同济大学 机械与能源工程学院， 上海 201804
出版日期:2019-03-28发布日期:2019-03-28通讯作者:奚鹰，男，教授，博士生导师，电话(Tel.)：18017430565；E-mail：yingxi@tongji.edu.cn.作者简介:郑钰馨(1989-)，女，安徽省宿州市人，博士生，现主要从事机械设计和机械系统动力学研究.基金资助:国家自然科学基金（51475331）资助项目Elastodynamics Analysis of Pure Torsional Model of Spur Gear
ZHENG Yuxin,XI Ying,YUAN Lang,BU WanghuiSchool of Mechanical Engineering, Tongji University, Shanghai 201804, China
Online:2019-03-28Published:2019-03-28摘要/Abstract
摘要： 为研究非线性因素对直齿轮纯扭转模型弹性动力学的影响，根据达朗贝尔原理，采用微位移思想，建立4自由度直齿轮纯扭转动力学模型.首先，通过Runge-Kutta法结合时间离散法求解系统在齿轮啮合误差、时变啮合刚度和啮合间隙等非线性因素影响下的时变方程，得到系统振动的响应以及对应频谱图.其次，结合非线性特性分析理论，通过改变系统的啮合刚度、激励频率和齿侧间隙，获得系统动态响应的全局分岔图和最大Lyapunov指数.然后，综合运用时间历程曲线、相空间轨线、Poincáre映射图和功率谱，定量和定性分析系统的周期运动、拟周期运动和混沌运动.最后，考虑非线性因素耦合作用对系统的影响，为齿轮传动系统的非线性特性分析提供一套较为完整的方法.
关键词: 直齿轮, 纯扭转动力学模型, 分岔, 最大Lyapunov指数, Poincáre映射图
Abstract: In order to study the influence of nonlinear factors on the elastodynamics of spur gear’s pure torsional model, a pure torsional dynamic model of four-degree-of-freedom spur gear is established by using the principle of D’Alembert and the method of micro-displacement. Firstly, a time-varying equation set is solved by Runge-Kutta and time-dispersion methods with the consideration of the nonlinear factors such as gear meshing error, time-varying meshing stiffness and meshing gap, and the dynamic response and the corresponding spectrum of the system are obtained. Next, combined with the nonlinear analysis theory, the global bifurcation diagram and the maximum Lyapunov exponent are obtained by changing the meshing stiffness, the excitation frequency and the tooth side clearance of the system. Then, the periodic motion, quasi-periodic motion and chaos of the system are analyzed from the quantitative and qualitative point of view respectively by using the time history plot, phase space trajectory, Poincáre map and power spectrum. Finally, the coupling influence of nonlinear factors on the system are considered, which provides a complete method for the nonlinear characteristic analysis of gear transmission system.
Key words: spur gear, pure torsional dynamic model, bifurcation, maximum Lyapunov exponent, Poincáre map
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