Archive | 2019
Crack detection in a shaft using finite difference technique
Abstract
Fatigue cracks arise in a rotor shaft due to cyclic loading. A growing crack in a machine element may lead to a calamitous failure of the machinery. Identification of crack at an early stage supports in safe and economic running of machinery. The appearance of crack in a shaft reduces local stiffness and causes a slope discontinuity in the shaft elastic line during vibration. Detection of slope discontinuity reveals the presence of crack in a shaft. However, in the presence of measurement noise, identification of slope discontinuity is difficult. In the present work, finite element model of a cracked simply supported shaft is considered for the simulation work. A transverse surface crack is considered for the cracked model. The shaft is assumed to be non-rotating and an external sinusoidal forcing is used to excite the shaft. To imitate actual experimentation, Gaussian noise is added in the simulated cracked shaft response. A dominant peak is observed at the crack position, which is obtained by using the central finite difference approximation on the simulated response of simply supported shaft. The method is used for the localization of the cracks present in the shaft. It is based on detecting the slope discontinuity in the elastic line of the shaft. The finite difference method based evaluation is also implemented for varying crack depth ratios at different signal to noise ratio (SNR).