高重合度摆线内齿轮副时变啮合刚度计算与齿间载荷分配研究

doi:10.3901/JME.2018.21.101

机械工程学报 ›› 2018, Vol. 54 ›› Issue (21): 101-112.doi: 10.3901/JME.2018.21.101

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高重合度摆线内齿轮副时变啮合刚度计算与齿间载荷分配研究

贵新成¹, 李立顺¹, 李红勋¹, 詹隽青¹, 薛兴东²

1. 陆军军事交通学院国家应急交通运输装备工程技术研究中心天津 300161;
2. 北京数之行科技有限公司产品研发部北京 100048

收稿日期:2018-06-20 修回日期:2018-08-14 出版日期:2018-11-05 发布日期:2018-11-05
通讯作者: 詹隽青(通信作者),男,1960年出生,博士,教授,博士研究生导师。主要研究方向为军用车辆传动技术和总体设计、特种车辆底盘设计与整车改装。E-mail:zjquing@263.net
作者简介:贵新成,男,1990年出生,博士研究生。主要研究方向为军用车辆设计与试验工程。E-mail:gns2018@126.com;李立顺,男,1971年出生,博士,教授,硕士研究生导师。主要研究方向为特种车辆装备设计与试验。E-mail:lilili58815@sohu.com;李红勋,男,1981年出生,博士研究生,副研究员。主要研究方向为军用特种车辆装备设计与仿真。E-mail:lihongxun2008@163.com

Time-varying Mesh Stiffness Calculation and Load Distribution among Teeth of Cycloid Internal Gear Pair with High Contact Ratio

GUI Xincheng¹, LI Lishun¹, LI Hongxun¹, ZHAN Junqing¹, XUE Xingdong²

1. National Emergency Transportation Equipment Engineering Research Center, Army Military Transportation University, Tianjin 300161;
2. Product Research and Development Department, Beijing Data Expert Technology Inc., Beijing 100048

Received:2018-06-20 Revised:2018-08-14 Online:2018-11-05 Published:2018-11-05

摘要/Abstract

摘要： 高重合度摆线内齿轮副时变啮合刚度计算和齿间载荷分配是其动力学分析和强度设计的基础，由于是多齿啮合，齿间载荷分配非常复杂，属于静不定问题。结合现有文献，考虑了真实的过渡曲线和精确的轮齿建模，采用更为准确的齿面赫兹接触刚度计算方法，基于势能法建立了与摆线齿形相适应的单轮齿对啮合综合刚度模型，针对该齿轮副的传动特点，构建了其变形协调方程，提出了多齿啮合齿间载荷分配模型。为验证所建模型的正确性并提高仿真分析效率，在ABAQUS中利用Python脚本编程进行二次开发，实现了精确化建模、参数化分析和自动化操作，根据齿轮加载接触分析结果和基于有限元法的轮齿对受载啮合刚度计算方法，得到了不同负载转矩作用下单轮齿对、多轮齿对的啮合综合刚度和轮齿啮合力。对比表明，计算结果趋势吻合、数值接近，验证了建模分析的正确性，可为动力学分析和强度计算提供基础。

关键词: 摆线齿轮, 齿间载荷分配, 啮合刚度, 势能法, 有限元法

Abstract: Time-varying meshing stiffness calculation and load distribution among teeth of cycloid internal gear pair with high contact ratio are the foundation of dynamics analysis and strength design. Because of the multi-teeth meshing, the load distribution among teeth is very complex and belongs to the statically indeterminate problem. In line with the existing literatures, considering the real transition curve and the exact tooth modeling, a more accurate method is utilized to calculate tooth surface Hertz contact stiffness, and the single tooth pair meshing synthesizing stiffness model fitting cycloid tooth shape is established by the potential energy method. According to its transmission characteristic, deformation compatibility equations are constructed and the load distribution model among teeth of multi-tooth meshing is proposed. In order to verify the correctness of the above model and improve the efficiency of simulation analysis, Python script programming is employed for secondary development in ABAQUS, which realizes accurate modeling, parametric analysis and automatic operation. On the basis of gear loaded contact analysis resulting and meshing stiffness calculation method of single tooth pair based on finite element method, the changing curves of meshing synthesizing stiffness and tooth meshing force in single-tooth meshing and multi-tooth meshing under different torques are obtained respectively. A comparison of the two methods shows that their results have coincident variation trend and closed numerical values, which verifies the correctness of the modeling and analysis and provides the foundation for dynamic analysis and strength calculation.

Key words: cycloid gear, finite element method, load distribution among teeth, meshing stiffness, potential energy method

中图分类号:

TH132

贵新成, 李立顺, 李红勋, 詹隽青, 薛兴东. 高重合度摆线内齿轮副时变啮合刚度计算与齿间载荷分配研究[J]. 机械工程学报, 2018, 54(21): 101-112.

GUI Xincheng, LI Lishun, LI Hongxun, ZHAN Junqing, XUE Xingdong. Time-varying Mesh Stiffness Calculation and Load Distribution among Teeth of Cycloid Internal Gear Pair with High Contact Ratio[J]. Journal of Mechanical Engineering, 2018, 54(21): 101-112.

参考文献

[1] FIGLIOLINI G,STACHEL H,ANGELES J. On martin disteli's spatial cycloidal gearing[J]. Mechanism and Machine Theory,2013,60(1):73-89.
[2] 贵新成,詹隽青,叶鹏,等. 高重合度内啮合复合摆线齿轮传动设计与分析[J]. 机械工程学报,2017,53(1):55-64. GUI Xincheng,ZHAN Junqing,YE Peng,et al. Design and analysis of internal compound cycloid gear transmission with high contact ratio[J]. Journal of Mechanical Engineering,2017,53(1):55-64.
[3] 李剑锋,王钧效,王寿祐,等. 直齿圆锥齿轮齿向载荷分布及齿间载荷分配[J]. 山东工业大学学报,1996,26(4):445-450. LI Jianfeng,WANG Junxiao,WANG Shouyou,et al. Load distribution along contact lines and among contact pairs of straight bevel gear[J]. Journal of Shandong University of Technology,1996,26(4):445-450.
[4] 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 correction and tooth crack dynamic modeling[J]. Journal of Mechanical Engineering,2013,49(11):153-160.
[5] LIANG Xihui,LIU Zhiliang,PAN Jun,et al. Spur gear tooth pitting propagation assessment using model-based analysis[J]. Chinese Journal of Mechanical Engineering,2017,30(6):1369-1382.
[6] NARESH K R,ANAND P. Mesh stiffness measurement of cracked spur gear by photoelasticity technique[J]. Measurement,2015,73(1):439-452.
[7] MA Hui,PANG Xu,FENG Ranjiao,et al. Improved time-varying mesh stiffness model of cracked spur gears[J]. Engineering Failure Analysis,2015,55(1):271-287.
[8] 李亚鹏. 齿轮时变啮合刚度改进计算方法[J]. 机械传动,2010,34(5):22-26. LI Yapeng. Study on improved algorithm of gear time-varying meshing stiffness[J]. Journal of Mechanical Transmission,2010,34(5):22-26.
[9] 冯松,毛军红,谢友柏. 齿轮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.
[10] LIANG Xihui,ZHANG Hongsheng,LIU Libin,et al. The influence of tooth pitting on the mesh stiffness of a pair of external spur gears[J]. Mechanism and Machine Theory,2016,106(1):1-15.
[11] 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.
[12] WU Siyan,ZUO Mingjian,ANAND P. Simulation of spur gear dynamics and estimation of fault growth[J]. Journal of Sound and Vibration,2008,317(3):608-624.
[13] CHAARIF,FAKHFAKH T,HADDAR M. Analytical modeling of spur gear tooth crack and influence on gearmesh stiffness[J]. European Journal of Mechanics A/Sliod,2009,28(3):461-468.
[14] 马辉,逄旭,宋荣泽,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,2014,35(6):864-866,884. MA Hui,PANG Xu,SONG Rongze,et al. Time-varying mesh stiffness calculation of spur gears based on improved energy method[J]. Journal of Northeastern University,2014,35(6):864-866,884.
[15] CHEN Zaigang,ZHAI Wanming,SHAO Yimin,et al. Analytical model for mesh stiffness calculation of spur gear pair with non-uniformly distributed tooth root crack[J]. Engineering Failure Analysis,2016,66(1):502-514.
[16] NARESH K R,ANAND P. Experimental measurement of spur gear mesh stiffness using digital image correlation technique[J]. Measurement,2017,111(1):93-104.
[17] 唐进元,王志伟,雷敦财. 载荷与齿轮啮合刚度、重合度的关系研究[J]. 机械传动,2014,38(6):1-4. TANG Jinyuan,WANG Zhiwei,LEI Duncai. Study on the relationship between load and gear mesh stiffness,contact ratio[J]. Journal of Mechanical Transmission,2014,38(6):1-4.
[18] 周驰,田程,丁炜琦,等. 基于有限元法的准双曲面齿轮时变啮合特性研究[J]. 机械工程学报,2016,52(15):36-43. ZHOU Chi,TIAN Cheng,DING Weiqi,et al. Analysis of hypoid gear time-varying mesh characteristics based on the finite element method[J]. Journal of Mechanical Engineering,2016,52(15):36-43.
[19] COOLEY C G,LIU Chunguang,DAI Xiang,et al. Gear tooth mesh stiffness:A comparison of calculation approaches[J]. Mechanism and Machine Theory,2016,105(1):540-553.
[20] 刘鹏,赵韩,黄康,等. 基于势能法的微线段齿轮啮合刚度模型研究[J]. 应用力学学报,2015,32(6):1069-1074. LIU Peng,ZHAO Han,HUANG Kang,et al. Research on mesh stiffness model of micro-segments gear based on potential energy method[J]. Chinese Journal of Applied Mechanics,2015,32(6):1069-1074.
[21] CONELL R W. Compliance and stress sensitivity of spur gear teeth[J]. Journal of Mechanical Design,1981,103(2):447-459.
[22] 贵新成,李红勋,李立顺,等. 基于范成法加工摆线内齿轮副的齿根过渡曲线分析[J]. 军事交通学院学报,2017,19(9):91-95. GUI Xincheng,LI Hongxun,LI Lishun,et al. Root fillet curve of internal cycloid gear based on generating method[J]. Journal of Military Transportation University,2017,19(9):91-95.
[23] 王庆. 齿轮系统动态设计[M]. 北京:气象出版社,2014. WANG Qing. Gear system dynamic design[M]. Beijing:China Meteorological Press,2014.
[24] 李润方,王建军. 齿轮系统动力学:振动·冲击·噪声[M]. 北京:科学出版社,1997. LI Runfang,WANG Jianjun. Gear system dynamics:Vibration·impact·noise[M]. Beijing:Science Press,1997.
[25] SAINSOT 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.
[26] LIANG Xihui,ZUO M J,PATEL T H. Evaluating the time-varying mesh stiffness of a planetary gear set using the potential energy method[J]. Journal of Mechanical Engineering Science,2014,228(3):535-547.
[27] 陈鹏飞,秦伟,徐波. 摆线针轮啮合传动的等效接触扭转刚度计算[J]. 机械科学与技术,2014,33(4):506-510. CHEN Pengfei,QIN Wei,XU Bo. Calculation of equivalent contact torsional stiffness for cycloid meshing[J]. Mechanical Science and Technology for Aerospace Engineering,2014,33(4):506-510.
[28] 何小萍,许立新. 新型同轴对转摆线针轮传动的受力分析[J]. 机械研究与应用,2015,28(6):49-51,55. HE Xiaoping,XU Lixin. Force analysis of a new coaxial counter rotating cycloid pin gear transmission[J]. Mechanical Research & Application,2015,28(6):49-51,55.
[29] 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,2013,47(11):23-29. TANG Jinyuan,PU Taiping. Spiral bevel gear meshing stiffness calculations based on the finite element method[J]. Journal of Mechanical Engineering,2013,47(11):23-29.
[30] LIANG Xihui,ZHANG Hongsheng,ZUO M J,et al. Three new models for evaluation of standard involute spur gear mesh stiffness[J]. Mechanical Systems and Signal Processing,2018,101(1):424-434.
[31] 周欣,邓康耀,田中旭,等. 渐开线齿轮传动的扭转刚度研究[J]. 机械传动,2017,41(6):46-51. ZHOU Xin,DENG Kangyao,TIAN Zhongxu,et al. Research of the torsion stiffness of involute gear transmission[J]. Journal of Mechanical Transmission,2017,41(6):46-51.
[32] MA Hui,ZENG Jin,FENG Ranjiao,et al. An improved analytical method for mesh stiffness calculation of spur gears with tip relief[J]. Mechanism and Machine Theory,2016,98(1):64-80.
[33] XIE Chongyang,HUA Lin,LAN Jian,et al. Improved analytical models for mesh stiffness and load sharing ratio of spur gears considering structure coupling effect[J]. Mechanical Systems and Signal Processing,2018,111(1):331-347.

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高重合度摆线内齿轮副时变啮合刚度计算与齿间载荷分配研究

Time-varying Mesh Stiffness Calculation and Load Distribution among Teeth of Cycloid Internal Gear Pair with High Contact Ratio

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