含Lugre动摩擦及间隙的振动系统的动力学分析

Dynamic Analysis of the Vibration System with Lugre Dynamic Friction and Clearance

通过对单列圆柱滚子轴承的简化,建立一类含Lugre动摩擦及间隙的两自由度碰撞振动系统动力学模型,分析系统的运动过程,利用数值仿真方法探讨激振频率和间隙变化对系统动力学行为的影响。结果表明,随着激振频率的递增,系统的运动状态由混沌演化为逆周期倍化分岔及Hopf分岔,同时多周期运动也演变为单周期运动;而当频率一定且间隙在一定的范围内变化时,系统的运动在混沌状态和逆周期倍化分岔状态之间变化,动力学行为较为复杂。但若将间隙控制在一定范围内时,随着激振频率的增加,系统的运动周期会越来越少,振动形式变得不再复杂,有关结论揭示了频率和间隙对系统稳定性的影响。

The dynamic model of a 2-DOF impact vibration system with Lugre dynamic friction and clearance is established by simplifying a single row of cylindrical roller bearings.The motion process of the system is analyzed.The influence of the excitation frequency and clearance on the dynamic behavior of the system is analyzed by numerical simulation.The results show that with the increase of the excitation frequency,the motion state of the system evolves from the chaos to the inverse period-doubling bifurcation and the Hopf bifurcation,and multi-cycle motion also evolves into single-cycle motion.When the frequency is constant,and the gap changes within a certain range,the motion of the system changes alternatively between the chaotic motion state and the inverse period-doubling bifurcation state,the dynamic behavior is more complex.However,if the gap is controlled within a certain range,the periodical motion phenomenon of the system will become less and less with the increase of the excitation frequency,and the vibration form will become less complicated.This conclusion reveals the influence of frequency and clearance on system stability.