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系統識別號 U0002-1409200713093000
中文論文名稱 直型管科氏質量流率計之分析
英文論文名稱 Analysis of a Straight Tube Coriolis Mass Flowmeter
校院名稱 淡江大學
系所名稱(中) 航空太空工程學系碩士班
系所名稱(英) Department of Aerospace Engineering
學年度 95
學期 2
出版年 96
研究生中文姓名 吳季桓
研究生英文姓名 Chi-Huan Wu
學號 692370892
學位類別 碩士
語文別 英文
口試日期 2007-07-24
論文頁數 53頁
口試委員 指導教授-田豐
委員-吳登淵
委員-張永康
中文關鍵字 科氏質量流計  有限元素法 
英文關鍵字 Coriolis mass flowmeter  Finite element method 
學科別分類 學科別應用科學航空太空
中文摘要 科氏流量計為一工業應用上相當精確的質量流量計, 其常被應用於測量飛行器燃油之消耗狀況.科氏流量計的數學模式可以藉由振動樑的理論來推導, 並以之分析管流的振動. 在流體為不可壓縮和非黏滯流的假設之下, 則該直管可視為是Timoshenko樑. 再藉由 Hamilton 的原理來推得控制方程式(governing equation). 為了更容易找出自然振動頻率, 本文將四個自由度的形狀函數(shape function)用三階多項式來表示, 再藉由Langrange 方程式
推得樑的運動方程式. 由於經有此方式得到的運動方程式過於複雜, 因此本文採用有限元素法來求解運動方程式.
最後數值結果顯示ANSYS的mode shape很接近Matlab所求的, 也確認了相位差正比於質量流率.
英文摘要 Coriolis mass flowmeter is an useful tool to
measurement flowrate precisely, the purpose of the research is to analyze a Straight tube Coriolis mass flowmeter, it has been more than fifteen years since finite element method was implemented to
the analysis of Coriolis flowmeter. The Coriolis mass flowmeter is modelled by using the theory of vibrating beams. We idealize the fluid as incompressible and inviscid, the tube is represented as
Timoshenko beam. The governing equations were derived by Hamilton's principle. In order to find out natural frequencies easily, we use a third order polynomial shape function for four degrees of freedom including two displacement and two slope and determine the weak form
of equation of motion by Lagrange's equation .The numerical results shows that the mode shape of Matlab is identical to ones of Ansys, and confirm the phase diffenence is proportional to the mass flowrate.
論文目次 Contents

Chinses Abstract i
Abstract ii
Acknowledgement iii
Nomenclature iv
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Working Principle of Coriolis flowmeter . . . . . . . . . . . 3
2 Timoshenko Beam Theory 6
2.1 Straight Tube . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Finite Element Method 13
3.1 Straight Tube . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 Numerical Example 24
4.1 Configuration of the Tubes . . . . . . . . . . . . . . . . . . 24
4.2 The results of Ansys and Matlab . . . . . . . . . . . . . . 26
4.3 Analytical and Numerical Results . . . . . . . . . . . . . . 27
4.4 The mode shape of tubes . . . . . . . . . . . . . . . . . . . 28
4.4.1 Ansys . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.4.2 Matlab . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.4.3 Ansys vs Matlab . . . . . . . . . . . . . . . . . . . 30
4.4.4 Magnitude of mode shape . . . . . . . . . . . . . . 31
5 Conclusion 38
5.1 conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . 38
A Euler beam theorem 39
B Equilibrium Equation 45
Bibliography 52

List of Tables
4.1 The measurements of straight and u tube . . . . . . . . . . 25
4.2 The comparison between Ansys and Matlab when tube is
full of water . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 The comparison between Ansys and Matlab when tube is
none of water . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.4 Analytical vs Numerical results . . . . . . . . . . . . . . . 27
4.5 Natural frequencies and mode shape of Ansys . . . . . . . 28
4.6 Natural frequencies and mode shape of Matlab . . . . . . . 29
4.7 The comparison of Natural frequencies and mode shape between
Ansys and Matlab . . . . . . . . . . . . . . . . . . . 30
4.8 First mode: Eigenvectors . . . . . . . . . . . . . . . . . . . 31
4.9 Second mode: Eigenvectors . . . . . . . . . . . . . . . . . . 33
4.10 Third mode: Eigenvectors . . . . . . . . . . . . . . . . . . 35

List of Figures
1.1 Straight tube Coriolis meter . . . . . . . . . . . . . . . . . 5
2.1 Timoshenko Beam . . . . . . . . . . . . . . . . . . . . . . 7
4.1 The measurements of straight and u tube . . . . . . . . . . 24
4.2 Phase difference is proportional to the velocity . . . . . . . 37
A.1 Beam element with positive nodal displacements, rotations,
forces, and moments . . . . . . . . . . . . . . . . . . . . . 39
A.2 Differential Beam Element . . . . . . . . . . . . . . . . . . 40
A.3 Deformation of a beam in pure bending . . . . . . . . . . . 41
A.4 Normal stresses in a beam of linearly elastic material: (a)
side view of beam showing distribution of normal stresses,
and (b) cross section of beam showing the Z axis as the
neutral axis of the cross section. . . . . . . . . . . . . . . . 41
A.5 Curvature of a beam . . . . . . . . . . . . . . . . . . . . . 44
B.1 Local axes of the deformed beam at O0 and A0 . . . . . . . 46
B.2 Free body diagram of deformed beam. (a) applied forces per
unit length and force stress resultants; (b) applied moments
per unit length and moment stress resultants. . . . . . . . 47
參考文獻 Bibliography
[1] Lin, “Micro-gas flow standard and measurement techniques,” Measurement Information,
vol. 75, pp. 10–14, September 2000.
[2] ——, “Market analysis of coriolis mass flow meter,” Measurement Information,
vol. 71, p. 75, Janury 2000.
[3] G. S. Peter Enoksson and E. Stemme, “A silicon resonant sensor structure for coriolis
mass-flow measurement,” Journal of Microelectromechanical Systems, vol. 6, no. 2,
pp. 119–125, 1997.
[4] J. C. R. S. D. Sparks, R. Smith and N. Najafi, “A portable mems coriolis mass flow
sensor,” in IEEE Sensors Conference, no. 33, October 2003, p. 90.
[5] Lou, “Mass flow sensor and mems techniques,” Measurement Information, vol. 75,
pp. 15–21, September 2000.
[6] G. Housner, “Bending vibration of a pipe line containing flowing fluid,” ASME
Journal of Applied Mechanics, vol. 19, no. 2, pp. 205–208, 1952.
[7] M. Paidoussis and N. Issid, “Dynamics stability of pipes conveying fluid,” Journal
of Sound and Vibration, vol. 33, no. 3, pp. 267–294, 1974.
[8] S. Noah and G. Hopkins, “Dynamics stability of elastically supported pipes conveying
pulsating fluid,” Journal of Sound and Vibration, vol. 71, no. 1, pp. 103–116,
1980.
[9] G. Sultan and J. Hemp, “Modelling of a coriolis mass flowmeter,” Journal of Sound
and Vibration, vol. 132, no. 3, pp. 473–489, 1989.
[10] E. F. K. J. Stephen H. Crandall, Dean C. Karnopp and D. C. Pridmore-Brown,
Dynamics of Mechanical and Electromechanical Systems, S. H. Crandall, Ed.
McGRAW-HILL Inc., 1968.
[11] A. Kohli and B. Nakra, “Vibration analysis of straight and curve tubes conveying
fluid by means of a straight beam finite element,” Journal of Sound and Vibration,
vol. 93, no. 2, pp. 307–311, 1984.
[12] H. Raszillier and F. Durst, “Coriolis-effect in mass flow metering,” Archive of Applied
Mechanics, vol. 61, no. 3, pp. 192–214, 1991.
[13] G. E. P. C. P. Stack, R. B. Garnett, “A finite element for the vibration analysis of a
fluid-conveying timoshenko beam,” in Collection of Technical Papers - AIAA/ASME
Structures, Structural Dynamics and Materials Conference. Publ by AIAA, Washington,
DC, USA, April 1993, pp. 2120–2129.
[14] R. M. Rivello, Theory and Analysis of Flight Structures. CENTER BOOK CO.,
1971.
[15] J. S. RAO, ROTOR DYNAMICS. New Age International Ltd., 1996.
[16] S. S. RAO, Mechanical Vibrations. Prentice Hall, 2005.
[17] L.-K. C. Jong-Shyong Wu, “Free vibrations of a circularly curved timoshenko beam
normal to its initial plane using finite curved beam elements,” Computers and Structures,
vol. 82, pp. 2525–2540, 2004.
[18] J. Kirkhope, “Out-of-plane vibration of thick circular ring,” Journal of the Engineering
Mechanics Division, vol. 102, pp. 239–243, 1976.
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