三自由度齿轮传动系统的分岔与混沌研究

苟向锋; 陈代林

三自由度齿轮传动系统的分岔与混沌研究

1.
兰州交通大学机电工程学院, 兰州 730070

基金项目:

国家自然科学基金项目(51365025、11172119)资助.

详细信息

作者简介:
苟向锋(1974-),教授,硕士,研究方向为非线性动力学及控制,gouxf@mail.lzjtu.cn

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- 文章访问数: 458
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- 被引次数: 0
出版历程
- 收稿日期: 2012-11-04
- 刊出日期: 2015-06-10

Research on Bifurcation and Chaos of 3-DOF Gear Transmission System

1.
School of Mechanical Engineering Lanzhou Jiaotong University, Lanzhou 730070

摘要

摘要: 为研究齿轮传动系统中齿侧间隙等非线性因素对系统振动特性的影响, 综合考虑齿侧间隙、时变啮合刚度、综合啮合误差和轴承纵向响应, 建立了三自由度单级直齿轮副传动系统的扭转振动非线性动力学模型;采用变步长4-5阶Runge-kutta法, 对系统运动的状态方程进行了数值求解;并构建了系统的Poincaré截面, 得到了系统的分岔图。结合系统最大Lyapunov指数谱、Poincaré映射图及FFT频谱图, 分析了系统在激励频率变化时的动力学特性, 发现系统在不同激励频率下会发生Hopf分岔、鞍结分岔及倍化分岔, 给出了系统的分岔值, 分别得到了系统经Hopf分岔和鞍结分岔通向混沌运动的两种过程。
- 动力学 /
- 非线性系统 /
- Runge-kutta法 /
- 齿轮 /
- Hopf分岔
Abstract: In order to investigate the influence of the backlash and other nonlinear factors to system vibration, a nonlinear dynamic model of a single-stage spur gear pair system with three degree-of-freedom is established in this paper, wherein the backlash, the time-varying stiffness, the torsion motion and the transmission error are consid-ered. The nonlinear three-degree-of-freedom equations are solved by employing variable step-size Runge-kutta methods and the bifurcation diagrams are obtained. The nonlinear dynamic characteristic of the system is discussed for the varying of the exciting frequency, classified based on bifurcation diagrams, top Lyapunov exponent (TLE) diagram, Poincaré maps and FFT spectrum. The Hopf bifurcation, saddle-node bifurcation and doubling bifurcation are found in the different values of the exciting frequency and their bifurcation points are given. There are two routes from periodic motion to chaos motion. The one is from period-4 motion to chaos by Hopf bifurcation, and the other is from period-3 motion and period-3 by saddle-node bifurcation.
- chaos theory /
- degrees of freedom (mechanics) /
- differential equations /
- dynamics /
- errors

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参考文献(17)

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