Analytical algorithm for time-varying meshing stiffness of modified herringbone gear pair

修形人字齿轮副时变啮合刚度的解析算法

School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China

Received: 12 August 2021

Abstract

This paper jointly uses the slicing method and the potential energy method to propose an analytical algorithm that considers the meshing stiffness of the modified herringbone gear pair and its axial force. The calculation results are compared with the finite element and ISO calculation results to verify the accuracy of the analytical algorithm. The algorithm is used to analyze the influence of modification on meshing stiffness of the herringbone gear pair. The calculation results show that the modification length, axial modification and the meshing stiffness of the single pair of herringbone gears and the time-varying meshing stiffness of the herringbone gear pair decrease with the increase of tooth profile modification. The mean value of time-varying meshing stiffness decreases with the increase of tooth profile modification. It decreases first and then tends to be stable with the increase of tooth profile modification length and axial modification. The variance of time-varying meshing stiffness increases first and then decreases with the increase of tooth profile modification of the pinion. It decreases with the increase of tooth profile modification of the herringbone gear, increases first and then decreases and then tends to be stable with the increase of tooth profile modification length. The variance decreases with the increase of axial modification of the pinion. It decreases first and then increases and tends to be stable with the increase of axial modification of the herringbone gear.

摘要

将切片法与势能法相结合, 提出了一种考虑轴向力和修形的人字齿轮副啮合刚度解析算法, 并将计算结果与有限元和ISO计算结果进行比较, 验证该算法的准确性。利用该算法分析修形对人字齿轮副啮合刚度的影响, 计算结果表明: 齿廓修形量、修形长度和齿向修形量的增加, 均使单对轮齿啮合刚度及人字齿轮副时变啮合刚度减小; 时变啮合刚度均值随着齿廓修形量增加而减小, 随着齿廓修形长度和齿向修形量的增加先下降后平稳; 时变啮合刚度方差随着小齿轮齿廓修形量增加先增大后减小, 随着大齿轮齿廓修形量增加而减小, 随着齿廓修形长度增加先增大后减小, 随着小齿轮齿向修形量增加而减小, 随着大齿轮齿向修形量增加先减小后增大。