臺灣博碩士論文加值系統

於齒輪系統之非線性動態分析中，嚙合剛性的分析，一般均用數學上的技巧，如：傅立葉級數(Fourier series)展開或方波函數來模擬，但這與實驗方法所量測出的結果有很大的誤差。
本研究所提出之方式由齒條刀具創成漸開線齒形(involute tooth profile)，再由齒形輪廓計算出嚙合剛性，並利用此剛性來分析對齒輪系統之非線性動態影響。齒條刀具的主要創成參數有，直邊段參數、圓角段夾角、壓力角、齒厚、齒深等，其中齒深則由齒根高、齒冠高與齒頂隙所構成。其中，壓力角，齒深與齒數，這些參數會影響到齒形輪廓的成形，並造成嚙合剛性有不一樣的計算結果。本文即在討論壓力角、齒深、齒數如何影響嚙合剛性，進而造成齒輪系統之非線性動態行為。
由分析結果顯示，接觸率與嚙合剛性都會造成齒輪動態性能有所影響。高接觸比齒系對於整體的系統響應會較小，且高轉速下能平穩運轉；高嚙合剛性會使系統響應增大。此系統理論模型能快速求解出響應進而預先分析運轉情況，選用適當齒系於機械傳動。

The analysis of the mesh stiffness in the nonlinear dynamic gear train was simulated by applying mathematical technique such as Fourier series, rectangular wave function. However, the error always exists between practical experience and mathematical technique.
This study is focused on the involute tooth profile of generation of the rack cutter and evaluated the mesh stiffness by using tooth profile. Furthermore, the effect of the mesh stiffness affected the non-linear dynamic behavior of the gear train. The generated parameters of the rack cutter included line and fillet parts, pressure angle, and tooth depth (which included root tooth, addendum, and clearance). These can affect the tooth profile and evaluation of the mesh stiffness. In this study, the parameters design how to affect the tooth profile, mesh stiffness, and non-linear dynamic behavior.
According to the results, the dynamic behavior of gear train was affected by the contact ratio and mesh stiffness. The system response was small for the gear train of high contact ratio as stable action at high speed. The response can be increased for high mesh stiffness. This theoretical model of system can be quickly solved response to pre-analysis a situation of the motion and selected the gear train in the mechanical transmission.

摘要 I
ABSTRACT II
CONTENTS III
LIST OF TABLES VI
LIST OF FIGURES VII
NOMENCLATURE XII

CHARTER 1
INTRODUCTION 1
1-1 Motivation of Research 1
1-2 Literature Review 2
1-2-1 Types of Geared System Models 2
1-2-2 Geared System 4
1-2-3 Gear Mesh Stiffness 7
1-3 Outlines 9

CHAPTER 2
MODEL AND DYNAMIC CHARACTERISTIC OF THE MULTI-MESH GEAR TRAIN 10
2-1 Configuration of System Model 10
2-2 The System Equation of Motion 12
CHARPTER 3
ANALYSIS OF TIME-VARYING GEAR MESH STIFFNESS 18
3-1 Generation of the Spur Gear 19
3-1-1 Rack Cutter 19
3-1-2 Coordinate Transformation 21
3-1-3 Generation of a Locus of Rack Cutter 24
3-1-4 Tangent and Normal to a Plane Curve 25
3-1-5 Envelop of a Locus of Rack Cutter 27
3-1-6 Generation of Involute Tooth Profile 30
3-2 Analysis of Time-Varying Gear Mesh Stiffness 32
3-2-1 Evaluation of Gear Mesh Stiffness 33
3-2-2 Time-Varying Gear Mesh Stiffness 39
3-2-3 Variation of Stiffness due to the Number of Contact Pairs 40

CHARPTER 4
NUMERICAL RESULTS AND DISCUSSIONS 50
4-1 Numerical Results Compared with the Published Paper 50
4-2 Gear Mesh Stiffness Analysis 52
4-3 Computation of Gear Mesh Stiffness 53
4-4 Dynamic Analysis of System Model 55

CHARPTER 5
CONCLUSIONS AND FUTURE STUDY 92
5-1 Conclusion 92
5-1 Future Studies 93
REFERENCE 94

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