含碰摩悬臂转子系统的动态响应分析

Analysis on dynamic response of overhung rotor system with rubbing

文中建立了一个受碰摩影响的不平衡悬臂转子系统的力学模型,根据Lagrange法推导出系统的运动方程,运用4阶Runge-Kutta法对该模型进行数值计算,结合周期分岔图、碰撞分岔图、最大力矩图、占空比图、Poincaré截面图、轴心轨迹图和轴心位移时间历程图研究了系统的动力学特性,着重分析了偏心量和阻尼系数的变化对转子系统响应的影响,辨识出了转子系统的运动周期、冲击次数、所受最大力矩及冲击时间的占比。研究表明:含碰摩悬臂转子系统具有单周期、多周期、准周期和混沌运动等复杂动力学行为;随着偏心量的增加,系统混沌运动区域增大且碰撞冲击程度愈来愈剧烈,系统的稳定性降低;随着阻尼系数的增加,系统混沌运动大幅度减少,趋于较为稳定的周期运动。上述结论有助于认识含碰摩悬臂转子系统的运动规律。

In this article, the mechanical model of the unbalanced overhung rotor system with rubbing is set up, and the motion equation of the system is deduced with the help of the Lagrange method. The fourth-order Runge-Kutta method is used for numerical calculation. The dynamic characteristics of the system are explored in combination with the cycle bifurcation diagram, the impact bifurcation diagram, the maximum moment diagram, the duty cycle diagram, the Poincaré section diagram, the axis locus diagram and the axis displacement time history diagram. Efforts are made to analyze the influence of the eccentricity and the ever-changing damping coefficient upon the response of the rotor system on one hand and identify the rotor system’s movement cycle, impact frequency, maximum torque and proportion of time on the other hand. The results show that the overhung rotor system with rubbing has complex dynamic behaviors such as single period, multiple periods, quasi period and chaotic motion. With the ever-increasing eccentricity, the chaotic motion region of the system increases and the impact becomes increasingly severe. As a result, the system stability decreases. With the increase of the damping coefficient, the chaotic motion of the system greatly reduces and tends to be stable in a period. These conclusions are helpful to explore the motion law of the overhung rotor system with rubbing.