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研究生:鄧博文
研究生(外文):Bo- Wen Deng
論文名稱:氣動壓軸承之轉子系統非線性動態分析
論文名稱(外文):Nonlinear Dynamic Analysis of a Rotor System with Aerodynamic Journal Bearings
指導教授:蕭庭郎
指導教授(外文):Ting-Nung Shiau
學位類別:碩士
校院名稱:國立中正大學
系所名稱:機械工程所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2006
畢業學年度:95
語文別:英文
論文頁數:97
中文關鍵詞:氣動壓軸承有限差分法雷諾方程式
外文關鍵詞:the Reynolds equationFinite Difference Methodthe aerodynamic bearing
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隨著科技發展,高轉速機械已成為近代機械設計之主流。氣體軸承在工業上的應用被視為一種較理想之軸承,其特色是無摩擦耗損、不需潤滑系統、可在特殊環境下操作和使用壽命長等優點,是其它傳統軸承所無法達到的。
本研究主要是針對氣動壓軸承轉子系統進行特性分析與參數鑑別。在特性分析方面,首先利用有限差分法推導非線性可壓縮氣體雷諾方程式,求出氣體軸承力量,再將此力量加至轉子系統運動方程式中,利用數值積分方法便可以求得系統響應,接著再採用最小平方遞推演算法 (Recursive Least Square) 與卡爾曼濾波演算法 (Kalman Filter),便可以鑑別出氣動壓軸承的阻尼參數與剛性參數。
由分析結果顯示,最小平方遞推演算法與卡爾曼濾波演算法,兩者所得鑑別參數相當接近。將此鑑別後的系統響應與數值計算所得到的系統響應比較,兩者之系統響應軌跡非常接近,說明鑑別後的軸承模型可以非常準確地模擬原氣動壓軸承,並可以快速求解出系統響應,減少電腦運算時間。
With the development of technology, high rotational speed machines become the mainstream of the mechanical design recently. The aerodynamic bearing is regarded as an ideal bearing which has many superior characteristics than the conventional bearing. The characteristics include no waste of contact, no need for lubrication, capability of working on unusual environment, long life of working and so forth.
This study is focused on the aerodynamic bearing-rotor system characteristics analysis and bearing parameter identification. In the analysis of system characteristics, Finite Difference Method (FDM) is employed to solve the Reynolds equation, which is used to calculate the nonlinear compressible gas force of the gas bearing. By applying the gas bearing force to system equations of motion, the system response can be determined by the numerical integration method. Using the Recursive Least Square Method and the Kalman Filter Method, bearing parameters can be identified from the system response. The parameters include the damping and stiffness coefficients of the aerodynamic bearing.
According to the results of identification, both parameters identified by the Recursive Least Square Method and the Kalman Filter Method are in good agreement. The identified system responses are very close to those from numerical integration. The results show that the aerodynamic bearing force can be precisely identified and the system response can be quickly solved with less computer time.
CONTENTS

摘要 I
ABSTRACT II
CONTENTS III
LIST OF TABLES VI
LIST OF FIGURES VIII
NOMENCLATURE X

CHAPTER PAGE

CHAPTER 1 INTRODUCTION
1-1 Motivation of Research 1
1-2 Literature Review 2
1-2-1 Gas Film Bearings 2
1-2-2 Stability of the Rotor System Mounted with Journal Bearings 5
1-2-3 Identification of Gas Bearings 6
1-3 Outlines 7

CHAPTER 2 ANALYSIS OF THE AERODYNAMIC BEARING-ROTOR SYSTEM
2-1 Reynolds Equations for Gas bearings 8
2-1-1 The Aerostatic Reynolds Equations 9
2-1-2 The Aerodynamic Reynolds Equations 13
2-3 Successive Over Relation Method for Reynolds Equations 17
2-4 Forces of the Aerodynamic Bearings 18
2-5 The System Equations of Motion 19

CHAPTER 3 PARAMETERS IDENTIFICATION OF AERODYNAMIC BEARINGS
3-1 Appropriate Mathematical Model 26
3-2 Methods of Parameters Identification 28
3-2-1 Recursive Least Square Method (RLS) 28
3-2-2 Kalman Filter Method (KF) 33

CHAPTER 4 NUMERICAL RESULTS AND DISCUSSIONS
4-1 The Pressure Distribution of the Aerostatic Bearing 38
4-2 The Aerodynamic Bearing Forces 39
4-3 The System Response of the Aerodynamic Bearing under Different External Forces 44
4-4 The System Response of the Aerodynamic Bearing under Different System Parameters 45
4-5 Identification of the Aerodynamic Bearing Forces 46

CHAPTER 5 CONCLUSIONS AND FUTURE STUDY
5-1 Conclusions 91
5-2 Future Study 92

REFERENCE 93
REFERENCE
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