force, and mass flow rate to multiply the detected phase difference by an appropriate proportionality constant to calculate the mass flow rate of the fluid flowing through measuring tube 101. Converter 111 transmits the calculated data on the mass flow rate of the fluid to an integrated production control system such as a distributed control system (DCS) or an external device such as a personal computer (PC). [Prior art documents] [Patent documents]
[0012] [Patent Document 1] Japanese Patent Application Publication No. 54-52570 [Patent Document 2] JP 2002-13961 A [Non-patent literature]
[0013] [Non-Patent Document 1] JIS B 7555 Flow measurement method using Coriolis meters (mass flow, density and volumetric flow measurement) Summary of the Invention [Problem to be solved by the invention]
[0014] In the above-mentioned conventional technology, the measurement sensitivity of the mass flow rate is proportional to the magnitude of the phase difference. The magnitude of the phase difference is determined by geometric elements of the device, such as the shape of the measurement tube 101 and the positions of the sensors 102 and 103. The shape of the measurement tube 101 is strongly restricted by the size of the flowmeter, etc. In addition, adjustment of the positions of the sensors 102 and 103 is restricted by a trade-off between the magnitude of the phase difference and the signal strength induced in the sensors 102 and 103. As described above, there are various restrictions on increasing the phase difference, and therefore, in the conventional technology, it is difficult to increase the measurement sensitivity.
[0015] The present invention has been made in view of the above, and an object of the present invention is to provide a Coriolis mass flowmeter that makes it possible to easily increase the measurement sensitivity. [Means for solving the problem]
[0016] The present invention provides a Coriolis mass flowmeter comprising: a measuring tube which is fixed at both ends and has a shape which is rotationally symmetrical about an axis serving as an axis, and through which a fluid to be measured flows from one end side to the other end side of the both ends; an excitation unit which applies rotational vibration to the measuring tube about the axis; a sensor unit which detects a displacement, velocity or acceleration which occurs in the measuring tube in a direction of a Coriolis force acting on the rotationally vibrated measuring tube and which is proportional to the amplitude of the rotational vibration; and a calculation unit which calculates the mass flow rate of the fluid based on the detected displacement, velocity or acceleration.
[0017] According to the present invention, there is an effect that the measurement sensitivity can be easily increased. [Brief description of the drawings]
[0018] [Figure 1] FIG. 1 is an explanatory diagram illustrating a configuration example of a Coriolis mass flowmeter according to an embodiment. [Diagram 2] FIG. 2 is a graph illustrating a frequency response in a measurement tube of the Coriolis mass flowmeter according to the embodiment. [Diagram 3] FIG. 3 is an explanatory diagram for explaining the dimensional relationship of the measurement pipe. [Figure 4] FIG. 4 is an explanatory diagram for explaining the Coriolis force acting on the measurement tube. [Diagram 5] FIG. 5 is a block diagram illustrating an example of a functional configuration of the converter. [Figure 6] FIG. 6 is an explanatory diagram for explaining an outline of the configuration and operation of a conventional Coriolis mass flowmeter. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0019] A Coriolis mass flowmeter according to an embodiment of the present invention will be described in detail below with reference to the drawings. Note that the present invention is not limited to the embodiment described below.
[0020] Fig. 1 is an explanatory diagram showing a configuration example of a Coriolis mass flowmeter according to an embodiment. As shown in Fig. 1, in a Coriolis mass flowmeter 100, a measurement tube 1 through which a fluid to be measured flows has a shape that is rotationally symmetrical by 180° about a vertical Z-axis, for example.
[0021] The measuring tube 1 is fixed on the X-axis, that is, both ends, the inlet side where the fluid flows in and the outlet side where the fluid flows out, are fixed by support members 1a. The fluid flows from the inlet side to the outlet side of the measuring tube 1 fixed by the support members 1a.
[0022] The measuring tube 1 is U-shaped and has a tube section 1b extending from the inlet side in the positive Z-axis direction, a tube section 1c bent at a right angle from tube section 1b and extending in the X-axis direction, and a tube section 1d bent at a right angle from tube section 1c and extending toward the outlet side (negative Z-axis direction).
[0023] Although the measurement tube 1 is U-shaped in this embodiment, it may be a bow shape (U-shape) or a V-shape that is rotationally symmetrical by 180° about the Z axis.
[0024] Exciters 2 and 3 are installed on the inlet and outlet sides of the measurement tube 1, specifically on the upper parts of the tube sections 1b and 1d. The operation of the exciters 2 and 3 is controlled by a converter 12, and they apply a harmonic excitation force in the Y direction to the measurement tube 1. At this time, the exciters 2 and 3 are composed of coils with the same number of turns and magnets with the same magnetic force, for example, but the coils are wound in opposite directions and connected in parallel by conductors, so that they are driven in opposite phases to each other. As a result, the exciters 2 and 3 resonate the measurement tube 1 in a vibration mode (torsion mode) that twists around the Z axis.
[0025] Fig. 2 is a graph for explaining the frequency response in the measurement tube 1 of the Coriolis mass flowmeter 100 according to the embodiment. Graph G shown in Fig. 2 shows the frequency response of the measurement tube 1 when the horizontal axis is frequency (Frequency) and the vertical axis is vibration strength (Gain). As shown in graph G, in the measurement tube 1, the resonance frequency F2 of the torsion mode is higher than the resonance frequency F1 of the flexure mode.
[0026] Since the vibration amplitude of this torsional mode is minute, the amplitude due to the excitation force of the exciters 2 and 3 can be regarded as a rotational vibration around the Z-axis of the measurement tube 1. In other words, the exciters 2 and 3 are an example of an excitation unit. Note that the configuration for applying a rotational vibration around the Z-axis to the measurement tube 1 is not limited to the above-mentioned configuration using the exciters 2 and 3. For example, the excitation unit may be a single exciter that causes the measurement tube 1 to rotate and vibrate.
[0027] FIG. 3 is an explanatory diagram for explaining the dimensional relationship of the measurement pipe 1. As shown in FIG. 3, the length of the pipe parts 1b and 1d is L pl The length of the pipe section 1c is L bm The rotation angle (torsion angle) of the measuring tube 1 around the Z axis is θ. The rotation angle of the measuring tube 1 around the X axis is φ.
[0028] When rotational vibration about the Z-axis is applied to the measurement tube 1, the equation of motion of the measurement tube 1 is given by the following formula (1) using the dimensional relationship in FIG.
[0029]
number
[0030] However, J θ is the moment of inertia around the Z axis. D θ is the damping coefficient for the movement of the measuring tube 1 around the Z axis. K θ is the elastic modulus which acts as a restoring force against the torsional motion of the measuring tube 1 around the Z axis. F ex0 is the amplitude of the excitation force of exciters 2 and 3. ω θnis the driving frequency of the measuring tubes 1, 2 controlled by the converter 12.
[0031] From the equation of motion shown in formula (1), the torsion angle θ of the measuring tube 1 after a sufficient amount of time has passed is given by the following formula (2). θ is the phase lag of the vibration of the measuring tube 1 relative to the excitation force of the exciters 2 and 3.
[0032]
number
[0033] Furthermore, when looking at pipe section 1b of measuring tube 1 on the inlet side, pipe section 1b bends slightly in the Y direction, so it can be considered as a rotational vibration around the X axis. Similarly, when looking at pipe section 1d of measuring tube 1 on the outlet side, pipe section 1d bends slightly in the Y direction, so it can be considered as a rotational vibration around the X axis, but because the driving directions of exciters 2 and 3 are opposite, the rotations around the X axis on the inlet side and outlet side are also opposite.
[0034] At this time, the minute length dL pl Coriolis force dF acting on c Using the dimensional relationship in Figure 3, Q is expressed by the following formula (3). A is the cross-sectional area of the measuring tube 1 perpendicular to the flow velocity. v is the flow velocity of the fluid flowing inside. ρ is the density of the fluid. Q m is the mass flow rate (ρAv).
[0035]
number
[0036] The flow velocity vector 7 of the fluid on the inlet side and the flow velocity vector 8 of the fluid on the inlet side are in a relationship of inverse vectors. In addition, the rotation of the tube section 1b on the inlet side and the tube section 1d on the outlet side is also the same, so the Coriolis force acting on the infinitesimal length of the tube section 1d of the measuring tube 1 on the outlet side is also dF c Therefore, the Coriolis forces 9 and 10 acting on the measurement tube 1 deflect (displace) the measurement tube 1 in the Y direction.
[0037] Fig. 4 is an explanatory diagram for explaining the Coriolis force acting on the measurement tube 1. In Fig. 4, the deflection of the measurement tube 1 due to the Coriolis force acting on the measurement tube 1 is indicated by a dotted line.
[0038] As shown in Fig. 4, when the measurement tube 1 is viewed on the YZ plane, the measurement tube 1 can be regarded as a cantilever beam receiving a uniformly distributed load resulting from the Coriolis force. This uniformly distributed load is expressed by the following formula (4).
[0039]
number
[0040] When the measurement tube 1 is regarded as a cantilever, the deflection 11 of the cantilever is proportional to the uniformly distributed load. Therefore, the displacement y in the Y direction at the end of the measurement tube 1 is p is expressed by the following formula (5): where K is the proportional coefficient between the deflection amount 11 and the uniformly distributed load.
[0041]
number
[0042] As shown in formula (5), the displacement, velocity, or acceleration in the Y direction of the measurement tube 1 due to Coriolis forces 9, 10 acting on the measurement tube 1 is proportional to the mass flow rate. The sensor 4 installed on the Z axis of the measurement tube 1 detects this displacement, velocity, or acceleration in the Y direction. Specifically, the sensor 4 is installed on the tube section 1c of the measurement tube 1, that is, at the end of the measurement tube 1 when it is considered as a cantilever beam.
[0043] Converter 12 processes the signal corresponding to the displacement, velocity, or acceleration in the Y direction received from sensor 4, and calculates the mass flow rate of the fluid flowing in measuring tube 1 by multiplying it by an appropriate proportionality constant shown in equation (5) above. Converter 12 transmits data indicating the calculated mass flow rate of the fluid to an integrated production control system such as a DCS, or an external device such as a PC. Converter 12 is an example of a calculation unit.
[0044] 5 is a block diagram showing an example of a functional configuration of the converter 12. As shown in FIG. 5, the converter 12 includes a communication unit 13, a storage unit 14, and a control unit 15.
[0045] The communication unit 13 is a communication interface that, under the control of the control unit 15, transmits drive signals to the exciters 2 and 3, receives signals detected by the sensor 4, and transmits data indicating the mass flow rate to external devices.
[0046] The storage unit 14 is a non-volatile memory or the like, and stores setting information 14a, history information 14b, etc. The setting information 14a is data describing various setting contents including a proportional constant for calculating the mass flow rate of a fluid from a displacement, velocity, or acceleration in the Y direction. The history information 14b is data in which the detection results (values of displacement, velocity, or acceleration in the Y direction) of the sensor 4 and the history of the calculation results (values of mass flow rate) are listed in chronological order with, for example, a time stamp attached.
[0047] The control unit 15 is, for example, a computer realized by a processor, and includes an excitation control unit 15a, a signal processing unit 15b, a flow rate calculation unit 15c, and a data transmission unit 15d.
[0048] The excitation control unit 15a controls the driving (excitation) of the exciters 2 and 3 by outputting a driving signal to the exciters 2 and 3 via the communication unit 13. Specifically, the excitation control unit 15a drives the exciters 2 and 3 with a predetermined excitation force and vibration drive number set by the setting information 14a.
[0049] The signal processing unit 15b processes the signal received from the sensor 4 via the communication unit 13 and converts it into a value of displacement, velocity, or acceleration in the Y direction. For example, the signal processing unit 15b receives a signal from the sensor 4 after a certain time has elapsed since the excitation control unit 15a drives the exciters 2 and 3 with a predetermined excitation force and vibration drive number. Next, the signal processing unit 15b processes the signal received from the sensor 4 to obtain the value of displacement, velocity, or acceleration in the Y direction at the point where the torsion mode has settled.
[0050] Based on the value of the displacement, velocity or acceleration in the Y direction converted by the signal processing unit 15b, the flow rate calculation unit 15c multiplies the value by a proportionality constant set by the setting information 14a to calculate the mass flow rate of the fluid flowing in the measuring pipe 1. The flow rate calculation unit 15c adds a timestamp to the calculated mass flow rate, the value of the displacement, velocity or acceleration in the Y direction that was the basis of the calculation, and the like, and stores them in the history information 14b.
[0051] The data transmission unit 15d transmits data indicating the mass flow rate of the fluid calculated by the flow rate calculation unit 15c to an external device via the communication unit 13. For example, the data transmission unit 15d transmits the most recent mass flow rate included in the history information 14b to the external device together with a timestamp, etc. The data transmission unit 15d may also transmit the mass flow rate updated in the history information 14b to the external device together with a timestamp, etc. at a predetermined time interval.
[0052] (effect) The Coriolis mass flowmeter 100 includes a measurement tube 1 that is fixed at both ends, has a shape rotationally symmetrical about the Z axis with the center of both ends being the center, and through which a fluid to be measured flows from one end to the other end. The Coriolis mass flowmeter 100 includes an excitation unit that applies rotational vibration about the Z axis to the measurement tube 1. The Coriolis mass flowmeter 100 includes a sensor unit that detects a displacement, velocity, or acceleration that occurs in the measurement tube 1 in proportion to the amplitude of the rotational vibration in the Y direction of Coriolis forces 9, 10 acting on the rotationally vibrated measurement tube 1. The Coriolis mass flowmeter 100 includes a calculation unit that calculates the mass flow rate of the fluid based on the detected displacement, velocity, or acceleration.
[0053] For this reason, in the Coriolis mass flowmeter 100, the larger the rotational vibration, the larger the displacement, velocity, or acceleration occurring in the measuring tube 1 detected by the sensor unit, making it possible to sense the mass flow rate with high sensitivity. For example, in the Coriolis mass flowmeter 100, the measurement sensitivity of the mass flow rate can be easily increased by increasing the rotational vibration.
[0054] Moreover, the excitation unit includes a first excitation unit (exciter 2) provided on one end side of the measurement tube 1 and a second excitation unit (exciter 3) provided on the other end side of the measurement tube 1, and the first excitation unit and the second excitation unit are driven in opposite phases to each other to give rotational vibration. As a result, in the Coriolis mass flowmeter 100, the moment applied to the rotational vibration (torsion) can be increased, and the measurement tube 1 can be vibrated with sufficient amplitude even when the natural angular frequency of the measurement tube 1 becomes high.
[0055] Moreover, in the Coriolis mass flowmeter 100, one sensor unit is provided on the Z axis. As a result, in the Coriolis mass flowmeter 100, noise due to differences between multiple sensors can be reduced compared to a conventional Coriolis mass flowmeter having two sensors for detecting a phase difference.
[0056] The measurement tube 1 is U-shaped and has a first tube section (tube section 1b) extending from one end, a second tube section (tube section 1c) bending at a right angle from the first tube section and extending, and a third tube section (tube section 1d) bending at a right angle from the second tube section and extending to the other end. In the resonant motion of such a U-shaped Coriolis mass flowmeter, the resonant frequency F2 of the torsion mode is generally higher than the resonant frequency F1 of the bending mode. Therefore, in the Coriolis mass flowmeter 100 using the U-shaped measurement tube 1, it is possible to make the measurement less susceptible to the effects of external vibrations having a relatively low frequency.
[0057] The calculation unit calculates the mass flow rate based on the displacement, velocity, or acceleration detected at the end of the U-shape using equation (5). This allows the Coriolis mass flowmeter 100 to calculate the mass flow rate based on the displacement, velocity, or acceleration detected at the end of the U-shape.
[0058] Some examples of combinations of the disclosed technical features are set out below.
[0059] (1) A measuring tube having both ends fixed, a shape rotationally symmetrical about the center of both ends, and through which a fluid to be measured flows from one end side to the other end side of both ends; an excitation unit that applies rotational vibration about the axis to the measuring tube; a sensor unit that detects a displacement, a velocity, or an acceleration occurring in the measurement tube in proportion to an amplitude of the rotational vibration in a direction of a Coriolis force acting on the measurement tube that is rotationally vibrated; A calculation unit that calculates a mass flow rate of the fluid based on the detected displacement, the detected velocity, or the detected acceleration; A Coriolis mass flowmeter comprising:
[0060] (2) The excitation unit includes a first excitation unit provided on one side of the axis of the measurement tube and a second excitation unit provided on the other side of the axis of the measurement tube, and the first excitation unit and the second excitation unit are driven in opposite phases to each other to provide the rotational vibration. 2. A Coriolis mass flowmeter according to claim 1.
[0061] (3) The sensor unit is provided on the axis. 3. The Coriolis mass flowmeter according to claim 1, wherein the first and second coriolis mass flowmeters are arranged in a first and second directions.
[0062] (4) The measuring tube has a U-shape including a first tube portion extending from the one end side, a second tube portion bending at a right angle to extend from the first tube portion, and a third tube portion bending at a right angle from the second tube portion to extend to the other end side. The Coriolis mass flowmeter according to any one of (1) to (3) above.
[0063] (5) The calculation unit calculates the displacement as y p , the proportional coefficient between the deflection of the measuring tube and the uniformly distributed load is K, the torsion angle of the measuring tube in the rotational vibration is θ, and the mass flow rate is Q m , the amplitude of the rotational vibration is F ex0 , the width of the second tube portion is L bm , the damping coefficient for the movement of the measuring tube around the axis is D θ , the driving frequency of the excitation unit is ω θ and the phase lag with respect to the excitation force of the excitation part is φ θBased on the formula (5), Calculating the mass flow rate based on the displacement, the velocity, or the acceleration. A Coriolis mass flowmeter according to (4). [Explanation of symbols]
[0064] 100...Coriolis mass flowmeter 1, 101...Measuring tube 1a...Support member 1b~1d…Pipe section 2, 3, 104...Exciter 4, 102, 103…Sensor 5, 6, 105...Excitation force 7, 8, 106, 107...Flow velocity vector 9, 10, 108, 109...Coriolis force 11…Amount of deflection 12, 111...Converter 13…Communications Department 14...Storage section 14a…Setting information 14b…Historical information 15...Control section 15a...Excitation control section 15b...Signal processing section 15c...Flow rate calculation section 15d…Data transmission section 110...Torsion vibration F1, F2…resonance frequency G...Graph
Claims
1. a measurement tube having both ends fixed, a shape rotationally symmetrical about the center of the both ends, and through which a fluid to be measured flows from one end side to the other end side of the both ends; an excitation unit that applies rotational vibration about the axis to the measuring tube; a sensor unit that detects a displacement, a velocity, or an acceleration occurring in the measurement tube in proportion to an amplitude of the rotational vibration in a direction of a Coriolis force acting on the measurement tube that is rotationally vibrated; A calculation unit that calculates a mass flow rate of the fluid based on the detected displacement, the detected velocity, or the detected acceleration; A Coriolis mass flowmeter comprising:
2. the excitation unit includes a first excitation unit provided on one side of the axis of the measurement tube and a second excitation unit provided on the other side of the axis of the measurement tube, and the first excitation unit and the second excitation unit are driven in opposite phases to each other to provide the rotational vibration.
2. The Coriolis mass flowmeter according to claim 1 .
3. The sensor unit is provided on the axis.
2. The Coriolis mass flowmeter according to claim 1 .
4. The measuring tube has a U-shape including a first tube portion extending from the one end side, a second tube portion bending at a right angle to extend from the first tube portion, and a third tube portion bending at a right angle from the second tube portion to extend to the other end side.
2. The Coriolis mass flowmeter according to claim 1 .
5. The calculation unit calculates the displacement as y p , the proportional coefficient between the deflection of the measuring tube and the uniformly distributed load is K, the torsion angle of the measuring tube in the rotational vibration is θ, and the mass flow rate is Q m , the amplitude of the rotational vibration is F ex0 , the width of the second tube portion is L bm , the damping coefficient for the movement of the measuring tube around the axis is D θ , the driving frequency of the excitation unit is ω θ and the phase lag with respect to the excitation force of the excitation part is φ θ Based on the following equation (1), [0010] Calculating the mass flow rate based on the displacement, the velocity, or the acceleration.
5. A Coriolis mass flowmeter according to claim 4.
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