Impact of residual stress on the time-varying meshing stiffness of helical gears and its dynamic analysis

LUO Jiayuan; YAN Bo; GAO Cong

doi:10.16578/j.issn.1004.2539.2025.03.006

您当前的位置：

首页 >

文章列表页 >

Impact of residual stress on the time-varying meshing stiffness of helical gears and its dynamic analysis

Theory·Research | 更新时间：2025-03-20

- Impact of residual stress on the time-varying meshing stiffness of helical gears and its dynamic analysis
- Journal of Mechanical Transmission Vol. 49, Issue 3, Pages: 40-47(2025)
- 作者机构：
  
  1.重庆交通大学机电与车辆工程学院，重庆 400074
  2.重庆长安汽车股份有限公司，重庆 400023
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2025.03.006
  CLC： TH132
- Received：10 November 2023，
  
  Published：15 March 2025
- 稿件说明：
移动端阅览
罗家元，严博，高聪. 残余应力对斜齿轮时变啮合刚度的影响及其动力学分析［J］. 机械传动，2025，49（3）：40-47.

LUO Jiayuan，YAN Bo，GAO Cong. Impact of residual stress on the time-varying meshing stiffness of helical gears and its dynamic analysis［J］. Journal of Mechanical Transmission，2025，49（3）：40-47.
罗家元，严博，高聪. 残余应力对斜齿轮时变啮合刚度的影响及其动力学分析［J］. 机械传动，2025，49（3）：40-47. DOI： 10.16578/j.issn.1004.2539.2025.03.006.

LUO Jiayuan，YAN Bo，GAO Cong. Impact of residual stress on the time-varying meshing stiffness of helical gears and its dynamic analysis［J］. Journal of Mechanical Transmission，2025，49（3）：40-47. DOI： 10.16578/j.issn.1004.2539.2025.03.006.

摘要

目的

淬火热处理作为齿轮重要强化工艺会产生较高的残余应力，进而影响齿轮啮合刚度及动态性能。在分析淬火残余应力分布规律的基础上，揭示残余应力对齿轮啮合动态特性的量化影响。

方法

基于直接热-力耦合法建立齿轮淬火仿真模型并求解淬火残余应力，结合单节点法将该残余应力作为预应力求解斜齿轮副的时变啮合刚度；并以此为基础，利用集中参数法建立斜齿轮副的10自由度动力学模型，使用龙格-库塔法进行数值求解，得到斜齿轮副的振动响应动载荷时域图和频域图。

结果

与不考虑残余应力相比，存在残余应力的单齿弯曲变形在4齿啮合区域变大、在5齿啮合区域变小，接触变形无明显变化，啮合刚度和动载荷的时域峰值变大，啮频处的动载荷频域幅值谱密度增大。

Abstract

Objective

As an important strengthening process for gears

the quenching heat treatment will generate relatively high residual stress

which will further affect the meshing stiffness and dynamic performance of gears. Based on the analysis of the distribution law of quenching residual stress

the quantitative impact of residual stress on the meshing dynamic characteristics of gears was revealed.

Methods

A gear quenching simulation model was established based on the direct thermo-mechanical coupling method to solve the quenching residual stress. Combined with the single node method

this residual stress was regarded as the prestress to solve the time-varying meshing stiffness of the helical gear pair. Based on this

the lumped parameter method was used to establish a 10-degree-of-freedom dynamic model of the helical gear pair. The Runge-Kutta method was used for numerical solution

and the time domain diagram and frequency domain diagram of the dynamic load during the vibration response of the helical gear pair were obtained.

Results

Compared with the situation without considering the residual stress

the bending deformation of a single tooth becomes larger in the four-tooth meshing area and smaller in the five-tooth meshing area. The contact deformation does not change much

and the time domain peak values of meshing stiffness and dynamic load become larger

the dynamic load frequency domain amplitude spectral density at the meshing frequency increases.

关键词

Keywords

references

雷亚国，罗希，刘宗尧，等 . 行星轮系动力学新模型及其故障响应特性研究［J］. 机械工程学报， 2016 ， 52 （ 13 ）： 111 - 122 .

LEI Yaguo ， LUO Xi ， LIU Zongyao ， et al . A new dynamic model of planetary gear sets and research on fault response characteristics ［J］. Journal of Mechanical Engineering ， 2016 ， 52 （ 13 ）： 111 - 122 .

冯松，毛军红，谢友柏 . 齿面磨损对齿轮啮合刚度影响的计算与分析［J］. 机械工程学报， 2015 ， 51 （ 15 ）： 27 - 32 .

FENG Song ， MAO Junhong ， XIE Youbai . Analysis and calculation of gear mesh stiffness with tooth wear ［J］. Journal of Mechanical Engineering ， 2015 ， 51 （ 15 ）： 27 - 32 .

ENDO H ， RANDALL R B ， GOSSELIN C . Differential diagnosis of spall vs. cracks in the gear tooth fillet region：experimental validation ［J］. Mechanical Systems and Signal Processing ， 2009 ， 23 （ 3 ）： 636 - 651 .

YANG D C H ， LIN J Y . Hertzian damping，tooth friction and bending elasticity in gear impact dynamics ［J］. Journal of Mechanisms Transmissions and Automation in Design ， 1987 ， 109 （ 2 ）： 189 - 196 .

唐进元，蒲太平 . 基于有限元法的螺旋锥齿轮啮合刚度计算［J］. 机械工程学报， 2011 ， 47 （ 11 ）： 23 - 29 .

TANG Jinyuan ， PU Taiping . Spiral bevel gear meshing stiffness calculations based on the finite element method ［J］. Journal of Mechanical Engineering ， 2011 ， 47 （ 11 ）： 23 - 29 .

FENG M J ， MA H ， LI Z W ， et al . An improved analytical method for calculating time-varying mesh stiffness of helical gears ［J］. Meccanica ， 2017 ， 53 ： 1131 - 1145 .

廖平，魏静，张爱强，等 . 一种弧齿锥齿轮时变啮合刚度和传动误差半解析计算方法［J］. 机械传动， 2019 ， 43 （ 12 ）： 50 - 56 .

LIAO Ping ， WEI Jing ， ZHANG Aiqiang ， et al . A semi-analytical calculation method for time-varying meshing stiffness and transmission error of spiral bevel gear ［J］. Journal of Mechanical Transmission ， 2019 ， 43 （ 12 ）： 50 - 56 .

孟宗，石桂霞，王福林，等 . 基于时变啮合刚度的裂纹故障齿轮振动特征分析［J］. 机械工程学报， 2020 ， 56 （ 17 ）： 108 - 115 .

MENG Zong ， SHI Guixia ， WANG Fulin ， et al . Vibration characteristic analysis of cracked gear based on time-varying meshing stiffness ［J］. Journal of Mechanical Engineering ， 2020 ， 56 （ 17 ）： 108 - 115 .

陈勇，李金锴，臧立彬，等 . 疲劳点蚀斜齿轮动力学仿真预测与故障识别试验研究［J］. 机械工程学报， 2021 ， 57 （ 9 ）： 61 - 70 .

CHEN Yong ， LI Jinkai ， ZANG Libin ， et al . Dynamic simulation and experimental identification for fatigue pitting helical gear fault ［J］. Journal of Mechanical Engineering ， 2021 ， 57 （ 9 ）： 61 - 70 .

陈庆红，陈丙三 . 齿根裂纹下的行星齿轮系统动力学特性研究［J］. 机床与液压， 2023 ， 51 （ 16 ）： 81 - 89 .

CHEN Qinghong ， CHEN Bingsan . Study on dynamic characteristics of planetary gear system with root crack ［J］. Machine Tool & Hydraulics ， 2023 ， 51 （ 16 ）： 81 - 89 .

王刚强 . 修形斜齿轮啮合刚度解析模型与系统振动特性研究［D］. 重庆：重庆大学， 2018 ： 7 - 16 .

WANG Gangqiang . An analytical model for the meshing stiffness of helical gears with modification and system vibration characteristics ［D］. Chongqing ： Chongqing University ， 2018 ： 7 - 16 .

DOANE D V ， KIRKALDY J S . Hardenability concepts with applications to steel ［C］// Proceedings of a Symposium Held at the Sheraton-Chicago Hotel ， October 24 - 26 ， 1977 . New York ： Metallurgical Society of AIME ， 1978 ： 78 - 83 .

ŞI˙MŞI˙R C ， GÜR C H . A mathematical framework for simulation of thermal processing of materials：application to steel quenching ［J］. Turkish Journal of Engineering & Environmental Sciences ， 2008 ， 32 （ 2 ）： 85 - 100 .

TOTTEN G ， HOWES M ， INOUE T . Handbook of residual stress and deformation of steel ［M］. Materials Park，OH ： ASM International ， 2002 ： 248 - 312 .

杜国君，杨志强，刘小蛮 . 渗碳圆柱齿轮淬火过程的数值模拟［J］. 工程力学， 2013 ， 30 （ 1 ）： 407 - 412 .

DU Guojun ， YANG Zhiqiang ， LIU Xiaoman . Quenching process simulation of carburized cylindrical gear ［J］. Engineering Mechanics ， 2013 ， 30 （ 1 ）： 407 - 412 .

徐港辉 . 斜齿轮传动系统中齿轮-轴承耦合动力学建模与振动特性分析［D］. 上海：上海大学， 2020 ： 69 - 90 .

XU Ganghui . Vibration modelling and analysis of helical gear transmission system based on gear-bearing coupling dynamics ［D］. Shanghai ： Shanghai University ， 2020 ： 69 - 90 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Discrete element simulation and test study on the barrel finishing process of aviation gears

Finite element analysis of effect of double shot peening on residual stress of 18CrNiMo7-6 gear steel

Low fluctuation stiffness design method for vibration reduction of helical gears

Robust Optimization Design for Combined Tooth Surface Modification of Helical Gear Pair Considering Load Variation Domain

Study on the Influence of Modified Design on the Dynamic Characteristics of the Helical Gear System

Related Author

ZHAO Zemin

LI Guihua

ZHU Guangzhao

TANG Jinyuan

LI Xin

LIU Qingsong

WANG Zhen

SUN Hao

Related Institution

AECC Harbin Dongan Engine Co., Ltd.

State Key Laboratory of Precision Manufacturing for Extreme Service Performance, Central South University

School of Aerospace Engineering, Zhengzhou University of Aeronautics

Henan Aerospace Hydraulic Pneumatic Technology Co., Ltd.

AECC Hunan Aviation Powerplant Research Institute

⁰