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 shaft response

do not possess sufficient information to detect the crack position, 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 to detect

by Fast Fourier Transform (FFT). Han et al.3 used the index of wavelet packet

energy rate for the crack detection in beams. Shekhar

et al.4 used the mechanical impedance concept to detect the crack. They

compared the differences of cracked and uncracked beam and found that there is

a major difference in the mobility of cracked and uncracked/intact beam, and on

the basis of that they found the damage position along the shaft. M 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 used proposed

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

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

finding the crack position.

Doucka et al. 8 used CWT with the ‘symmetrical4’ analyzing wavelet (something missing).

M Rucka 9 uses CWT

with ‘gauss4’ (missing). Papadopoulos et al. (2004)

10 used Discrete wavelet transform (DWT)

with ‘db3’ (missing) for the detection of crack in beam they calculate

compliancy matrix as a function of crack

depth and angular position and used Bspline curve fitting (first crack model

then detection). Wie Fan, Pizhong Qiao 11 used two dimensional

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

of crack in plate structure. M Rucka 12 used

the higher order modes of the cantilever beam to detect the damage. They used

CWT with gauss4 wavelet.

In the present

work, forced vibration response is obtained using finite element analysis. Timoshenko model is used to . 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 DWT a suitable length of the shaft is chosen for clear

visualization of the spikes due to the crack present in the shaft. It is

found that a shaft of length 1 m discretized into 160 or more elements gives better

and clear spikes at the crack position. For the

practical implementation, noise is added to the response of the shaft and it is

found that the crack is detected by the ‘sym4’ wavelet up to the 4% of the noise.