Abstract: Aimming directly at trivial problems of mathematical model for involute tooth profile of noncircular gears, based on the theory of shapping with cutter, A new method was raised. Firstly, set up the mathematical model for involute tooth profile of circular gears of cutter. Secondly, established another mathematical model for relationship of geometry position between the cutter and semifinished product of noncircular gears. Finally, combined the two mesh equations together,and then got the mathematical model. The mathematical model is simple, unified and applicable.

Key words: Mathematical model , Involute tooth profile , Shapping with cutter , Mesh equation

摘要： 针对目前非圆齿轮渐开线齿廓数学方程比较繁琐的问题,提出以插齿刀加工非圆齿轮理论为基础,
获得非圆齿轮渐开线齿廓曲线数学模型的方法。首先建立插齿刀的渐开线圆柱齿轮齿廓的数学模型,再建立插齿
刀与非圆齿轮毛坯即节曲线在相互啮合时的几何位置关系,使其作纯滚动,最后用啮合方程将这两个模型结合起
来。此数学模型简单统一,适用范围广泛。

关键词: 数学模型 , 渐开线齿廓 , 插齿加工 , 啮合方程