盤狀刀具創成蝸桿與蝸輪之特性分析

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，亦可以提供一般傳統正齒輪及螺旋齒輪無法達成之大減速比效果，又蝸桿蝸輪組為多齒接觸，接觸比較高，因而可應用在須較高負荷的場合。由於工業界對於定位精度與穩定度之要求日益升高的情況下，高接觸比之蝸桿蝸輪組所帶來之效益也日益顯著。為提高蝸桿蝸輪組之接觸比，可將蝸桿與蝸輪之軸交錯角設定為非90°，以此種方式增加了蝸桿蝸輪組之接觸比，使得機構的結構更為緊湊。 本研究將利用齒輪原理以及電腦輔助設計技術，針對盤狀刀具創成之蝸桿蝸輪組，進行其齒面數學模式的建立並以程式語言建構所推導之蝸桿蝸輪組齒面數學模式，並以電腦繪圖軟體建構並繪製模型。此外，本研究亦將以程式語言模擬此機構運動中之運動狀況，針對蝸桿與蝸輪兩齒面間的接觸情形進行模擬與分析研究，探討正常裝配狀況下與具有裝配誤差狀況下蝸桿蝸輪組之傳動特性及接觸齒印大小、分佈位置與形狀的差異等，此分析結果可供蝸桿蝸輪設計與製造者之重要參考。

Worm gear sets can conquer the tooth 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 that spur and helical gear sets could not offer. Besides, the worm gear set has a larger contact ratio which enables its loading capability. In order to increase the contact ratio of a worm gear set, the worm gear set can be generated with a non-ninety-degree crossing angle. This kind of generating method not only increase the contact ratio of worm gear sets, but also make the transmission mechanism more compact.

In this research, the mathematical model of a worm gear set is developed based on the theory of gearing and the technique of computer aided design. The worm is generated by a disc-type grinding wheel and worm gear is generated by a fly-cutter. Based on the developed mathematical model, a computer graph of the worm gear set is presented. Besides, tooth contact analysis of the worm gear set is also performed to calculate the location of the contact points. Meanwhile, contact patterns and transmission errors of the worm gear set with assemble errors are also investigated. The analysis results are most helpful to the designers and manufacturers.