漸開線少齒差行星傳動機構齒型之研究

Abstract

少齒差行星齒輪傳動機構(PDSTND)具有結構緊湊及高減速比的優 勢，然而其具有相當多的干涉與限制條件，是相當困難的設計問題。本研 究目標針對兩種PDSTND(K-H-V型和2K-H型)的齒型進行最佳化分 析，並採用漸開線移位齒輪。2K-H型可想像成兩組K-H-V型結合。最 佳化目標包含兩種，一種是單獨針對接觸比的單一目標，另一種是將接觸 比與工作壓力角以權重的方式組合而成的目標函數。 本研究提出以三種齒高方案，分別為全高齒、短齒、對全高齒作齒頂 變動來進行設計。文獻只有探討K-H-V設計，為了與文獻中的K-H-V 型公平比較，本研究採用跟文獻相同的基本參數。並在不低於文獻設計的 效率下，以組合差分進化法進行K-H-V型最佳化設計，找出最佳齒型。 此外本研究也針對2K-H型進行最佳化設計，並對K-H-V型與2K-H型 兩者之間性能進行比較。

For the planetary drive with small teeth number difference (PDSTND), there are many advantages such as compact design, high speed reduction ratio, small specific sliding and small contact stress. However, its design is a very difficult task because of many interferences and constraints. This study is to seek the optimum tooth profiles of two kinds of PDSTND (K-H-V and 2K-H types) with profile shifted involute gears. The 2K-H type is considered a two-stage K-H-V type. Two kinds of the objective function are optimized: one is to minimize the reciprocal of the contact ratio and the other is to minimize some weighted combinations of the reciprocal of the contact ratio and the working pressure angle. The study proposes using three schemes for the height of profile shifted involute gears, i.e., full depth tooth, stub tooth and variation in addendum of full depth tooth. The optimum designs of only the K-H-V type have been discussed in the literature. To compare with the previous designs fairly, the same basic design parameters are used and the efficiency is constrained to be not less than that of the previous designs. In the study, the optimization problems are solved using the combined-mutation differential evolution algorithm. The optimum design of the 2K-H type is also investigated. The comparison of performance between the K-H-V and 2K-H types is provided.