Steady State and Transient Vibration Analysis of an Exponentially Graded Rotor Bearing System Having a Slant Crack

Abstract

The dynamic behaviour of a slant-cracked exponentially graded (EG) rotor-bearing system has been investigated using the finite element method for flexural vibrations. A two nodded EG rotor element has been developed based on the Timoshenko beam theory. Local flexibility coefficients (LFCs) of a slant-cracked EG shaft element have been derived using fracture mechanics concepts to develop the stiffness matrix of a cracked EG element. The steady-state and transient vibration responses of cracked and uncracked rotor systems have been simulated using the Houbolt time marching method. When a crack is present in the shaft, the subharmonic frequency peaks are centred on operating speed in the steady-state frequency responses, whereas on critical speed in the transient frequency responses at an interval frequency corresponding to the torsional frequency. It has been found that the crack parameters such as crack depth and location, temperature gradients and torsional frequencies have a significant influence on natural frequencies and dynamic responses, which could be implemented for efficient rotor crack detection methodologies.