臺灣博碩士論文加值系統

擺線減速機在現代工業上的使用越來越普遍，與傳統減速機中的行星式減速機相比，擺線減速機的優勢在於：高承載力、低背隙、較大的減速比範圍、穩定的動態受力、體積小與較高的工作效率等優點。理論上，不具修形之擺線減速機中的擺線盤與外環針齒為全齒接觸，但實際應用上，為了製造允差、與預留潤滑空間，擺線盤齒形設計需要予以修形，這使得擺線盤由全齒接觸變為局部齒接觸，故此對於修形後的受力表現，值得加以探討研究。由於擺線減速機複雜的運動模式，以理論分析有其極限和困難，所以對擺線減速機的受力分析，使用有限元素法分析可以在工程上獲得有效且可接受的結果。本論文旨在使用有限元素分析軟體於擺線減速機之受力分析，並探討其中軟體之參數設定及穩定性；除此之外，並將分析之結果與理論分析之結果做一比較，以增加軟體分析的正確性。

Cycloidal speed reducers have been applied in modern engineering universally. Compared with the traditional planetary gear reducer, cycloidal speed reducers have the characteristics of high load ability, low-backlash, high-ratio, reliable functioning in dynamical load conditions, compact, and high efficiency. Theoretically, the teeth of cycloid disk are in contact with appropriate rollers on the outer stationary case simultaneously. But in practical application, in order to compensate the manufacturing errors and reserve the space for lubricating, the cycloid teeth have to be modified. Thus the teeth of cycloid disk are not all at simultaneous contact with rollers anymore. It is necessary to understand the changes of force reaction of the cycloid dick after the profile modification. Due to the complex motion of cycloid disk, it is difficult to analyze the force reaction by theoretical method; therefore, the force analysis using finite element method has been implemented in this work. The goal of the thesis is to analyze the force condition of a cycloidal speed reducer using finite element method. The parameters and stability of the FEM software are discussed. In additional, the results of FEA are compared with those of theoretical method such that the correctness of FEA can be furthered assured.

致謝 I
摘要 II
Abstract III
目錄 IV
圖目錄 VI
表目錄 X
符號說明 XI
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.2.1 擺線減速機 2
1.2.2 漸開線齒輪FEM分析 5
1.3 研究動機與目的 6
1.4 論文架構 7
第二章 接觸力量之理論分析方法 8
2.1 前言 8
2.2 擺線減速機靜態受力分析 8
2.2.1 參數設定 8
2.2.2 靜力平衡 12
2.3 結果算例 17
第三章 ANSYS使用環境與APDL分析流程 19
3.1 前言 19
3.2 ANSYS 介紹 20
3.3 APDL在本文的應用 22
3.4 APDL 指令簡介 22
3.4.1 擺線盤自行網格規劃 23
3.4.2 邊界負載與求解 31
3.5 小結 36
第四章 以有限元素軟體分析減速機之受力 37
4.1 前言 37
4.2 有限元素軟體環境介紹 37
4.2.1 單元類型介紹 39
4.2.2 接觸設置介紹 40
4.3 一階擺線減速機FEM分析流程 43
4.3.1 前處理 44
4.4 求解與結果 50
4.4.1 分析結果之收斂表現 50
4.4.2 未修形有限元分析 52
4.4.3 理論分析結果 56
4.4.4 FEM分析之修形齒型 57
4.5 結果討論 61
4.5.1 未修形模型之有限元分析與理論推導比較 61
4.5.2 未修形模型與修形模型FEM分析比較 66
4.6 小結 71
第五章 結論與未來方向 74
5.1 結論 74
5.2 未來方向 75
參考文獻 76
附錄 79
A 本文APDL操作流程所使用的指令介紹 79
B 本文一階擺線減速機APDL分析流程之程式碼 88

[1]Blagojevic, M., Marjanovic, N., Djordjevic, Z., Stojanovic, B., Disic, A., "A New Design of a Two-Stage Cycloidal Speed Reducer," ASME J. Mech. Des, Vol.133, 085001-1~7. (2011)
[2] Braren, L.K., Gear Transmission, US Patent 1694031. (1928)
[3] Malhotra, S. K. and Parameswaran, M. A., "Analysis of a Cycloid Speed Reducer," Mech. Mach. Theory Vol. 18, No. 6, pp. 491-499. (1983)
[4]Litvin, F., and Feng, P., "Computerized Design and Generation of Cycloidal Gear," Mech. Mach. Theory, Vol. 31, No. 7, pp. 891-911. (1996)
[5] Chmurawa, M., and Lokiec, A., "Distribution of Loads in Cycloidal Planetary Gear (Cyclo) Including Modification of Equidistant," Proceedings of the 16th European ADAMS User Conference. (2001)
[6] Chmurawa, M., and John A., "FEM in Numerical Analysis of Stress and Displacement Distribution in Planetary Wheel of Cycloidal Gear," NAA 2000, LNCS 1988, Spring-Verlag Berlin Heidelberg, pp. 772-799. (2001)
[7] Gorla, C., Davoli, P., Rosa, F., Longoni, C., Chiozzi, F., Samarani, A., "Theoretical and Experimental Analysis of a Cycloidal Speed Reducer," ASME J. Mech. Des., Vol. 130, No. 11, pp. 1126041-1126048. (2008)
[8]Blagojevic, M., Nikolic-Stanojevic, V., Marjanovic, N., Veljovic, L., "Analysis of Cycloid Drive Dynamic Behavior," Scientific Technical Review, Vol. LIX, No 1, pp. 52-56. (2009)
[9]Blagojevic, M., Marjanovic, N., Dordevic, Z., Stojanovic, B., "Stress and Strain State of Single-Stage Cycloidal speed reducer," IRMES, pp. 553-558. (2011)
[10]林灣松，"二階擺線減速機之運動誤差分析與設計"，碩士論文，國立台灣大學機械工程學系，台北，台灣。(2013)
[11]Li, J.-F., Xu M.-T., Wang, S.-U., "Finite Element Analysis of Instantaneous Mesh Stiffness of Cylindrical Gears," Commun. Numer. Meth. Engng, Vol. 15, pp. 579-587. (1999)
[12] Litvin, L.F., Fuentes, A., Fan, Q., Handschuh, R.F., "Computerized Design, Simulation of Meshing, and Contact and Stress Analysis of Face-Milled Formate Generated Spiral Bevel Gears," Mech. Mach. Theory Vol. 37, pp. 441-459. (2001)
[13] Li, S.-T., "Gear Contact Model and Loaded Tooth Contact Analysis of a Three-Dimensional, Thin-Rimmed Gear," ASME J. Mech. Des, Vol. 124, pp. 511-517. (2002)
[14] Chen, Y.-C., and Tsay, C.-B., "Stress Analysis of a Helical Gear Set with Localized Bearing Contact" Finite Elem Anal Des, Vol. 38, pp. 707-723. (2002)
[15] 林世豪，"小軸交角直齒錐形齒輪對之齒面接觸應力分析"，碩士論文，清雲科技大學，桃園，台灣。(2008)
[16] Gonzalez-Perez, I., Iserte, J.L., Fuentes, A., "Implementation of Hertz Theory and Validation of a Finite Element model for stress analysis of gear dives with localized bearing contact," Mech. Mach. Theory Vol. 46, pp. 765-783. (2011)
[17] 伍志明，"直傘齒輪有限元素應力分析之研究"，碩士論文，台灣科技大學，台北，台灣。(2012)
[18]李輝煌，"ANSYS 工程分析基礎與觀念"，高立圖書有限公司，台北，台灣。(1999)
[19] 黛曙光，謝桂蘭，黃雲清，"ANSYS 參數化編程與命令手冊"，機械工業出版社，北京，中國。(2009)
[20]李兵，何正嘉，陳雪峰，"ANSYS Workbench 設計、仿真與優化"，清華大學出版社，北京，中國。(2008)
[21] 李力行，"機械設計手冊"，第五版，第九篇 - 輪系，第三章 – 擺線針輪行星傳動，機械工業出版社，北京，中國。(2010)