An algorithm for localization of fatigue crack in spinning rotor based on proof by negation

Abstract

This paper presents an innovative signal-based approach for detection and localization of a fatigue crack induced in spinning rotors. For development of the algorithm and demonstration of the its capabilities, a conventional rotor supported by rigid end bearings has been considered. In this demonstration, a cracked rotor is simulated using finite elements with four degrees of freedom per node. The model accounts for the gyroscopic effects caused by the offset disc and the breathing of the fatigue crack. The gyroscopic effects are accounted for by the introduction of the gyroscopic matrix in the finite element formulation, and the crack breathing effect is considered by introduction of the crack excitation function in the equations of motion The developed algorithm can also be used to simultaneously determine the magnitude and direction of the disc unbalance relative to the crack front. Also, the algorithm is used to validate the crack location hypothesis at a single node by introducing a variable crack location flag vector. The crack location flag vector with the highest crack stiffness value accurately represents the true crack location.