摩擦自激振动系统的非线性动力学特征与分岔控制研究
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摘要
摩擦自激振动现象广泛存在于工程领域和日常生活中,由其引起的机械部件的磨损、表面的破坏、疲劳破坏和产生噪声,对工业生产和人们的生活环境造成了不小的影响,越来越引起人们的重视。目前摩擦自激振动等滞后非光滑动力学机理还未被深入认识,关于摩擦自激振动的理论研究缺乏系统性,难以总结参数影响的规律,工程实际情况中常见的参数非定常性、多自由度内共振等影响因素往往被忽略。另外,针对摩擦自激振动的非线性主动控制策略研究还刚刚开始。本文以机械系统中的摩擦自激振动为研究对象,对摩擦自激振动系统的非线性动力学特性和分岔控制进行了深入细致的研究,主要工作及创造性成果如下:
通过对机床摩擦颤振、钻杆颤振、汽车驱动系统颤振和制动系统啸叫等摩擦自激振动系统的结构特性研究,建立了一类具有代表性的双质体—传输带摩擦自激系统动力学模型。为深入探讨摩擦自激振动的非线性动力学机理及摩擦自激振动的分岔控制等研究奠定了基础。
利用李亚普诺夫理论对摩擦自激振动系统的稳定性进行分析,求出系统运动的平衡点,对平衡点稳定性进行判断,确定系统的临界失稳速度。利用平均法求得摩擦自激振动系统的近似解析定常解。分析可知随着传输带速度减小,系统静平衡状态失稳,出现纯滑动和粘滑形式的摩擦自激振动。分析系统参数变化与系统振动的关系,发现正压力比值的变化对自激振动有较大影响。
考虑了内共振因素对摩擦自激振动的影响,利用数值方法分析非内共振、1:2内共振和1:3内共振三种情况下,摩擦自激振动系统的非线性动力学特性。设计了摩擦自激振动实验平台,并进行实验研究。结果发现内共振状态对摩擦自激系统的非线性动力学特性有重要影响。
针对摩擦自激振动的非线性特点,提出Washout滤波器方法对摩擦自激振动进行分岔控制。控制在临近分岔点处引入,通过Washout滤波器方法确定非线性控制器的线性增益,应用规范型直接法计算其非线性增益,将系统亚临界Hopf分岔控制为超临界Hopf分岔,使受控系统的自激振动幅值大大降低。理论分析和数值仿真表明该控制方法的有效性。
研究开发了基于虚拟仪器技术的振动信号采集分析系统,实现了变步长随机共振和经验模式分解算法,增强了提取微弱振动信号特征和捕捉非稳定信号的能力,弥补了传统信号分析系统的不足。
Self-excited vibrations induced by friction widely exist in fields of engineering and dailylife. Usually, the unwanted self-excited vibrations cause an early wear of the contacting parts of machines. It seems that up to now not all the possible nonlinear phenomena have been properly understood. Especially such conditions as parameter change and internal resonance have seldom been considered in a multiple-degree-of-freedom system. And study on nonlinear active control strategy is just started. The aim of this paper is to deeply investigate nonlinear characteristics and bifurcation control of self-excited vibration, which results in the following conclusions.
Based on extensive studies on various self-excited systems with friction, a typical“mass-on-moving-belt”model is derived and established for describing friction-induced vibration. The dynamical model lays the foundation for deep studies on nonlinear characteristics and bifurcation control of self-excited vibration.
Then the stability of the established system is analyzed analytically using Lyapunov theories. After calculating equilibrium points of the system and analyzing the stability of them, crucial velocity at which the system becomes unstable is obtained eventually. And the approximate analytical solutions of the system are derived by means of KBM method. By analyzing relationship between parameters and vibrations of the system, it is found that normal pressure ratio plays an important role in self-excited vibration.
Considered important effect of internal resonance, nonlinear dynamical behaviors of the system under non-internal resonance, 1:2 internal resonance and 1:3 internal resonance conditions are numerically investigated respectively. An experimental bench for testing frictional self-excited vibrations is designed and built up. Analytical and experimental results show that internal resonance condition plays an important role in the friction-induced self-excited vibration.
The Washout filter technique is used to control self-excited vibration caused by friction. The point at which Hopf bifurcation to be introduced is analyzed and determined. Then the linear control gain of Washout filer controller is calculated according to Hopf bifurcation condition. The nonlinear control gain is obtained based on the rule transferring sub-critical Hopf bifurcation to super-critical one. The analytical and numerical results show that the vibration amplitude of controlled system is greatly reduced comparing to the uncontrolled one and washout filter method is an effective way in control on self-excited vibration.
A portable vibration signal measurement and analysis system based on virtual instrument technology is developed after implementing such signal processing algorithms as Step-changed Stochastic Resonance and Empirical Mode Decomposition. These abundant functions enhance the ability of feature extraction from weak and unstable vibration signals.
通过对机床摩擦颤振、钻杆颤振、汽车驱动系统颤振和制动系统啸叫等摩擦自激振动系统的结构特性研究,建立了一类具有代表性的双质体—传输带摩擦自激系统动力学模型。为深入探讨摩擦自激振动的非线性动力学机理及摩擦自激振动的分岔控制等研究奠定了基础。
利用李亚普诺夫理论对摩擦自激振动系统的稳定性进行分析,求出系统运动的平衡点,对平衡点稳定性进行判断,确定系统的临界失稳速度。利用平均法求得摩擦自激振动系统的近似解析定常解。分析可知随着传输带速度减小,系统静平衡状态失稳,出现纯滑动和粘滑形式的摩擦自激振动。分析系统参数变化与系统振动的关系,发现正压力比值的变化对自激振动有较大影响。
考虑了内共振因素对摩擦自激振动的影响,利用数值方法分析非内共振、1:2内共振和1:3内共振三种情况下,摩擦自激振动系统的非线性动力学特性。设计了摩擦自激振动实验平台,并进行实验研究。结果发现内共振状态对摩擦自激系统的非线性动力学特性有重要影响。
针对摩擦自激振动的非线性特点,提出Washout滤波器方法对摩擦自激振动进行分岔控制。控制在临近分岔点处引入,通过Washout滤波器方法确定非线性控制器的线性增益,应用规范型直接法计算其非线性增益,将系统亚临界Hopf分岔控制为超临界Hopf分岔,使受控系统的自激振动幅值大大降低。理论分析和数值仿真表明该控制方法的有效性。
研究开发了基于虚拟仪器技术的振动信号采集分析系统,实现了变步长随机共振和经验模式分解算法,增强了提取微弱振动信号特征和捕捉非稳定信号的能力,弥补了传统信号分析系统的不足。
Self-excited vibrations induced by friction widely exist in fields of engineering and dailylife. Usually, the unwanted self-excited vibrations cause an early wear of the contacting parts of machines. It seems that up to now not all the possible nonlinear phenomena have been properly understood. Especially such conditions as parameter change and internal resonance have seldom been considered in a multiple-degree-of-freedom system. And study on nonlinear active control strategy is just started. The aim of this paper is to deeply investigate nonlinear characteristics and bifurcation control of self-excited vibration, which results in the following conclusions.
Based on extensive studies on various self-excited systems with friction, a typical“mass-on-moving-belt”model is derived and established for describing friction-induced vibration. The dynamical model lays the foundation for deep studies on nonlinear characteristics and bifurcation control of self-excited vibration.
Then the stability of the established system is analyzed analytically using Lyapunov theories. After calculating equilibrium points of the system and analyzing the stability of them, crucial velocity at which the system becomes unstable is obtained eventually. And the approximate analytical solutions of the system are derived by means of KBM method. By analyzing relationship between parameters and vibrations of the system, it is found that normal pressure ratio plays an important role in self-excited vibration.
Considered important effect of internal resonance, nonlinear dynamical behaviors of the system under non-internal resonance, 1:2 internal resonance and 1:3 internal resonance conditions are numerically investigated respectively. An experimental bench for testing frictional self-excited vibrations is designed and built up. Analytical and experimental results show that internal resonance condition plays an important role in the friction-induced self-excited vibration.
The Washout filter technique is used to control self-excited vibration caused by friction. The point at which Hopf bifurcation to be introduced is analyzed and determined. Then the linear control gain of Washout filer controller is calculated according to Hopf bifurcation condition. The nonlinear control gain is obtained based on the rule transferring sub-critical Hopf bifurcation to super-critical one. The analytical and numerical results show that the vibration amplitude of controlled system is greatly reduced comparing to the uncontrolled one and washout filter method is an effective way in control on self-excited vibration.
A portable vibration signal measurement and analysis system based on virtual instrument technology is developed after implementing such signal processing algorithms as Step-changed Stochastic Resonance and Empirical Mode Decomposition. These abundant functions enhance the ability of feature extraction from weak and unstable vibration signals.
引文
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