臺灣博碩士論文加值系統

　　擺線傳動器(Cycloidal drives)在工業上應用甚廣，具有傳動速比範圍大、體積小、重量輕、運轉平穩、承載能力大、高效率與壽命長等特點。本研究的主要目的在於針對具修整齒形之擺線輪的擺線傳動器，進行其特性分析，並決定齒形修整量之最佳組合，以期能得到更佳之傳動性。

　　首先應用共軛曲面理論，建立具修整齒形之擺線輪的一般化曲面設計模式，然後建立其齒形接觸分析模式。再以其為依據，利用最佳化方法，在提供潤滑所需的油膜厚度及容忍少量的製造與裝配誤差的條件下，以降低瞬時速比誤差及傳動誤差為目標，決定符合所需之擺線輪修整齒形的等距與移距之最佳組合。文中並以實例設計與分析，探討該傳動器的多種特性，並驗證所建立的各模式之正確性。

　　本文建立了擺線傳動器之曲面設計、齒形接觸分析及擺線輪修整齒形之最佳化的模式，將有助於研發高性能的擺線傳動器，提升目前齒輪傳動的相關產業之技術水準。

　　Cycloidal drives are used in many machinery. They have some advantages, such as larger range of speed ratio, more compact, lighter weight, higher capacity, and higher efficiency, etc. The main purpose of this study is to investigate the characteristics of the drives with modified tooth profiles and to determine the optimum amounts of tooth modifications such that they have better characteristics.

　　Based on the theory of conjugate surfaces, a general model for the profile design of the cycloidal wheel without or with various tooth modifications is developed. Then, the model for the tooth contact analysis is evolved. Consequently, subjected to the required lubricant thickness and the tolerance for the assembly and manufacture errors, an optimization technique is applied to determine the amounts of tooth modifications such that the instantaneous velocity ratio error and the transmission error can be minimized. Examples are included to verify the correctness of the models developed and to demonstrate the characteristics of the drives.

　　The models developed should be an aid for designing the cycloidal drives with better performance, and they are also useful for the development of other gear mechanisms.

目　錄

中文摘要‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧i
英文摘要‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ii
致謝‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧iii
目錄‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧iv
表目錄‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧vii
圖目錄‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧viii
符號說明‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧xiv

第一章　前言‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧1
　1-1　研究動機‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧1
　1-2　文獻回顧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧3
　　1-2-1　曲面設計‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧3
　　1-2-2　齒形修整‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧5
　　1-2-3　齒形接觸分析‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧5
　　1-2-4　最佳化設計‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧6
　1-3　研究目的與方法‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧7
　1-4　本文內容‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧7

第二章　曲面設計‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧8
　2-1　標準齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧8
　　2-1-1　齊次坐標轉換矩陣‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧8
　　2-1-2　共軛曲面與包絡理論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧10
　　2-1-3　坐標轉換矩陣‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧13
　　2-1-4　齒形曲線方程式‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧15
　2-2　修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧17
　　2-2-1　修整齒形方法‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧17
　　2-2-2　坐標轉換矩陣‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧18
　　2-2-3　齒形曲線方程式‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧20
　2-3　實例分析‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧21
　　2-3-1　標準齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧21
　　2-3-2　修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧23
　　　2-3-2-1　轉角修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧23
　　　2-3-2-2　等距修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧26
　　　2-3-2-3　移距修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧27
　　　2-3-2-4　等距加移距修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧29
　2-4　本章結論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧31

第三章　齒形接觸分析‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧32
　3-1　坐標轉換矩陣‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧32
　3-2　齒形接觸分析‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧34
　3-3　實例分析‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧36
　　3-3-1　標準齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧36
　　3-3-2　修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧36
　　　3-3-2-1　轉角修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧38
　　　3-3-2-2　等距修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧39
　　　3-3-2-3　移距修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧48
　　　3-3-2-4　等距加移距修整齒形‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧55
　3-4　本章結論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧64

第四章　齒形最佳化‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧66
　4-1　設計需求‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧66
　4-2　數學模式‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧67
　　4-2-1　設計變數‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧67
　　4-2-2　目標函數‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧67
　　4-2-3　限制條件‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧68
　4-3　實例設計與分析‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧68
　　4-3-1　降低瞬時速比誤差‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧69
　　4-3-2　降低傳動誤差‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧73
　　4-3-3　同時降低瞬時速比誤差及傳動誤差‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧76
　　4-3-4　降低傳動誤差(加重w3=4)‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧79
　4-4　本章結論‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧82

第五章　結論與建議‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧84

參考文獻‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧86

附錄A　等距、移距及等距加移距修整之齒形曲線與徑向距離等不同組合別相關曲線圖‧‧‧‧‧‧93

附錄B　等距、移距與等距加移距修整齒形之瞬時速比與傳動誤差等不同組合別相關曲線圖‧‧‧106

附錄C　等距加移距修整齒形之瞬時速比與傳動誤差平均值、誤差百分比、變動量及變動係數等
　　　　不同組合別相關曲線圖‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧119

附錄D　最佳設計結果之齒形曲線、徑向距離、瞬時速比與傳動誤差之曲線圖‧‧‧‧‧‧‧‧‧131

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