修整型刮齒刀所創成螺旋齒輪之數學模式與接觸分析

Abstract

螺旋齒輪現今多利用CNC之滾齒機來加工製造，且有許多的研究利用假想齒條刀模擬滾刀創成螺旋齒輪，並將所創成的齒輪對進行相關的接觸分析。本研究則是由假想齒條刀模擬磨輪來創成一刮齒刀，並利用刮齒刀再來創成螺旋齒輪，模擬一般齒輪在滾齒程序後，所進行的精加工刮齒程序；在創成過程中，刮齒刀旋轉軸與被創成齒輪旋轉軸之間具有一交錯角，為空間中交錯軸的嚙合運動。本論文依據齒輪原理與創成機構，推導出一修整型刮齒刀之齒面數學模式，並利用直進式刮齒方式創成出齒輪之齒面數學模式，而後再利用所建立的齒輪數學模式進行齒輪特性分析，其中包括刮齒刀所創成齒輪的齒面差異比較與齒面接觸分析比較。修整型刮齒刀的齒面，是由漸開線形與圓弧線形構成的複合線形所組成，以及具有隆齒修整的齒面，因此被創成齒輪之齒面會受刮齒刀外型所影響，而使得被創成齒輪對之運動誤差曲線為近似拋物線形曲線。

In general, most of helical gears are generated by a CNC machine with Hob cutters. Many scholars have proceeded some studies on generation methods for helical gears that were generated by Hob cutters and then performed the tooth contact analysis of the generated gear pair. In this study, an imaginary rack-cutter is adopted to simulate a grinding wheel to generate a shaving cutter. The shaving cutter is then used for the helical gear generation to simulate the precision cutting of the gear. Shaving is a gear finishing process after gear hobbing process. The modified shaving cutter and the helical gear rotate with crossed axes in 3-dimentioanl space.In this study, the geometry of a modified shaving cutter was constructed at first, and the mathematical model of the helical gear shaved with plunge shaving by a modified shaving cutter was also developed. According to this mathematical model and tooth contact analysis, the gear surface deviation and kinematical error of the generated helical gear pair are investigated. The modified shaving cutter was modified with crowning modification along the lead direction and profile modification. The profile of the modified shaving cutter has crowned tooth modification and is composed of an involute curve and a circular-arc curve. The kinematical error curve of helical gear pair generated by modified shaving cutters approximates to a parabolic curve.