Dynamic modeling and vibration analysis of cracked rotor-bearing system based on rigid body element method

Rotor crack occurs frequently in rotating machinery. It is of great significance to study the vibration mechanisms of the cracked rotor-bearing system, which can provide proofs for crack online monitoring. In this paper, a new dynamic model of the cracked rotor-bearing system is developed using the rigid body element (RBE) method, and vibration response analysis is then carried out. The rotor is discretized as a set of RBEs, and each two adjacent RBEs is connected by an elastic joint (EJ). Each EJ is modeled with six imaginary springs (three translational springs and three rotational springs). The breathing crack is modeled through time-varying stiffnesses of imaginary springs, which are obtained using real-time parameters (area, cross-section moment of inertia, and polar moment of inertia) in four processes (crack fully closed, crack partially opened, crack fully opened, and crack partially closed) in a full rotation angle. The interactions of adjacent RBEs are then given based on the force and moment analysis, and the bearing forces are obtained based on two models (i.e., equivalent spring-damper model, and Gupta bearing model). The equations of motions of the cracked rotor-bearing system are developed through Newton-Euler equations and solved by the fourth-order Runge-Kutta-Fehlberg method with a step-changing criterion. The displacement responses are then obtained, and the frequency spectrums of displacement responses and their instantaneous frequencies (IFs) under different rotation speeds are analyzed. Simulation results of the cracked rotor-bearing system are in good agreement with previously published results and experiment results. What’s more, analysis results show that the frequency spectrum of IF can be an indicator for online monitoring of the rotor crack.