Application of non-symmetric bending principles on modelling fatigue crack behaviour and vibration of a cracked rotor

Many studies on cracked rotors developed crack breathing models that assume that the neutral axis of bending always remains horizontal for simplification. These models may generate significant discrepancies and thus there is a need to develop more sophisticated models to look into the shifting of the neutral axis for a cracked rotor. Herein, a case study on the shifting of the neutral axis for a cracked rotor is firstly performed by using a three-dimensional finite element model to confirm that the neutral axis becomes inclined as the cracked rotor rotates. In response to this finding, non-symmetric bending principles are used to develop a new crack breathing model which has the advantage of being able to numerically calculate the inclination angle of the neutral axis. When compared to an existing crack model in the literature that assumes that the neutral axis remains horizontal (HNA model), the proposed model is relatively less stiff in bending as a result of an overall lower area moment of inertia. Using the harmonic balance method, a two-dimensional finite element vibration model of a cracked rotor was devised by employing the proposed crack breathing model and the HNA model for validation. It can be found that the vibration amplitudes of the first three frequency components are similar between the two models for shallow cracks and significantly differed for deep cracks. This result highlights the potential of the proposed model for modelling and detecting mid-to-late-stage cracks in rotors.