齿轮系统的共存周期运动及其吸引域  

Study on Coexisting Periodic Solutions and Their Global Stability of a Nonlinear Gear System

作　　者：王娟[1] 李同杰[1,2] 李政民卿 

机构地区：[1]安徽科技学院机电与车辆工程学院,安徽凤阳233100 [2]南京航空航天大学机电学院,南京210016

出　　处：《机械设计与研究》2013年第4期48-50,共3页Machine Design And Research

基　　金：国家自然科学基金资助项目(51105194);安徽省高校优秀青年人才基金资助项目(2012SQL139);安徽科技学院自然科学一般资助项目(ZRC2013382)

摘　　要：基于经典的间隙单齿轮副非线性动力学模型,采用伪不动点追踪法研究了齿轮系统共存的周期解,采用胞映射方法研究了各共存周期解的全局稳定性。结果发现,在考查参数下,齿轮系统存在3种不同形怎的周期运动,即分别是周期1解(0.634 6,0.062 5)、周期2解(-0.141 4,-0.150 5)和周期4解(-0.2053,-0.151 8)。其中,周期1解不具备长期运动稳定性;周期2解的吸引域面积较大且连续,具有较高的局部稳定性;周期4解的吸引域不连续,运动的初值稳定性较差。The coexisting periodic solutions and their global stability of a nonlinear gear system are studied in this paper.Based on the classical nonlinear gear dynamic model,quasi-fixed-point tracing method is used to study the coexisting periodic solutions and cell-to-cell mapping method is used to study the global attracting domain of every coexisting periodic solution.The results reveal that the gear system has 3 coexisting periodic solutions,comong which which period-1 solution（0.634 6,0.062 5） doesn’t have long-term moment stability,period-2 solution（-0.141 4,-0.150 5） has a good local stability,and period-4 solution（-0.205 3,-0.151 8） has a poor local stability.

关 键 词：齿轮非线性动力学模型 伪不动点追踪法 胞映射方法 系统共存周期解 全局稳定性 

分 类 号：TH132.425[机械工程—机械制造及自动化]