General harmonic balance solution of a cracked rotor-bearing-disk system for harmonic and sub-harmonic analysis: Analytical and experimental approach

The effect of crack depth of a rotor-bearing-disk system on vibration amplitudes and whirl orbit shapes is investigated through a general harmonic balance technique and experimental verification. Two models of the crack, which are the breathing and the open crack models, are considered. Finite element models and general harmonic balance solutions are derived for breathing and open cracks which are valid for damped and undamped rotor systems. It is found via waterfall plots of the system with a breathing crack that there are large vibration amplitudes at critical values of crack depth and rotor speed for a slight unbalance in the system. The high vibration amplitudes at the backward whirl appear at earlier crack depths than those of the forward whirl for both crack models. Resonance peaks at the second, third and fourth subcritical speeds emerge as the crack depth increases. It is shown that the unique signature of orbits for the breathing crack model which have been verified experimentally can be used as an indication of a breathing crack in the shaft. In addition, the veering in the critical frequencies has been noticed in the open crack case.