Nonlinear Vibrations of Rotor-Bearing Systems Supported by Squeeze Film Dampers Due to Unbalance Excitation

Abstract

Abstract In this paper, nonlinear dynamic behaviors of a multi-mass flexible rotor-bearing system supported by short length Squeeze Film Damper (SFD) due to the unbalance excitation are presented. The rotordynamic model of the system is developed by using 1D Timoshenko beam elements for flexible shafts, lumped inertias for disks, linear springs and viscous dampers for bearings and structural damping for the system. The nonlinear SFD model is based on the analytical solution of Reynolds equation for open ends short length SFDs assuming circular-centered orbit motion. The SFD’s nonlinear damping coefficient matrix and mass coefficient matrix generated because of fluid inertia are obtained. In this model, rotor system matrices and nonlinear SFD coefficient matrices are incorporated to obtain the full system mass, gyroscopic, damping and stiffness matrices. Harmonic Balance Method (HBM) is used to represent the resulting nonlinear differential equations of motion as a set of nonlinear algebraic equations. Newton’s Method with arc-length continuation is utilized as the solution method for the set of nonlinear algebraic equations obtained. A rotor of a small turbojet engine, details of which is available in the literature, is considered as an example. Different nonlinear responses of the rotordynamic system are investigated in order to observe the effects of SFD’s diameter, clearance and length parameters and the amount of unbalance loadings and their locations.