Nonlinear vibration analysis of a cracked rotor-ball bearing system during flight maneuvers

This paper focuses on the nonlinear responses of a cracked rotor-ball bearing system caused by aircraft flight maneuvers. The equations of motion of the system are formulated with the consideration of the breathing mechanism of a transverse crack and the maneuver load of a climbing-diving flight. The fourth order Runge-Kutta method is employed to detect the nonlinear responses of the system, which are reflected by bifurcation diagrams, power spectrums, maximum Lyapunov exponent, phase portraits and Poincaré sections. It is shown that the super-harmonic responses of the system are affected significantly by the maneuver load under sub-critical speeds. Plenty of quasi-periodic motions are obtained, and a variety of complex nonlinear behaviors including bifurcations and jumping phenomenon are observed near 1/4, 1/3, 2/5 and 1/2 critical speeds when the maneuver load increases from 0 to 10 g. The nonlinear responses of the system influenced by crack stiffness, bearing clearance and rotor eccentricity are also investigated. Chaotic motions are demonstrated when the crack stiffness or the bearing clearance increases across a critical value. However, the responses maintain quasi-periodic when the rotor eccentricity changes. The results will contribute to a better understanding of the nonlinear dynamic behaviors of cracked rotors in flight maneuvers.