臺灣博碩士論文加值系統

相較於傳統漸開線齒輪，擺線行星齒輪機構因齒形為短齒高，可透過少齒差來達成較高的減速比，並且可由多齒對嚙合予以分擔較多負載、吸收瞬間衝擊，近年來多應用在機械手臂、土木機械等減速傳動上。由於多齒對嚙合屬靜不定力學問題，雖然目前有限元素法(Finite Element Method) 已具備相當程度的分析能力，但仍未能有效率的模擬接觸應力及其接觸齒對之接觸斑；特別是利用有限元素法來分析因背隙需求所設計之修整齒廓時，設計工作之複雜度會提高且變得更加費時。
本研究旨在建立一演算法，可用於分析擺線行星傳動機構在不同修整、不同組裝或加工誤差的組合狀況下之接觸特性，包含傳動誤差、背隙、以及接觸齒對的受載分析。同時在論文中亦根據所建立分析模型，探討不同齒形修整參數及組裝誤差影響下的背隙、傳動誤差、受載傳動誤差負載分配以及應力分布。
本論文研究之齒形修整係採移距與等距修整，分析結果可歸納為下列幾點：(1) 修整參數對傳動連續性的影響最大，亦即齒對嚙合時產生振動與否是歸因於間隙大小的適切性，此一特性也可在背隙的分析結果中觀察到；(2) 偏心誤差對傳動誤差的影響遠大於加工誤差；(3) 不同修整參數的受載接觸齒輪對會因不同修整狀況而使嚙合時分配負載的齒數不同，也因而有不同的負載分配結果；(4) 所有接觸應力的模擬結果皆為馬鞍型應力分布，且邊緣發生應力集中效應; (5) 不論何種組裝誤差下，受載傳動誤差值以及其最大最小之差值皆會比未受載之傳動誤差大，因受負載會造成曲軸上一領先轉角。
根據以上分析結果，確知本論文所建立之受載齒對接觸分析模型，可確實分析齒廓修整參數以及組裝加工誤差對接觸齒對之影響，此分析方法與工具可作為未來設計與優化擺線行星齒輪傳動機構的參考。

Cycloid planetary gear drives have many advantages in comparison of the conventional involute planetary gear drives, such as high gear ratio, good performances in sharing the transmitted load, and shock absorbing ability. Although modern FEM software offer good solving possibility, it is not efficient to simulate the contact stress and the corresponding contact pattern of the tooth pairs. Especially it will be more expensive in time while designing modified cycloid profile for backlash control by using FEM.
The aim of the thesis is to propose an approach to analyze the contact characteristics of the cycloid planetary gear drives with modified flanks, including the transmission errors, backlashes and the loads acting among the contact cycloid-pin tooth-pairs. In the proposed model, the influence of the relevant errors on shared loads and the contact stress are considered. On the other hand, backlash and transmission errors due to the flank modification and errors will be also analyzed in the thesis.
The results of this thesis may be summarized as follows: Modification parameters have strong influences to the continuity of transmission, which means it causes vibrations or not during meshing due to the suitability of clearance, and similar situation can be found in results of backlash; Eccentric errors influence the transmission errors much more than manufacturing errors; Modification causes the difference of load sharing factor on the basis of the tooth number shared the load during engaging; All the contact simulation results illustrate a saddle-shaped contact pattern with concentrated stresses on the face-end ; No matter which kind of assembly errors, the values of Loaded Transmission Errors(LTEs) and the max-to-min values are always larger than Transmission Errors(TEs) because the load always causes a leading angle on crankshaft.
The above results are summarized the contact results influence by modification and assembly errors, and proposes an aid for analyzing the contact characteristics under loading, which helps designing the cycloid drives with better performance in the future.

摘要 i
Abstract ii
Acknowledgments iii
Table of Contents iv
List of Figures viii
List of Tables xv
Nomenclature xvi
1. Introductions 1
1.1 Background and Motivation 1
1.2 Literature Review 2
1.3 Scope and Objective 5
1.4 Thesis Outline 7
2. Theoretical Background 8
2.1 Constructive Structure of Cycloid Planetary Gear drives 8
2.1.1 Principle 8
2.1.2 Design Parameters 9
2.1.3 Reduction Ratio 10
2.1.4 Definition of Ideal Assembly Conditions 13
2.2 Mathematical Models of Theoretical Cycloid Tooth Flanks 14
2.3 Mathematical Models of Modified Cycloid Tooth Flanks 15
2.3.1 Types of Flank Modification 15
2.3.2 Mathematical Equations of Modified Tooth Flanks 22
2.4 Tooth Contact Analysis Models 23
2.4.1 Mesh Relation Using the Instant Center Method 23
2.4.2 Contact Point of Theoretical Cycloid Tooth-Pairs 24
2.4.3 Effective displacements along the contact normal 25
2.5 Loaded Tooth Contact Analysis Model 26
2.5.1 Basic Model 26
2.5.2 Loaded Transmission Errors 29
3. Tooth Contact Analysis of Modified Cycloid Gear Pair 30
3.1 Tooth Contact Analysis under Error-free conditions 30
3.1.1 Geometrical Relation of Gear Meshing 30
3.1.2 Contact Points of Modified Cycloid Tooth-Pairs 31
3.2 Tooth Contact Analysis with Assembly Errors 38
3.2.1 Definitions of Assembly Errors 38
3.2.2 Mesh Relation 40
3.2.3 Contact Points of Modified Cycloid Tooth-Pairs with Assembly Errors 44
3.3 Kinematic Performances 52
3.3.1 Transmission Errors 52
3.3.2 Backlashes 53
4. Loaded Tooth Contact Analysis of Cycloid Gear 54
4.1 Basic Relations for LTCA Model 54
4.1.1 Concept of Stiffness Model 54
4.1.2 Relations of Deformations and Displacements 54
4.1.3 Relations of load equilibrium 56
4.2 Flank Separation Distance of Contact Tooth-Pairs 57
4.3 Formulation of equation sets 58
5. Study Cases for Numerical Analysis 60
5.1 Gearing Data 60
5.2 Modification Parameters 60
5.3 Assembly and Manufacturing Errors 61
6. Kinematic Performances of the Cycloid Stage with Modified Flanks 64
6.1 Transmission Error 64
6.1.1 Error-free Conditions 64
6.1.2 Conditions with Eccentric Error of the Center of the Cycloid Disc 68
6.1.3 Eccentric Error of the center of the Pin-Wheels’ Pitch Circle 71
6.1.4 Pin Radius Errors 73
6.1.5 Pitch Circle Radius Errors of the Pin-Wheel 75
6.2 Backlash 78
6.2.1 Error-free Conditions 78
6.2.2 Eccentric Error of the Center of the Cycloid Disc 79
6.2.3 Eccentric Error of the Center of the Pin-Wheel Pitch Circle 81
6.2.4 Pin Radius Error 82
6.2.5 Pitch Circle Radius Error of the Pin-Wheel 83
6.3 Summary 84
6.3.1 Transmission Error 84
6.3.2 Backlash 85
7. Loaded Tooth Contact Analysis of the Cycloid Stage 87
7.1 Theoretical Cycloid Tooth-Pairs without Errors 87
7.1.1 Load sharing 87
7.1.2 Contact stress distribution on tooth flanks 88
7.1.3 Reaction loads of rolling bearings 88
7.1.4 Transmitted torque of crankshafts 89
7.1.5 Loaded transmission errors 90
7.2 Modified Cycloid Tooth-Pairs without Errors 91
7.2.1 Load Sharing 91
7.2.2 Contact stress distribution on tooth flanks 93
7.2.3 Contact stress 95
7.2.4 Reaction loads of rolling bearing 97
7.2.5 Transmitted torque of crankshafts 99
7.2.6 Loaded Transmission errors 100
7.3 Modified Cycloid Tooth-Pairs with Errors 102
7.3.1 Load Sharing 102
7.3.2 Contact Stress 109
7.3.3 Loaded Transmission errors 117
7.4 Summary 121
7.4.1 Load Sharing 121
7.4.2 Contact Stress Distribution 121
7.4.3 Maximum Contact Stress 122
7.4.4 Loaded Transmission Error 123
8. Conclusions and Future Works 124
8.1 Conclusions 124
8.1.2 Transmission Error 126
8.1.3 Backlash 127
8.1.4 Load Sharing 128
8.1.5 Contact Stress Distribution 128
8.1.6 Maximum Contact Stress 129
8.1.7 Loaded Transmission Error 129
8.2 Future Works 131
References 132
Appendix A: Eccentric Error – Cycloid Disc 136
Appendix B: Eccentric Error – Pin-Wheels 144

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