旋转机械耦合传动系统参激振动分析与控制

以一类旋转机械传动系统的扭振为研究对象,考虑轴系时变刚度变化和非线性摩擦阻尼力的影响,根据Lagrange原理建立了一类旋转机械传动系统的耦合非线性动力学方程,利用多尺度方法推导出了系统的平均方程,并根据Hopf分岔理论给出了系统发生Hopf分岔的充要条件及周期运动稳定性的判别方法,分析了参数共振和内共振条件下系统的分岔特性。为抑制传动系统因亚临界Hopf分岔引起的失稳振荡,引入非线性反馈控制,对系统的Hopf分岔点进行转移并控制周期运动的稳定性和幅值。研究结果为非线性旋转机械参激振动的分析及控制提供了有效方法。

Parametric Vibration Analysis and Control in Coupling Rotating Mechanical Drive System

Taking the torsional vibration of a kind of rotating machanical drive system as the research object,considering the influences of time-varying stiffness and nonlinear friction damping,a coupled nonlinear dynamic equation of rotating mechanical drive system was obtained on the basis of Lagrange theory.The average equation of system was deduced with the aid of method of multiple scales.Besides,according to Hopf bifurcation theory the necessary and sufficient conditions of Hopf bifurcation and the judgment method of periodic motion’s stability were given,and the bifurcation characteristics of system were analyzed under the condition of parametric resonance and internal resonance.In order to suppress instability oscillation of drive system caused by subcritical Hopf bifurcation,a nonlinear feedback control was introduced.After including the controller,the Hopf bifurcation points of system can be transferred,and the stability and amplitude of limit cycle were controlled.Through above study,an effective method was provided for parametric vibration ananlysis and control in nonlinear rotating machineries.