Study of the Oscillation Modes of a Coriolis Flowmeter Using a Parametric Finite Element Model, Verified by the Results of Modal Testing

Abstract

The paper describes the calculated and experimental determination of the oscillation modes of a Coriolis flowmeter. To define the estimated parametric oscillation modes, we formed a model of the volumetric flowmeter finite element. The model allows the evaluation of the impact of changes in the meter size and the medium density on the flowmeter frequency. The results of the calculations of the finite element model were verified by modal tests of the flowmeter.

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Procedia Engineering 150 ( 2016 ) 336 – 340
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of ICIE 2016
doi: 10.1016/j.proeng.2016.07.027
ScienceDirect
Available online at www.sciencedirect.com
International Conference on Industrial Engineering, ICIE 2016
Study of the Oscillation Modes of a Coriolis Flowmeter Using a
Parametric Finite Element Model, Verified by the Results of Modal
Testing
A.A. Yausheva,*, P.A. Taranenkoa, V.A. Loginovskiyb
aSouth Ural State University, 76, Lenin Avenue, Chelyabinsk, 454080, The Russian Federation
b Elmetro Grupp, Chelyabinsk, 454106, The Russian Federation
Abstract
The paper describes the calculated and experimental determination of the oscillation modes of a Coriolis flowmeter. To define
the estimated parametric oscillation modes, we formed a model of the volumetric flowmeter finite element. The model allows the
evaluation of the impact of changes in the meter size and the medium density on the flowmeter frequency. The results of the
calculations of the finite element model were verified by modal tests of the flowmeter.
© 2016 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the organizing committee of ICIE 2016.
Keywords: Coriolis flowmeter; finite element method; modal analysis;
A Coriolis flowmeter is used to measure the mass flow of liquids and gases. It consists of a case and two U-
shaped oscillating tubes through which the fluid is moving. The body of the flowmeter and its measuring part are
shown in Fig. 1. The tubes make steady forced oscillations with a resonance frequency in the opposite direction to
each other from the XY plane. The translatory motion of the fluid in the rotational motion around the X axis of the
tube causes Coriolis acceleration and, thus, Coriolis force. This force is directed against the tube movement it gets
from the coil, that is, when the tube moves along the Z-axis, the Coriolis force for the fluid flowing inside is directed
against the Z-axis. As soon as the liquid passes the tube bend, the direction of the Coriolis force is reversed. The
Coriolis force causes a phase shift, being proportional to the mass flow rate, for the mechanical oscillations of two
measuring tubes taking place at measuring coil installation.
* Corresponding author. Tel.: +7-351-272-37-44.
E-mail address: iaushevaa@susu.ac.ru
© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of ICIE 2016

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A.A. Yaushev et al. / Procedia Engineering 150 ( 2016 ) 336 – 340
A design overview of a Coriolis flowmeter is given in [1, 2], and a detailed description of the principle of
operation is given in [3].
Fig. 1. Coriolis flowmeter: 1 – process connection flange; 2 – flow tubes; 3 – current controller; 4 – support; 5 –measuring coils; 6 – drive coil;
7 – weights
To understand the dynamics of mechanical systems is of great importance for the creation and improvement of
new designs as well as for solving the problems associated with the mechanical vibrations of existing structures. An
effective tool for studying the dynamic properties of the system is the modeling of the dynamic behavior of
structures using the finite element method [4, 5]. Verification by mode test results is important for designing a finite
element model [6, 7]. Using this model it is necessary to develop the flowmeter verification technology in site [8, 9].
Hence, to estimate the frequencies and modes of the flowmeter a finite volume model is formed (Fig. 2a). It
consists of the elements of prismatic shape with twenty nodes and a tetrahedral shape with ten nodes. To determine
the optimal size of the element, frequency calculations of flowmeter oscillations and forms for different sizes of
elements were made. The dependence of the frequency of flowmeter oscillations on the number of nodes in the
model, as the flowmeter operates, is shown in Fig. 2b.
Fig. 2 Finite element model of flowmeter (ɚ); dependence of the frequency of flowmeter oscillations on the number of nodes (b)
The accuracy of flow measurement is affected by the location of the flowmeter working frequency relative to
other frequencies of the device parts. For example, in [10-13] the influence of the density of the medium measured,
the tubes’ pressure and the geometric sizes of the flowmeter on its first frequency are considered. To assess the
impact of the geometrical and technical parameters on the forms of flowmeter oscillations a finite element model,
verified by modal test results, is appropriate.
The generated finite element model is a parameterized one. To analyze the frequencies and modes of vibrations
of the flowmeter the possibility to shift the support, and to change the mass of weights and the liquid density in
tubes is provided. The weight mass varies due to changes in density of the materials used, and the density of fluid is
changed by specifying the equivalent density of the tube material.

338 A.A. Yaushev et al. / Procedia Engineering 150 ( 2016 ) 336 – 340
Modal tests of the flowmeter [14, 15] were made by using the following hardware and software:
xLMS SCADAS – a 40-channel measuring system for generating an excitation signal of vibrations, collecting and
processing of dynamic signals;
xSpectral Testing module of software package LMS Test.Lab for modal testing and processing of the results;
xmodal vibration shaker TMS2100E11;
xforce sensor PCB 208C03 with sensitivity equal to 2,2 mV / N;
xthree-piezoaccelerometers PCB 356A32 with the sensitivity of 100 mV / g;
xthree-single-point Polytec CLV-3D laser vibrometer.
The test configuration is shown in Fig. 3, 4. The flowmeter is freely suspended on elastic ropes. The broadband
random excitation signal is generated by the computer in the range of 20 to 400 Hz with the help of the LMS Test
Lab program. The excitation signal is formed on the LMS Scadas generator, transformed to an amplifier and then to
the modal shaker. The shaker is suspended with rods and connected to the case base of the flowmeter. To control the
forced oscillations between the flowmeter and shakers the force sensor is installed. The three-laser vibrometer [16]
measures in a non-contact way three components of the vibration velocity of the tubes. Opposite all of the coils on
both sides of the flowmeter case six holes are made for technical measurements. Case oscillations are measured
using three-component accelerometers mounted on its surface.
Fig. 3. Test configuration: 1 – flowmeter; 2 – laser vibrometer; 3 – accelerometers; 4 – SCADAS; 5 – computer; 6 – amplifier; 7 – modal shaker;
8 – force sensor; 9 – rodes; 10 – opening in the flowmeter for making measurements by laser vibrometer
Fig. 4. Photos experimental stand

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A.A. Yaushev et al. / Procedia Engineering 150 ( 2016 ) 336 – 340
When the modal shaker excited oscillations, we recorded the excitation signal with a force sensor, measured the
vibration velocities of the point on the tube with the three-laser vibrometer, and measured the case vibration
accelerations with accelerometers. Calculating the excitation signals and the responses we obtained the frequency
transfer functions. Then, the experiment was repeated with a laser vibrometer measurement at another point. We
used 6 points on the tubes for measurements. The averaged frequency transfer functions obtained were processed
using a PolyMax algorithm [17, 18] and we identified the characteristic frequencies, the shape and the decrements of
the flowmeter oscillations.
In the frequency range under study, which is up to 400 Hz, we identified ten forms of natural vibrations of the
tubes and three forms of the case vibrations. The forms of flowmeter oscillations, in the range less than 200 Hz, are
of great practical value. The first natural frequency of the case oscillation is 236 Hz. The table 1 shows a comparison
of the calculated and experimental forms and frequencies of natural oscillations of the flowmeter measuring tubes.
The modal assurance criterion (MAC) is used to compare waveforms [18, 19].
Table 1. Comparison of the calculated and experimental forms and natural frequencies of the flowmeter tube oscillations
Form
ζ
Descriptionofoscillationforms
Experiment
Frequency,Hz
Calculation
Frequency,Hz
Error
%
ʺʤˁ
1AntiphaseoscillationsoftubesinXYplane88.891.93.50.93
2InphaseoscillationsoftubesinXYplane94.095.51.60.87
3AntiphaseoscillationsoftubesoftheXYplane116.8117.40.50.79
4InphaseoscillationsoftubesinXYplane128.6126.81.40.76
5InphaseoscillationsoftubesinXYplane157.4162.43.20.91
6AntiphaseoscillationsoftubesoftheXYplane174.7175.40.40.97
The discrepancy between the calculated and experimental flowmeter frequencies does not exceed 4%, thus, the
finite element model of the flowmeter reflects accurately the properties of the actual flowmeter design. Using the
finite element model, we obtained for the first and six flowmeter frequencies the effect estimates for the support
shifting, for changing both the mass of weights and liquid density placed in the tubes (Fig. 5). The frequency of
forced vibrations coincides with the first natural frequency when using the flowmeter. The sixth form of natural
vibrations is similar to a waveform of forced flowmeter of the Coriolis force.
Fig. 5. Dependence of the first and second flowmeter frequencies on the flowmeter parameters
With the use of the finite element model created it is possible to avoid an unacceptable coincidence of the
flowmeter natural frequencies and the three harmonics frequency of the electrical network when creating a new and
improved flowmeter. The results obtained from the verified finite element model allow a sufficiently high reliability

340 A.A. Yaushev et al. / Procedia Engineering 150 ( 2016 ) 336 – 340
in assessing the changes of flowmeter frequencies and, correspondingly, the flow measurement accuracy when
changing the geometric dimensions and technical parameters of the flowmeter system.
The experiments were carried out using the equipment center "Experimental Mechanics" SUSU.
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