球形齒輪之數學模式及接觸分析

Abstract

球形齒輪有可容許垂直軸向裝配誤差之特性，其特性類似圓錐形齒輪，許多學者已進行圓錐形齒輪之研究，且有不錯之成果。而雖然球形齒輪之實際加工技術在很早的時候已經被發展出來，但有關球形齒輪的研究則尚未開始著手進行，因此，若能建立出球形齒輪的數學模式，則可利用此數學模式來進行球形齒輪之相關分析，更進一步了解球形齒輪的特性及應用上之限制。 本論文依據齒輪原理與創成機構推導出凸狀球形齒輪及凹狀球形齒輪之齒形數學模式，並利用所建立之球形齒輪數學模式進行電腦模擬，其中包括：球形齒輪之齒面過切分析、接觸分析及齒印分析。齒面過切分析主要探討球形齒輪之齒面過切位置及過切發生的球形角，接觸分析則討論球形齒輪分別在具有裝配誤差及理想狀況時之運動誤差及接觸點位置，另外，齒印分析探討球形齒輪在受力變形後其接觸橢圓之位置及大小。

The spherical gears have a characteristic what can tolerate the perpendicular axes misalignment. It’s like the bevel gears. There were many scholars haven proceeded some studies and built some good results. Although the techniques of manufacture the spherical gears had been developed. But the research do not proceed about the spherical gears. Therefore, if we can build the mathematical model of spherical gears then we can start some analysis about spherical gears. For this reason, we can understand some characteristics and limit of used about spherical gears further. In this thesis, we will according to the theory of gears and the mechanism of cutting to develop the mathematical model of spherical gears. Then, we will follow this mathematical model of spherical gears to proceed the computer analysis. Those are about: undercutting analysis of spherical gears, teeth contact analysis (TCA) and contact pattern analysis of spherical gears. The undercutting analysis probe the position of undercutting line and the spherical angle of spherical gears. Teeth contact analysis probe the kinematic error and the position of contact point of spherical gears with misalignment and ideal case. Another contact pattern analysis probe the positions and size of contact pattern of spherical gears.