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Cracked rotors have nonlinear spring characteristics of a piecewise linear type due to an open-closed mechanism of cracks. There have been many studies on the dynamic behaviour of cracked rotors in order to develop fault diagnosis systems for detecting cracks. However, most of these studies concern the change in resonance phenomena mainly due to cracks in rotor systems with linear supports. In many practical rotor systems, various kinds of nonlinear spring characteristics may exist due to mechanical elements, such as nonlinear bearing supports, and the rotor systems become nonlinear. Therefore, existing fault diagnosis systems are unable to detect cracks in such nonlinear rotor systems which are supported by nonlinear bearings. In this paper, we study the vibrational behaviour of a cracked rotor with nonlinear bearing supports and focus on the effect of combined resonances caused by a crack and nonlinear bearing supports. In particular, we investigate in detail the resonance phenomena of a harmonic resonance and a II2-order subharmonic resonance by numerical simulations using a PWL model and theoretical solutions using a PS model. The results show that the dynamic behaviours of a cracked rotor in a nonlinear rotor system are obviously different from those in a rotor system with linear supports, and the change in vibrational behaviour of a harmonic resonance and a 1!2-order subharmonic resonance are significant due to changes of angular positions of an unbalance.

Resonance with Respect to Angular Positions of an Unbalance of a Cracked Rotor in a Nonlinear Rotor System