Influence of crack breathing model on nonlinear dynamics of a cracked rotor

Fatigue cracking of the rotor shaft is an important fault observed in the rotating machinery, which can lead to catastrophic failure. The paper addresses the influence of the crack breathing models on the nonlinear vibration characteristics of the cracked rotors. Nonlinear dynamics of the cracked rotor is investigated using two well-known crack models, i.e. switching crack model and response-dependent breathing crack model. Equations of motion for the cracked rotor are systematically presented for both the models. Through numerical simulations, the dynamic response for both the crack models is compared for the subcritical speed region for the rotor. Distinct differences have been found in bifurcation, amplitude, orbit and Poincaré map when carrying out the comparison between two models for the assumed rotor parameters. Switching crack modelling reveals chaotic, quasi-periodic and subharmonic vibration response for deeper cracks. Rotor system enters into chaos or quasi-periodic motion directly from periodic motion, and leaves the chaos via route of quasi-period. Transient chaos behaviour is also observed for the first time in the case of cracked rotor. Contrary to this, more realistic breathing crack model reveals no evidence of chaotic, quasi-periodic and subsynchronous vibrations in the response. Unbalance eccentricity level and its phase, crack depth and damping are found to have considerable influence on the bifurcation phenomena of the cracked rotor modelled using switching crack model.