保角映射法分析直齿轮轮齿变形

TOOTH DEFLECTION ANALYSIS OF SPUR GEAR BY MEANS OF CONFORMAL MAPPING METHOD

分析了用平面弹性理论的复变函数法求直齿轮轮齿变形的理论──保角映射法，完成了求载荷作用点位移的解析解，用具有１０个分式项表达的映射函数，提高了映射齿形精度，得到计算轮齿变形的精确解；用该法计算得到赫兹接触下的变形值与Ｔｅｒａｕｃｈｉ集中载荷法求得轮齿变形的结果对比，精度大大提高；并将该结果与著名的Ｗｅｂｅｒ及Ｌｕｎｄｅｒｇ公式对比，证明该法是可靠的。

The tooth deflection of spur gear was calculated by the conformal mapping method which is the complex potentials approach in two dimensional elasticity theory.The analytic solution was deritived for determining the displacement at force active Point.The mapping function was expressed by ten fractional terms, the accuracy of the mapping shape of tooth was increased and the exact solution of tooth deflections was obstained. The compution results of tooth deflections under Hertz contact given by this method were contrasted to those by Terauchi's concentrated load method, the accuracy of the results by this method was greatly increased ,and compared with those Weber's and Lunderg's formuls, this method was confirmed to be reliable.