裂纹转子系统的混沌响应控制方法研究

Controlling Chaos of Nonlinear Response in Rotor Containing a Crack

研究了轴上含裂纹的单盘转子系统出现混沌响应时的混沌控制问题。在采用开闭裂纹模型的基础上,推导了单盘裂纹转子的运动方程。在综合了延迟反馈和正弦周期微扰等控制方法特点的基础上,提出了正弦延迟反馈的控制混沌方法。由仿真结果可以看出,可以通过计算最大Lyapunov指数来选择控制参数。调整控制参数,可以将裂纹转子由混沌运动分别控制到协调运动、周期2运动和周期4运动上。

We aim to study controlling nonlinear chaotic response in the Jeffcott rotor containing a crack in shaft. Considering the opening and closing of crack in rotation, we derive the motion equations of rotor. Based on the Delay Feedback Control （DFC） method and perturbation of sinusoid periodic excitation, the novel chaos control scheme——Sinusoid Delay Feedback（SDF） method——is presented. By choosing the appropriate coefficients, the chaotic response can be so controlled as to become gradually a periodic motion. By computing the largest Lyapunov exponent, the optimal control coefficients can be selected. From simulation results, it is shown that varying the weight coefficient and amplitude coefficient, the chaotic response of rotor containing a crack can be so controlled as to become gradually a synchronous, periodic-2 or periodic-4 motion.