保角映射法求解渐开线直齿轮齿根应力

CALCULATION OF INVOLUTE SPUR GEAR ROOT STRESS BY CONFORMAL MAPPING METHOD

目前国际上确定渐开线齿轮齿廓保角映射函数的方法均为数值回归法，计算复杂，映射精度的提高受到限制．为此，本文给出了渐开线齿轮齿廓保角映射函数的解析解，计算方便，使映射精度大幅度提高。以上述工作为基础，笔者给出了渐开线直齿轮齿根应力的解析公式，并由算例证实了计算结果和边界元法计算值之间的一致性。

Up to now, the conformal mapping function for tooth profile of involute gear isdetermined by numerical regression method. Its calculation is complicated and the mappingaccuracy is limited. In this paper, an analytical formula is given of conformal mapping functionfor the tooth profile of involute gear. The calculation is easy and the mapping accuracy is greatlyimproved. An analytical solution to root stress of involute spur gear is presented in the paper.Good agreement with the result of boundary element solution is achieved in an example providedwhich validates the present solution.