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

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

Structural Design and Parameter Optimization | 更新时间：2026-05-27

- Study on maximum sliding rate of planetary gear train with center distance error and optimization of modification coefficient
- Journal of Mechanical Transmission Vol. 50, Issue 3, Pages: 23-30(2026)
- 作者机构：
  
  辽宁科技大学机械工程与自动化学院，鞍山 114051
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2026.03.003
  CLC： TH111;TH132
- Received：16 October 2024，
  
  Revised：2024-11-13，
  
  Published：15 March 2026
- 稿件说明：
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李传祥，陈东，王朝阳，等. 含中心距误差的行星轮系最大滑动率与变位系数优化的研究［J］. 机械传动，2026，50（3）：23-30.

LI Chuanxiang，CHEN Dong，WANG Zhaoyang，et al. Study on maximum sliding rate of planetary gear train with center distance error and optimization of modification coefficient［J］. Journal of Mechanical Transmission，2026，50（3）：23-30.
李传祥，陈东，王朝阳，等. 含中心距误差的行星轮系最大滑动率与变位系数优化的研究［J］. 机械传动，2026，50（3）：23-30. DOI： 10.16578/j.issn.1004.2539.2026.03.003.

LI Chuanxiang，CHEN Dong，WANG Zhaoyang，et al. Study on maximum sliding rate of planetary gear train with center distance error and optimization of modification coefficient［J］. Journal of Mechanical Transmission，2026，50（3）：23-30. DOI： 10.16578/j.issn.1004.2539.2026.03.003.

摘要

目的

针对打捆装备行星减速器在重载时易发生齿面磨损和胶合失效的问题，研究含中心距误差的3K-Ⅰ型行星轮系最大滑动率及其影响因素，旨在通过优化变位系数提升传动性能与寿命。

方法

首先，基于齿轮啮合原理，推导了含中心距误差的行星轮系最大滑动率计算式；其次，利用控制变量法分析了变位系数和齿数比对最大滑动率的影响规律；再次，基于等滑动率原则，结合根切与重合度等约束条件，构建了以各齿轮对滑动率差值之和最小为目标的优化模型；最后，利用Matlab软件进行非线性约束优化求解，并对比分析了将中心距误差等作为设计变量的不同优化方案。

结果

结果表明，变位系数是影响最大滑动率的主导因素。对比发现，将中心距误差作为优化设计变量的方案最为合理，该方案在给定误差范围内显著降低了各齿轮对间的最大滑动率及其差值，其中3对齿轮副的滑动率差值分别降低了19.6%、90.9%、96.1%，有效改善了齿面的滑动平衡性，为行星轮系设计提供了参考。

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.

关键词

Keywords

references

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