Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears with Large Tooth Number Cracks

Jiao Wei; Xu Kejun; Qin Haiqin

doi:10.16578/j.issn.1004.2539.2023.06.002

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Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears with Large Tooth Number Cracks

Theory·Research | 更新时间：2023-08-14

- Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears with Large Tooth Number Cracks
- Journal of Mechanical Transmission Vol. 47, Issue 6, Pages: 8-15(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.1004.2539.2023.06.002
  CLC：
- Published：15 June 2023，
  
  Received：12 April 2022，
  
  Revised：19 April 2022，
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焦为,徐可君,秦海勤.大齿数裂纹直齿轮时变啮合刚度算法研究[J].机械传动,2023,47(06):8-15.

Jiao Wei,Xu Kejun,Qin Haiqin.Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears with Large Tooth Number Cracks[J].Journal of Mechanical Transmission,2023,47(06):8-15.
焦为,徐可君,秦海勤.大齿数裂纹直齿轮时变啮合刚度算法研究[J].机械传动,2023,47(06):8-15. DOI： 10.16578/j.issn.1004.2539.2023.06.002.

Jiao Wei,Xu Kejun,Qin Haiqin.Research on the Time-varying Meshing Stiffness Algorithm of Spur Gears with Large Tooth Number Cracks[J].Journal of Mechanical Transmission,2023,47(06):8-15. DOI： 10.16578/j.issn.1004.2539.2023.06.002.

摘要

针对齿数大于41的直齿轮，基于切齿几何和齿轮啮合原理，明确渐开线齿廓起点和渐开线与基圆交点的区别，引入过渡曲线参数方程，对基于能量法的时变啮合刚度计算公式进行改进，全面建立了不同裂纹水平的故障轮齿模型。在此基础上，以斜线作为有效齿厚削减限制线，使得裂纹轮齿模型更严格、考虑因素更全面。参考有限元法计算结果，分别讨论了模型修正、裂纹程度、有效齿厚削减限制线具体形式等因素对时变啮合刚度的影响。计算结果表明，未修正轮齿模型会导致大齿数裂纹齿轮时变啮合刚度计算结果偏小；啮合刚度降低程度随裂纹水平的增大而不断增加。根据裂纹水平给出了有效齿厚削减限制线的建模建议：当裂纹水平较低时，有效齿厚削减限制线宜采用直线；当裂纹水平较高时，采用直线会产生较大误差；采用斜线不仅便于计算，同时能够满足计算精度需求，具有更强的实用性。

Abstract

For spur gears with more than 41 teeth

based on the geometry of cutting teeth and the principle of gear meshing

the difference between the starting point of the involute profile and the intersection of the involute and the base circle is clarified

and the transition curve parameter equation is introduced to calculate the time-varying meshing stiffness based on the energy method. The formula has been improved

and the faulty gear tooth models with different crack degrees are comprehensively established. On this basis

the oblique line is used as the effective tooth thickness reduction limit line

which makes the crack tooth model stricter and the considerations more comprehensive. With reference to the calculation results of the finite element method

the effects of model correction

crack extent

and the specific form of the effective tooth thickness reduction limit line on the time-varying meshing stiffness are discussed respectively. The calculation results show that the uncorrected gear tooth model will lead to a small calculation result of the time-varying meshing stiffness of gears with large numbers of teeth; the reduction degree of meshing stiffness increases with the increase of the crack level. According to the degree of cracks

the modeling suggestion for the effective tooth thickness reduction limit line is given: when the crack level is low

the effective tooth thickness reduction limit line should be a straight line; when the crack level is high

using a straight line will cause significant errors. Using a diagonal line is not only convenient for calculation

but also can meet the requirements of calculation accuracy and has stronger practicability.

关键词

大齿数齿根裂纹不同裂纹程度有效齿厚削减限制线时变啮合刚度

Keywords

Large numbers of teethTooth root crackDifferent degrees of cracksEffective tooth thickness reduction limit lineTime-varying meshing stiffness

references

程礼，李思路，郭立，等.某型发动机减速器齿轮毂裂纹故障研究［J］.噪声与振动控制，2017，37（2）：158-162.

CHENG Li，LI Silu，GUO Li，et al.Research on crack failure of gear hub of a certain type of engine reducer［J］.Noise and Vibration Control，2017，37（2）：158-162.

MENG Z，SHI G，WANG F.Vibration response and fault characteristics analysis of gear based on time-varying mesh stiffness［J］.Mechanism and Machine Theory，2020，148：103786.

JIANG H，LIU F.Mesh stiffness modelling and dynamic simulation of helical gears with tooth crack propagation［J］.Meccanica，2020，55（6）：1215-1236.

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 calculation method of meshing stiffness of spur bevel gears［J］.Journal of Mechanical Transmission，2021，45（9）：62-67.

CHEN Z，SHAO Y.Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth［J］.Engineering Failure Analysis，2011，18（8）：2149-2164.

VERMA J G，KUMAR S，KANKAR P K.Crack growth modeling in spur gear tooth and its effect on mesh stiffness using extended finite element method［J］.Engineering Failure Analysis，2018，94：109-120.

冯娜娜，吴海淼.齿轮故障对直齿轮副时变啮合刚度的影响研究［J］.机械传动，2021，45（1）：99-103.

FENG Na'na，WU Haimiao.Research on the influence of gear fault on the time-varying mesh stiffness of spur gear pair［J］.Journal of Mechanical Transmission，2021，45（1）：99-103.

孙光耀，穆塔里夫·阿赫迈德，王鹏程.斜齿轮裂纹应力强度因子与J积分的计算分析［J］.机械传动，2020，44（10）：74-79.

SUN Guangyao，MUTARIF Ahmed，WANG Pengcheng.Calculation and analysis of stress intensity factor and J integral for helical gear cracks［J］.Journal of Mechanical Transmission，2020，44（10）：74-79.

王金文，马夏悦，刘子豪，等.随机风载下含裂纹故障风机增速箱动力学研究［J］.机械传动，2022，46（1）：33-41.

WANG Jinwen，MA Xiayue，LIU Zihao，et al.Dynamics of the fan speed-increasing box with cracks under random wind load［J］.Journal of Mechanical Transmission，2022，46（1）：33-41.

NING J，CHEN Z，WANG Y，et al.Vibration feature of spur gear transmission with non-uniform depth distribution of tooth root crack along tooth width［J］.Engineering Failure Analysis，2021，129：105713.

万志国，贺王鹏，廖楠楠，等.齿根裂纹与齿面剥落故障的振动响应机理研究［J］.西安电子科技大学学报，2021，48（6）：131-137.

WAN Zhiguo，HE Wangpeng，LIAO Nannan，et al.Study on vibration response mechanism of tooth root crack and tooth surface spalling failure［J］.Journal of Xidian University，2021，48（6）：131-137.

谢福起，巫世晶，李小勇，等.含齿根裂纹风电行星齿轮传动系统动态特性研究［J］.计算机集成制造系统，2022，28（8）：2343-2352.

XIE Fuqi，WU Shijing，LI Xiaoyong，et al.Research on dynamic characteristics of wind power planetary gear transmission system with root cracks［J］.Computer Integrated Manufacturing Systems，2022，28（8）：2343-2352.

刘启坤，吴胜利，李智，等.圆柱直齿轮齿根裂纹扩展路径仿真及其影响因素分析［J］.机械传动，2021，45（10）：29-35.

LIU Qikun，WU Shengli，LI Zhi，et al.Simulation of spur gear tooth root crack propagation path and analysis of its influencing factors［J］.Journal of Mechanical Transmission，2021，45（10）：29-35.

赖俊杰，王衍学，蒋超阳.直齿轮轮齿双侧裂纹对其刚度影响的研究［J］.机械传动，2021，45（4）：20-28.

LAI Junjie，WANG Yanxue，JIANG Chaoyang.Study on the effect of double-sided cracks on spur gear teeth on its stiffness［J］.Journal of Mechanical Transmission，2021，45（4）：20-28.

ZHANG C，DONG H，WANG D，et al.A new effective mesh stiffness calculation method with accurate contact deformation model for spur and helical gear pairs［J］.Mechanism and Machine Theory，2022，171：104762.

YANG L，WANG L，YU W，et al.Investigation of tooth crack opening state on time varying meshing stiffness and dynamic response of spur gear pair［J］.Engineering Failure Analysis，2021，121：105181.

ZHAO J，HOU L，LI Z，et al.Prediction of tribological and dynamical behaviors of spur gear pair considering tooth root crack［J］.Engineering Failure Analysis，2022，135：106145.

徐克根.渐开线齿轮齿根过渡曲线计算及在UG中精确建立齿轮三维模型［J］.装备制造技术，2019（11）：168-171.

XU Kegen.Calculation of tooth root transition curve of involute gear and accurate establishment of 3D model of gear in UG［J］.Equipment Manufacturing Technology，2019（11）：168-171.

田培棠.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，2012：95-110.

TIAN Peitang.Geometric calculation principle and practical algorithm of cylindrical gears［M］.Beijing：National Defense Industry Press，2012：95-110.

ZOUARI S，MAATAR M，FAKHFAKH T，et al.Following spur gear crack propagation in the tooth foot by finite element method［J］.Journal of Failure Analysis and Prevention，2010，10（6）：531-539.

吴序堂.齿轮啮合原理［M］.北京：机械工业出版社，1982：15-25.

WU Xutang.Principle of gear meshing［M］.Beijing：Machinery Industry Press，1982：15-25.

MA H，LI Z，FENG M，et al.Time-varying mesh stiffness calculation of spur gears with spalling defect［J］.Engineering Failure Analysis，2016，66：166-176.

MOHAMMED O D，RANTATALO M，AIDANPAAI J O.Improving mesh stiffness calculation of cracked gears for the purpose of vibration-based fault analysis［J］.Engineering Failure Analysis，2013，34：235-251.

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.

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