Finite element analysis of multi-disk rotor-bearing system with transverse crack

Abstract

The vibration analysis of rotating systems is pronounced as a key function in all the fields of engineering. The behavior of the rotor systems are mainly resulting from the excitations from its rotating elements. There are several numerical methods present to analyze the rotor-bearing systems. Finite element method is a key tool for dynamic analysis of rotor bearing system. The current study describes a multi disk, variable cross section
rotor-bearing system with transverse crack on xisymmetric elements supported on bearings in a fixed frame. The shaft in the rotor-bearing system is assumed to obey Euler- Bernoulli beam theory. The equation of motion of the rotor-bearing system is derived by Lagrangian approach along with finite element method. Finite element model is used for vibration analysis by including rotary inertia and gyroscopic moments with consistent matrix approach. The rotor bearing system consists of two bearings and two rigid disks. One disk is overhung and the other one is placed between the bearings. Internal damping of the shaft and linear stiffness parameter of the bearings are taken into account to obtain the response of the rotor-bearing system. The rotor has variable cross-section throughout the configuration. The disks are modeled as rigid and have mass unbalance forces. The critical speed, unbalance response and natural whirls are analyzed for the typical rotor-bearing system with transverse crack. Analysis includes the effect of crack depths, crack location and spin speed. The results are compared with the results obtained from finite element analysis. The bearing configurations are undamped isotropic and orthotropic. The natural whirl speeds are analyzed for the synchronous whirl for both the uncracked and cracked rotor bearing system using Campbell diagrams. The effect of transverse crack over the starting point of the system instability regions in the rotating speed axis with zero asymmetric angle is examined. Further, Houbolt’s time integration scheme is used to obtain the phase diagrams and frequency response for both the bearing cases to study the stability threshold. Analyses are carried out by using numerical computing software.