The research on non-linear characteristics of a cracked rotor and reconstruction of the crack forces

Abstract

The non-linear characteristics of a cracked rotor are investigated in this paper. It is known that the cracked rotor system becomes non-linear when the rotor is not in a weight-dominant condition. In the case of the crack opening, the rotor is weakened not only in the crack direction but also in the perpendicular direction of the crack, and the breathing of the crack is determined by the vibration in the crack direction. Based on these assumptions, a model of a cracked rotor can be established in rotating coordinates and the governing equations can also be obtained. The discontinuities of the governing equations make it very difficult to obtain the vibration response of this kind of model analytically, so the numerical simulation method is applied. The chaos and bifurcation phenomena is observed through the numerical results. According to the results obtained in this paper, the Lyapunov exponent calculated from the simulated time series is proven to be effective in judging the chaotic property of a system. The non-linear effect of a crack can be reconstructed by using the state space theory when considering the crack as an external force.