Introduction Megdalena Rucka uses CWT with ‘gauss4’

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.

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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.