非90°交錯角之ZN型蝸輪與ZK型蝸桿之接觸分析

Abstract

一般齒輪當齒數太少時，齒輪之齒面會產生過切現象，尤其是單段高減速比齒輪組其輸入軸之齒數很少時，但是蝸桿蝸輪組可以克服此問題，因此，蝸桿蝸輪組可提供一般正齒輪和螺旋齒輪無法提供的大減速比功能。蝸桿蝸輪組屬於高接觸比的傳動機構，提高接觸比除了可以提高定位精度和穩定度之外，亦可增加蝸桿蝸輪組之負載能力，更可以廣泛地使用在某些特定的環境。本論文所探討之蝸桿蝸輪組具有非90度之交錯角，除了可以增加齒輪組之接觸比，亦可藉由改變蝸桿蝸輪組之交錯角以獲得不同之特性，增加其應用性。 本論文將應用齒輪原理以及電腦輔助設計技術，對於ZN型蝸輪與ZK型蝸桿，分別進行其齒面數學模式的建立，再依據所推導之齒面數學模式和齒面接觸分析技術，探討蝸桿蝸輪組兩嚙合齒面之接觸情形，包括運動誤差、瞬時接觸齒數、平均接觸比、接觸比與接觸齒印。本研究亦討論不同之設計參數與交錯角對於蝸桿蝸輪組之接觸情形，並且探討蝸桿蝸輪組在具有裝配誤差時，其接觸情形與接觸齒印。

Tooth undercutting may occur for conventional gear sets with a small number of teeth, especially for a single stage gear-set with a high reduction gear ratio. Nevertheless, worm gear sets can conquer this issue which spur and helical gear sets could not provide. Worm gear sets are transmission mechanism of high contact ratios. Increasing the contact ratio of a worm gear set not only improve position precision and stability, but also increase load capacity of the worm gear set, which enables it to apply to some particular environments. In this research, the worm gear set with a non-ninety-degree crossing angle not only increase the contact ratio but also obtain different properties by changing the crossing angle of a worm gear set. In this research, the mathematical models for the ZN type worm gear and the ZK type worm are developed based on the theory of gearing and the technique of computer aided design. According to the developed mathematical models and the tooth contact analysis technique, contact situations of a worm gear set, including kinematic error, instantaneous contact teeth, average contact ratio, contact ratio and contact ellipse are investigated. Besides, the influence of different design parameter and different crossing angle on the contact situation of a worm gear set are also studied. Furthermore, contact situation and contact ellipse of a worm gear set under ideal and error assembly conditions are investigated.