内载荷激励下齿轮系统分岔和混沌特性分析  

Bifurcation and Chaos Analysis of Nonlinear Dynamics in A Spur Gear Pair System with the Internal Loads Incentive

作　　者：刘魁 Liu Kui(Chongqing West EMU of Chongqing Vehicle Section,Chengdu Railway Bureau,Chongqing 401122,China)

机构地区：[1]成都铁路局重庆车辆段重庆西动车所,重庆401122

出　　处：《宁夏大学学报（自然科学版）》2018年第3期212-216,共5页Journal of Ningxia University(Natural Science Edition)

基　　金：甘肃省国际科技合作计划项目(1104WCGA195);甘肃省高校科研基金资助项目(212084)

摘　　要：建立了一种单自由度直齿轮副系统的非线性动力学模型,该模型综合考虑引起齿轮内载荷的时变啮合刚度、齿轮传动误差和啮合冲击等因素.运用五阶自适应Runge-Kutta方法给出了系统随内载荷变化的分岔图及其相对应的最大Lyapunov指数图,并结合相图、Poincare映射图、动载荷和FFT频谱图对系统的动力学特性进行了分析.结果表明,较小的内载荷有利于齿轮保持稳定的运行.另外,通过齿轮的动载荷历程,得到了齿轮的啮合冲击状态与系统参数之间的关系.A nonlinear dynamics model for a spur gear pair system is established where the time varying stiffness, gear the transmission error and meshing impact are considered, which causing the gear internal loads incentive. The dynamic behavior of the gear with variation of internal excitation is investigated by fifth order adaptive Runge Kutta calculating its bifurcation diagram, its maximum Lyapunov exponent, the phase portrait, Poincare section, dynamic load and FFT spectrum. It turns out that the smaller internal loads incentive is conducive to stable operation of the gear. By the dynamic load course of gear, the relationship between the state of gear meshing and system parameters is presented.

关 键 词：非线性动力学 分岔 最大LYAPUNOV指数 动载荷 FFT频谱 

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]