臺灣博碩士論文加值系統

在本論文中，將討論含開啟裂縫或開合裂縫的齒輪轉子軸承系統的動態特性。首先，發展一個含開啟裂縫的齒輪轉子系統的簡單解析模型來計算含開啟裂縫的齒輪轉子系統的自然頻率、臨界轉速、穩態響應及穩定性。在裂縫模擬方面，將裂縫所造成轉軸局部撓屈的現象，利用能量平衡的觀念以一組線性彈簧取代。因為裂縫的影響，將造成一個週期性的時變系統。利用快速傅立葉轉換(FFT)可以將時域的振動響應轉換成頻域的頻譜圖來研究裂縫的影響。並利用傅羅凱理論(Floquet theory)計算出系統的穩定性。此外，本文發展有限元素模型來分析含開啟或開合裂縫的齒輪轉子軸承系統的自然頻率、臨界轉速、穩態響應及穩定性。

In this thesis, the dynamic analysis of a geared rotor-bearing system with an open crack or a breathing crack is discussed. A simple analytic model of a geared rotor system is developed by taking into account the effect of an open transverse surface crack for determination of natural frequencies, critical speeds, and stability of the system. The existing crack results in a local flexibility of the shaft and it is replaced by a set of springs based on the balance of energy. The effect of the crack results in a periodic time-varying system. From the response time histories, the FFT spectra can be obtained for investigating the effects of crack. The Floquet theory is used to examine the stability of the first variation equations with periodic coefficients. Finite element models are developed for geared rotor-bearing system with an open transverse surface crack and with a breathing transverse surface crack for determination of natural frequencies, critical speeds, dynamic response and stability.
The results show that additional instability regions of the shaft’s spin speed are observed when a crack occurs on the shaft. The influences of the crack on the stability of the system are significant as the depth increases to an evident value.

CONTENTS
Page
ABSTRACTi
CONTENTSii
LIST OF TABLESv
LIST OF FIGUREvi
NOMENCLATUREx
CHAPTER
IINTRODUCTION1
1.1 Motivation and Objective1
1.2 Literature Review2
1.2.1 Mathematical Models for Geared Rotor Dynamic2
1.2.2 Mathematical Models for Crack5
1.3 Dissertation Outline8
IIFLEXIBILITY PARAMETERS OF CRACK10
2.1 Basic Theory10
2.2 Derivation of flexibility parameters15
2.3 Results and Discussion16
III SIMPLE ANALYTIC MODEL FOR GEARED
ROTOR SYSTEM WITH AN OPEN CRACK21
3.1 Equation Formulation21
3.1.1 Disk22
3.1.2 Gear Mesh23
3.1.3 Cracked Shaft27
3.1.4 System Equations of Motion34
3.2 Numerical Method Used for Stability Analysis36
3.3 Numerical Results and Discussion37
3.3.1 Free Vibrations37
3.3.2 Effect of Crack38
3.3.3 Stability38
3.3.4 Conclusions40
IV FINITE ELEMENT MODEL FOR GEARED
ROTOR-BEARING SYSTEM WITH AN OPEN CRACK49
4.1 Equation Formulation49
4.1.1 Bearing Support50
4.1.2 Rotor Shaft with an Open Crack50
4.1.3 System Equations of Motion55
4.1 Numerical Results and Discussion56
4.2.1 Free Vibrations56
4.2.2 Effect of Crack58
4.2.3 Stability59
4.2 Conclusions60
V FINITE ELEMENT MODEL FOR GEARED
ROTOR-BEARING SYSTEM WITH A BREATHING CRACK78
5.1 Crack Model with a Breathing Crack78
5.2 System Equations of Motion80
5.3 Numerical Results and Discussion81
5.4 Conclusions82
VI CONCLUSIONS91
REFERENCES94
APPENDIX A 101
PUBLICATION LIST109
VITA111

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