摩擦碰撞振动系统的周期运动和分岔
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摘要
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.
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.
引文
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[16] 罗冠炜,徐岩,谢建华.冲击消振器的概周期碰振运动分析[J].爆炸与冲击,2003,23(4):360-367.
[2] 朱喜锋,罗冠炜.两自由度含间隙弹性碰撞系统的颤碰运动分析[J].振动与冲击,2015,34(15):195-200.
[3] 吕小红,罗冠炜.小型振动冲击式打桩机的非线性动力学分析[J].工程力学,2013,30(11):227-232.
[4] 吕小红.冲击振动系统的粘滞振动及分岔特性研究[D].兰州:兰州交通大学,2016:18-21.
[5] 朱喜锋.含间隙机械系统的动力学特性及参数匹配规律研究[D].兰州:兰州交通大学,2016:25-30.
[6] LUO G W,ZHU X F,SHI Y Q.Dynamics of a two-degree-of freedom periodically-forced system with a rigid stop:diversity and evolution of periodic-impact motions[J].Journal of Sound & Vibration,2015,334(6):338-362.
[7] 罗冠炜,谢建华.冲击振动落砂机的周期运动稳定性与分叉[J].机械工程学报,2003,39(1):74-78.
[8] 赵琳燕,侍玉青,姜春霞.一类存在间隙和摩擦的分段光滑振动系统的动力学特性[J].兰州交通大学学报,2014,33(3):41-45.
[9] 侍玉青,赵琳燕,姜春霞.含摩擦和间隙振动系统的低频动力学特征[J].兰州交通大学学报,2017,36(6):8-12.
[10] LI Y,FENG Z C.Bifurcation and chaos in friction-induced vibration[J].Communications in Nonlinear Science & Numerical Simulation,2004,9(6):633-647.
[11] LUO G W,LV X H,SHI Y Q.Vibro-impact dynamics of a two-degree-of freedom periodically-forced system with a clearance:diversity and parameter matching of periodic-impact motions[J].International Journal of Non-Linear Mechanics,2014,65(4):173-195.
[12] SOUZA S L T D,CALDAS I L.Controlling chaotic orbits in mechanical systems with impacts[J].Chaos Solitons & Fractals,2004,19(1):171-178.
[13] PETERKA F.Bifurcations and transition phenomena in an impact oscillator[J].Chaos,Solitons & Fractals,1996,7(10):1635-1647.
[14] WAGG D J.Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator[J].Chaos Solitons & Fractals,2004,22(3):541-548.
[15] 罗冠炜,褚衍东,苟向锋.一类碰撞振动系统的概周期运动及混沌形成过程[J].机械强度,2005,27(4):445-451.
[16] 罗冠炜,徐岩,谢建华.冲击消振器的概周期碰振运动分析[J].爆炸与冲击,2003,23(4):360-367.