• CN:11-2187/TH
  • ISSN:0577-6686

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

• 机械动力学 • 上一篇    下一篇

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. 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. 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: 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

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