非圆齿轮行星轮系非线性动力学特性分析  

Analysis of nonlinear dynamic characteristics of non-circular planetary gear systems

作　　者：董长斌 李龙坤 刘永平[1] DONG Changbin;LI Longkun;LIU Yongping(School of Mechanical and Electrical Engineering,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学机电工程学院,兰州730050

出　　处：《哈尔滨工业大学学报》2024年第8期94-102,共9页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金(52265008);甘肃省青年科学基金(23JRRA751);甘肃省教育厅:高校教师创新基金(2023A-021)。

摘　　要：为解决非圆齿轮行星轮系动力学模型不完善、非线性动力学特性难以获取等问题,提出了一种非圆齿轮行星轮系动力学建模方法,并聚焦于时变参数激励下系统的动态响应机制,对非圆齿轮行星轮系非线性动力学特性进行研究。为精确分析系统非线性振动,对非圆齿轮齿侧间隙函数进行了拟合,在综合考虑齿面摩擦、时变啮合刚度、黏弹性阻尼、静态传递误差的基础上,通过引入相对位移坐标消除非线性方程的变量耦合。在此基础上,建立非圆齿轮行星轮系传动系统的动力学模型,并利用四阶变步长Runge-Kutta数值方法对系统非线性动力学方程组进行求解。获取了分岔图、时域图、相轨迹以及Poincaré映射,得到阻尼、齿面摩擦、时变啮合刚度等控制参数激励下系统的动态响应分布规律。结果表明:随各激励参数取值不同,系统呈现出混沌和周期运动相互过渡状态;合理选取激励参数,可减小系统在混沌与周期运动之间的时间间隔,快速进入稳定运动状态。研究成果可为抑制非圆齿轮行星轮系传动系统非线性振动、预测系统的动力学行为提供理论依据。To solve the problems of imperfect dynamic model and difficulty in obtaining nonlinear dynamic characteristics of non-circular planetary gear systems,a dynamic modeling method of non-circular planetary gear systems is proposed.The focus is on the dynamic response mechanism of the system under time-varying parameter excitation,aiming to study the nonlinear dynamic characteristics of non-circular planetary gear systems.In order to accurately analyze the nonlinear vibration of the system,the backlash function of non-circular gear is fitted.By considering the combined effects of tooth surface friction,time-varying meshing stiffness,viscoelastic damping and static transfer error,the variable coupling of nonlinear equations is eliminated by introducing relative displacement coordinates.On this basis,the dynamic model of non-circular planetary gear systems is established,and the fourth-order variable step Runge-Kutta numerical method is used to solve the nonlinear dynamic equations of the system.Bifurcation diagram,time domain diagram,phase trajectory and Poincarémap are obtained to reveal the distribution pattern of system’s the dynamic response under the influence of control parameters such as damping,tooth surface friction and time-varying meshing stiffness.The results show that with the different values of excitation parameters,the system presents a transition state between chaotic and periodic motion depending on the values of various excitation parameters.By selecting appropriate excitation parameters,the time interval between chaos and periodic motion can be reduced,leading to a quicker transition to a stable motion state.The research results can provide a theoretical basis for suppressing nonlinear vibrations of non-circular planetary gear systems and predicting the dynamic behavior of the system.

关 键 词：非圆齿轮行星轮系 非线性特性 激励参数 分岔 混沌 

分 类 号：TH132.424[机械工程—机械制造及自动化]