蝸桿蝸輪組是屬於空間交錯軸(crossed-axis)傳動機構，具有高傳動減速比，體積較小、噪音低、結構緊湊以及承載能力大等特點，而雙包絡蝸桿蝸輪組可以比蝸桿蝸輪組更高的接觸比(Contact Ratio)，定位精度及負載的傳遞也較好。 本研究針對ZN型雙包絡蝸桿及螺旋齒輪的搭配，從設計、模擬及分析進行一系列之研究，並有系統的建立ZN型雙包絡蝸桿及螺旋齒輪的研究流程。首先根據齒輪原理(Theory of Gearing)，採用軌跡法利用齒輪型車刀推導出ZN型雙包絡蝸桿齒面數學模式，再利用齒條刀與嚙合方程式推導出具轉位修整之螺旋齒輪齒面數學模式。根據推導出之ZN型雙包絡蝸桿與螺旋齒輪先進行干涉檢查，透過蝸桿包絡半徑參數修整再進行齒面接觸分析(Tooth Contact Analysis, TCA)，探討不同包絡半徑下的傳動誤差與接觸軌跡。最後根據齒面接觸分析的結果找出最佳的參數，進行有限元素法應力分析，並計算螺旋齒輪各齒間負載分布及嚙合效率。 ;Worm gear set is a spatial crossed-axis transmission mechanism, which has the characteristics of high reduction ratio, compact, low noise, compact structure and large load carrying capacity. The double-enveloping worm gear set has a higher contact ratio than the cylindrical worm gear set. The accuracy and load transfer are also better. This research aims at the study of the combination of ZN-type double-enveloping worm and helical gear, including design, simulation, and analysis. Firstly, the Theory of Gearing is used to derived the mathematical model of ZN-type double-enveloping worm by using the gear-type cutter. Then, the helical gear with profile shifting is derived. Based on the model of ZN-type double-enveloping worm and helical gear, the interference was inspected, and the worm enveloping radius was adjusted. Tooth contact analysis was used to explore the transmission error and contact path under various enveloping radius of the worm. According to the results of the tooth contact analysis, the best parameters are found to perform the finite element stress analysis. estimating the load distribution and meshing efficiency between the helical gear teeth.
