HOPF BIFURCATION OF A ROTOR-SLIDING BEARING SYSTEM

A new numeric-analytical method for Hopf bifurcation of a rotor-bearing system is presented according to the Hopf bifurcation theory and Floquet stability theory.The method comprises a modified shooting method for calculating periodic solutions,a calculation method for determining the stability of the solutions,and a prediction correction procedure for tracing the solutions,etc.The software package realized with these techniques was used for efficient and accurate study of Hopf bifurcation behaviors of rotor-sliding bearing systems.The results show that there exists an unstable subcritical limit cycle for small E s ,the journal center eccentricity ratio at a critical instability.A stable supercritical limit cycle exists for large E s .When supercritical bifurcation occurs,limit cycle appears as soon as the rotor speed exceeds its threshold value,and the limit cycle does not become unstable until the rotor speed surpasses the threshold speed a lot.When subcritical bifurcation occurs,the behavior of rotor is more complicated.In addition to existence of an unstable limit cycle below the threshold speed,there are large-amplitude stable limit cycles both above and below the threshold speed.That explains why jump phenomena and hysteresis in the amplitude may occur in a rotor-sliding bearing system.