基于接触有限元法的齿轮多齿时变啮合刚度数值分析

Numerical analysis of multi-tooth time-varying meshing stiffness of gear based on contact finite element method

针对传统齿轮刚度计算中,无法准确考虑齿轮啮合时由接触和惯性因素引起变形的问题,采用接触有限元法计算齿轮的多齿时变啮合刚度,并将计算结果分别与石川法和改进石川法的计算结果进行比较.在计算中采用参考单元辅助解决动态分析时无法提取各子步接触变形的问题.结果表明,接触有限元法与石川法的计算结果较吻合,最大值相差12.4%;与考虑轮体变形的改进石川法相比更加吻合,最大值相差10.2%;该方法计算的刚度曲线反映出由接触变形而导致齿轮实际重合度小于理论重合度的现象,计算结果较石川法和改进石川法更能反映真实情况。

As to the problem that the deformation caused by contact and inertia during gear meshing can not be accurately considered in traditional calculation of gear stiffness, the multi-tooth time-varying meshing stiffness of gear is calculated by contact finite element method, and then the calculation results are respectively compared with that obtained by Ishikawa method and improved Ishikawa method. The reference elements are used to solve the problem that the contact deformation of every sub-step can not be extracted in dynamic analysis. It shows that, the calculation result of contact finite element method matches that of Ishikawa method, and the maximum difference is 12.4% ; the result matches better with that of improved Ishikawa method which considers the gear body deformation, and the maximum difference is 10.2% ; the stiffness curve obtained by the method can reflect the phenomenon that, due to contact deformation, the practical overlap ratio is smaller than the theoretical one and the calculated results of the method can better reflect the realistic situation than those of Ishikawa method and improved Ishikawa method.