含多状态啮合与时变参量的直齿锥齿轮动态特性  

Dynamic characteristics of spur bevel gear transmission system with multi-state meshing and time varying parameters

作　　者：苟向锋[1] 李谷雨 朱凌云[1] GOU Xiangfeng;LI Guyu;ZHU Lingyun(School of Mechanical Engineering,Tiangong University,Tianjin 300387,China)

机构地区：[1]天津工业大学机械工程学院,天津300387

出　　处：《振动与冲击》2022年第23期86-93,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51365025);天津市自然科学基金项目(18JCYBJC88800)。

摘　　要：为研究直齿锥齿轮传动的动态特性,建立考虑多状态啮合特性的直齿锥齿轮传动系统弯-扭-轴动力学模型。根据锥齿轮啮合原理,用微元法计算系统载荷分配率和时变啮合刚度。以某汽车差速器中直齿锥齿轮参数为例,采用变步长四阶Lunge-Kutta法求解系统非线性动力学方程。定义三种不同Poincaré截面,结合正压力时间历程图、相图、Poincaré映射图、分岔图及最大Lyapunov指数,研究啮合频率与综合传递误差对系统动力学特性的影响。研究结果可为直齿锥齿轮传动系统参数设计及动态特性控制提供理论依据。Here, to study dynamic characteristics of spur bevel gear transmission, a bending-torsional-axial coupled dynamic model for spur bevel gear transmission system considering multi-state meshing characteristics was established. According to the meshing principle of bevel gears, load distribution rate and time-varying meshing stiffness of the system were calculated with the micro element method. Taking parameters of spur bevel gears in a certain automobile differential as an example, nonlinear dynamic equations of the system were numerically solved using the variable step size fourth-order Runge-Kutta method. 3 different Poincaré sections were defined. Positive pressure time-history diagram, phase diagram, Poincaré map diagram, bifurcation diagram and maximum Lyapunov exponent were combined to study effects of meshing frequency and comprehensive transmission error on dynamic characteristics of the system. It was shown that the study results can provide a theoretical basis for parametric design and dynamic characteristics control of spur bevel gear transmission system.

关 键 词：直齿锥齿轮 多状态啮合 时变参量 非线性动力学 微元法 

分 类 号：TH132[机械工程—机械制造及自动化] O322[理学—一般力学与力学基础]