摩擦碰撞振动系统的周期运动和分岔

Periodic Motion and Bifurcation of a Frictional Impact Vibration System

含间隙和摩擦的机械部件广泛存在于机械和交通等领域.而研究间隙和摩擦对系统动力学的影响可用以优化机械系统;因此建立了含双侧间隙的摩擦碰撞振动系统的动力学模型.采用四阶Runge-Kutta数值方法研究了该摩擦碰撞振动系统的动力学行为,分析了基准参数下该系统的粘滞与纯滑移周期振动特点.讨论了不同参数对粘滞行为和颤碰振动的影响.研究结果表明:在低频下,随着间隙值b的增大,系统发生粘滞的时间会减小,滑移的时间会增加.当摩擦力较大时,系统的纯滑移运动会逐渐消失,而主要存在粘滞振动.周期运动与混沌运动之间的转迁主要通过倍化分岔、逆倍化分岔、Bare-grazing分岔、Hopf分岔、以及Neimark-Sacker分岔来实现.由此可知,间隙值和摩擦对系统的动力学特性影响很大.

Mechanical components with clearance and friction widely exist in the fields of machinery and transportation.Studying the influence of clearance and friction on system dynamics can optimize the mechanical system.Therefore,a dynamic model of the vibro-impact system with bilateral clearances and friction is established.The dynamic behavior of the vibro-impact system with friction is studied by four order Runge-Kutta numerical method.The characteristics of sticking and pure sliding periodic vibration of this system under reference parameters are revealed.The influence of different parameters on sticking behavior and chattering-impact vibration is analyzed.The results show that the viscous time of the system will decrease and the slip time will increase with the enlargement of the gap value under the low frequency.When the friction is great,the pure sliding motion of the system will gradually disappear,and it mainly focuses on sticking vibration.Periodic motion and chaotic motion transit to each other mainly through Double bifurcation,inverse Double bifurcation,Bare-grazing bifurcation,Hopf bifurcation and Neimark-Sacker bifurcation.It can be concluded that the clearance value and friction have a great influence on the dynamic characteristics of the system.