Analysis of Stability and Unbalance Response of Flexible Rotor Supported on Hydrodynamic Porous Journal Bearing

Abstract

Rotating machines are one of the most important and widely used machineries in modern engineering world. Now-a-days modern rotating equipments have a number of complicated accessories attached with it and they are also made extremely flexible. They are also required to run at higher speed, much higher than their first critical speed. Fluid-film bearings supporting the rotating shafts play an important role in the dynamic behaviour of the rotors because of their stiffness and damping properties. Hydrodynamic bearings are one of the most widely used bearings to support the rotating shafts. Rotor-bearing systems exhibit a wide variety of phenomena pertaining to its operations which if not properly addressed and rectified may lead to catastrophic failure of the system. One such rotor-bearing phenomenon is the self-acting rotor vibrations induced by the hydrodynamic bearings and popularly known as oil-whirl and oil-whip which have severe repercussion on the functioning of the rotors. Another important area of rotor dynamics is the unbalance response of the rotors supported on the hydrodynamic journal bearings. Due to the inherent unbalance present in the rotor-bearing system high amplitude of vibrations are observed when the rotor is operated near its critical speed. In this context, a study of the rotorbearing system considering the non-linearity of the oil-film forces is necessary. In this thesis a methodology has been proposed to study stability and the unbalance response of a flexible rotor supported on two identical porous hydrodynamic journal bearing. Timoshenko Beam theory has been used for finite element formulation of the rotor. Finite hydrodynamic porous oil-film bearing is trajectories are shown. The stability curves have been drawn for different rotorbearing parameters. The effect of bearing location is also studied. Then unbalance is introduced in the model. Waterfall diagrams are obtained to study unbalance, oil-whirl for different rotor-bearing parameters. It has been observed that at low spin speed, unbalance is the major driving force and with an increase in the spin speed, oil-film forces take over as the major cause of vibration. Thus, whirling of the rotor gradually changes from synchronous to sub-synchronous. Waterfall diagrams are obtained for both run-up and run-down processes. Distinct dynamic behaviours are observed for run-up and run-down, which is known as hysteresis. Bifurcation analysis of the rotor-bearing system has also been carried out and PoincarD maps, time response, FFT-spectrum, dynamic trajectories and bifurcation diagrams have been utilized as diagnostic tools to study the non-linear dynamics of the rotor-bearing system. It has been found that the dynamic behaviour of the system can be periodic and quasi-periodic depending on the operating conditions. Also it is observed that when rotating speed is increased the rotor-bearing system undergoes Hopf Bifurcation. Initially, analysis of rotors supported on porous journal bearings have been carried out with an assumption that the lubricating fluid enters the clearance space of the bearing with a zero tangential velocity at the porous medium. However, earlier investigations suggest that this assumption is at best an approximation only. Therefore, the effect of tangential slip velocity using Beavers-Joseph criterion has also been carried out. Th....