Comparative Study of FFT and Wavelet Techniques for Induction Machine Having Bearing Fault

IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

ISSN 2320 – 6020

Comparative Study of FFT and Wavelet Techniques for Induction Machine Having Bearing Fault Ashish Kamal and V. K. Giri ABSTRACT- Motor Current Signature Analysis (MCSA) has been successfully used for fault diagnosis in induction machines.

The current spectrum of the induction machine for locating characteristic fault frequencies is used in MCSA. The spectrum is obtained using a Fast Fourier Transformation (FFT) that is performed on the signal under analysis. The fault frequencies occur in the motor current spectra are unique for different motor faults. However FFT does not always achieve good results with nonconstant load torque. Other signal processing methods, such Wavelet transforms techniques may also be used for analysis. These techniques are capable of revealing aspects of data like trends, breakdown points, and discontinuities in higher derivatives, and self similarity which are not available in FFT analysis. In the present paper, the comparisons of various techniques are discussed to analyze the experimental results obtained.

KEYWORD - Induction Motor, Bearing fault, Wavelet transform, Fast Fourier transforms

INTRODUCTION Advances in digital signal processing technology have enabled researchers to process more data in less time. As a result, information that is not previously available can be extracted from the collected data. In the light of these developments, condition monitoring via MCSA has recently drawn more attention from researchers. MCSA focuses its efforts on the spectral analysis of the stator current and has been successfully used in the detection of broken rotor bars, bearing damage and the dynamic eccentricity [1]. MCSA analyzes the stator current in search of current harmonics directly related to new rotating flux components, which are caused by faults in the motor flux distribution [2]. The advantage of this technique is that it is well recognized nowadays as a standard due to its simplicity: It needs only one current sensor per machine and is based on straightforward signal processing techniques such as Fast Fourier transforms (FFT). But, Fourier analysis has also some other serious drawbacks. One of them may be that time information is lost in transforming to the frequency domain. When looking at a Fourier transform of a signal, it is impossible to tell when a particular event has taken place.

If it is a stationary signal – this drawback isn't very important. However, most interesting signals contain numerous non-stationary or transitory characteristics: drift, trends, abrupt changes, and beginnings and ends of events.

These characteristics are often the most important part of the signal, and Fourier analysis is not suitable in detecting them.

The aim of this paper is to discuss the importance of FFT and wavelet transforms methods for stator-current analysis to detect the bearing faults in induction machines.

BEARING FAULT A characteristic frequency đ?‘“đ?‘“đ?‘?đ?‘? can be associated with each type of bearing fault. This frequency corresponds to the periodicity of occurrence of the abnormal physical phenomenon related to the existence of the fault. For example if one considers a hole on the outer raceway, then, as the rolling elements move over the defect, they are regularly in contact with the hole which produces an effect on the machine at a given frequency. The characteristic frequencies are functions of the bearing geometry and the mechanical rotor frequency đ?‘“đ?‘“đ?‘&#x;đ?‘&#x; . A detailed calculation of these frequencies can be found in [4]. The frequencies of the two fault types considered here, are given by Outer Raceway đ?‘“đ?‘“đ?‘œđ?‘œ =

đ?‘ đ?‘ đ?‘?đ?‘?

đ?‘“đ?‘“đ?‘œđ?‘œ =

đ?‘ đ?‘ đ?‘?đ?‘?

đ??¸đ??¸

đ?‘“đ?‘“đ?‘&#x;đ?‘&#x; ďż˝1 −

đ??ˇđ??ˇ đ?‘?đ?‘?

cos ���

(1)

đ?‘“đ?‘“đ?‘&#x;đ?‘&#x; ďż˝1 +

đ??ˇđ??ˇ đ?‘?đ?‘?

cos ���

(2)

Inner Raceway • Author Ashish kamal is currently pursuing master of technology program in Power Electronics and Drives from Madan Mohan Malaviya Engineering College, Gorakhpur, Uttar Pradesh, India.. E-mail: hsihsamtec@gmail.com. • Co-Author V. K. Giri is currently Professor and Head

of Department of Electrical Department in Madan Mohan Malaviya Engineering College, Gorakhpur, Uttar Pradesh, India. E-mail:girivkmmm@gmail.com.

đ??¸đ??¸

đ??ˇđ??ˇđ?‘?đ?‘?

đ??ˇđ??ˇđ?‘?đ?‘?

Where đ?‘ đ?‘ đ?‘?đ?‘? is the number of balls, đ??ˇđ??ˇđ?‘?đ?‘? & đ??ˇđ??ˇđ?‘?đ?‘? are the inner and outer raceway diameters, and β is the slip angle as shown in Fig. 1.

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

ISSN 2320 – 6020 Where, the arctangent function here returns values of phase between -p and +p , a full range of 2p radians.

Using the rectangular to polar conversion function to FFT (A) convert the complex array to its magnitude and phase đ?‘ đ?‘ (Ď•) is equivalent to using the preceding formulas.

FAULT DETECTION USING WAVELET TRANSFORM Fourier analysis uses the basic functions sin (t), cos (t), and exp(it). In the frequency domain, these functions are perfectly localized, but they are not localized in the time domain, resulting in a difficult to analyze or synthesize complex signals presenting fast local variations such as transients or abrupt changes [5]. To overcome the difficulties involved, it is possible to "window" the signal using a regular function, which is zero or nearly zero outside a time segment [-m, m]. The results in the windowedFourier transform [6]: đ??şđ??şđ?‘ đ?‘ (đ?‘¤đ?‘¤, đ?‘Ąđ?‘Ą) = âˆŤ đ?‘ đ?‘ (đ?‘˘đ?‘˘)đ?‘”đ?‘”(đ?‘Ąđ?‘Ą − đ?‘˘đ?‘˘) đ?‘’đ?‘’ đ?‘–đ?‘–đ?‘–đ?‘–đ?‘–đ?‘– đ?‘‘đ?‘‘đ?‘‘đ?‘‘

(5)

Shifting and scaling a different window function, called in this case mother wavelet, it is obtained the so called Wavelet Transform.

Fig. 1: Geometrical characteristics of the rolling-element bearings

√đ?‘Žđ?‘Ž

FAULT DETECTION USING FAST FOURIER TRANSFORMS (FFT) To detect the fault, spectrum is obtained using a Fast Fourier Transformation (FFT) that is performed on the signal under analysis. But, the FFT in the stator current is quite difficult to apply with accuracy due to problems such as frequency resolution, magnitude accuracy at steady state, and more generally, due to data processing [3]. The present paper discusses new methods (Wavelet transform) based on statorcurrent analysis for online fault detection in induction machines, which would overcome the averaging problems of classical FFT. This section also discusses bearing faults of induction motors which can be online detected with help of MCSA. The Power spectrum is computed from the basic FFT function. The power spectrum shows power as the mean squared amplitude at each frequency line. The amplitude of the FFT is related to the number of points in the timedomain signal. The following equation can be used to compute the amplitude and phase versus frequency from the FFT. Amplitude spectrum in quantity peak Magnitude[FFT(A)] = N ďż˝đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘…đ?‘… [FFT (A)]2 +đ??źđ??źđ??źđ??źđ??źđ??ź [FFT (A)]2 = (3) đ?‘ đ?‘ Phase spectrum in radians = Phase[FFT(A)] = arctangent ďż˝

img [FFT (A)] real [FFT (A)]

ďż˝

(4)

1

đ??şđ??şđ?‘ đ?‘ (đ?‘¤đ?‘¤, đ?‘Ąđ?‘Ą) = âˆŤ đ?‘ đ?‘ ďż˝ ďż˝ đ?œ‘đ?œ‘ ďż˝

đ?‘Ąđ?‘Ąâˆ’đ?‘˘đ?‘˘ đ?‘Žđ?‘Ž

ďż˝ đ?‘‘đ?‘‘đ?‘‘đ?‘‘

(6)

Where, a is the scale factor, u is the shift, Ď• (t) is the mother wavelet and đ??şđ??şđ?‘ đ?‘ (đ?‘¤đ?‘¤, đ?‘Ąđ?‘Ą) is the wavelet transform of function s(t).

The discrete version of Wavelet Transform, DWT, consists in sampling not the signal or not the transform but sampling the scaling and shifted parameters. This result in high frequency resolution at low frequencies and high time resolution at high frequencies, removing the redundant information . A discrete signal x[n] could be decomposed: đ?‘—đ?‘— −1 đ?‘Ľđ?‘Ľ[đ?‘›đ?‘›] = ∑đ?‘˜đ?‘˜ đ?‘Žđ?‘Žđ?‘—đ?‘—đ?‘—đ?‘— ,đ?‘˜đ?‘˜ đ?œ™đ?œ™đ?‘—đ?‘—đ?‘—đ?‘— ,đ?‘˜đ?‘˜ [đ?‘›đ?‘›] + ∑đ?‘—đ?‘— =đ?‘—đ?‘—đ?‘—đ?‘— ∑đ?‘˜đ?‘˜ đ?‘‘đ?‘‘đ?‘—đ?‘— ,đ?‘˜đ?‘˜ đ?œ‘đ?œ‘đ?‘—đ?‘— ,đ?‘˜đ?‘˜ [đ?‘›đ?‘›] (7)

Where, Ď•[n] = Scaling function đ?‘—đ?‘— 0

đ?œ™đ?œ™đ?‘—đ?‘—đ?‘—đ?‘— ,đ?‘˜đ?‘˜ [đ?‘›đ?‘›]=2 2 đ?œ™đ?œ™(2đ?‘—đ?‘— đ?‘œđ?‘œ đ?‘›đ?‘› − đ?‘˜đ?‘˜): Scaling function at scale s=2đ?‘—đ?‘— đ?‘œđ?‘œ shifted by “kâ€?. φ (n)= Mother wavelet đ?‘—đ?‘—

đ?œ‘đ?œ‘đ?‘—đ?‘—đ?‘—đ?‘— ,đ?‘˜đ?‘˜ [đ?‘›đ?‘›] = 22 đ?œ‘đ?œ‘(2đ?‘—đ?‘— đ?‘›đ?‘› − đ?‘˜đ?‘˜): Scaling function at scale s=2đ?‘—đ?‘— shifted by “kâ€?. đ?‘Žđ?‘Žđ?‘—đ?‘—đ?‘—đ?‘— ,đ?‘˜đ?‘˜ : Coefficient of approximation at scale s=2đ?‘—đ?‘—đ?‘—đ?‘— đ?‘‘đ?‘‘đ?‘—đ?‘— ,đ?‘˜đ?‘˜ : Coefficient of detail at scale s=2đ?‘—đ?‘— N= 2đ?‘—đ?‘— : being N the number of sample of samples of x[n]

In order words, a discrete signal could be constructed by means of a sum of a j − jo details plus a one approximation of a signal at scale s = 2đ?‘—đ?‘— đ?‘œđ?‘œ .The details and the approximations at different scales could be obtained by means of a tree decomposition showed in Fig. 2.

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

Fig. 2: Wavelet Tree Decomposition

ISSN 2320 – 6020

Fig. 4: Frequency Spectrum of Induction Motor having Bearing Fault

RESULT AND ANALYSIS The frequency spectrum of stator current of healthy induction motor is shown in fig. 3. From the fig. 3, it can be seen that the fundamental frequency (50Hz) has maximum amplitude of 103 db and other harmonic components has a range of amplitudes from -4 db to 90 db.

Hence, the presence of harmonics component fundamental frequency in the current spectrum can detected by transforming signal from time-domain frequency-domain. But, the percentage of change magnitude is not clearly visible in frequency domain.

of be to in

1. FFT ANALYSIS Fig. 5 shows the FFT analysis of current spectrum of healthy induction motor. Where, the relative magnitude of harmonics component is shown.

Fig. 3: Frequency Spectrum of Healthy Induction Motor

The stator current of induction motor having bearing fault, leads to fig. 4. It can be seen from the fig. that harmonic components has a magnitude range slightly larger than as in case of healthy induction motor i.e. 0 db to 90 db.

Fig. 5: FFT Analysis of Current Spectrum of Healthy Induction Motor

In case of healthy induction motor, 48 Hz, 49 Hz, 51 Hz and 52 HZ frequency has a relative magnitude 6 %, 12%, 14 % and 8 %. It can be seen in fig. 5.

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IJBSTR RESEARCH PAPER VOL 1 [ISSUE 7] JULY 2013

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Fig. 6: FFT Analysis of Current Spectrum of Induction Motor having Bearing Fault.

Fig. 6 shows the FFT of current spectrum of induction motor having bearing fault. It can be seen from fig.6 that even the frequency 48, 49, 51, and 52 has increased their relative magnitude, but also other frequency harmonic has also increased their magnitude.

Since, a particular order of frequency is fixed for certain type of fault. But, the FFT analysis of a signal is not capable to identify the certain fault.

2. WAVELET ANALYSIS

Fig.8: Decomposition of Stator Current of Induction Motor having bearing fault at 12 Levels

Now in fig.8, the waveform of decomposition level 12 has magnitude 4 units. This rise in magnitude shows the presence of damage in the motor. The frequency of waveform of decomposition level 12 alters slightly.

The wavelet analysis is performed on current spectrum of both healthy and damage bearing motor. The decomposition level is set at 12, to obtain lower frequency order.

CONCLUSION Fig. 7, Shows the decomposition of stator current spectrum at level 12. It can be seen from the fig. that decomposition at level 12, the magnitude of lower frequency is 2.

In this paper, Motor current signature analysis for the detection of induction motor faults based on FFT and wavelet analysis of stator current are discussed with some experimental results which are useful for online diagnosis in industrial applications. MCSA detects changes in a machine’s permeance by examining the current signals and uses the current spectrum of the machine for locating characteristic fault frequencies. The spectrum is obtained using a Fast Fourier Transformation (FFT) that is performed on the signal under analysis. The fault frequencies that occur in the motor current spectra are unique for different motor faults. However this method does not always achieve good results with not constant load torque. Therefore, this paper proposes a different signal processing methods: Wavelet Transform. The wavelet transform determines the sinusoidal frequency and the phase content of the local sections of a signal as it changes over time. At last, we can conclude that the wavelet analysis can effectively diagnose bearing fault in induction motor.

REFERENCES 1.

Fig.7: Decomposition of Stator Current of Healthy Induction Motor at 12 Levels

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Neelam Mehala, Ratna Dahiya “An Approach of Condition Monitoring of Induction Motor Using MCSA”, International Journal of Systems Applications, Engineering & Development, Volume 1, Issue 1, pp. 13-17, 2007.

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