Gear fault detection using vibration analysis and continuous wavelet transform

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Procedia Materials Science 5 (2014) 1846 – 1852
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© 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
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2211-8128 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Selection and peer-review under responsibility of Organizing Committee of AMME 2014
doi:10.1016/j.mspro.2014.07.492
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Kiran Vemekar et al. / Procedia Materials Science 5 (2014) 1846 - 1852
In an engine manufacturing industry, defects in gears may be arises during the assembly process in production line.
Therefore, it is necessary to identity and eliminate the defective engines going into the market. Each component of
engine equipment has a different signature in time and frequency spectrum.Time domain represents the dynamic
responses depend on the interaction of many components of the system. In time versus frequency domain, wavelet
transform (WT) facilitates multi-resolution analysis and hence, becomes popular to extract characteristics features of
non-stationary vibrations signals.
Wavelet analysis are informative in scale (frequency)-time domain, compared with conventional vibration
spectrum analysis which gives frequency domain information. (Peng et al. 2003). Tse et al. (2004) used exact
wavelet analysis for machine fault diagnosis. Saravanan et al. (2010) examined the spur gear box fault detection
using discrete wavelet for feature extraction and artificial neural network used as a classifier. Chandran et al. (2012)
application of Laplace wavelet kurtosis used for fault diagnosis of gears. Al-Badour et al. (2011) time, frequency and
wavelet analysis used study blade and shaft vibrations of turbo-machinery. Amamath (2008) made an attempt
experimentally with help of vibration and acoustic signalsfor fault detection of helical gear using Daubechie wavelet.
Srikanth (2008) used conventional vibration analysis for the fault detection of two stroke internal combustion (IC)
engines. The purpose of this paper is to extend the application of Fourier transform and continuous wavelets for fault
diagnosis of gear used in internal combustion engine.
1.1 Fourier transform
Fourier transform (FT) is most widely used in vibration signal analysis. It simply converts given signal from time
domain to frequency domain by integrating the given function over the entire time period. The integral Fourier
transform for a non-periodic function x(t) is given by,
x(f) =
XCM)eiwC du
(1)
X(w) =
x(t) e~lu>t dt
(2)
Where, tuis fundamental frequency.Using these equations, a signal can be transformed into the frequency domain
and back again. The FT is well suited to analyze stationary periodic functions-which will exactly repeat themselves
once over period, without modification.Fourier transform is particularly used to convert a function from the
continuous time to the continuous frequency domain, where as fast Fourier transform (FFT) is an efficient algorithm
to compute the discrete Fourier transform and it’s inverse. FT technique earned much of the importance in
processing stationary signal. FFT is the one of the extension of it.
1.2 Wavelet Transform
The FT is not very useful for analyzing non-stationary signals since it fail to describe the frequency content of a
signal at particular time. In signal processing, the limitation of FT led to the introduction of new Time-frequency
analysis called Wavelet transform (WT). It is improved version of Fourier transform, can be used for analysing the
components of a stationary signal.
Generally conventional data processing is computed in time or frequency domain. Wavelet processing combines
both time and frequency. In simple language, we use term called ‘time-frequency’ analysis. A wavelet is a basis
function characterized by, two aspects, one is its shape and amplitude, which is chosen by user. Second one is its
scale (frequency) and time (location) relative to the signal.
The continuous wavelet transform can be used to generate spectrograms which show the frequency content of
signals as a function of time. A continuous-time wavelet transform of x(t) is defined as:
CWT Xv(a,b) =^fZ,xCt)W*(^ dt, {a,bcR,a*0
(3)
In above equation \|/ (t) is a continuous function in time domain as well as the frequency domain called the mother
wavelet and y* (t) indicates complex conjugate of the analysing wavelet y (t). The parameter ‘a’ is termed as scaling
1848
Kiran Vernekar et al. /Procedia Materials Science 5 (2014) 1846 - 1852
parameter and ‘b’ is the translation parameter. The transformed signal Xv(a,b)is a function of the translation
parameter ‘b’ and the scale parameter ‘a’. In WT, signal energy is normalized by dividing the wavelet coefficients
by -r= at each scale.
Vial
1.2.1 Morlet Wavelet
The Morlet wavelet transform is belongs to CWT family. It is one of the most popular wavelet used in practice
and its mother wavelet is given by,
lit
wo \
•P(t) — 7F
eJWot — e 2 / 6 2
V7T \
(4)
In above equation, w0 refers to central frequency of the mother wavelet. The term e 2 involved in above
equation is specifically used for correcting the non-zero mean of the complex sinusoid, and in most of cases, it can
be negligible when w0>5. Therefore when the central frequency w0>5, the mother wavelet redefined as follows;
«P(t) = 4^ e>°£e~T
(5)
V7T
2. Experimental studies
The test rig setup was constructed to study fault detection of gear used in IC engine. The details about the
experimental setup and experimental procedure are discussed in the following subsections.
2.1 Experimental setup description
The below figures shows the Line sketch and experimental engine test setup used for fault detection of gear used in
internal combustion engine. The experiments were conducted on the Kawasaki Bajaj KB-100 two stroke spark
ignition engine. In practice, the engine conditions are monitored at idle speed, which is nearer to 1000 rpm.
Therefore the experiment has been carried out at constant rotational engine speed of 1080 rpm at 4th gear position.
Here the engine speed refers to the rotational speed of the crank. The engine was driven by using 3 Hp DC motor.
The data has been acquired by using NI 9234 data acquisition (DAQ) card and analysed using Lab View 10.0
software from National Instruments (NI). Piezoelectric accelerometer with an operating frequency range between 1
to 5000 Hz was used to pick up vibration signals from the gear box casing.
D.C. Motor
Gear wheel
Fig. 1. Line sketch experimental setup.
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Kiran Vernekar et al. / Procedia Materials Science 5 (2014) 1846 – 1852
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