Bifurcation analysis of rotor-squeeze film damper system with fluid inertia

This paper focuses on the bifurcation behaviors of a rigid rotor-squeeze film damper system considering the effect of fluid inertia. The equations of motion of the system are formulated considering π oil film model with fluid inertia. Then the averaging method is employed to obtain the bifurcation equation of the system model. By using the C-L method, three different modes of bifurcation behaviors are found from the three regions divided by the transition sets, namely bifurcation set and hysteresis set in system parameter plane. By changing the value of Reynolds number that reflects the fluid inertia of the squeeze film damper, the hysteresis set is moved obviously; it is shown that the fluid inertia plays an important role in determining the bifurcation behaviors of the system. Meanwhile, the bifurcation behaviors of system are affected significantly by the fluid inertia when the bearing coefficient locates within a certain region. Thus in this situation, the fluid inertia must be taken into account for theoretical analysis. Direct numerical simulation is also carried out by using the 4th order Runge-Kutta method to verify the theoretical results. The results obtained in this paper will provide a fundamental theory for designing an effective squeeze film damper.