A Kineto-Static Model for a Cracked Shaft Flexible Bearing System With Linear-Angular Coupled DOF in Bending

In this paper, a model for vibration of a cracked rotor shaft flexible bearing system with linear-angular coupled DOF in bending is proposed. A vector approach on the change of the system’s angular momentum at a steady state has been used to derive the equation of motion leading to a linear time-variant system. By considering the forces and moments in the kinematic pairs of the shaft and bearing, an equivalent coupled 4-DOF complex spring is analytically introduced to simulate the system at a low rotating speed with the crack as an external force. Consequently, the Kineto-static response has been obtained by restricting the system to strong parameters. Viability of the model for investigating the complex response of a shallow-crack rotor bearing system has been demonstrated by analysis and features in time history and frequency spectra explored for crack detection. Various scenarios are considered, and the presented results concur with the published literature.