含侧隙非线性齿轮传动系统的分岔与混沌分析  

BIFURCATION AND CHAOS IN A NONLINEAR DYNAMIC MODEL OF SPUR GEAR WITH BACKLASH

作　　者：王晓笋[1] 巫世晶[1] 周旭辉 李群力[1] 

机构地区：[1]武汉大学动力与机械学院,武汉430072 [2]中船重工集团第719所,武汉430064

出　　处：《振动与冲击》2008年第1期53-56,共4页Journal of Vibration and Shock

基　　金：湖北省流体机械与动力工程装备技术重点实验基金项目(2007208010011);武汉大学博士点基金(502-265145)

摘　　要：建立了包含齿侧间隙的齿轮传动系统非线性动力学模型,引入相对啮合位移将模型降为单自由度系统,并对模型进行无量纲化处理。计算了系统随外载荷和齿侧间隙变化的分岔图与对应的最大李雅谱诺夫指数图,分析了系统动力学特性的变化情况,并计算了周期状态和混沌状态下的相空间轨线、Poincare截面和关联维数,以不同的定性与定量分析方法对系统进行了细致地研究。A nonlinear dynamic model for gear trains including backlash is built.It is reduced to a system with a single degree of freedom by introducing the relative gear mesh displacement and its dimensionless equation of motion is given.The dynamic behavior of the gear train with variation of external excitation and backlash is investigated by calculating its bifurcation diagram and its maximum lyapunov exponent.The phase portrait,the Poincare section and the correlation dimension are computed under periodic and chaotic states.The nonlinear model is analyzed deliberatedly with different qualitative and quantitative methods.

关 键 词：齿轮传动系统 齿侧间隙 外载荷 最大李雅谱诺夫指数 分岔图 关联维数 POINCARE截面 

分 类 号：TH113[机械工程—机械设计及理论] O322[理学—一般力学与力学基础]