非對稱齒形之蝸桿蝸輪組之特性分析

Abstract

蝸桿蝸輪組是空間交錯軸(Cross Axes)的傳動機構，其基本元件為蝸桿和蝸輪，是常見的傳動齒輪系之一。本研究先依據ZN型蝸桿之切削方式，利用左右為直邊且非對稱之刀具，模擬刀具與蝸桿之間的滾削機構，推導出非對稱齒形之ZN型蝸桿之齒面方程式。利用此蝸桿之齒面數學模式，配合蝸桿型滾刀與蝸輪之切削機構關係和嚙合方程式，便可得到蝸輪之齒面數學模式。利用推導出之蝸桿蝸輪組的齒面數學模式，便可進行蝸桿蝸輪之間的齒面接觸分析(Tooth Contact Analysis, TCA)與有限元素法(Finite Element Method, FEM)齒輪應力分析，再將分析所得之結果，與一般對稱齒形之ZN型蝸桿蝸輪組作比較，探討其差異與優劣，以做為設計與製造之依據，以求非對稱齒形蝸桿蝸輪組於單方向旋轉時，相較於對稱齒形之蝸桿蝸輪組，具有較佳的強度，延長其使用壽命。 而其他型之蝸桿蝸輪組，如ZE型和ZK型，亦可採用相似之方法，建立其非對稱齒形之蝸桿蝸輪組的數學模式，經由接觸分析與應力分析，瞭解其傳動機構之特性。

The worm gear set, which is composed of a worm and worm gear, is one of the cross axes transmission mechanisms. Based on the cutting method and the asymmetric straight-sided cutter, the mathematical model of the asymmetric ZN-type worm surfaces is developed. The mathematical model of the worm gear surfaces can be obtained by applying the cutting mechanism of the worm gear hobbing process and the equation of meshing between the hob cutter and the produced worm gear surfaces. Based on the developed mathematical model of the worm gear set surfaces, the tooth contact analysis of the worm gear set is performed and the finite element stress analysis is also investigated. By comparing the analysis results of an asymmetric ZN-type worm gear set with a symmetric ZN-type worm gear set, it is most helpful to the design and manufacture of the worm gear sets. It is found that the strength of the asymmetric ZN-type worm gear set is higher than that of the symmetric ones. Therefore, the asymmetric ZN-type worm set is suitable for one direction rotation transmissions. For other types of worm gear set, eg. ZE-type and ZK-type, the same method and developing procedures can be used. Based on the developed mathematical model of the asymmetric worm gear set, the characteristics of the worm gear set are obtained by applying the contact analysis and stress analysis.