Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears Based on an Improved Potential Energy Method

Xu Kejun; Jiao Wei; Qin Haiqin

doi:10.16578/j.issn.1004.2539.2023.02.001

您当前的位置：

首页 >

文章列表页 >

Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears Based on an Improved Potential Energy Method

Theory·Research | 更新时间：2023-02-25

- Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears Based on an Improved Potential Energy Method
- Journal of Mechanical Transmission Vol. 47, Issue 2, Pages: 1-7(2023)
- 作者机构：
  
  海军航空大学航空机械工程与指挥系（青岛校区），山东青岛 266041
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2023.02.001
  CLC：
- Published：15 February 2023，
  
  Received：06 January 2022，
  
  Revised：31 March 2022，
扫描看全文
徐可君,焦为,秦海勤.基于改进势能法的直齿轮时变啮合刚度计算方法研究[J].机械传动,2023,47(02):1-7.

Xu Kejun,Jiao Wei,Qin Haiqin.Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears Based on an Improved Potential Energy Method[J].Journal of Mechanical Transmission,2023,47(02):1-7.
徐可君,焦为,秦海勤.基于改进势能法的直齿轮时变啮合刚度计算方法研究[J].机械传动,2023,47(02):1-7. DOI： 10.16578/j.issn.1004.2539.2023.02.001.

Xu Kejun,Jiao Wei,Qin Haiqin.Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears Based on an Improved Potential Energy Method[J].Journal of Mechanical Transmission,2023,47(02):1-7. DOI： 10.16578/j.issn.1004.2539.2023.02.001.

摘要

以势能法为基础，将轮齿全齿廓分为渐开线部分和过渡曲线部分，提出一种改进的直齿轮时变啮合刚度计算方法。该方法考虑了齿根过渡曲线的参数方程，基于渐开线起始点半径、基圆半径和齿根圆半径的相对大小关系，建立了不同齿数情况下的轮齿模型，对渐开线齿廓部分的积分上限进行了修正，使得轮齿模型更为精确。对不同齿数情况下的轮齿时变啮合刚度进行计算，将改进前后方法的计算结果进行对比。结果表明，由于渐开线齿廓起始点半径和基圆半径不重合导致的计算误差会随着齿数的增加而增大；对于齿数相差较大的轮齿进行时变啮合刚度计算时，应根据齿数大小分情况进行啮合刚度计算；若用统一的轮齿模型进行计算，可能会带来较大的计算误差。参考有限元法计算结果，分析了误差产生的原因，验证了本文中所提方法的有效性。

Abstract

Based on the potential energy method

the full tooth profile of the gear teeth is divided into the involute part and the transition curve part

and an improved calculation method for the time-varying meshing stiffness of spur gears is proposed. Using this method

the parametric equation of the tooth root transition curve is considered

and based on the relative size relationship between the radius of the involute starting point

the radius of the base circle and the radius of the root circle

the tooth model with different numbers of teeth is established. A part of the integral upper limit has been corrected to make the gear tooth model more accurate. The time-varying meshing stiffness of gear teeth under different numbers of teeth is calculated

and the calculation results with this method before and after the improvement are compared. The results show that the calculation error caused by the non-coincidence of the starting point radius and the base circle radius of the involute tooth profile will increase with the increase of the number of teeth; when calculating the time-varying meshing stiffness of the teeth with a large difference in the number of teeth

the meshing stiffness calculation should be carried out according to the size of the teeth. There might be a large calculation error when the uniform gear model is used for calculation. Referring to the calculation results of the finite element method

the causes of errors are analyzed

and the effectiveness of the method proposed is verified.

关键词

改进势能法直齿轮时变啮合刚度不同轮齿模型

Keywords

Improved potential energy methodSpur gearTime-varying meshing stiffnessDifferent gear models

references

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．

TIAN X H.Dynamic simulation for system response of gearbox including localized gear faults［D］.Edmonton：University of Alberta，2004：19-49.

SAINSOT A P，VELEX P，DUVERGER O.Contribution of gear body to tooth deflections-a new bidimensional analytical formula［J］.Journal of Mechanical Design，2004，126（4）：748-752.

CHAARI F，FAKHFAKH T，HADDAR M.Analytical modelling of spur gear tooth crack and influence on gear mesh stiffness［J］.European Journal of Mechanics/A Solids，2008，28（3）：461-468.

万志国，訾艳阳，曹宏瑞，等.时变啮合刚度算法修正与齿根裂纹动力学建模［J］.机械工程学报，2013，49（11）：153-160.

WAN Zhiguo，ZI Yanyang，CAO Hongrui，et al.Time-varying mesh stiffness algorithm modification and root crack dynamic modeling［J］.Journal of Mechanical Engineering，2013，49（11）：153-160.

杨云，李朝阳，李轩.基于能量法的摆线针轮传动啮合刚度理论研究［J］.机械传动，2018，42（9）：7-12.

YANG Yun，LI Chaoyang，LI Xuan.Theoretical research on meshing stiffness of cycloidal pinwheel transmission based on energy method［J］.Journal of Mechanical Transmission，2018，42（9）：7-12.

孙亚林.基于集中参数模型的齿轮系轮齿裂纹故障振动特性研究［D］.广州：华南理工大学，2019：8-26.

SUN Yalin.Research on fault vibration characteristics of gear train tooth cracks based on lumped parameter model［D］.Guangzhou：South China University of Technology，2019：8-26.

张涛，何泽银，殷时蓉，等.考虑时变摩擦的直齿轮副啮合刚度计算及其影响因素分析［J］.机械传动，2019，43（9）：54-59.

ZHANG Tao，HE Zeyin，YIN Shirong，et al.Calculation of meshing stiffness of spur gear pair considering time-varying friction and analysis of its influencing factors［J］.Journal of Mechanical Transmission，2019，43（9）：54-59.

王晓鹏，刘世军，李纪强.基于几何学和势能法的直齿轮副时变啮合刚度精确建模及应用［J］.机械传动，2020，44（3）：91-96.

WANG Xiaopeng，LIU Shijun，LI Jiqiang.Accurate modeling and application of time-varying mesh stiffness of spur gear pair based on geometry and potential energy method［J］.Journal of Mechanical Transmission，2020，44（3）：91-96.

黄金凤，张飞斌，崔玲丽，等.基于全齿廓普遍方程的齿轮时变啮合刚度改进算法［J］.机械制造与自动化，2019，48（1）：40-44.

HUANG Jinfeng，ZHANG Feibin，CUI Lingli，et al.Improved algorithm for time-varying meshing stiffness of gears based on universal equation of full profile［J］.Machine Building and Automation，2019，48（1）：40-44.

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.Analysis of vibration characteristics of cracked faulty gears based on time-varying mesh stiffness［J］.Journal of Mechanical Engineering，2020，56（17）：108-115.

马辉，逄旭，宋溶泽，等.基于改进能量法的直齿轮时变啮合刚度计算［J］.东北大学学报（自然科学版），2014，35（6）：863-866，884.

MA Hui，PANG Xu，SONG Rongze，et al.Calculation of time-varying mesh stiffness of spur gears based on improved energy method［J］.Journal of Northeastern University （Natural Science Edition），2014，35（6）：863-866，884.

CHEN Z G，ZHOU Z W，ZHAI W M，et al.Improved analytical calculation model of spur gear mesh excitations with tooth profile deviations［J］.Mechanism and Machine Theory，2019，149：103838.

陈思宇，谭儒龙，郭晓东.直齿锥齿轮啮合刚度计算方法研究［J］.机械传动，2021，45（9）：62-67.

CHEN Siyu，TAN Rulong，GUO Xiaodong.Research on the calculation method of meshing stiffness of spur bevel gears［J］.Journal of Mechanical Transmission，2021，45（9）：62-67.

刘炀，崔熙，王结鑫.考虑磨损的直齿轮啮合刚度计算与分析［J］.机械传动，2021，45（1）：65-70.

LIU Yang，CUI Xi，WANG Jiexin.Calculation and analysis of meshing stiffness of spur gears considering wear［J］.Journal of Mechanical Transmission，2021，45（1）：65-70.

DAI H，LONG X，CHEN F，et al.An improved analytical model for gear mesh stiffness calculation［J］.Mechanism and Machine Theory，2021，159：104262.

CHEN Z，NING J，WANG K，et al.An improved dynamic model of spur gear transmission considering coupling effect between gear neighboring teeth［J］.Nonlinear Dynamics，2021，106（1）：1-19.

WANG G，LUO Q，ZOU S.Time-varying meshing stiffness calculation of an internal gear pair with small tooth number difference by considering the multi-tooth contact problem［J］.Journal of Mechanical Science and Technology，2021，35（9）：4073-4083.

SUN Z，CHEN S，HU Z，et al.Improved mesh stiffness calculation model of comprehensive modification gears considering actual manufacturing［J］.Mechanism and Machine Theory，2022，167：104470.

田培棠，田凌.圆柱齿轮几何计算原理及实用算法［M］.北京：国防工业出版社，2012：95-97.

TIAN Peitang，TIAN Ling.The geometric calculation principle and practical algorithm of cylindrical gears［M］.Beijing：National Defense Industry Press，2012：95-97.

郭忠，张艳冬.基于APDL的渐开线直齿圆柱齿轮参数化精确建模［J］.机械制造与自动化，2010，40（3）：33-36.

GUO Zhong，ZHANG Yandong.Parametric accurate modeling of involute spur gears based on APDL［J］.Machine Building and Automation，2010，40（3）：33-36.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Numercial Calculation of Time-varying Meshing Stiffness of Spur Gear based on Weber Energy Method

Meshing Stiffness Calculation of Spur Bevel Gears Considering the Tooth Pair Coupling

Study on the Spalling Fault Degradation Mechanism and Dynamic Model of Gear Tooth Surfaces

Study on Vibration Reduction Method by Gear Staggering Phase Tuning

Dynamic Response Analysis of the Cracked Fault Gear System Based on the Finite Element Model

Related Author

Li Bingqian

Liang Juke

Wang Zhiqiang

Xu Hongbin

Xu Taojin

Yang Changhui

Zhang Chu

Li Feifei

Related Institution

School of Mechanical Engineering, Chongqing University of Technology

Key Laboratory of Automobile Part Manufacturing Technology of Ministry of Education,Chongqing University of Technology

School of Mechanical Engineering, Dalian University of Technology

School of Management Science and Engineering, Chongqing Technology and Business University

College of Traffic and Transportation, Chongqing Jiaotong University

⁰