Study on maximum sliding rate of planetary gear train with center distance error and optimization of modification coefficient

LI Chuanxiang; CHEN Dong; WANG Zhaoyang; WANG Xiao; XU Huanping

doi:10.16578/j.issn.1004.2539.2026.03.003

Abstract：[Objective]Aiming at the problems of severe tooth surface wear and gluing failure in the planetary reducers of baling equipment under heavy loads,the maximum sliding rate and its influencing factors in a 3K-I planetary gear train with center distance errors were investigated to enhance transmission performance and prolong service life by optimizing the modification coefficients.[Methods]Firstly,based on the gear meshing principle,the calculation formulas for the maximum sliding rate of the planetary gear train with center distance errors were derived.Secondly,the control variable method was used to analyze the specific influence of the modification coefficient and tooth number ratio on the maximum sliding rate.Thirdly,based on the equal sliding rate principle and combined with constraints such as undercutting and contact ratio,an optimization model using the weighted average method was constructed,aiming to minimize the sum of the sliding rate differences among gear pairs.Finally,nonlinear constrained optimization was solved using the fmincon command in Matlab,and different optimization schemes,such as taking the center distance error as a design variable,were comparatively analyzed.[Results]The results show that the modification coefficient is the dominant factor affecting the maximum sliding rate.The comparative analysis reveals that the scheme treating the center distance error as an optimization design variable is the most reasonable.Within the given error range of[-0.1,0.1]mm,this scheme significantly reduces both the maximum sliding rates and their differences among the gear pairs.Specifically,the sliding rate differences of the three gear pairs are decreased by 19.6%,90.9%,and 96.1%,respectively.This effectively improves the sliding balance of the tooth surfaces and provides a reference for the design of planetary gear trains.