Numerical simulations of steady-state of two-crack rotor system supported by radial active magnetic bearings

Abstract

The steady-state response of a two-crack rotor system is investigated by computational simulations in the paper. The rotor system supported by radial active magnetic bearings is excited by centrifugal forces of discs unbalances. A flexibility matrix of Bernoulli beam element takes into account coupling phenomena between directions of vibration. The phenomenon occurs in cracked rotors. The couplings express relations between vibration in different directions, i.e. bending-torsion, bending-longitudinal, and torsion-longitudinal. The flexibility matrix elements of the cracked rotor are derived using the concepts of fracture mechanics for transverse surface crack. Partial opening/closing of cracks implemented in motion equations is determined by sign of stress intensity factor for mode I. The factor is computed for the crack edge. The motion equations are nonlinear because the system response depends on breathing of cracks and nonlinear force coupling is introduced by radial active magnetic bearings. Parametric studies of the system response were carried out in order to examine influence of various angles between two cracks. Several recommendations for detection of cracks and monitoring of the cracked rotor are suggested.