谐波平衡
非线性系统
振动
机械
扭矩
数值延拓
控制理论(社会学)
摄动(天文学)
刚度
数值积分
有限元法
经典力学
物理
振幅
数学
数学分析
工程类
计算机科学
结构工程
声学
光学
控制(管理)
量子力学
人工智能
分叉
热力学
作者
Cheon-Jae Bahk,Robert G. Parker
出处
期刊:Journal of Computational and Nonlinear Dynamics
[ASME International]
日期:2010-10-22
卷期号:6 (2)
被引量:86
摘要
Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. At resonance, the resulting vibration causes tooth separation leading to nonlinear effects such as jump phenomena and subharmonic resonance. This work examines the nonlinear dynamics of planetary gears by numerical and analytical methods over the meaningful mesh frequency ranges. Concise, closed-form approximations for the dynamic response are obtained by perturbation analysis. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. Correlation between the amplitude of response and external torque demonstrates that tooth separation occurs even under large torque. The harmonic balance method with arclength continuation confirms the perturbation solutions. The accuracy of the analytical and harmonic balance solutions is evaluated by parallel finite element and numerical integration simulations.
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