球齿轮传动的齿面接触分析和应力分析

Research of the Tooth Contact and Stress Analysis of Spherical Gear Drives

球齿轮是一种新型的二维齿轮传动机构。在建立了球齿轮数学模型的基础上,得到了球齿轮传动的啮合模型,并进行了齿面接触特性分析,通过解非线性方程组,可得到接触点在齿面的位置。分析了球齿轮齿面的结构特征,针对球齿轮传动的接触形式表现为轮齿凸面与马鞍面之间的点接触,对啮合齿面的接触椭圆进行了分析计算,总结出了球齿轮在任一偏摆平面内啮合传动时接触椭圆的变化规律:在轮齿根部和顶部啮合时,接触椭圆较小,因而接触应力较大;而在轮齿中部啮合时,接触椭圆较大,所以接触应力较小。采用有限元的方法对球齿轮轮齿进行了弯曲应力和接触应力分析,分析结果进一步验证了接触椭圆变化规律的正确性。以上结论对进一步研究球齿轮的传动理论与实际应用具有重要的指导意义。

The spherical gear is a new gear-driven mechanism with a double degree of freedom. Based on the mathematical models of spherical gears, the meshing model is obtained and tooth contact analysis is performed, so the location of contact points on teeth surfaces is received by using nonlinear solver. The structural shape of the tooth surface is studied. To the point contact form of meshing spherical gears between a convexity and a saddle surface, contact ellipses of meshing tooth surfaces are studied, and then the movement rule of contact ellipses when spherical gear pairs mesh in any swaying plane that passes through polar axes of spherical gear pairs is gained： Contact ellipses are little on teeth base and teeth tip, so contact stress is large; Contact ellipses are relatively large on teeth midposition, so contact stress is little. Finite element analysis is applied to perform bending stress analysis and tooth contaet stress analysis, and the result validates the correctness of the movement rule of contact ellipses. The study is useful for further investigations in transmission theory and practical applications of spherical gear pairs.