Bifurcation Analysis of a Transversely Cracked Nonlinear Jeffcott Rotor System at Different Resonance Cases

Abstract

This work focuses on the dynamical behaviour and bifurcations of a vertically supported Jeffcott rotor system having a transverse crack and nonlinear stiffness characteristics at the primary, sub-harmonic, and super-harmonic resonance cases. The nonlinear restoring force due to the bearing-clearance, the crack breathing, the disc eccentricity, and the orientation angle between the crack and imbalance direction are considered in the system model. The equations governing the system motion are derived and solved analytically by applying the Multiple Scales Perturbation Technique (MSPT). The slow-flow modulating equations are obtained and the spinning speed response curve is plotted. The whirling orbit and amplitude spectrum are constructed in the three considered resonance cases. The acquired results provide a better understanding of the main reasons of the superand sub-harmonic resonance excitations. In additions, we concluded that the suitable resonance case that can be used for early detections of the cracks in the rotating shafts is the sub-harmonic resonance case. Finally, the obtained results are confirmed numerically and compared with the work published in the literature.