差曲面拓扑的齿轮啮合刚度计算与承载接触分析

基于齿条-齿轮等切共轭产形原理,构建齿面数值模型、ease-off差齿面,对ease-off蕴含的齿面啮合信息进行解析,获得了齿面接触路径、传动误差、接触线瀑布图;综合ease-off拓扑仿真与轮齿刚度非线性单元耦合解析,给出了修形拓扑齿面的啮合刚度、承载传动误差的计算方法。沿接触路径遍历接触线序列,获得了轮齿时变啮合刚度、承载传动误差与载荷分布图;给出了2阶抛物面对称与对角拓扑两种修形形式算例,求出了系列载荷作用下的啮合刚度、承载传动误差、齿面载荷分布。结果显示:随着载荷的增加,轮齿啮合刚度时变效应明显减弱;承载传动误差波动与啮合刚度、修形梯度密切相关;对角修形在啮合刚度、传动误差、载荷分布特性方面好于对称修形。 

Calculation of gear meshing stiffness and loaded tooth contact analysis based on ease-off surface topology

Based on the theory of rack-gear equal-tangential conjugate generating, the construction of numerical model of tooth surface and ease-off surface of gears was presented. Through analysis on the tooth surface meshing information of ease-off surface implication, the contact path, transmission errors and falls of contact line were obtained. Combining the ease-off simulation of tooth surface and the non-linear element coupling gear stiffness analysis, the computational method on time-varying meshing stiffness, loaded transmission errors for the modified tooth surface was presented. The computation was done by traversing the sequence contact lines according to the contact path, then the tooth meshing stiffness, loaded transmission errors and load distribution map were obtained. Two examples on topological tooth surface for symmetrical and bias modification of the 2-order paraboloid were acquired, and a series of results for the tooth meshing stiffness, loaded transmission errors and load distribution map under varied loads were gained. Results showed that the varied effects of tooth meshing stiffness weakened obviously with the increasing loads, and the fluctuation of loaded transmission errors was closely related to meshing stiffness and modification gradient of tooth surface. The bias modification was better than the symmetrical one in the performance of meshing stiffness, loaded transmission errors and load distribution.