质量-弹簧-带摩擦自激振动系统的分岔特性及其控制研究  

Bifurcation characteristics and control of a mass-spring-belt friction self-excited vibration system

作　　者：李小彭[1] 孙德华[1] 岳冰[1] 王丹[1] 闻邦椿[1] 

机构地区：[1]东北大学机械工程与自动化学院,沈阳110819

出　　处：《振动与冲击》2015年第15期28-32,44,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(51275079);中央高校基本业务费专项科研基金(N110403009);新世纪优秀人才支持计划(NCET-10-0301)资助项目

摘　　要：为了深入研究摩擦自激振动系统的非光滑动力学机理,建立了含有Stribeck摩擦模型的具有代表性的质量-弹簧-带摩擦自激振动系统非线性动力学模型。利用数值仿真方法分析了自激振动系统在不同参数下的分岔特性,仿真结果表明:进给速度、阻尼系数和动静摩擦系数比均是影响系统运动状态的主要因素;进给速度较低时系统进行准周期振动,当进给速度达到0.4944时,系统开始出现超临界Hopf分岔现象;阻尼系数和动静摩擦系数比变化时系统有与进给速度变化时类似的特性。针对系统中存在的分岔现象,提出了Washout滤波器方法对其进行分岔控制。对比引入Washout滤波器前后系统的相图,得到Washout滤波器能使受控系统的自激振动振幅明显减小,拓扑结构得到明显改善,这间接的表明了在原系统中加入Washout滤波器设计的非线性控制器对摩擦系统进行分岔控制是一种比较有效的方法。In order to deeply study the non-smooth dynamic mechanism of a friction self-excited vibration system,a nonlinear dynamic model for a typical mass-spring-belt friction self-excited vibration system containing a Stribeck friction model was established. Secondly,the bifurcation characteristics of the system under different parameters were analyzed by using the numerical simulation method. The results showed that feed speed,damping coefficient and ratio of dynamicstatic friction coefficients are the main factors affecting the system motion state; quasi-period vibration happens when the feed speed is lower and the supercritical Hopf bifurcation appears when the feed speed is 0. 4944; the system＇s characteristics with variation of damping coefficient and ratio of dynamic-static friction coefficients are similar to those with variation of feed speed. Thirdly,Washout filter method was used to control bifurcation phenomena existing in the system.By comparing the phase diagrams of the system behore and after introducing Washout filter,the results showed that the amplitude of the controlled system is reduced and its topologic structure is improved obviously after introducing Washout filter,so adding Washout filter into the system is a more effective method for bifurcation control of a mass-spring-belt friction self-excited vibration system with nonlinear controllers.

关 键 词：自激振动 摩擦模型 Washout滤波器 分岔控制 

分 类 号：TH113.1[机械工程—机械设计及理论]