Mehdi Arehpanahi S.
H.
H Sadeghi J.
Milimonfared H. R. Akbari Roknabadi
Department of Electrical Engineering, Amir kabir University of Technology
Number 421, Hafez Ave, Tehran, Iran
Tel: +98(21) 64543363, Fax: +98(21) 6413969
Abstract The fault of broken rotor bars in a three phase induction motor is diagnosed by using the wavelet multiresolution analysis .in this paper. Daubechies wavelet is selected as the wavelet base and the wavelet coefficient is obtained from the wavelet transform of current derivative signal of the faulty induction motor. The wavelet reconstruction of a signal branch is processed. The signals energy in different levels is compared together. Simulation result show that different broken rotor bar have different energy in level three. Based on this number of broken rotor bar is obtained.
I. INTRODUCTION identify rotor bar faults, Most of witch are strongly dependent on detecting the twice slip frequency modulation due to the speed or torque in stator current [3-
4]. Several published works are related to rotor bar failures in squirrel cage induction motor are based on machine current signature analysis [5]. In this way fast
Fourier transform is used to show the effect of this fault on frequency spectrum of current signal. Broken rotor bars in squirrel cage induction machine results the presence of two sidebands at frequency ( 1
±
2 s ) f around the main frequency component in the stator current spectrum [6]. Estimation of rotor resistance is another
The most popular way of converting electrical energy to mechanical energy is squirrel cage induction motor.
These motors play a crucial rule in modern industrial plants, however there are adverse service conditions. This approach, which is reported in [7]. Although the Fourier transform is an effective method, it is useful for stationary signal processing and the transform signal may lose some time domain information. The limitation of Fourier risk of motor failing can be remarkably reduced if normal service conditions can be arranged in advance [1]. The occurrence of mechanical fault on induction motors results in an asymmetry in the winding and/or eccentricity transform is analyzing non-stationary signals lead to the introduction of time-frequency or time scale signal processing tools, assuming the independence of each frequency channel when the original signal is of air gap, which leads to a change in the air gap space harmonics distribution [2].
In recent years rotor fault diagnosis has became a challenging topic for many electric machine researchers. decomposed. The task of distinguishing the fault conditions from the normal conditions based on the resultant FFT spectrum is a difficult one. This is due to the fact that the stator current is a non-stationary signal
The majority of all rotor failures are caused by combination of various stresses [3], namely:
•
Thermal stresses due to thermal overload and unbalance, hot spot or excessive losses, sparking
•
Magnetic stresses caused by electromagnetic whose properties vary with respect to the time variant normal operation conditions of the motors such as load torque and power operation supply. Short-Time Fourier transform, which windows the input signal, overcomes time location problems to some extent. However by forces, unbalanced magnetic pull, electromagnetic noise and vibration.
•
Dynamic stresses arising from shaft torque, components, this approach does not provide either multiple resolution or temporal resolution [8]. This centrifugal forces and cyclic stresses. assumption may be considered as the limitation of this
Mechanical stresses due to loose lamination, fatigued parts, bearing failure and, etc .
Since 1980 rotor bar fault detection has became a challenging issue and it still attracts researcher attention.
Different diagnosis techniques have been developed to approach. Wavelet transform is a method for time varying or non-stationary signal analysis, and uses a new description of spectral decomposition via the scaling concept. Wavelet theory provides a unified framework for a number of techniques, which have been developed for various signals processing application [9]. Another
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method for detection of rotor broken bar is using wavelet transform and signal energy in sixteenth level which is reported in [10]. In [10] the difference between levels is very close together therefore fault diagnosis is to be difficult. This paper proposes a new method for mechanical fault feature extraction of three-phase squirrel cage induction motor based on wavelet packet decomposition is then expressed as : x ( t )
=
j k Z
C ( j , k )
ψ j , k
( t )
(2) and approximation, which is the projection of
W
0
0
( n )
=
W j
2
+ l
1
+
1
( n ) x ( n ),
=
W j
2 l
+
1
( n )
= i
L
2
−
1
=
0 h
0
( i ) W j l
( 2 j
L
2
−
1 i
=
0 h
1
( i ) W j l
( 2 j i
− n ) x (t ) onto approximation apace
V j
+
1 and detail space
W j
+
1 is also divided. Wavelet packet Decomposition adds redundancy to the transformation by expanding each packet recursively.
The transformation of the input sequence can be described iteratively as follows given a low pass filter decomposition of stator current derivative for better identification. Wavelet is a time frequency analysis tool originated from seismic signal analysis, which uses narrow windows for high frequency component [11]. The window width of wavelet analysis is automatically adjusted for various frequency components. Two important characteristics, i.e. time localization ability and multi-resolution analysis, make wavelet very attractive for
{ h
1
( l )} l
L
=
2
0 a high pass filter
{ h
0
( l )} l
L
=
2
0 having a finite impulse response of size k, and a decomposition Depth j.
In Fig.1 an example is shown for such a division. The original space is divided into detail the purpose of fault detection and diagnosis. The underlying idea of proposed method is to use wavelet packet decomposition to decompose the stator current derivative into time-frequency spectrum, and use the result to calculate and to choose proper feature coefficient which best describe the mechanical faults. The feature signature for broken rotor bar is presented in this paper.
The remainder of this paper is organized as follows. i
− n )
(3) and approximation spaces by the high pass filter h
0
Section 2 describes the fundamentals of wavelet packet decomposition and the proposed feature coefficients and energy level. Using the feature energy level analysis to the broken rotor bar is presented in section 3. Simulation results on a small induction motor are presented in section
4. where wavelet.
Wavelet packet decomposition (WPD) is an extension of wavelet transform that is obtained by generalizing the link between multi-resolution approximation and wavelets.
For multi-resolution analysis (MRA), a space decomposed into lower resolution space space
W j
+
1
ψ j , k
( t )
=
2 j / 2 ψ
( 2
. At each level j j − k )
is used for dyadic
V j
+
1
V j is
and a detail
, signal is divided into detail and low pass filter h
1 , respectively. And then the detail space is still divided into two sub-spaces, detail space and approximation space. The result detail signal is further divided. The recursive splitting of vector space is represented in a binary tree in Fig. 3.b, where the node of binary tree is labeled by its depth j and node number k
II. WAVELET PACKET DECOMPOSITION [8]
For any given signal x ( t )
∈
L
2
( R ) the discrete wavelet transform is defined as inner production of the wavelet function and the signal, that is :
C ( j , k )
= n
∑
∈
Z x ( n )
ψ j , k
( n )
(1) where, x ( n ) is the signal to be analyzed and
ψ j , k
( n ) is the discrete wavelet function. The wavelet and corresponding space is denoted as
W j k
. It is proved that there are more than 2
2 j
−
1
different wavelet packet orthonormal bases included in a full wavelet packet binary tree of depth j. Each of this packets has a limited time support as well as frequency support. For any of the wavelet packet tree, the wavelet packet coefficients are given as : d j , k
[ n ]
=< x ( t ),
ψ j , k
( t
−
2 j n )
>
(4)
The set of functions: W j,n = ( W j,n,k ( x ), k
∈
Z ) is the ( j , n ) wavelet packet. For positive values of integers j and n , wavelet packets are organized in trees. The tree in Fig. 6-
40 is created to give a maximum level decomposition equal to 3. For each scale j , the possible values of parameter n are: 0, 1, ..., 2 j -1.
The notation W j,n , where j denotes scale parameter and n the frequency parameter, is consistent with the usual depth-position tree labeling :
W
0,0
= (
φ( x- k, k
∈
Z) and W 1 1=
ψ (
x/2-k, k
∈
Z)
It turns out that the library of wavelet packet bases contains the wavelet basis and also several other bases.
More precisely, let V 0 denote the space (spanned by the family W 0,0 ) in which the signal to be analyzed lies; then
(W d ,1 ; d
≥
1) is an orthogonal basis of V 0 . For every strictly positive integer D , ( W D,0 , ( W d,1 ; 1
≤ d
≤
D )) is an orthogonal basis of V 0 . The discrete wavelet transform
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provides, at each instant of time, a set of coefficients for different levels.
In this study we use Winding Function Method (WFM) for three phase squirrel cage induction motor simulation using MATLAB software. Then one, two, three and four rotor bar is broken for fault analysis and broken rotor bar detection. Simulation results” stator current “are shown in
Fig. 3, 4, 5, 6 and 7 respectively.
5
4
3
2
1
)
A t n e rr u
C
0
-1
-2
-3
-4
-5
0 50 100 150 200
Time (ms)
250 300 350
Figure 1 : The wavelet packet filter bank decomposition and the corresponding binary tree. h0 :high pass filter h1: low pass filter
Figure 3 : healthy stator current
Figure 2 Wavelet packets organized in a tree, scale j defines depth and frequency n defines position in the tree
These coefficients are used for fault detection. This index can be interpreted as the amount of “energy “in the signal. Specific level. Using this index, we can explore the “energy” distribution of the measured stator current derivative to determine whether the motor is healthy or not.
2
1
)
( t e rr u
C
0
-1
-2
-3
-4
-5
0
5
4
3
50 100 150 200
Time (ms)
250 300
Figure 4: one broken rotor bar stator current
350
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6
4
2
)
A t e rr u
C
0
-2
-4
-6
0
6
4
2 e rr
)
( t 0
-2
-4
-6
0
50 100 150 200
Time (ms)
250 300
Figure 5 two rotor broken bar stator current
50 100 150 200
Time (ms)
250 300
Figure 6: three rotors broken bar stator current
350
350 higher than signal and can be seen signal details better.
Fig. 8 and 9 show stator current derivative for one and four broken rotor bar respectively. We calculate value of five levels stator current derivative energy for five conditions (healthy, 1, 2, 3 and 4 broken rotor bars) and put results in the table I. Daubechies orthonormal wavelet basis of order 10 is used for this analysis. Length of observation window is 19 cycles and contain 3872 point
(sample rate=10 KHz ). In all cases, induction motor is running in 80% of full load torque. Table 1 shows variation of energy of each detail stator current derivative for each scale. This energy is normalized by total signal energy like per unit systems. According table I results energy in level three is different by number of rotor bars clearly that can be used in broken rotor bar detection.
0.05
)
( t e rr u
C
0
-0.05
-0.1
-0.15
-0.2
-0.25
0
0.25
0.2
0.15
0.1
50 100 150 200
Time (ms)
250 300 350
Figure 8 : one rotor broken bar stator current derivative
6
4
2
)
( t e rr u
C
0
-2
-4
0.05
)
A t n e rr u
C
0
-0.05
-0.1
-0.15
-0.2
-0.25
0.25
0.2
0.15
0.1
-6
0 50 100 250 300 350
0 50 100 150 200
Time (ms)
250 300 350
150 200
Time (ms)
Figure 7: four rotors broken bar stator current
Figure 9: four rotors broken bar stator current derivative
For stator current analysis we use stator current derivative energy because in derivative, signal variation is
The difference between signals is on the energy level that is shown in table 1. In table 1, energy levels in five
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scales are shown that in third level difference between broken rotor bars is higher than others. Energy level in third level is the best way for broken bar rotor detection.
Table 1 : energy of each scale in healthy and faulty cases
Level
1
2
3
4
Number of broken bars
0 1 2 3 4
0.54 0.03 0.57 0.49
0.56 1.21 1.08 0.03
0.38
0.68
4.45 23.01 18.5 16.48
13.46
2.91 6.42 5.09 5.64
3.78
5 0.34 0.42 1.55 1.6
0.98
All number in table is normalized in present
IV. CONCLUSION
[7] J. L. De. Castro and Manzanedo, B. Novo and M. P. Donsion
“ Detection Of Broken Rotor Bars In Induction Mchines
Based on Rotor Resistance Estimation ” Espoo Finland,
ICEM 2000, 28-30 August 2000, pp. 859-862
[8] W. T. Thomson, I. D. Stewart, “ On-line Current Monitoring
For Fault Diagnosis Inverter /fed Induction Motor ”, Life management of power plants, International Conference, 1994, pp. 66-73
[9] Zhongming Ye ,Bin Wu and A. R. Sadeghian, “ Signature
Analysis on Induction Motor Mechanical Faults by Wavelet
Packet Decomposition ” IEEE Industrial Application, 2001, pp. 1022-1029
[10] K. Abbaszadeh, J. Milimonfared, H. Haji and H. A. Toliyat,
“ Broken Bar Detection In Induction Motor Via Wavelet
Transformation ”, The 27 th
Annual Conference of the IEEE
Industrial Electronics Society, 2001, pp. 95-99
[11] Cao Zhitong, Chen Hongping, He Guoguage and Ewen
/Ritchie, “ Rotor Fault Diagnosis of Induction Motor Based on Wavelet Reconstruction ” Electrical Machines and Systems,
2001. ICEMS 2001. Proceedings of the Fifth International
Conference Vol. 1, pp.374-377
Signal decomposition via wavelet transform and wavelet packet provides a good approach of multiresolution analysis. The decomposed signals are independent due to the orthogonality of the wavelet function. There is no redundant information in the decomposed frequency bands.
Based on the information from a set of independent frequency bands, mechanical condition monitoring and fault diagnosis can be performed effectively.
This work shows a new approach in detection of broken rotor bars in squirrel cage induction motors having only stator line current derivatives as input. The detection is based on the Discrete Wavelet Decomposition method.
It shows that the effectiveness of the proposed method for this kind of fault. 3-hp squirrel cage induction motor with cast aluminum rotor bars is utilized in for our simulations.
The result can be used as an extra feature for the proposed
Bayes minimum error classifier.
REFRENCES
[1] H. Bonnet, G. C. Soukup, “ Cause and Analysis of Stator
Rotor Failures in Three-Phase Squirrel Cage Induction
Motor ”, IEEE Transaction on Industry Applications, Vol. 28,
No. 4, July/August 1992
[2] Hargis, B. G. Gaydon and K. Kamash,” The Detection of
Rotor Bar Failures in Induction Motors ” IEEE International
Conference on electrical Machine Design and Applications,
1982, pp. 216-220
[3] W. Deleroi, “ Squirrel Cage Motor with Broken Bar In The
Rotor in the Rotor Physical Phenomena and Their
Experimental Assessment ” Pro. ICEM’82, Budapest,
Hungary, 1982, pp. 767-770
[4] G. B. Kliman, J. Stein, “ Methods of Motor Current Signature
Analysis ” Electric Machine and Power Systems, 1992, pp.
463-474
[5] Benbouzid and M. Vieira, “Induction Motor Fault Detection and Localization Using Stator Current, Advanced Signature
Processing Technique ” IEEE Trans. Industrial Application
1995, Vol. 3 ,No. 1
[6] S. L. Ho, W. L. Chan and H. W. Leung, “ Application of
Statistical Signal Processing for Condition Monitoring of
Rotor Faults in Induction Motor ” Electrical Machines and
Drives, Sixth International Conference, 1993, pp. 97-102
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