• CN：11-2187/TH
  • ISSN：0577-6686
机械工程学报

›› 2011, Vol. 47 ›› Issue (21): 76-83.

• 论文 • 上一篇    下一篇

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行星齿轮系扭转非线性振动建模与运动分岔特性研究

李同杰;朱如鹏;鲍和云;项昌乐;刘辉   

  1. 南京航空航天大学机电学院;安徽科技学院工学院;北京理工大学机械与车辆学院
  • 发布日期:2011-11-05

Nonlinear Torsional Vibration Modeling and Bifurcation Characteristic Study of a Planetary Gear Train

LI Tongjie;ZHU Rupeng;BAO Heyun;XIANG Changle;LIU Hui   

  1. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics College of Engineering, Anhui Science & Technology University School of Mechanical and Vehicular Engineering, Beijing Institute of Technology
  • Published:2011-11-05

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摘要： 建立行星齿轮系扭转非线性振动模型，模型中考虑了行星齿轮系各齿轮副间的时变啮合刚度、齿侧间隙以及综合传递误差等非线性因素；推导出系统的量纲一振动微分方程，采用数值积分方法研究行星齿轮的运动特性随转速以及齿侧间隙等参数的分岔特性，结合Poincaré图形分析，研究转速、啮合阻尼以及齿侧间隙等参数对系统分岔特性的影响。结果发现，随着转速的逐渐增大，系统会通过激变途径进入到混沌运动，而随着齿侧间隙的逐渐增大，系统会通过倍周期分岔途径进入到混沌。阻尼过小将会导致行星齿轮系统的稳态运动由短周期运动向复杂运动转变。齿侧间隙是影响系统运动分岔特性的重要因素，但是影响范围主要限于量纲一齿侧间隙大于3.5的大间隙区段。

关键词: 非线性振动, 分岔, 混沌, 行星齿轮系

Abstract: A nonlinear torsional vibration model of a planetary gear train with errors of transmission, time varying meshing stiffness and gear backlashes is established and dimensionless equations of the system are derived. The solution of the equations is carried out by using the method of numerical integration. By comparing with Poincaré maps and bifurcation diagrams, the bifurcation properties of the system are studied. The influences of some bifurcation parameters such as rotational speed, damping coefficient and gear backlashes on the bifurcation properties of the system are assessed. The study results reveal that the system’s motion state will change into chaos in the way of crisis as speed increase and period doubling bifurcation is the way to chaos as backlashes increase. A smaller damping coefficient will make the system’s periodic motion state change into complex state. Gear backlashes have a strong impact on the system’s bifurcation characteristic when dimensionless the backlashes is bigger than 3.5.

Key words: Bifurcation, Chaos, Nonlinear vibration, Planetary gear set

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