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

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

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

- Impact of radial modification coefficient of bevel gears on load-bearing characteristics of differential
- Journal of Mechanical Transmission Vol. 50, Issue 3, Pages: 38-46(2026)
- 作者机构：
  
  1.郑州航空工业管理学院创新创业中心，郑州 450046
  2.郑州航空工业管理学院机械工程学院，郑州 450046
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2026.03.005
  CLC： TH132
- Received：03 March 2025，
  
  Published：15 March 2026
- 稿件说明：
移动端阅览
席俊杰，暴梦浩，梁兆威，等. 锥齿轮径向变位系数对差速器承载特性的影响［J］. 机械传动，2026，50（3）：38-46.

XI Junjie，BAO Menghao，LIANG Zhaowei，et al. Impact of radial modification coefficient of bevel gears on load-bearing characteristics of differential［J］. Journal of Mechanical Transmission，2026，50（3）：38-46.
席俊杰，暴梦浩，梁兆威，等. 锥齿轮径向变位系数对差速器承载特性的影响［J］. 机械传动，2026，50（3）：38-46. DOI： 10.16578/j.issn.1004.2539.2026.03.005.

XI Junjie，BAO Menghao，LIANG Zhaowei，et al. Impact of radial modification coefficient of bevel gears on load-bearing characteristics of differential［J］. Journal of Mechanical Transmission，2026，50（3）：38-46. DOI： 10.16578/j.issn.1004.2539.2026.03.005.

摘要

目的

国内外学者已针对不同变位系数下齿轮的动态特性开展研究，但关于径向变位系数与载荷双重变量对差速器锥齿轮应力变化规律的影响仍不明确。依托现有研究基础，重点探究不同径向变位系数、不同载荷条件下差速器行星齿轮副的等效应力变化规律，并对差速器锥齿轮进行模态分析。

方法

首先，以径向变位系数为自变量，对行星齿轮及半轴齿轮分别进行径向正变位及径向负变位的构型；其次，以半轴齿轮所受转矩为自变量，对不同径向变位系数的行星齿轮及半轴齿轮模型在边界条件上施加3种转矩；最后，使用非线性接触分析单元进行接触和力学性能分析，求解齿轮应力分布。

结果

结果表明，在锥齿轮啮合时，应力最大位置处于齿轮根部；在不同转矩的加载下，随着行星齿轮的径向变位系数

从0.1增至0.2时，齿根处最大应力减小，啮合线处平均应力增大；当半轴齿轮径向变位系数

从-0.1减小至-0.2时，齿轮齿根处最大应力增大，啮合线处平均应力也增大。对差速器行星齿轮及半轴齿轮进行模态分析的结果显示，随着正、负变位系数的增加，半轴齿轮、行星齿轮的最大固有频率与最大空间位移逐渐增加。

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

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

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.

关键词

Keywords

references

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