质量-弹簧-带摩擦自激振动系统的分岔特性及其控制研究

李小彭,孙德华,岳冰,王丹,闻邦椿

振动与冲击 ›› 2015, Vol. 34 ›› Issue (15) : 28-32.

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (15) : 28-32.
论文

质量-弹簧-带摩擦自激振动系统的分岔特性及其控制研究

  • 李小彭,孙德华,岳冰,王丹,闻邦椿
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Study on Bifurcation Characteristics and Control of the Mass-Spring-Belt Friction Self-Excited Vibration System

  • LI Xiao-peng,  SUN De-hua,  YUE Bing,  WANG Dan,  WEN Bang-chun
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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。

Abstract

In order to deeply study the non-smooth dynamic mechanism of self-excited vibration, the friction self-excited vibration system model containing the Stribeck friction model is established, which is a nonlinear dynamical mass-spring-belt model. Secondly, the bifurcation characteristics of the system under different parameters are analyzed by using numerical simulation method. The results show that feed speed, damping coefficient and ratio of dynamic-static friction coefficient are the main factors affecting the system motion state. Quasi-period fluctuation happened in low feed speed region and the supercritical Hopf bifurcation appeared at the system when the feed speed is 0.4944. The system appeared to be the similar rules with different damping coefficient and ratio of dynamic-static friction coefficient. Thirdly, the Washout filter method is designed to control the bifurcation phenomenon existed in the system. By contrast the phase diagrams pre and post, results show that the amplitude of controlled system is reduced and the topology is improved obviously after introducing the Washout filter. All demonstrate adding Washout filter into the system to control the bifurcation phenomenon is a more effective method.
 

关键词

自激振动 / 摩擦模型 / Washout滤波器 / 分岔控制

Key words

self-excited vibration
/ friction model / washout filter / bifurcation control

引用本文

导出引用
李小彭,孙德华,岳冰,王丹,闻邦椿. 质量-弹簧-带摩擦自激振动系统的分岔特性及其控制研究[J]. 振动与冲击, 2015, 34(15): 28-32
LI Xiao-peng, SUN De-hua, YUE Bing, WANG Dan, WEN Bang-chun. Study on Bifurcation Characteristics and Control of the Mass-Spring-Belt Friction Self-Excited Vibration System[J]. Journal of Vibration and Shock, 2015, 34(15): 28-32

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