内啮合斜齿轮副齿面接触应力与有限元分析

Contact stress of gear tooth surfaces and finite element analysis of internal meshing helical gear

针对数控内齿珩轮强力珩齿时被珩工件齿面应力分布规律问题,首次提出采用内啮合斜齿轮传动模型模拟替代内齿珩轮强力珩齿运动。以典型的Hertz接触理论为基础,首先计算节点P处齿面应力,其次通过计算内啮合传动啮合线上不同啮合点位置的综合曲率,引入压比系数,分析齿数为123的内齿轮分别与齿数为13、33、73、103的外圆柱斜齿轮在不同啮合线上的齿面应力分布情况。建立内啮合斜齿轮三维模型,利用三维有限元方法分别分析齿数为123的内齿轮分别与齿数为13、33、73的外圆柱斜齿轮的三个内啮合齿轮副在啮合线任意位置上的应力分布情况。结果表明:一对内啮合的齿轮副齿数差越大,且重合度小于2时,齿根处应力最大、节线附近处突然变大;齿数差越小时,齿根处应力最大。为此,内齿珩轮强力珩齿时尽可能采用齿数差较小的珩齿形式,以便控制被珩齿轮齿形挖根和中凹误差现象。

For the problem of tooth surface stress distribution of work piece honed by a NC internal honing wheel, internal helical gear transmission model has been used in this paper to replace internal power honing movement. Firstly, the tooth surface stress of pitch point P is calculated based on Hertz Contact Principle. Secondly, through calculating the synthetic curvatures of different pitch points in meshing line of internal transmission and introducing pressure ratio, the tooth surface stress distributions at different meshing positions have been analyzed when an internal gear with teeth number of 123 is respectively meshed with external helical gears with teeth number of 13, 33, 73 and 103. 3 D models of internal meshing helical gear pair is established, the stress distributions at any position in meshing line have been studied by three-dimensional finite element software when an internal gear with teeth number of 123 is respectively meshed with external helical gears with teeth number of 13, 33 and 73. The results show that: when the teeth number difference between a pair of internal gears is larger, as well as the contact ratio is less than 2, the stress at tooth root is largest, and the stress nearby pitch line increases suddenly; while the teeth number difference is smaller, the stress at tooth root is largest. Therefore, teeth number difference should be as small as possible, as proposed in this paper, to control concave tooth profile error during internal power honing using an internal honing wheel.