Impact of radial modification coefficient of bevel gears on load-bearing characteristics of differential

XI Junjie; BAO Menghao; LIANG Zhaowei; LI Kaixuan; ZENG Guang; ZHANG Yishuai; LIU Yuanpeng

doi:10.16578/j.issn.1004.2539.2026.03.005

Abstract：[Objective]Scholars at home and abroad have conducted research on the dynamic characteristics of gears under different modification coefficients.However,the influence of the dual variables of radial modification coefficient and load on the stress variation law of differential bevel gears remains unclear.Based on the existing research foundation,the variation law of equivalent stress of differential planetary gear pairs under different radial modification coefficients and different load conditions was mainly explored,and the modal analysis of differential bevel gears was also carried out.[Methods]Firstly,with the radial modification coefficient as the independent variable,separate configurations of positive and negative radial modifications were created for the planetary gear and side gear.Secondly,taking the torque applied to the side gear as the independent variable,three types of torques were imposed on the boundary conditions of the planetary gear and side gear models with different radial modification coefficients.Finally,non-linear contact analysis elements were employed to conduct contact and mechanical performance analyses and solve for the stress distribution of the gears.[Results]The results indicate that the maximum stress position of the bevel gears during meshing occurs at the gear roots.Under different torque loadings,as the radial modification coefficient x1 of the planetary gear increases from 0.1 to 0.2,the maximum stress at the tooth root decreases,while the average stress along the meshing line increases.When the radial modification coefficient x2 of the side gear decreases from-0.1 to-0.2,the maximum stress at the tooth root of the gear increases,and so does the average stress along the meshing line.The modal analysis results of the planetary gear and side gear in the differential show that as the positive and negative modification coefficients increase,the maximum natural frequency and maximum spatial displacement of both the side gear and planetary gear gradually increase.