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.