基于齿根圆角圆心所在位置的时变啮合刚度修正模型

因接触齿对数的变化以及接触位置变化，将导致作为齿轮系统动力学的最重要的内部激励-时变啮合刚度发生变化。然而，目前的研究不能精确的采用解析模型来计算齿根圆与基圆之间的势能，将导致时变啮合刚度的计算误差。针对这个问题，本文基于势能法，提出了一个精确考虑齿根圆与基圆之间的势能的计算时变啮合刚度的解析模型，根据齿根圆角圆心所在位置，研究了不同参数条件下轮齿时变啮合刚度的算法，与有限元仿真结果的对比表明：本文提出的修正算法能更为精确地计算轮齿的时变啮合刚度，可减小解析法计算刚度的误差，为齿轮振动分析提供了一个新的途径。
Abstract：Variation of contact teeth pairs’ number and contact positions causes the time varying meshing stiffness, as the most important internal excitation of gear dynamic systems, to change.However, most of the current studies can’t adopt a precise analytical model to calculate potential energy between a tooth root circle and a gear base circle, and lead to calculation errors of the time-varying meshing stiffness.Here, aiming at this problem, based on the potential energy method, an analytical model to calculate the time-varying mesh stiffness and accurately consider potential energy between a gear base circle and a tooth root circle was proposed.According to the location of tooth root fillet’s center, the algorithm to calculate the time-varying meshing stiffness under conditions of different parameters was studied.Comparing the calculation results with those of finite element simulation, it was shown that the modified algorithm proposed here can more precisely calculate the time-varying meshing stiffness of gear teeth; this method provides a new way for gear system vibration analysis.