Vibration Analysis of Cantilever Beam With Two Inclined Cracks and Its Implementation in Fault Diagnosis

Abstract

Cracks present in mechanical members reduce the service life of the member. The presence of a crack doesn't necessarily mean the worthlessness of the member rather it plainly indicates the reduction in full load application of the member. The natural frequencies are characteristics of a particular member, and they get modified with the introduction of crack. Modal analysis provides a mean to determine those vibration characteristics both for cracked and uncracked beam. The present research aims to determine the vibration response of a cantilever beam with two inclined cracks to both free and forced excitations when the inclination angle of the crack changes. Results obtained from ANSYS for free, and forced oscillation have been presented. Experimentally, free vibration analysis has been done, and natural frequencies have been obtained from Frequency Response plots, and it has been compared to the values obtained from ANSYS. Using both these vibration methods, both surface and internal cracks can be located and in some cases their magnitude can be estimated by only considering their response to vibration excitations. Three-dimensional surface plots of natural frequencies have been plotted to take into account all angle combinations for both cracks. Mode shapes of the uncracked beam and cracked beam with specific angle combination have been plotted that can be used for crack identification by comparing the values of total deformation. Fuzzy Logic has been applied to predict the expected location of the crack, its severity and its inclination. Percentage variation in relative natural frequencies of cracked beam to uncracked beam has been used as input in the Fuzzy system. Surface plots using Fuzzy Logic Designer of MATLAB have been generated to obtain the dependence of output on specific input parameters.