Identification of Multiple Cracks in a Shaft System
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Fatigue cracks present in the shaft of a machine make it susceptible to the catastrophic failure. Hence, it is important to detect all the potentially dangerous cracks present in the shaft before failure occurs. Assessment of damage severity is also important to predict the remaining life, to schedule the maintenance and to prepare the inventory. In the present work, an identification methodology has been developed; which identifies the number of cracks, their locations on the shaft, their sizes, and the orientation angle of cracks. The methodology uses transverse forced responses of the shaft system at different frequencies of a harmonic excitation. First, a multi-crack detection and localization algorithm (MCDLA) is developed. Transverse forced vibrations of a non-rotating cracked shaft in two orthogonal planes are analyzed with the help of the finite element method by using the Timoshenko beam theory. The presence of a crack in a shaft introduces a slope discontinuity in the elastic line of the shaft. This causes a jump in the value of the curvature of the shaft elastic line, and it is difficult to measure in the presence of measurement noise. In the present work, the shaft curvature is obtained by approximating forced responses of the shaft at consecutive axial measurement locations by a quadratic polynomial. The effect of noise is reduced by utilising forced responses of the shaft at several frequencies. This stage of the algorithm gives the number of cracks and their approximate locations over the shaft. Information obtained from the first algorithm is used in the second algorithm, the multi-crack localization and sizing algorithm (MCLSA), to find out the size and more accurate location of cracks. The MCLSA uses the multi-objective genetic algorithms to solve an optimization problem giving the size and accurate location of the cracks. Responses of the shaft at several frequencies are used to define objective functions in the genetic algorithm (GA). The proposed two stage methodology is tested with numerically simulated noisy forced responses from the finite element modeling of a simply supported shaft having two cracks. Themethodology identifies very well the presence of cracks and also estimates quite accurately the location and the size of cracks on the shaft. Initially, the identification algorithm is tested with cracks of known orientation, i.e. assuming that all the cracks have the same and known orientation angle. Hence, the identification algorithm is developed for identifying two unknowns per crack, i.e. the size and the location. Later, the crack orientation angle is introduced as another crack parameter and the identification algorithm is tested with cracks of unknown orientation angle. First, the algorithm is tested for open cracks then for breathing cracks. From numerical simulations, it is shown that the first algorithm, i.e. the MCDLA, work well in these situation also. It gives the number of cracks present in the shaft and its approximate location over it. A new method is proposed to find out the crack orientation angle for open cracks as well as for breathing cracks. It consists of taking measurements of the shaft deflection at regular angular orientations of the shaft. Next, the MCDLA is tested for a real cracked shaft in a laboratory test set-up. Initially, measurements were taken using eddy current sensors, which did not give good results. Nex.
Supervisor: R. Tiwari AND S. Talukdar