摘要
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。
Taking the torsional vibration of a kind of rotating machanical drive system as the re- search 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 bi- furcation and the judgment method of periodic motion＇s stability were given,and the bifurcation char acteristics of system were analyzed under the condition of parametric resonance and internal reso- nance. In order to suppress instability oscillation of drive system caused by subcritical Hopf bifurca- tion, 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 in nonlinear rotating machineries. provided for parametric vibration ananlysis and control in nonlinear rotating machineries.
出处
《中国机械工程》
EI
CAS
CSCD
北大核心
2012年第12期1461-1466,共6页
China Mechanical Engineering
基金
国家自然科学基金资助项目(61104040)
河北省自然科学基金-钢铁联合研究基金资助项目(E2012203090)
关键词
旋转机械
扭振
分岔控制
耦合非线性系统
rotating machinery
torsional vibration
bifurcation control
coupling nonlinear system
