椭圆齿轮传动系统非线性动态特性分析  

Analysis of nonlinear dynamic characteristic of elliptic gear transmission system

作　　者：董长斌 刘永平[1] 魏永峭 邓海青 许杰 DONG Chang-bin;LIU Yong-ping;WEI Yong-qiao;DENG Hai-qing;Xu Jie(School of Mechanical&Electronical 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：《吉林大学学报（工学版）》2020年第2期483-493,共11页Journal of Jilin University:Engineering and Technology Edition

基　　金：国家自然科学基金项目(51765032);兰州市科技局项目(2017-4-104);甘肃省自然科学基金项目(18JR3RA140).

摘　　要：为获得椭圆齿轮副工作时的振动规律,以实现其稳定、高效传动,在分析椭圆齿轮固有特性的基础上对椭圆齿轮非线性动力学特性进行了研究。以齿轮动力学理论为基础,建立考虑时变啮合刚度、齿侧间隙、静态传递误差、粘弹性阻尼的椭圆齿轮非线性动力学模型,利用四阶变步长Runge-Kutta数值方法对椭圆齿轮传动系统非线性动力学方程进行求解,绘制了系统的位移响应,相轨迹以及Poincaré映射,得到激励频率、阻尼比、时变啮合刚度、以及内部激励4个控制参数对传动系统动态响应的影响。椭圆齿轮副动力学模型的建立、求解和参数影响分析可以为后续的动态设计、不同参数下的振动响应趋势预测以及降噪提供一定的理论依据。In order to obtain the vibration law of elliptic gear pair and realize its stable and efficient transmission,the nonlinear dynamic characteristics of elliptic gear were studied based on the analysis of the inherent characteristics of elliptic gear. Based on the theory of gear dynamics,a nonlinear dynamic model of elliptic gear with time-varying meshing stiffness,backlash,static transmission error and viscoelastic damping is established. The nonlinear dynamic equation of elliptic gear transmission system is solved by the fourth-order variable step Runge-Kutta numerical method, and the displacement response, phase trajectory and Poincaré mapping of the system are plotted. The effects of excitation frequency,damping ratio,time-varying mesh stiffness,and internal excitation parameters on the dynamic response of the transmission system are obtained. The establishment,solution and parameter analysis of dynamic model of elliptic gear pair can provide a theoretical basis for subsequent dynamic design,vibration response trend prediction and noise reduction under different parameters.

关 键 词：机械制造自动化 椭圆齿轮 动态特性 非线性响应 

分 类 号：TH132.424[机械工程—机械制造及自动化]