以圓弧形滾齒刀創成之球形齒輪的齒面數學模式和接觸分析

Abstract

球形齒輪早已使用多時，但目前尚未見有以圓弧形滾齒刀創成之球形齒輪，亦無對此類具有齒面修整之球形齒輪進行齒面接觸研究。因此，建立此類具有齒面修整之球形齒輪的齒面數學模式並進行其特性研究分析，探討此類對球形齒輪在具有裝配誤差狀態下對齒輪組傳動的影響，將可對球形齒輪之齒面修整的特性更為瞭解，並有助於本文所提之球形齒輪齒面修整技術在球形齒輪上的運用。 本論文依據齒輪原理與球形齒輪之創成機構，以推導用圓弧形滾齒刀來創成具有齒形修整之球形齒輪的齒面數學模式，而本文提出此圓弧形滾齒刀之滾削創成也可用具有圓弧剖面之曲線狀齒條刀來加以模擬。針對此類具齒形修整之球形齒輪，應用齒輪嚙合原理建立其齒面接觸分析模式，並輔以電腦輔助分析程式之開發，進行齒面修整之球形齒輪的齒面接觸模擬與特性分析，探討具有裝配誤差狀態下齒輪組之運動誤差。

Spherical gears have been used for years, however, spherical gears generated by a hob cutter with circular-arc profiles have not found yet. Besides, there is no research on the tooth contact analysis of this type of spherical gears with tooth profile modification. Therefore, to establish the mathematical model of this type of gears and to investigate the contact characteristic of the gear pairs are most helpful to the applications of this tooth modified spherical gears. In this research, the tooth mathematical model of the spherical gears with modified tooth profiles, generated by a hob cutter with circular-arc profiles, is developed based on the theory of gearing and the spherical gear generation mechanism. A concept of applying the curvilinear-tooth rack cutter with circular-arc profiles to simulate the hobbing generation of a hob cutter with circular-arc profiles is proposed. Based on the developed tooth mathematical model of the modified spherical gear as well as the theory of gear meshing and the developed tooth contact analysis computer simulation programs, the tooth contact simulations, characteristic analysis and kinematical errors of the gear pairs under various assembly errors are performed and discussed.