Bifurcation analysis of a flexible balanced cracked rotor-bearing system

The dynamic analysis of cracked rotors is of considerable current interest. In the present paper, the effect of the presence of a transverse crack in a rotor supported by two hydrodynamic journal bearings is investigated. A nonlinear model of a flexible cracked rotor-bearing system is proposed. The model of the hydrodynamic forces is derived based on the assumption of a short bearing approximation and a half-Sommerfeld boundary condition. The system of nonlinear differential equations is integrated numerically using the Runge-Kutta method. The effect of the crack depth on the motion of the journal center in the vicinity of the stability limit is investigated. Bifurcation diagrams and Poincaré maps are used to determine the effect of the crack on the stability limit and on the journal motion.