The dynamics of a rotor system with a shaft having a slant crack. A qualitative analysis using a simple rotor model.

In this study, a qualitative analysis of a transverse vibration of a rotor system with a crack that grows at an angle of 45 degrees toward the axis of the shaft is presented. Based on the assumption that the bending stiffness of the shaft changes synchronously with the opening/closing behavior of the crack caused by the torsional vibration of the shaft, the equation of motion of a simple rotor system with a shaft having a slant crack is represented by a differential equation with parametric excitation in the coordinate system rotating at the operating speed of the rotor. It is shown by the solution that the steady-state response of the rotor system with a slant crack on its shaft induced by imbalance contains the frequencies represented by mΩ+ nωT/2 ; m=1, 2, ..., and n=0, 1, 2, ..., where Ω is the operating speed of the rotor, and ωT is the frequency of torsional vibration of the rotor system.