系統識別號 | U0002-1409200713093000 |
---|---|
DOI | 10.6846/TKU.2007.00395 |
論文名稱(中文) | 直型管科氏質量流率計之分析 |
論文名稱(英文) | Analysis of a Straight Tube Coriolis Mass Flowmeter |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 航空太空工程學系碩士班 |
系所名稱(英文) | Department of Aerospace Engineering |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 95 |
學期 | 2 |
出版年 | 96 |
研究生(中文) | 吳季桓 |
研究生(英文) | Chi-Huan Wu |
學號 | 692370892 |
學位類別 | 碩士 |
語言別 | 英文 |
第二語言別 | |
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 |
關鍵字(中) |
科氏質量流計 有限元素法 |
關鍵字(英) |
Coriolis mass flowmeter Finite element method |
第三語言關鍵字 | |
學科別分類 | |
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. |
第三語言摘要 | |
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 |
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