Shaft [1] used continuous wavelet transform (CWT) with Mexican

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.

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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.