- Email: [email protected]
A Fault Diagnosis Approach for Broken Rotor Bars Based on EMD and Envelope Analysis
Jun. 2007
Journal of China University of Mining & Technology
Vol.17
No.2
J China Univ Mining & Technol 2007, 17(2): 0205–0209
A Fault Diagnosis Approach for Broken Rotor Bars Based on EMD and Envelope Analysis ZHANG Jian-wen, ZHU Ning-hui, YANG Li, YAO Qi, LU Qing School of Information & Electrical Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China Abstract: Empirical Mode Decomposition (EMD) used to deal with non-linear and non-stable signals, is a time-frequency analytical method that has been developed recently. In this paper the EMD method is used to filter the noise from the stator current signal that arises when rotor bars break. Then a Hilbert Transform is used to extract the envelope from the filtered signal. With the EMD method again, the frequency band containing the fault characteristic-frequency components, 2sf, can be extracted from the signal's envelope. The last step is to use a Fast Fourier Transform (FFT) method to extract the fault characteristic frequency. This frequency can be detected in actual data from a faulty motor, as shown by example. Compared to the Extend Park Vector method this method is proved to be more sensitive under light motor load. Key words: EMD; analysis of envelope; fault of broken rotor bar CLC number: TM 343+.3
1
Introduction
At present, the most widely used method of detecting broken rotor bars in squirrel-cage induction motors is analyzing the stator current. When a rotor bar breaks the stator current will have spectral components, at a frequency of 1±2sf (f is the supply fundamental frequency; s is the per-unit slip), in every phase of the motor due to the broken bar. Therefore, broken rotor bars can be diagnosed by detecting these spectral components (1±2sf) in the stator current; the status of the broken rotor bars can be qualitatively estimated from the amplitude of the sideband frequencies (1±2sf). However, it is often difficult to effectively detect the sideband frequencies due to interference from the fundamental driving frequency. Electric motor monitoring and diagnosis via both a Park-vector and an extended Park-vector (EPV), which analyzes the squared modulus of the Parkvector from a spectral standpoint, approach has been put forward [1]. The EPV method transforms the fundamental components of the three-phase current into direct current, which makes obvious the side- band frequency at 2sf generated by faults such as broken
rotor bars or cracked end-rings. Despite the great improvement in detecting broken rotor bars with the EPV approach, the characteristic fault-frequency (2sf) can not be detected when the load is light or nonexistent. In this paper a new method combining Empirical Mode Decomposition (EMD) and Envelope Spectrum analysis is proposed for detecting broken rotor bars.
2
Basic Principles of Envelope Spectrum Analysis and EMD
A widely used method of mechanical fault diagnosis is analysis of the envelope spectrum of various signals. For example the envelopes of vibration signals are often analyzed to extract useful components. Typically, there are three methods for extraction of the envelope of these signals: amplitude demodulation of the Hilbert transform; filter-demodulation, or; high-pass absolute value demodulation. Considering the Hilbert transform, the actual signal is combined with its Hilbert transform, also called the quadrature function of the signal, to form what is known as the analytic signal. This is a complex func-
Received 07 September 2006; accepted 10 November 2006 Projects 50504015 supported by the National Natural Science Foundation of China and OC4499 by the Science Technology Foundation of China University of Mining & Technology Corresponding author. Tel: +86-516-83995728; E-mail address:[email protected]
206
Journal of China University of Mining & Technology
tion, the real part being the signal itself and the imaginary part being the transform. The amplitude of the analytic signal contains the desired information in our case. Concerning filter-demodulation, the original signal is demodulated and the resulting signal normalized to zero mean. If this signal is passed through a high-pass filter, with cut-off frequency f, the envelope, composed of frequencies above f, will be obtained. Concerning high-pass absolute value demodulation, the signal, which has zero mean value, is processed through a high-pass filter. The absolute value of the result is then passed through a low-pass filter to give the desired information. The frequency components of this envelope signal depend upon the choice of low-pass frequency. Furthermore, in an electrical fault diagnosis wavelet and wavelet packet analysis are also used to extract the envelopes of signals [2–4]. In most of the above mentioned methods the original signal must be filtered in various ways before applying amplitude demodulation. Although there is no need to pre-filter signals in the wavelets transform, it is necessary to choose a proper wavelet basis, which is hard for a novice to do. In this paper a new method, based on EMD, is introduced as a way to extract envelopes of signals to further diagnose machine faults. EMD decomposes a signal into different frequency components ranging from high to low according to the characteristics of the signal. This method needs neither pre-filtering of the original signal, like in the amplitude demodulation of Hilbert transform method requires, nor choosing a wavelet basis like in the wavelet transform. EMD is self-adapting for signal decomposing. EMD, proposed by Norden E. Huang of NASA in 1998, has recently been regarded as a breakthrough method that does not require the limitations of linearity and stationarity required of spectral analysis methods based on the Fourier transform. EMD is mainly used to analyze non-linear and non-stationary signals. EMD has been successfully applied to biomedical engineering, environment engineering and fault diagnosis [5]. This paper introduces the principles and algorithm of the EMD method. EMD, and Hilbert envelope analysis, are applied to fault diagnosis of broken rotor bars in induction type motors. The approach is shown to be effective at extracting the fault characteristic frequency of broken rotor bars. 2.1
Fundamental principles of EMD
EMD is a method of decomposing a non-linear and non-stationary signal into a series of zero-mean amplitude-modulation frequency-modulation (AM-FM) components that represent the characteristic time scale of the observation. This is done by iteratively conducting a sifting process. The zero-mean AM-FM components are called Intrinsic Mode Functions
Vol.17
No.2
(IMFs); they must satisfy the following requirements: 1) the number of extrema and the number of zero crossings in the IMF must either be equal or differ at most by one; and 2) at any point the mean value of the envelopes defined by the local maxima and local minima must be zero. In a short, the signal is locally symmetric concerning the time axis. The sifting process to find the IMFs of a signal x(t) comprises the following steps: 1) Find the positions and amplitudes of all local maxima, and all local minima, in the input signal x(t). Then create an upper envelope by cubic spline interpolation of the local maxima, and a lower envelope by cubic spline interpolation of the local minima. Calculate the mean of the upper and lower envelopes; this is defined as m1 (t ) . Subtract the envelope mean signal, m1 (t ) , from the original input signal. (1) h1 (t ) = x (t ) − m1 (t ) Check whether h1 (t ) meets the requirements to be an IMF. If not, treat h1 (t ) as new data and repeat the previous process. Then set (2) h11 (t ) = h1 (t ) − m11 (t ) Repeat this sifting procedure k times until h1k (t ) is an IMF; this is designated as the first IMF. (3) c1 (t ) = h1k (t ) 2) Subtract c1 (t ) from the input signal and define the remainder, r1 (t ) , as the first residue. Since the residue, r1 (t ) , still contains information related to longer period components treat it as a new data stream and repeat the above-described sifting process. This procedure can be repeated j times to generate j residues, rj (t ) , resulting in: ⎧ r1 (t ) − c2 (t ) = r2 (t ) ⎪ (4) # ⎨ ⎪ r (t ) − c (t ) = r (t ) n n ⎩ n −1 The sifting process is stopped when either of two criteria are met: 1) the component cn(t), or the residue rn(t), becomes so small as to be considered inconsequential, or 2) the residue, rn(t), becomes a monotonic function from which an IMF can not be extracted. By summing up equations (3) and (4) we finally obtain n
x(t ) = ∑ Cimf i (t ) + rn (t )
(5)
i =1
In other words, the original signal can now be represented as the sum of a set of Intrinsic Mode Functions plus a residue. 2.2
Envelope of IMFs [6]
Now apply the Hilbert transform to all IMFs, c j (t ) , in (5). H [c j (t )] =
1 ∞ c j (t ) dτ π ∫ −∞ t − τ
(6)
ZHANG Jian-wen et al
A Fault Diagnosis Approach for Broken Rotor Bars Based on EMD and Envelope Analysis
After the Hilbert transform, H[cj(t)] and cj(t) together form a complex signal Zj(t). Z j (t ) = c j (t ) + iH [c j (t )]
(7)
So, the envelope of every IMF, cj(t), is given by a j (t ) = c j (t ) 2 + H [c j (t )]2
3
(8)
Applications in the Diagnosis of Broken Rotor Bars Based on EMD and Envelope Spectrum
Consider a squirrel-cage, asynchronous motor with a broken rotor bar. Reference [7] describes how the stator current is amplitude and frequency modulated (AM-FM) due to fluctuations induced by the broken bar. The carrier is the supply frequency, f, and the modulation frequency is the characteristic frequency 2sf. Furthermore, the extent of the fault may be estimated from the amplitude of the 2sf component. The fundamental frequency component, f, and the modulation component, 2sf, of the stator current can be obtained by EMD and then analyzed by studying the corresponding envelope spectra. Broken rotor bars can be detected so long as the modulation component, 2sf, is present.
This approach has been tested. The results are described below. The asynchronous motor used for the experiment is a three-phase 50 Hz, four-pole 7.5 kW squirrel-cage induction machine. One of its rotor bars was intentionally broken. The three-phase current was measured with a DL1540 digital memory scope under both full load and no load. The EMD and Hilbert envelope analysis was applied to any phase current. The results are compared with the EPV method. Under no load conditions the fault motor speed is, n=1491 r/min, 2sf=0.6 Hz Under full load the fault motor speed is, n=1433 r/min, 2sf=1.47 Hz. Fig. 1 shows the three-phase stator current measured by the DL1540 digital memory scope. Fig. 1a shows the stator current when the load is full and Fig. 1b shows the stator current under no load. It is clear that, under full load, the stator current envelope of this motor is different from that of a healthy one. The current envelope from a healthy motor looks like a straight line, but there are clear fluctuations in motor current in the presence of the broken rotor bar. The fluctuation is not apparent when the load is light or absent.
(a) Full load
Fig. 1
(b) No load
Stator current of the broken rotor-bar motor
In references [8–9], the EPV approach was shown to be effective when applied to heavily loaded machines. Interested readers are referred there for more
details. After applying the EPV transform to the three phase stator current under full and no load, results as shown in Fig. 2a and Fig. 2b could be obtained.
(a) Full load
Fig. 2
207
(b) Light load
Results of three-phase stator current’s EPV
208
Journal of China University of Mining & Technology
The characteristic frequency of the broken rotor bars at 2sf=4.47 Hz can be detected clearly when under full load. But unloaded, the motor current shows no sign of the 2sf=0.6 Hz signal. This indicates that the EPV approach can only be applied to heavily loaded motors because the diagnostic results depend on the loading of the motor. In the following paragraphs the broken-rotor-bar fault will be diagnosed using the combined method of EMD and Hilbert spectrum analysis. First, any one of the three phase stator currents is decomposed through the EMD method. Fig. 3 shows the decomposition results.
Fig. 3
Fig. 4
Vol.17
Hilbert envelope of current from which the high frequencies have been filtered
EMD results of stator current when the load is light
In Fig. 3 the first three IMFs are high frequency components and the waves represent random noise, which is useless, so they can be filtered immediately. Then Hilbert envelope spectrum analysis is applied to the reconstituted current obtained by summing the remaining signals. The results are shown in Fig. 4. The modulation frequency, 2sf, can be separated from this signal after further EMD. Fig. 5 shows the results of all IMFs ranging from high to low frequency. The calculated characteristic frequency is expected around 0.6 Hz. Therefore a FFT was applied to the last IMFs. The eleventh IMF, after FFT, shows the characteristic frequency at 0.6 Hz) and its first harmonic at 4sf , 1.2 Hz. Fig. 6 shows these results.
Fig. 5
EMD results of the current’s Hilbert envelope
Fig. 6
Frequency spectrum of IMF11 of Fig. 5
No.2
ZHANG Jian-wen et al
A Fault Diagnosis Approach for Broken Rotor Bars Based on EMD and Envelope Analysis
4 Conclusions The EPV approach can effectively detect the characteristic, fault induced, frequency when the motor load is heavy. When the load is light it fails to do that. This paper proposes an approach based on the EMD and the Hilbert envelope spectrum to circumvent such limitations. The high frequency components of a current signal can be filtered effectively by EMD without using other methods. The current signal without high frequency components will represent the envelope of the current. To obtain the fault characteristic frequency, 2sf, again apply EMD to the reformed current envelope to obtain its IMFs, which can be extracted based
209
on frequency, from high to low. After doing an FFT transform on the IMF containing the characteristic frequency, 2sf, the fault characteristic frequency can be obtained. The results of analyzing the current signals from a faulty motor having an intentionally broken rotor bar indicate the effectiveness of this method for detecting the characteristic frequency and hence the fault. To complete such a diagnosis only one of the three phase currents is required while the EPV approach needs the complete three-phase current. This shows the advantage of this method again. The EMD method is not perfect, it has certain influences on the analysis of the stator current, especially in dealing with boundary problems. Therefore, this method still needs further improvement.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
Mejjarih, Benbouzid M. Monitoring and diagnosis of induction motors electrical faults using a current Park’s vector pattern learning approach. IEEE Trans. on Industry Application, 2000, 36(3): 730–735. Cheng J S, Yu D J. An envelope analysis approach based on wavelet transform. Journal of Hunan University (Natural Sciences Edition), 2000, 27(4): 76–80. (In Chinese) Li H, Song Z Y, Sun F R. Approach to extraction of fault features based on wavelet packet and envelope analysis. Journal of Vibration, Measurement & Diagnosis, 2003, 23(4): 291–294. (In Chinese) Li Z, Chen X C, Liu Z B. Envelopment analysis and its application in the fault diagnosis. Journal of Test and Measurement Technology, 2002, 16(2): 92–95. (In Chinese) Tan S W. The Research of Hilbert-Huang Transform Based on Multi-resolution Analysis [Ph.D. Dissertation]. Chongqing: Chongqing University, 2001. (In Chinese) Li H, Zhang H Q, Tang L W. Study on faults diagnosis of bearing based on EMD and envelope spectrum. Journal of Hebei University of Technology, 2005, 34(1): 11–16. (In Chinese) Xu B Q, Li H M, Sun L L, et al. A novel detection method for broken rotor bars in induction motors. Proceedings of the CSEE, 2004, 24(5): 115–119. (In Chinese) Liu Z X, Zhang Z, Yin X G, et al. A new approach of on-line condition monitoring and fault diagnosis for the squirrel-cage induction motor. Transactions of China Electrotechniacl Society, 2002, 17(1): 89–92. Wang P F, Hou X G, Xia L, et al. Diagnosis of induction motors electrical faults using a current park’s vector pattern learning approach. Journal of Wuhan Institute of Science and Technology, 2002, 15(5): 87–90. (In Chinese)
Journal of China University of Mining & Technology
Vol.17
No.2
J China Univ Mining & Technol 2007, 17(2): 0205–0209
A Fault Diagnosis Approach for Broken Rotor Bars Based on EMD and Envelope Analysis ZHANG Jian-wen, ZHU Ning-hui, YANG Li, YAO Qi, LU Qing School of Information & Electrical Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China Abstract: Empirical Mode Decomposition (EMD) used to deal with non-linear and non-stable signals, is a time-frequency analytical method that has been developed recently. In this paper the EMD method is used to filter the noise from the stator current signal that arises when rotor bars break. Then a Hilbert Transform is used to extract the envelope from the filtered signal. With the EMD method again, the frequency band containing the fault characteristic-frequency components, 2sf, can be extracted from the signal's envelope. The last step is to use a Fast Fourier Transform (FFT) method to extract the fault characteristic frequency. This frequency can be detected in actual data from a faulty motor, as shown by example. Compared to the Extend Park Vector method this method is proved to be more sensitive under light motor load. Key words: EMD; analysis of envelope; fault of broken rotor bar CLC number: TM 343+.3
1
Introduction
At present, the most widely used method of detecting broken rotor bars in squirrel-cage induction motors is analyzing the stator current. When a rotor bar breaks the stator current will have spectral components, at a frequency of 1±2sf (f is the supply fundamental frequency; s is the per-unit slip), in every phase of the motor due to the broken bar. Therefore, broken rotor bars can be diagnosed by detecting these spectral components (1±2sf) in the stator current; the status of the broken rotor bars can be qualitatively estimated from the amplitude of the sideband frequencies (1±2sf). However, it is often difficult to effectively detect the sideband frequencies due to interference from the fundamental driving frequency. Electric motor monitoring and diagnosis via both a Park-vector and an extended Park-vector (EPV), which analyzes the squared modulus of the Parkvector from a spectral standpoint, approach has been put forward [1]. The EPV method transforms the fundamental components of the three-phase current into direct current, which makes obvious the side- band frequency at 2sf generated by faults such as broken
rotor bars or cracked end-rings. Despite the great improvement in detecting broken rotor bars with the EPV approach, the characteristic fault-frequency (2sf) can not be detected when the load is light or nonexistent. In this paper a new method combining Empirical Mode Decomposition (EMD) and Envelope Spectrum analysis is proposed for detecting broken rotor bars.
2
Basic Principles of Envelope Spectrum Analysis and EMD
A widely used method of mechanical fault diagnosis is analysis of the envelope spectrum of various signals. For example the envelopes of vibration signals are often analyzed to extract useful components. Typically, there are three methods for extraction of the envelope of these signals: amplitude demodulation of the Hilbert transform; filter-demodulation, or; high-pass absolute value demodulation. Considering the Hilbert transform, the actual signal is combined with its Hilbert transform, also called the quadrature function of the signal, to form what is known as the analytic signal. This is a complex func-
Received 07 September 2006; accepted 10 November 2006 Projects 50504015 supported by the National Natural Science Foundation of China and OC4499 by the Science Technology Foundation of China University of Mining & Technology Corresponding author. Tel: +86-516-83995728; E-mail address:[email protected]
206
Journal of China University of Mining & Technology
tion, the real part being the signal itself and the imaginary part being the transform. The amplitude of the analytic signal contains the desired information in our case. Concerning filter-demodulation, the original signal is demodulated and the resulting signal normalized to zero mean. If this signal is passed through a high-pass filter, with cut-off frequency f, the envelope, composed of frequencies above f, will be obtained. Concerning high-pass absolute value demodulation, the signal, which has zero mean value, is processed through a high-pass filter. The absolute value of the result is then passed through a low-pass filter to give the desired information. The frequency components of this envelope signal depend upon the choice of low-pass frequency. Furthermore, in an electrical fault diagnosis wavelet and wavelet packet analysis are also used to extract the envelopes of signals [2–4]. In most of the above mentioned methods the original signal must be filtered in various ways before applying amplitude demodulation. Although there is no need to pre-filter signals in the wavelets transform, it is necessary to choose a proper wavelet basis, which is hard for a novice to do. In this paper a new method, based on EMD, is introduced as a way to extract envelopes of signals to further diagnose machine faults. EMD decomposes a signal into different frequency components ranging from high to low according to the characteristics of the signal. This method needs neither pre-filtering of the original signal, like in the amplitude demodulation of Hilbert transform method requires, nor choosing a wavelet basis like in the wavelet transform. EMD is self-adapting for signal decomposing. EMD, proposed by Norden E. Huang of NASA in 1998, has recently been regarded as a breakthrough method that does not require the limitations of linearity and stationarity required of spectral analysis methods based on the Fourier transform. EMD is mainly used to analyze non-linear and non-stationary signals. EMD has been successfully applied to biomedical engineering, environment engineering and fault diagnosis [5]. This paper introduces the principles and algorithm of the EMD method. EMD, and Hilbert envelope analysis, are applied to fault diagnosis of broken rotor bars in induction type motors. The approach is shown to be effective at extracting the fault characteristic frequency of broken rotor bars. 2.1
Fundamental principles of EMD
EMD is a method of decomposing a non-linear and non-stationary signal into a series of zero-mean amplitude-modulation frequency-modulation (AM-FM) components that represent the characteristic time scale of the observation. This is done by iteratively conducting a sifting process. The zero-mean AM-FM components are called Intrinsic Mode Functions
Vol.17
No.2
(IMFs); they must satisfy the following requirements: 1) the number of extrema and the number of zero crossings in the IMF must either be equal or differ at most by one; and 2) at any point the mean value of the envelopes defined by the local maxima and local minima must be zero. In a short, the signal is locally symmetric concerning the time axis. The sifting process to find the IMFs of a signal x(t) comprises the following steps: 1) Find the positions and amplitudes of all local maxima, and all local minima, in the input signal x(t). Then create an upper envelope by cubic spline interpolation of the local maxima, and a lower envelope by cubic spline interpolation of the local minima. Calculate the mean of the upper and lower envelopes; this is defined as m1 (t ) . Subtract the envelope mean signal, m1 (t ) , from the original input signal. (1) h1 (t ) = x (t ) − m1 (t ) Check whether h1 (t ) meets the requirements to be an IMF. If not, treat h1 (t ) as new data and repeat the previous process. Then set (2) h11 (t ) = h1 (t ) − m11 (t ) Repeat this sifting procedure k times until h1k (t ) is an IMF; this is designated as the first IMF. (3) c1 (t ) = h1k (t ) 2) Subtract c1 (t ) from the input signal and define the remainder, r1 (t ) , as the first residue. Since the residue, r1 (t ) , still contains information related to longer period components treat it as a new data stream and repeat the above-described sifting process. This procedure can be repeated j times to generate j residues, rj (t ) , resulting in: ⎧ r1 (t ) − c2 (t ) = r2 (t ) ⎪ (4) # ⎨ ⎪ r (t ) − c (t ) = r (t ) n n ⎩ n −1 The sifting process is stopped when either of two criteria are met: 1) the component cn(t), or the residue rn(t), becomes so small as to be considered inconsequential, or 2) the residue, rn(t), becomes a monotonic function from which an IMF can not be extracted. By summing up equations (3) and (4) we finally obtain n
x(t ) = ∑ Cimf i (t ) + rn (t )
(5)
i =1
In other words, the original signal can now be represented as the sum of a set of Intrinsic Mode Functions plus a residue. 2.2
Envelope of IMFs [6]
Now apply the Hilbert transform to all IMFs, c j (t ) , in (5). H [c j (t )] =
1 ∞ c j (t ) dτ π ∫ −∞ t − τ
(6)
ZHANG Jian-wen et al
A Fault Diagnosis Approach for Broken Rotor Bars Based on EMD and Envelope Analysis
After the Hilbert transform, H[cj(t)] and cj(t) together form a complex signal Zj(t). Z j (t ) = c j (t ) + iH [c j (t )]
(7)
So, the envelope of every IMF, cj(t), is given by a j (t ) = c j (t ) 2 + H [c j (t )]2
3
(8)
Applications in the Diagnosis of Broken Rotor Bars Based on EMD and Envelope Spectrum
Consider a squirrel-cage, asynchronous motor with a broken rotor bar. Reference [7] describes how the stator current is amplitude and frequency modulated (AM-FM) due to fluctuations induced by the broken bar. The carrier is the supply frequency, f, and the modulation frequency is the characteristic frequency 2sf. Furthermore, the extent of the fault may be estimated from the amplitude of the 2sf component. The fundamental frequency component, f, and the modulation component, 2sf, of the stator current can be obtained by EMD and then analyzed by studying the corresponding envelope spectra. Broken rotor bars can be detected so long as the modulation component, 2sf, is present.
This approach has been tested. The results are described below. The asynchronous motor used for the experiment is a three-phase 50 Hz, four-pole 7.5 kW squirrel-cage induction machine. One of its rotor bars was intentionally broken. The three-phase current was measured with a DL1540 digital memory scope under both full load and no load. The EMD and Hilbert envelope analysis was applied to any phase current. The results are compared with the EPV method. Under no load conditions the fault motor speed is, n=1491 r/min, 2sf=0.6 Hz Under full load the fault motor speed is, n=1433 r/min, 2sf=1.47 Hz. Fig. 1 shows the three-phase stator current measured by the DL1540 digital memory scope. Fig. 1a shows the stator current when the load is full and Fig. 1b shows the stator current under no load. It is clear that, under full load, the stator current envelope of this motor is different from that of a healthy one. The current envelope from a healthy motor looks like a straight line, but there are clear fluctuations in motor current in the presence of the broken rotor bar. The fluctuation is not apparent when the load is light or absent.
(a) Full load
Fig. 1
(b) No load
Stator current of the broken rotor-bar motor
In references [8–9], the EPV approach was shown to be effective when applied to heavily loaded machines. Interested readers are referred there for more
details. After applying the EPV transform to the three phase stator current under full and no load, results as shown in Fig. 2a and Fig. 2b could be obtained.
(a) Full load
Fig. 2
207
(b) Light load
Results of three-phase stator current’s EPV
208
Journal of China University of Mining & Technology
The characteristic frequency of the broken rotor bars at 2sf=4.47 Hz can be detected clearly when under full load. But unloaded, the motor current shows no sign of the 2sf=0.6 Hz signal. This indicates that the EPV approach can only be applied to heavily loaded motors because the diagnostic results depend on the loading of the motor. In the following paragraphs the broken-rotor-bar fault will be diagnosed using the combined method of EMD and Hilbert spectrum analysis. First, any one of the three phase stator currents is decomposed through the EMD method. Fig. 3 shows the decomposition results.
Fig. 3
Fig. 4
Vol.17
Hilbert envelope of current from which the high frequencies have been filtered
EMD results of stator current when the load is light
In Fig. 3 the first three IMFs are high frequency components and the waves represent random noise, which is useless, so they can be filtered immediately. Then Hilbert envelope spectrum analysis is applied to the reconstituted current obtained by summing the remaining signals. The results are shown in Fig. 4. The modulation frequency, 2sf, can be separated from this signal after further EMD. Fig. 5 shows the results of all IMFs ranging from high to low frequency. The calculated characteristic frequency is expected around 0.6 Hz. Therefore a FFT was applied to the last IMFs. The eleventh IMF, after FFT, shows the characteristic frequency at 0.6 Hz) and its first harmonic at 4sf , 1.2 Hz. Fig. 6 shows these results.
Fig. 5
EMD results of the current’s Hilbert envelope
Fig. 6
Frequency spectrum of IMF11 of Fig. 5
No.2
ZHANG Jian-wen et al
A Fault Diagnosis Approach for Broken Rotor Bars Based on EMD and Envelope Analysis
4 Conclusions The EPV approach can effectively detect the characteristic, fault induced, frequency when the motor load is heavy. When the load is light it fails to do that. This paper proposes an approach based on the EMD and the Hilbert envelope spectrum to circumvent such limitations. The high frequency components of a current signal can be filtered effectively by EMD without using other methods. The current signal without high frequency components will represent the envelope of the current. To obtain the fault characteristic frequency, 2sf, again apply EMD to the reformed current envelope to obtain its IMFs, which can be extracted based
209
on frequency, from high to low. After doing an FFT transform on the IMF containing the characteristic frequency, 2sf, the fault characteristic frequency can be obtained. The results of analyzing the current signals from a faulty motor having an intentionally broken rotor bar indicate the effectiveness of this method for detecting the characteristic frequency and hence the fault. To complete such a diagnosis only one of the three phase currents is required while the EPV approach needs the complete three-phase current. This shows the advantage of this method again. The EMD method is not perfect, it has certain influences on the analysis of the stator current, especially in dealing with boundary problems. Therefore, this method still needs further improvement.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
Mejjarih, Benbouzid M. Monitoring and diagnosis of induction motors electrical faults using a current Park’s vector pattern learning approach. IEEE Trans. on Industry Application, 2000, 36(3): 730–735. Cheng J S, Yu D J. An envelope analysis approach based on wavelet transform. Journal of Hunan University (Natural Sciences Edition), 2000, 27(4): 76–80. (In Chinese) Li H, Song Z Y, Sun F R. Approach to extraction of fault features based on wavelet packet and envelope analysis. Journal of Vibration, Measurement & Diagnosis, 2003, 23(4): 291–294. (In Chinese) Li Z, Chen X C, Liu Z B. Envelopment analysis and its application in the fault diagnosis. Journal of Test and Measurement Technology, 2002, 16(2): 92–95. (In Chinese) Tan S W. The Research of Hilbert-Huang Transform Based on Multi-resolution Analysis [Ph.D. Dissertation]. Chongqing: Chongqing University, 2001. (In Chinese) Li H, Zhang H Q, Tang L W. Study on faults diagnosis of bearing based on EMD and envelope spectrum. Journal of Hebei University of Technology, 2005, 34(1): 11–16. (In Chinese) Xu B Q, Li H M, Sun L L, et al. A novel detection method for broken rotor bars in induction motors. Proceedings of the CSEE, 2004, 24(5): 115–119. (In Chinese) Liu Z X, Zhang Z, Yin X G, et al. A new approach of on-line condition monitoring and fault diagnosis for the squirrel-cage induction motor. Transactions of China Electrotechniacl Society, 2002, 17(1): 89–92. Wang P F, Hou X G, Xia L, et al. Diagnosis of induction motors electrical faults using a current park’s vector pattern learning approach. Journal of Wuhan Institute of Science and Technology, 2002, 15(5): 87–90. (In Chinese)