飛刀創成之蝸輪與ZK型蝸桿之接觸分析

Abstract

蝸桿蝸輪組可以克服一般傳統齒輪組在特定的模數下齒數太少時，齒輪齒面會產生過切的現象之問題，因此蝸桿蝸輪組可提供傳統正齒輪及螺旋齒輪均無法提供之大減速比功能。此外，增加蝸桿蝸輪組之接觸比除了可以提高其定位精度與穩定度，同時亦可有提高負荷之優點，使之更能廣泛地應用於各種傳動系統之環境。為了提高蝸桿蝸輪組之接觸比，本論文將蝸桿以非90°之交錯角之創成機構切製蝸輪。此種方法增加了蝸桿蝸輪組之接觸比，使得傳動的結構更為緊湊，提供更高的負載。 本論文將利用齒輪原理以及電腦輔助設計技術，針對飛刀創成之蝸輪與ZK型蝸桿在非90˚交錯角之嚙合條件下，進行此蝸桿蝸輪組之齒面數學模式的建立。此外，在根據所推導之非90˚交錯角蝸桿蝸輪組數學模式和齒面分析技術，探討蝸桿蝸輪組兩齒面間之傳動誤差與接觸比。同時討論不同的交錯角對於非90˚交錯角蝸桿蝸輪組之運動誤差與接觸比之影響。

Worm gear sets can conquer the undercutting problem, which occurs due to the small number of teeth of conventional gear sets with some special modules. Therefore, worm gear sets can provide high gear ratio, which spur and helical gear sets could not offer. Besides, increasing the contact ratio of a worm gear set not only improves the orientation precision and transmission stability, but also increases the loading capacity of the worm gear set, which enables it to apply to various transmission systems. In order to increase the contact ratio of worm gear sets, the worm gear sets are generated with a non-ninety-degree crossing angle. This kind of worm gear generation increases the contact ratio of worm gear sets, and makes the transmission mechanism more compact, and provides a higher loading ability. In this research, a mathematical model for the worm gear, generated by a fly cutter, meshes with the ZK type worm with a non-ninety-degree crossing angle is developed based on the theory of gearing and the technique of computer aided design. According to the developed mathematical model and the tooth contact analysis technique, transmission errors and the contact ratios of the worm gear set with a non-ninety-degree crossing angle are investigated. Besides, the effect of different crossing angles on the transmission errors and contact ratios are also investigated.