A continuous model approach for cross-coupled bending vibrations of a rotor-bearing system with a transverse breathing crack

In this paper, the cross-coupled bending vibrations of a rotating shaft, with a breathing crack, mounted in resilient bearings are investigated. The equations of motion of the continuum and isotropic rotating model of the shaft follow the theory of Rayleigh. The governing equations are coupled in the two main directions, and the partial solution is obtained by solving a linear system of equations, for each time step, taking into account the non-linearity due to the breathing crack. The coupling is introduced in three different ways: the equations of motion, the resilient bearings and the crack. A main focus is made in the coupling introduction due to crack compliance variance while rotation with the cross-coupling terms of the local compliance matrix due to the crack to be calculated analytically as functions of the rotational angle. The three causes of coupling between the vertical and horizontal vibrations should be distinguished with regard to the effects that each one of them has on the dynamic response of the rotor. Inversely, the existence of each type of coupling in the frequency response could be used to identify the respective cause.