Identifying the Effect of Vibration on Crack Growth in Shaft Using Fuzzy Logic Algorithm

Abstract

Cracks in shafts can be identified as a significant factor for limiting the safe and reliable operation of machines. Engineers can predict faults using classical approaches. However, when artificial intelligence approaches are used, the forecasting time for crack diagnosis improves dramatically. The objective of this study is to detect the location and depth of the crack in the shaft using a fuzzy logic algorithm. Literature presents measurements of frequency, mode shape, and structural damping can be used to assess cracks. However, evaluating mode shape and structural deformation is more difficult than measuring frequency. Such criteria, however, are insufficiently sensitive to detect early flaws. This study employs changes in phase angle and natural frequency as crack indicators. To evaluate the natural frequencies and phase angles of the cracked shaft utilizing the change in stiffness matrices of the cracked element, theoretical calculations were performed using Matlab. To verify the theoretical values of natural frequencies, modal analysis was performed using Ansys. Good agreement is observed between the results. To detect the location and depth of the crack, the fuzzy logic technique uses first and second mode natural frequencies and their corresponding phase angles of the shaft as input parameters. The correlation coefficients for triangular, trapezoidal, and Gaussian membership functions are all close to one. Also, the average total errors of the three membership functions with the theoretical values are all less than 5%. This indicates that results obtained from all membership functions are close to the theoretical locations and depths of crack. So the proposed fuzzy logic technique would constitute an efficient tool for real-time crack identification.