系統識別號 | U0002-2002200908314800 |
---|---|
DOI | 10.6846/TKU.2009.01348 |
論文名稱(中文) | 撓性雙旋轉軸之有限元素法 |
論文名稱(英文) | Finite Element Method for Dual Flexible Rotary System |
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 | 97 |
學期 | 1 |
出版年 | 98 |
研究生(中文) | 洪于棻 |
研究生(英文) | Yu-Fen Hung |
學號 | 694370825 |
學位類別 | 碩士 |
語言別 | 英文 |
第二語言別 | |
口試日期 | 2009-01-08 |
論文頁數 | 82頁 |
口試委員 |
指導教授
-
田豐
委員 - 吳登淵 委員 - 楊智旭 |
關鍵字(中) |
雙軸承 有限元素法 擾性轉子系統 Matlab |
關鍵字(英) |
Twin spool Dual rotor Flexible rotary system Finite element method Matlab |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
這篇論文的主要目的在於使用有限元素來分析撓性雙旋轉軸。這個方法的優點在於計算過程中所用來計算撓性雙旋轉軸振動頻率的過程中,能夠有效增加它的準確度。此外,在建立撓性雙旋轉系統運動方程時,考慮了轉動慣性力矩、迴轉力矩效應與剪應力與應變的效應。 而不用像傳統的傳遞矩陣方法,需要額外一個一個的把特性矩陣加入 當撓性雙旋轉系統複雜性提高、所使用的節點數增加時,仍然保有了精確度。 |
英文摘要 |
The purpose of the research is that we hope to use a reduced order finite element method to analyze a dual rotating flexible shafts. The advantage of the proposed method is that the largest size of the matrices involved in computing the critical speed of rotating shaft increase it's accuracy. In addition, the effects of shear deformation, rotary inertia, gyroscopic moments and shear strain are all taken into account as well. However, that didn't like the traditional transfer matrix method need another to add the characteristic matrices. The accuracy of the obtained results from this method is high, which however inevitably demands computer memory intensivelyfor increasing number of nodes. |
第三語言摘要 | |
論文目次 |
Contents 致謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . i Chines Abstract . . . . . . . . . . . . . . . . . . . . . ii Abstract . . . . . . . . . . . . . . . . . . . . . . . . iii Nomenclature . . . . . . . . . . . . . . . . . . . . . . iv 1 Introduction . . . . . . . . . . . . . . . . . . . . .1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature Review . . . . . . . . . . . . . . . . . . 3 1.3 Research Method . . . . . . . . . . . . . . .. . . . . 4 2 Equation of Motion of the Flexible Dual-Rotor System ....5 3 The Finite Element Method ..............................12 3.1 Shape Function . . . . . . . . . . . . . . . . . . . 13 3.2 System Equation of Motion . . . . . . . . . . . . . . 16 3.3 Dual-Rotor Bearing . . . . . . . . . . . . . . . . . 19 3.4 Solution of Dual-Rotor Bearing System . . . . . . . 23 4 Numerical Examples .....................................25 5 Conclusion .............................................41 A The Equation of Motion................................. 42 A.1 Kinetic energy . . . . . . . . . . . . . . . . . . . 45 A.2 Potential Energy . . . . . . . . . . . . . . . . . . 48 A.2.1 Proof the Strain and Shear Strain Energy .. . . . . 48 A.3 Lagrange Equation . . . . . . . . . . . . ....... . . 57 B Finite Element Matrices . . . . . . . . . . . . . . . . 66 Bibliography . . . . . . . . . . . . . . . . . . . . . .74 List of Tables 4.1 Dimension of the shaft 1 and 2 in Example 4.1 (Unit : MKS) . . . . . . . . 26 4.2 Dimension of the disk shaft in Example 4.1 (Unit : MKS) . . . . . . . . . . 27 4.3 Dimension of the bearing in Example 4.1 (Unit : MKS) . . . . . . . . . . . 27 4.4 The critical speeds (rad/s) for inner-rotor in 4.1 . . . . . . . . . . . . . . . 27 4.5 The critical speeds (rad/s) for outer-rotor in 4.1 . . . . . . . . . . . . . . . 28 4.6 Nodal coordinate for the dual rotor system . . . . . . . . . . . . . . . . . . 34 4.7 Disk data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.8 Bearing stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.9 The critical speeds for inner-rotor in [13] . . . . . . . . . . . . . . . . . . . 36 4.10 The critical speeds for outer-rotor in [13] . . . . . . . . . . . . . . . . . . . 37 List of Figures 2.1 Twin Spool System[13] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Twin Spool System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 The Twin Spool coordinate system . . . . . . . . . . . . . . . . . . . . . . 7 2.4 The definitions of variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1 Internal force of each element . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Definition for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 Bearing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Dual-Rotor system model . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 Connect node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.1 The definitions of variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 A three-dimensional picture and section picture in Example 4.1 . . . . . . 26 4.3 The dual rotor system general by matlab . . . . . . . . . . . . . . . . . . . 28 4.4 The Campbell from [16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5 The Campbell from Matlab calculation (rad/s) . . . . . . . . . . . . . . . . 30 4.6 The innerrotor for the First mode 884Hz . . . . . . . . . . . . . . . . . . . 31 4.7 The outerrotor for the First mode 856Hz . . . . . . . . . . . . . . . . . . . 31 4.8 The innerrotor for the Second mode 1693Hz . . . . . . . . . . . . . . . . . 32 4.9 The outerrotor for the Second mode 1604Hz . . . . . . . . . . . . . . . . . 32 4.10 The innerrotor for the Third mode 2289Hz . . . . . . . . . . . . . . . . . . 33 4.11 The outerrotor for the Third mode 2271Hz . . . . . . . . . . . . . . . . . . 33 4.12 The dual rotor model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.13 A three-dimensional picture and section picture in Example 4.2 . . . . . . 35 4.14 The dual rotor system general by matlab . . . . . . . . . . . . . . . . . . . 36 4.15 The Campbell from Matlab calculation (rpm) . . . . . . . . . . . . . . . . 37 4.16 The innerrotor for the First mode 9448Hz . . . . . . . . . . . . . . . . . . 38 4.17 The outerrotor for the First mode 8396Hz . . . . . . . . . . . . . . . . . . 38 4.18 The innerrotor for the Second mode 12730Hz . . . . . . . . . . . . . . . . . 39 4.19 The outerrotor for the Second mode 12270Hz . . . . . . . . . . . . . . . . 39 4.20 The innerrotor for the Third mode 18180Hz . . . . . . . . . . . . . . . . . 40 4.21 The outerrotor for the Third mode 16780Hz . . . . . . . . . . . . . . . . . 40 A.1 The Twin Spool coordinate system . . . . . . . . . . . . . . . . . . . . . . 42 A.2 The definitions of variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 A.3 The shaft size model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 A.4 A single shaft model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 A.5 The shaft’s cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 A.6 Plane rotate to x axial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 A.7 strain energy 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 |
參考文獻 |
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