Introduction

Shaft

is the critical part of machinery, a crack present in the shaft may lead to a

catastrophic failure which may affect the entire power transmission system of

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

in a shaft affects flexibility of the shaft at or near the crack which affects

the entire dynamic vibration response of the shaft. This information is used to

find out the crack position. The shaft response doesn’t have sufficient

information to detect the crack position so it is needed to apply different

technique to detect the accurate crack position.

A lots of research is done to

detect the crack position, hong et al. (2002) used continuous wavelet transform

(CWT) with maxican hat wavelet with two vanishing moment and calculate lipschitz exponent to find out the damage. Sekhar (2004a) used CWT to detect the crack of a

rotor system which is not possible to detect by Fast Fourier Transform (FFT). Han

et al. (2005) used the index of wavelet packet energy rate for the crack

detection of beam. shekhar et al. (2005) 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 beam and on the basis of that they found the damage position of the

shaft. Rucka and wilde (2006a) uses CWT to found the damage location in plate

structures and beam.

Babu et al. (2008) applied

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

found that HHT gives better results with comparison to FFT and CWT for

detecting the small crack.

Sachin Kumar Singh et al. used a

finite element formulation of Timoshenko beam and defined crack probability

function based on this a multi crack localization and sizing algorithm (MCLSA) is developed for finding the crack position.

Doucka, S.Loutridis, A.trochidis

used continuous wavelet transform (CWT) with the ‘symmetrical4’ analyzing

wavelet, Megdalena Rucka uses CWT with ‘gauss4’ , Papadopoulos et al. (2004)

used Discrete wavelet transform (DWT) with ‘db3’ for the detection of crack in beam. Rucka and wilde (2007) compared the

derivatives and wavelet transform and found that wavelet

transform provides fine results with comparison to derivative for a noisy

signal. Magdalena Rucka (2011) used the higher order modes of the beam to

detect the damage; they used CWT with gauss4 wavelet.

Here in this work forced

vibration response of the Timoshenko shaft is generated, it is assumed that the

external forcing is applied in vertical direction only, this response 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 the shaft length greater than 120

gives better and clear spikes at the crack position. For the practical

implementation the 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.