A NOVEL NORMALIZATION PROCEDURE OF QUADRATIC COEFFICIENTS IN A MULTI-CRACK IDENTIFICATION ALGORITHM FOR A SHAFT SYSTEM

A multi-crack detection and localization algorithm was proposed by the authors [1], which defined crack probability functions (CPFs), as an indicator of presence of cracks in a cracked shaft. The algorithm was based on the normalization of quadratic coefficients obtained from forced responses of the cracked shaft with those obtained from the intact shaft. The algorithm identifies the number of cracks and their locations over the shaft span. In the present work, the normalization procedure is improved and a new parameter, the equivalent reduced stiffness (ERS) is defined. Forced responses of the intact shaft system are replaced by responses of the shaft system with its elastic constant, E, equal to ERS. The proposed modification is tested by numerically simulated responses with random noise. CPFs obtained using ERS are better indicator of presence of cracks than those obtained with elastic constant E. With this modification, forced responses of the shaft system near eigen frequencies can also be included where the signal-to-noise ratio is high. Next, the algorithm is tested for rotated cracks of unknown crack orientation angle, and a method is suggested to find out the crack orientation angle of the rotated cracks.