電腦輔助擺線減速機之運動誤差分析及可靠度分析

Computer-Aided Kinematic Error Analysis and Reliability Analysis of a Cycloidal Speed Reducer

高瑋璞(Wei-Pu Kao)

指導教授 ： 李志中

國立臺灣大學/工學院/機械工程學研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.11347

摘要

擺線減速機由於具有高減速比、高傳動效率、低噪音等優點，在工業界已應用一段時間。本文內容主要為針對具齒形修形的擺線減速機，運用齒輪原理來進行運動誤差的計算與分析；以及探討一階擺線減速機在針齒半徑上加入製造公差後，是否會發生干涉之可靠度分析。首先，本文藉由坐標轉換與齒輪嚙合原理來推導出擺線齒形參數式，並決定擺線齒輪的齒形修形量；接著進行齒面接觸分析來得到初始背隙與運動後實際的輸出角，並利用其結果來計算二階擺線減速機之運動誤差。另外，本文發展出電腦輔助的程式介面，方便設計者能簡單的得到計算後的運動誤差曲線。其次本文將針對一階擺線減速機之針齒，探討其加入製造公差後，在各個針齒與標稱尺度有差異的情況下，當曲柄輸入運轉一圈時，計算實際之輸出角，並分析不會發生干涉的可靠度及計算可靠度誤差，並且比較不同公差等級之結果。

關鍵字

擺線減速機 ； 齒形修形 ； 運動誤差分析 ； 可靠度分析

並列摘要

The cycloidal speed reducer has been commonly applied in industry because of its high reduction ratio, high transmission efficiency and low noise charactieristics. This thesis mainly investigates the kinematic errors of the cycloidal speed reducer with tooth modification as well as the reliability for the non-interference of the gear reducer with pin tolerance when assemblying.
The generation of the cycloid profile with tooth modification is derived via gear theory. Then, the tooth contact analysis is developed and a computer-aided program is developed for the designer to simulate the kinematic error of the cycloid reducer. The thesis subsequently discusses the reliability for non-interference during assembly when the pins are manufactured with tolerance. With various tolerance levels, the reliability of non-interference between pins and cycloid disc is calculated with Monte Carlo method. The overall kinematic error is also discussed in such conditions.

並列關鍵字

cycloidal speed reducer ； modification of tooth ； kinematic error ； relibility

參考文獻

[1] L.K. Braren, Gear Transmission, US Patent 1694031, 1928.

[2] F.L. Litvin and P.H. Feng, "Computerized design and generation of cycloidal gearings," Mechanism and Machine Theory, Vol.31, No.7, pp.891-911, 1996.

[3] J.G. Blanche and D.C.H. Yang, "Cycloid drives with machining tolerances," ASME Journal of Mechanical Design, Vol.111, No.3, pp.337-344, 1989.

[4] T.S. Lai, "Design and machining of the epicycloid planet gear of cycloid drives," The International Journal of Advanced Manufacturing Technology, Vol.28, No.7-8, pp.665-670, 2006.

[5] J.H. Shin and S.M. Kwon, "On the lobe profile design in a cycloid reducer using instant velocity center," Mechanism and Machine Theory, Vol.41, No.5, pp.596-616, 2006.