Shaftis the critical part of machinery.
A crack present in a shaft may lead tocatastrophic failure which may affect the entire power transmission system ofthe machinery. So the early detection of crack is very necessary. Presence ofcracks in a shaft affects flexibility of the shaft near the crack which affectsthe entire dynamic vibrational response of the shaft. This information can beused to find out the crack position.
The shaft responsedo not possess sufficient information to detect the crack position, so a differenttechnique is needed to be applied to detect the accurate crack position.A lot of research is done todetect the crack position. Hong et al. 1 used continuous wavelet transform(CWT) with Mexican hat wavelet of order two and calculated lipschitz exponent to find out the damage. Sekhar 2 usedCWT to detect the crack in a rotor system which was not possible to detectby Fast Fourier Transform (FFT).
Han et al.3 used the index of wavelet packetenergy rate for the crack detection in beams. Shekharet al.4 used the mechanical impedance concept to detect the crack. Theycompared the differences of cracked and uncracked beam and found that there isa major difference in the mobility of cracked and uncracked/intact beam, and onthe basis of that they found the damage position along the shaft. M Ruckaand Wilde 5 used CWT to find the damage location in plate structures and beams.Babu et al.
6 applied Hilbert-Huangtransform (HHT) to the cracked rotor for the damage detection and found thatHHT gives better results compared to FFT andCWT for detecting the small crack.Singh and Tiwari 7 used proposedcrack probability function as an indicator of crack in a shaft system. Based onthis a multi crack localization and sizing algorithm (MCLSA) is developed forfinding the crack position. Doucka et al. 8 used CWT with the ‘symmetrical4’ analyzing wavelet (something missing).M Rucka 9 uses CWTwith ‘gauss4’ (missing). Papadopoulos et al. (2004)10 used Discrete wavelet transform (DWT)with ‘db3’ (missing) for the detection of crack in beam they calculatecompliancy matrix as a function of crackdepth and angular position and used Bspline curve fitting (first crack modelthen detection).
Wie Fan, Pizhong Qiao 11 used two dimensionalcontinuous wavelet transform with gauss mother wavelet of order 2 for detectionof crack in plate structure. M Rucka 12 usedthe higher order modes of the cantilever beam to detect the damage. They usedCWT with gauss4 wavelet. In the presentwork, forced vibration response is obtained using finite element analysis. Timoshenko model is used to .
It is assumed that theexternal forcing is applied in vertical direction only. The shaft response invertical direction is taken as the input signal for the wavelet transform.Discrete wavelet transform (DWT) with different wavelet is analyzed and out ofwhich it is found that sym4 wavelet is most suitable for detecting the crackposition. For DWT a suitable length of the shaft is chosen for clearvisualization of the spikes due to the crack present in the shaft.
It isfound that a shaft of length 1 m discretized into 160 or more elements gives betterand clear spikes at the crack position. For thepractical implementation, noise is added to the response of the shaft and it isfound that the crack is detected by the ‘sym4’ wavelet up to the 4% of the noise.