Characterization and Reconstruction of Crack Forces for a Cracked de Laval Rotor Based on State Space Theory

A non-linear cracked rotor model accounting for shaft weakening parallel and perpendicular to the crack is investigated. The system equation bears discontinuity, and numerical treatment has been applied leading to bifurcation and chaos. Based on State Space Theory, the dynamics of the crack is reconstructed as a ‘crack force’ manifesting the action of the crack on the rotor. Further non-linear characteristics are reconstructed and could be adopted in condition monitoring of rotors. It is demonstrated that, the largest Lyapunov exponent of the simulated time series sufficiently indicates the system’s chaotic state. An interesting discussion and characterization of the cracked rotor is presented to emphasize the modeling.