Shaft is

the critical part of machinery. A crack present in a shaft may lead to

catastrophic failure which may affect the entire power transmission system of

the machinery. So the early detection of crack is very necessary. Presence of

cracks in a shaft affects flexibility of the shaft near the crack which affects

the entire dynamic vibrational response of the shaft. This information can be

used to find out the crack position. The crack position can’t be seen directly

from the shaft response, so a different technique is needed to be applied to

detect the accurate crack position. A lot of research is done to detect 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 used CWT to detect the crack in a rotor system which was

not possible by Fast Fourier Transform (FFT). Han et al. 3 used the index of

wavelet packet energy rate for the crack detection in beams. Sekhar et al. 4

used the mechanical impedance concept to detect the crack. They compared the

differences of cracked and intact beam and found that there is a major

difference in the mobility of cracked and intact beam, and on the basis of that

they found the damage position along the shaft. Rucka and Wilde 5 used CWT to

find the damage location in plate structures and beams. Babu et al. 6 applied

Hilbert-Huang transform (HHT) to the cracked rotor for the damage detection and

found that HHT gives better results compared to FFT and CWT for detecting the

small Crack.

Singh and Tiwari 7 proposed

crack probability function as an indicator of crack in a shaft system. Based on

this a multi crack localization and sizing algorithm (MCLSA) was developed for

finding the crack position. Doucka et al. 8 used CWT with sym4 mother wavelet

to detect the crack position. They also defined an intensity factor to relate

the size of the crack to the coefficients of the wavelet transform. Rucka and

Wilde 9 used CWT with gaus4 mother wavelet to detect the crack position in

cantilever beams. Papadopoulos et al. 10 calculated compliance matrix as a

function of crack depth and angular position and used B-spline curve fitting.

They used discrete wavelet transform (DWT) with ‘db3’ mother wavelet (missing)

for the detection of crack in beams. Fan and Pizhong 11 used two dimensional

continuous wavelet transform with gauss mother wavelet of order 2 for detection

of crack in plate structure. Rucka 12 used the higher order modes of the

cantilever beam to detect the damage. They used CWT with gaus4 mother wavelet.

In the present work, forced

vibration response is obtained using finite element analysis. It is assumed

that the external forcing is applied in vertical direction only. The shaft

response in vertical direction is taken as the input signal for the wavelet

transform. Discrete wavelet transform (DWT) with different wavelet is analyzed

and out of which it is found that sym4 wavelet is most suitable for detecting

the crack position. For the applicability of the method in the real field

problems noise is added to the signal.