Identification of the critical crack depths and locations of rotordynamic systems in backward whirl

The effect of crack depth of a rotor-bearing-disk system on vibration amplitudes is investigated. 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 with either breathing or open cracks which are valid for damped and undamped rotor systems. It is found via waterfall diagrams of the system with a breathing crack and slight unbalance that there are critical pairs of crack depth and frequency of large vibration amplitudes at the backward whirling frequencies. These high vibration amplitudes at the backward whirl appear at earlier crack depths than those at the forward whirl for both crack models. Resonance peaks at the second, third and fourth sub-harmonic frequencies emerge as the crack depth increases. It is shown that the orbit changes can be used as an indication of breathing crack propagation in the shaft. In addition, the veering in the critical frequencies has been clearly noticed in the open crack case.