臺灣博碩士論文加值系統

高速主軸廣泛使用於工業用機器，如航空發動機、蒸氣渦輪機、渦輪發電機、內燃機、往復式與離心式壓縮機等。而齒輪系統乃為現代動力傳輸最普遍機構之一，且經常合併轉子軸承系統以做為動力產生與輸出之用。由於高速與高精度傳輸之需求，齒輪轉子動力領域的研究愈顯重要。
振動會影響高速主軸系統的加工精度，而黏彈性支承可以降低系統的振動，並且增加主軸轉速的工作區間，因此考慮加裝黏彈性支承來改善這方面的問題。本文將探討的是具黏彈性支承之齒輪轉子軸承系統的動態特性之分析。
系統考慮側向與扭轉之間的耦合效應，藉著使用拉格朗至法及有限元素模型推導出齒輪轉子軸承系統之運動方程式，再以數值分析求出自然頻率，模態振型及穩態響應。首先分析黏彈性支承對系統穩態響應之影響，並分別對不同的黏彈性支承之剛性，損失因子和質量，以及齒輪在不同的轉軸位置對系統穩態響應之影響做探討。最後討論齒輪囓合的影響。
結果顯示，系統加裝黏彈性支承後，在低頻處會多出一個模態。當黏彈性支承的剛性或損失因子增加時，系統的剛性和阻尼隨之增加，所以系統的響應也將隨之減少。改變齒輪的位置將使系統的等效剛性產生變化，當齒輪越接近軸承則系統等效剛性越大使得響應變小。

High-speed spindle are generally employed in industrial machines such as aviation generator, steam and gas turbines, turbo-generators, internal combustion engines, reciprocating and centrifugal compressors. Gear system is one of the most common mechanisms for modern power transmission in theses industrial machines. The gear systems coupled with rotor-bearing systems are the source of power generation and power extraction. On account of the increasing demand for high speed and high accuracy transportation, the research in the field of geared rotor dynamics becomes very important.
The vibration significantly affects the performance of the high-speed spindle. The viscoelastic supports can reduce the vibration of the system and increase the working range of the high-speed spindle. Therefore, the viscoelastic supports are adopted to improve the problem. This study discusses the dynamic characteristics of the gear rotor-bearing system mounted on viscoelastic supports.
A finite element model of the geared rotor-bearing system mounted on viscoelastic supports is developed by taking account of the coupling effect of lateral-torsional motion. Then the system natural frequencies, mode shapes, and steady-state responses are determined. At first, the effects of viscoelastic supports on the system response are analyzed. And the steady-state response is investigated for various viscoelastic supports stiffness, various viscoelastic supports loss factor, various viscoelastic supports mass and various disk positions. The effect of gear mesh is also discussed.
As seen from results, one mode will be particularly induced in low frequency when gear rotor systems are mounted on viscoelastic supports. When the stiffness or the loss factor of the viscoelastic support increases, the system response will decrease. The gear position on the shaft will change the system equivalent stiffness. When the gear positions are closed to the bearing, the equivalent stiffness of the system will increase and the system response will decrease.

CONTENTS

摘要 I
ABSTRACT III
CONTENTS V
LIST OF TABLES VII
LIST OF FIGURES VIII
NOMENCLATURES XII
CHAPTERS PAGE

CHAPTER 1 INTRODUCTION
1-1 Motivation of Research 1
1-2 Literature Review 2
1-3 Outline 5

CHAPTER 2 THE MODEL OF GEARED ROTOR-BEARING
SYSTEM
2-1 Description of Geared Rotor-Bearing System 6
2-2 Equation Formulation 6
2-2-1 The disk 7
2-2-2 The gear mesh 8
2-2-3 Shaft elements 10
2-2-4 Bearing 12
2-2-5 Viscoelastic Supports 12
2-2-6 System equations of motion 15
2-3 Dynamic Analysis 15
2-3-1 Whirl speed analysis 16
2-3-2 Steady-state response analysis 17

CHAPTER 3 NUMERICAL RESULTS AND DISSCUSSIONS
3-1 The System Response with/without Viscoelastic Supports 22
3-2 The System Response versus Parameters of Viscoelastic Supports 23
3-3 The System Response versus Mass Ratios of Viscoelastic Support and Gear 25
3-4 The System Response versus Disk Positions 26
3-5 The Effects of Gear Mesh 27

CHAPTER 4 CONCLUSIONS AND FUTURE STUDY
4-1 Conclusions 62
4-2 Future work 63

REFERENCE 64
APPENDIX

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