A computational investigation of the transient response of an unbalanced rigid rotor flexibly supported and damped by short magnetorheological squeeze film dampers

Abstract

Due to manufacturing and assembly inaccuracies, real rotors are always slightly imbalanced. This produces their lateral vibration and forces that are transmitted through the bearings to the stationary parts. The oscillation of the system can be reduced if damping devices are added to the constraint elements. To achieve the optimum performance of the rotor in a wide range of angular velocities and when passing through the critical speeds their damping effect must be controllable. For this purpose, the application of semiactive magnetorheological (MR) dampers has been analysed. The investigated problem focuses on studying the influence of their damping effect and of its control on the amplitude of the rotor vibration, on the magnitude of the force transmitted to the rotor casing, and on the amount of dissipative power generated in the MR films. The developed mathematical model assumes cavitation in the lubricating layer, and the MR liquid is modelled as a Bingham material. The derivation of the equation governing the pressure distribution in the oil film is completed by a new methodology making it possible to determine the yielding shear stress needed for its solution. The equations of motion of the rotor are nonlinear due to the damping forces and to solve them a Runge–Kutta integration method was applied. Computer simulations show that a suitably proposed current–rotor angular speed relationship enables one to fully eliminate the resonance peaks and to achieve the optimum compromise between the attenuation of the rotor lateral vibration, the magnitude of the forces transmitted to the rotor casing and the amount of energy dissipated in the lubricating layers.