臺灣博碩士論文加值系統

摆线器已在工業上廣泛的應用，有鑒於此，本文主要針對次摆线於轉子幾何設計上的研究作討論。本文所研究的轉子分別有魯氏泵、摆齒泵、壓縮機以及摆线減速器等等。
在魯氏泵設計方面，本文提出一新的設計方法---變摆线曲線。並提出了一個可以達到高容積效率的設計流程以及達到高密閉性的設計流程。
在摆线減速器方面，提出了具有齒數差的兩種設計數學模式。這兩種設計中，一種為針輪外摆线嚙合，另一為針輪內摆线嚙合。依參數設計的結果，比較兩種設計的接觸力和曲率分析，利用曲率分析來推導出齒形不過切的條件，以及判斷齒形是否達到連續的情況。對於此兩種設計模式，亦可導出一個較簡單的非過切無因次數學模式，並衍生出可行設計區的方法，使得在此區域內的設計值皆不會有過切以及針輪間的干涉現象。
再者，此兩種設計的數學模式也可用於摆齒泵。此模式可推導出具有較好的泵效率以及密閉性之設計，其可行設計範圍可由過切分析所得到。此外，本文也應用了包絡或偏移量的觀念於摆齒泵設計上。在內外轉子之共軛曲線被產生後，便可算出兩共軛曲線之包絡線。被包絡的齒形不但可運用於摆齒泵而且也適用於壓縮機。文末，對於未包絡以及包絡後之轉子也同樣地作了容積效率以及密閉性分析。

The trochoidal derives is widely used in the industry. This thesis mainly discusses the trochoidal curve on the geometry design of Roots pump, gerotor, compressor and cycloidal speed reducer.
In the Roots pump design, we propose a new method that is an extended cycloid curve with a variable trochoid ratio. A design flow is presented on how to achieve high volumetric efficiency, and a design procedure on how to make a high sealing rotor is also discussed.
In the cycloidal speed reducer design, two types of design on the mathematical model with tooth differences are proposed. One is a pin wheel epitrochoid meshing and the other is a pin wheel hypotrochoid meshing. Using the parameters of the design result, then compare the analysis on their contact forces and assesses curvature which determines whether the cycloidal wheel has a non-undercutting or continuous condition on the tooth profile. For these two designs, simple dimensionless equations of non-undercutting would be derived and the feasible design regions without undercutting or interference between the adjacent pins would then be developed.
In addition, the two proposed mathematical models could be applied to the gerotor pump as well. The design with greater pump efficiency and sealing, and its feasible design region without undercutting would be determined by the undercutting analysis.
Besides, the ideas of envelope and offset are also added to the gerotor design. After the two conjugate curves are generated, their envelope curves would be proposed. The enveloped profiles could be exercised not only on the gerotor pump but also the compressor. Finally, the comparison with pump performance, such as volumetric efficiency and the sealing, would be presented for these designs, which include envelope and non-envelope rotor profiles.

Acknowledgement i
Abstract in Chinese ii
Abstract in English iii
Table of Contents iv
List of Tables ix
List of Figures x
Nomenclature xv

Chapter 1 Introduction
1.1 Types of Trochoids 1
1.2 Introduction of Roots pump 4
1.2.1 Roots Blower and Its Works 4
1.2.2 A Blower Used 5
1.2.3 Roots Vacuum Pump 5
1.2.4 Technical Considerations of Roots Pump 6
1.3 Introduction of a Cycloidal Speed Reducer 6
1.4 Introduction of a Gerotor Pump 8
1.5 References Review and Study Motivations 9
1.5.1 References Review for Roots Rotor 10
1.5.2 References Review for Trochoidal Drives 11
1.5.3 Thesis Outline 15

Chapter 2 Study on Tooth profile of a Roots Rotor with a Variable Trochoid Ratio
2.1 Introduction 18
2.2 Mathematical Model of Rotor Geometry 19
2.2.1 Mathematical Model of the Addendum Curve 19
2.2.2 Equation of Meshing 20
2.2.3 Mathematical Model of the Dedendum Curve 21
2.3 Curvature Analysis of the Rotor Profile 21
2.4 Undercutting analysis of the rotor profile 23
2.5 Design Method for the Extended Cycloid Curve with Variable Trochoid Ratio 24
2.5.1 Third-order Polynomial 25
2.5.2 Fifth-order Polynomial 25
2.5.3 Seventh-order Polynomial 25
2.5.4 Comparison of Volumetric Efficiency for the Variable Trochoid Ratio Designed Using Different-order Polynomials 26
2.5.5 Examples of Tooth Undercutting and Carryover 28
2.6 Design Procedure of the optimization of volumetric efficiency 28
2.6.1 Discussion on the Curve of the Trochoid Ratio Function 31
2.7 Design Procedure of High Sealing Property 32
2.8 Conclusion Remarks 36

Chapter 3 Geometry Design and Analysis for Trochoidal-Type Speed Reducers: with Conjugate Envelopes
3.1 Introduction 58
3.2 Geometric Design 59
3.2.1 Mathematical Model of Pin Wheel Epitrochoid Meshing 59
3.2.2 Mathematical Model of Pin Wheel Hypotrochoid Meshing 62
3.3 The Contact Forces of the Pin Wheel 64
3.4 Curvature and the Conditions of the Undercutting 67
3.4.1 Inflection Point 67
3.4.2 Extreme Value of the Radius of Curvature 68
3.5 Conclusion Remarks 72

Chapter 4 Geometric Design Using Hypotrochoid and Non-undercutting Conditions for an Internal Gear
4.1 Introduction 86
4.2 Geometric Design 87
4.3 Equation of Undercutting and Design Constraints 89
4.4 Numerical Examples and Discussion 94
4.4.1 Gerotor Design 94
4.4.2 Design of Cycloidal Speed Reducer 95
4.5 Conclusion Remarks 96

Chapter 5 Geometry Design and Feasible Design Region for Cycloidal Drives
5.1 Introduction 109
5.2 Geometric Design 110
5.3 Equation of Undercutting and Design Constraints 113
5.4 Numerical Examples and Discussion 117
5.4.1 Gerotor Design 117
5.4.2 Design of Cycloidal Speed Reducer 118
5.5 Conclusion Remarks 119

Chapter 6 Study on Geometry Design of a Gerotor pump with High Volumetric Efficiency
6.1 Introduction 133
6.2 Geometry Design of Cycloidal Pump 134
6.2.1 Mathematical Model 134
6.2.2 Mathematical Model of an Offset Curve 137
6.2.3 Equation of Undercutting 138
6.2.4 Equation of Curvature 141
6.3 Geometric Design and Discuss 142
6.3.1 Gerotor Designed with Epitrochoidal Curve 142
6.3.2 Gerotor Designed with Hypotrochoidal Curve 145
6.3.3 Gerotor Designed with Epicycloid and Hypocycloid 145
6.3.4 Comparison of the Volumetric Efficiency 146
6.4 Designed Gerotor with High Volumetric Efficiency 147
6.5 Conclusion Remarks 149

Chapter 7 Synthetic Conclusion and Further Prospects
7.1 Synthetic Conclusion 167
7.2 Future Prospects 169
References 171
SCI/EI Paper List 176

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