齿轮系统周期运动稳定性研究.pdf

齿轮系统周期运动稳定性研究 ———郜志英 　沈允文 　董海军等 齿轮系统周期运动稳定性研究 郜志英 　沈允文 　董海军 　刘梦军 西北工业大学 ,西安 ,7 10072 　　摘要 :针对含间隙的强非线性齿轮系统动力学模型 ,用数值方法研究了当系统参数和初始 条件变化时周期运动的稳定性 。基于 Flo quet 分岔理论将预测 - 校正算法用于讨论参数变化 时周期解的稳定性 ,得到精确的分岔点参数值 ;通过胞映射法求得周期吸引子的吸引域 , 引入 稳定性品质因子用以定量分析初始条件变化时周期运动的稳定性 。该研究结果可为非线性动 力学行为的分析和齿轮系统的设计提供参考 。 关键词 :非线性齿轮系统 ;周期运动 ;稳定性 ;数值分析 ( ) 中图分类号 : T H 113 　　　文章编号 :1004 - 132 Ⅹ2005 09 - 0757 - 04 Research on Stabil ity of Periodic Motion of Gear Systems Gao Zhiyin g 　Shen Yunwen 　Do ng Haij un 　Liu Men gj un Nort hwe st er n Polyt echnical U niver sit y , Xi ’an , 7 10072 Abstract :For t he dynamic mo del of st rongly nonlinear gear sy st em s wit h backla sh , t he st abilit y of p erio dic motion wa s st udied by numerical met ho ds w hen t he sy st em p aramet er s an d t he initial con di tion s were changed . Ba sed on t he Flo quet bif urcation t heory , t he p redict - cor rect met ho d wa s u sed to di scu ss t he st abilit y of p erio dic solution s wit h changing t he p aramet er s , an d t he p aramet er value s of bif urcation point s were obt ained accurat ely . The at t raction do main s of p erio dic at t ractor s are obt ained by u sin g t he cell mappin g met ho d , an d t he st abilit y f actor i s int ro duced to quantificationally analyze t he st abilit y of p erio dic motion wit h changin g t he initial con dition s. Accor ding to t he re search re sult s , t he p aramet er s and t he initial condition s can be p rop erly select ed , an d t he foun dation will be laid for a naly si s of nonlinear dynamic behavior an d de sign of t he gear sy st em s. Key w