Analysis of the nonlinear response of a cracked rotor considering the influence of coupling stiffness

This paper investigated the nonlinear response of a cracked rotor and its bifurcation. Based on the fracture mechanics, a crack model is constructed. Considering the opening and closing of crack, the direct and cross stiffness of shaft vary with rotation. The nonlinear motion equations for the cracked rotor were derived. To solve the equations, Newmark-β integration method was employed. The influences of rotation speed, crack depth and unbalance on a cracked rotor's nonlinear dynamics response were investigated. Period sampling of peak-to-peak (PSP) value diagram, is used to distinguish some nonlinear and linear response based on the fault diagnosis theory. Simulation results show that the PSP diagram is useful in reflecting the amplitude of the quasi-period and chaos response. In the response, there exists quasi-period motion near the 8/3 critical speeds when unbalance is large, which can be used to detect the crack. Sometimes quasi-period motion will lose its stability and go to chaos directly.