松动裂纹转子轴承系统周期运动分岔及稳定性分析

根据松动裂纹耦合故障转子轴承系统的非线性动力学方程,利用求解非线性非自治系统周期解的延拓打靶方法,研究了系统周期运动的分岔特性及其稳定性。研究发现,在较大和较小的偏心量作用下,系统的周期运动都由倍周期分岔而失稳,在适当的偏心量下,系统的周期运动以Hopf分岔形式失稳且稳定性较强。转轴裂纹和基础松动故障都使系统周期运动稳定性降低、系统Hopf分岔存在的偏心量范围变大。结论为转子轴承系统的安全稳定运行和振动的抑制及控制提供了理论参考。

On the Bifurcation and Stability of Periodic Motion of Rotor-Bearing Systems With Crack and Pedestal Looseness Fault

The bifurcation and stability of the periodic motion of rotor-bearing systems with crack and pedestal looseness fault were studied and the periodic solution of nonlinear non-autonomous system was obtained by continuation-shooting method. The following conclusions are drawn: the periodic motion of the rotor loses its stability by doubling bifurcation whether the unbalance in the system is high or low in unbalance-speed range. When the unbalance of the rotor is moderate, the periodic motion of the rotor loses its stability by Hopf bifurcation and the stability is stronger. The stability of periodic motion of the rotor decreases and the region of Hopf bifurcation becomes wider when crack and pedestal looseness exist in the rotor. The results may bring up the theoretical references for security running and vibration control of rotor-bearing systems.