The paper presents a new approach for detection of broken rotor bar fault in squirrel cage induction motors operating under varying load conditions. A mathematical model used in the presented method was developed using winding function approach to provide indication references for induction motor parameters under load variation. The model shows a strong relationship between broken rotor bar fault and stator current. The method is based on analysis of stator current using discrete wavelet transform. To verify the proposed method a squirrel cage induction motor with 1, 2 and 3 broken bars at no-load, half- and full-load conditions was investigated. Obtained experimental results confirmed the validity of the proposed approach

Chen, Zheng

Davydova, Anastasia

Lupin, Sergey

Shi, Pu

Vagapov, Yuriy

English

Glyndŵr University Research Online

 Glyndŵr University Research Online    Conference Paper   Broken bar fault diagnosis for induction machines under load variation condition using discrete Wavelet transform   Shi, P., Chen, Z., Vagapov, Y., Davydova, A. and Lupin, S.             This is a paper presented at the 12th IEEE East-West Design and Test Symposium EWDTS 2014, Kiev, 26-29 September, 2014.   Copyright of the author(s). Reproduced here with their permission and the permission of the conference organisers.          Recommended citation:  Shi, P., Chen, Z., Vagapov, Y., Davydova, A. and Lupin, S. (2014), ‘Broken bar fault diagnosis for induction machines under load variation condition using discrete Wavelet transform’, in: Proc. 12th IEEE East-West Design and Test Symposium EWDTS 2014, Kiev, 26-29 September, 2014, pp. 152-155. doi: 10.1109/EWDTS.2014.7027059  Abstract  The paper presents a new approach for detection of broken rotor bar fault in squirrel cage induction mo-tors operating under varying load conditions. A mathe-matical model used in the presented method was devel-oped using winding function approach to provide indi-cation references for induction motor parameters un-der load variation. The model shows a strong relation-ship between broken rotor bar fault and stator current. The method is based on analysis of stator current using discrete wavelet transform. To verify the proposed method a squirrel cage induction motor with 1, 2 and 3 broken bars at no-load, half- and full-load conditions was investigated. Obtained experimental results con-firmed the validity of the proposed approach.  1. Introduction  Accurate and prompt on-line fault detection and diag-nosis (FDD) of induction machines improves safety and reliability of industrial processes. Recent investiga-tions regarding induction motor reliability have re-vealed that 19% of the total motor faults are related to the rotor part [1].  Variety of methods, such as short time Fourier trans-form (STFT) [2], high resolution frequency estimation [3], and signal demodulation (SD) technique [4] have been proposed and developed to reduce the effect of the non-periodicity and non-stationary on the analysed signals. All above mentioned techniques are based on fast Fourier transform (FFT) and provide high quality discrimination between healthy and faulty conditions. However, FFT based approaches can not show fault evolution information in time domain. Wavelet analy-sis, which provides greater resolution in time for high frequency components and greater resolution in fre-quency for low frequency components, has been pro-posed to overcome this shortcoming.  Since the emergence of wavelet analysis, this method has been used with different approaches for the diagno-sis of rotor anomalies in induction machines such as wavelet ridge method [5] or wavelet coefficients analy-sis [6]. Following up these steps, approximations and details signals were investigated for reproducing the instantaneous evolution of rotor fault frequency com-ponents [7] and quantifying the fault extents [3]. How-ever, the majority of these methods track rotor fault frequency components on multi frequency bands, which make the diagnosis processes complicate. This paper proposes a new broken rotor bar fault  diagnostic method for diagnosis of squirrel cage induc-tion motors. This method is based on discrete wavelet coefficients and applicable for induction motors oper-ating under varying load conditions. In this paper, winding function approach (WFA) was used to develop a mathematical model to provide indication references for parameters under load variation. Stator current was used to demonstrate the relationship between this pa-rameter and broken rotor bar severity.  2. Model of three phase induction machine  To study the amplitude variation of currents, speed and torque components, WFA based coupled circuits model which accounts for all the space harmonics in the machine is adopted as shown in Fig. 1 [8]. The model of the induction motor is considered using the following assumptions: the air-gap is uniform and smooth; the magneto motive force (MMF) distri-bution in the air-gap is sinusoidal; the rotor bars are insulated from the rotor and there is no inter-bar cur-rent flows through the laminations; the permeability of machine armatures is assumed infinite; the eddy cur-rent, friction, windage losses, saturation and skin effect are neglected [8]. The mathematical model for the induction machine can be written as:                                                   where [Vs], [Vr], [Ir], [Rs], [Rr], [Φs], [Φr] are matrices that represent voltage, currents, resistance and flux linkage of the stator and rotor respectively.        s s s sdV R Idt   (1)       r r r rdV R Idt   (2) Broken Bar Fault Diagnosis for Induction Machines under  Load Variation Condition using Discrete Wavelet Transform Pu Shi, Zheng Chen, Yuriy Vagapov Glyndwr University, Plas Coch, Mold Road, Wrexham, LL11 2AW, UK Anastasia Davydova, Sergey Lupin National Research University of Electronic Technology,  Zelenograd, Moscow, 124498, Russia The mechanical equation of the machine is:                            where Tem is the electromagnetic torque produced by the machine, TL is the load torque, J is the inertia of the rotor and Ωm is the mechanical speed. It is also assumed that if as one of stator phase cur-rent, i(1‒2s)f is the arising current due to rotor asymme-try. The expression of if and i(1‒2s)f are:                             where ω = 2πf represents power supply angular frequency; If , I(1‒2s)f, af, and a(1‒2s)f represent the amplitude and initial phase of f and (1‒2s)f frequency characteristic components respectively. The fundamental magnetic flux can be expressed as:                       where Φ is magnitude of fundamental magnetic flux, aΦ is the initial phase of fundamental magnetic flux. The fundamental current if interacts with the funda-mental magnetic flux Φ generates torque:                       where P is the numbers of pole pair. Under the same rule, the arising current i(1‒2s)f due to broken bars interacts with the fundamental magnetic flux produces an oscillatory torque at frequency 2sf:   The amplitude of torque oscillation is:                      (7) demonstrates that the fundamental current interacting with supply current generates a constant torque. In contrast to (7), (8) shows ΔT(1‒2s)f  modulated by frequency 2sω, which leads to speed alternation component Δωr(t) according to motor rotating theory. The driving system incremental equation of motion is presented as: mem LdT T Jdt  (3) cos( )f f fi I t a  (4)         1 2 1 2 1 2cos 1 2s f s f s fi I s t a     (5)    cost t a   (6)  3 sinf f fT P I a a   (7)             1 2 1 2 1 21 2 1 2( ) 3 sin 2sin 2s f s f s fs fm s fT t P I s t a aT s t a a           (8)    1 2 1 23s fm s fT P I    (9)                 where J is the combined machine load inertia, ωr is the rotor rotate speed.  Taking the integration operation, the speed ripples caused by torque oscillation can be expressed as:        The amplitude of speed oscillation is:                        Due to rotor asymmetry, the (1±2s)f rotor currents generated by the corresponding EMFs produce two rotating fields at frequencies ±3sf and generate same EMF and current. As a consequence, this process gives rise to stator current components at frequencies:                       With the result of previous analysis, oscillation sig-nal distortion happens in current, speed and torque when broken rotor bars faults developed. Moreover, the amplitude of this oscillation depends on the factors of fault extent, operating conditions and the inertia. Therefore, the direct apply FFT to machine stator cur-rent under this circumstance seems ineffective.   3. Discrete wavelet transform  Discrete wavelet transform (DWT) decomposes a signal by passing it successively through high pass and low pass filters into its approximate and detailed ver-sions using multi resolution analysis (MRA) as seen in [9]. Each step of decomposition of the signal corre-sponds to a certain resolution. Fig. 2 shows two level wavelet decompositions. Here H and L are high-pass and low-pass filter respec-tively. At each level of scaling for various positions, the correlation between signal and wavelet are called wavelet coefficients. High pass filter coefficients are called detailed coefficient cDn and low pass filter coef-ficients are called approximate coefficients cAn. The first level of decomposition coefficients are cA1 and cD1, where cA1 is the approximate version of the original signal and cD1 is the detailed version of the original signal. At each decomposition level, the corre-sponding detailed and approximate coefficients have definite frequency bandwidths given by [0 ‒ fs/2l+1] for approximate coefficient cA1 and [fs/2l+1 ‒ fs/2l] for de-tailed one cD1 where fs is the sampling frequency, l denotes the decomposition level limited by the sam-pling frequency fs, where fs/2 is the corresponding Ny-quist frequency. At each step of decomposition the sampled dataset are down-sampling by a factor of 2↓,    1 2 ( )r s fdJ t T tdt   (10)         1 21 21 21cos 2 ( )2r s fs fms ft T t dtJTs t a asJ      (11)  1 22s fmrmTsJ  (12)  1 2brbf ks f  (13) Rotor barEnd ringEnd ring currentbkI( 1)b kI ( 2)b kI ( 1)b kI ( 2)b kI ( 3)b kI rkI( 1)r kI ( 2)r kI ( 1)r kI ( 2)r kI eILFig. 1. Elementary rotor loops and current definitions. which is denoted dyadic decomposition. The spectral frequency bands of different detailed coefficients are shown in the Table 1.  4. Broken rotor bar fault and quantitative diagnostic approach  The current component and its oscillation can be related to the fault rate in steady state condition. Char-acteristic current at frequency (1 ± 2ks)f merge in the stator current when rotor asymmetry happens. Among these arisen currents, frequency at (1 ± 2ks)f is the most suitable signal used for fault detection and quanti-tative diagnostic due to the evidently amplitude.  It is known that load level, fault extent are essential elements lead to motor variables variation. However, stator variables are constant values under normal con-dition and broken bar fault. In this paper, mean abso-lute value is used to represent the load level. Standard deviation (SD) is used to illustrate the oscillation caused by broken bars. The expression of mean abso-lute and standard deviation are presented in (14) and (15) and the calculated result shows in Table 3.                                            Table 4 shows the values of mean absolute and stan-dard deviation. Mean absolute represents the load variation, while standard deviation is used to represent signal oscillation. The ratio between standard deviation and mean absolute is introduced as an index for induc-tion motor broken bar quantitative diagnostic analysis. The ration of the amplitude of oscillation of stator cur-rent and its mean value is presented as:                            where SD represents standard deviation, meanabs represents mean absolute values. By calculating the fault index (16), it is much easier to diagnose the induction machines condition. As shown in Table 4, under healthy situation this index is around 1.67; when one broken rotor bar occurs, this index will drop to 1.40. As broken bars number in-crease, the index will continue drop to 1.36 and 1.31 under two and three broken bars. Table 4 has shown the obvious gap between these indexes.  11 Niimeanabs xN   (14)  211 NiiSD x meanabsN    (15) SDIndexmeanabs (16) Fig. 2. Wavelet analysis and synthesis of a signal S. SLHcA1LHcA2cD2cD1L'H'L'L'A2D2H'D1S'Analysis Synthesis/ReconstructionDecomposition Details Frequency Bands (Hz) Detail Level 1 2048 - 4096 Detail Level 2 1024-2048 Detail Level 3 512 - 1024 Detail Level 4 256 - 512 Detail Level 5 128 - 256 Detail Level 6 64 - 128 Detail Level 7 32 - 64 Detail Level 8 16 - 32 Detail Level 9 8 - 16 Detail Level 10 4 - 8 Table 1. Spectral frequency bands at different  decomposition levels Table 2. Specifications of an induction machine Specification Value Rated Power 3.7 kW Horse Power 5 HP Input Voltages 220/380 V Input Currents 13.8/8.0 A Pole pairs 1 Frequency 50 Hz Speed 3000 rpm Number of Stator Slots 36 EA Number of Rotor Bars 28 EA Healthy  No Load 50% 100% Mean abs 0.272 0.8505 1.5923 Standard Deviation 0.4543 1.4313 2.677 One broken bar  No Load 50% 100% Mean abs 0.3235 0.9523 1.7578 Standard Deviation 0.4546 1.3358 2.475 Two broken bars  No Load 50% 100% Mean abs 0.339 1.0028 1.8288 Standard Deviation 0.4641 1.3718 2.501 Three broken bars  No Load 50% 100% Mean abs 0.347 1.0628 1.9135 Standard Deviation 0.4566 1.3964 2.513 Table 3. Simulation result analysis based on  mean abs and SD values   No Load 50% 100% Healthy 1.67022 1.68289 1.6812 One broken Bar 1.40525 1.4027 1.4080 Two Broken Bars 1.36902 1.36796 1.3675 Three Broken Bars 1.31585 1.31388 1.3133 Table 4. Fault index ratio illustration of induction motor  No Load 30% 60% 100% Healthy 1.5 1.69 1.69 1.7 One broken Bar 1.41 1.39 1.4 1.4 Two Broken Bars 1.35 1.37 1.37 1.36 Three Broken Bars 1.32 1.33 1.32 1.33 Table 5. Experiment induction motor fault index ratio 5. Experimental test and results  The characteristics of the three phase induction ma-chine used in the tests are listed in Table 2. Among these tests, induction machines with healthy, one bro-ken bar, two broken bars and three broken bars under no-load, 30% load, 60% load and full load conditions are tested and compared. A current Hall effect sensor is placed in one line wire. The stator current is sampled at 5 kHz rate and transferred to a PC by an ADC-11 ac-quisition board. In each experiment, induction machine are start with no load condition for 30 second then 30%, 60% and full load are added and keep running for one min-ute. The experimental results are shown in Fig. 3(a-d).  Under healthy condition, the indexes are between 1.5-1.7; under one broken bar these values are around 1.4; under two broken bars these values are close to 1.35, while under three broken bars scenario, these ratios are 1.3 as shown in Table 5. The results demon-strate the ability of the proposed approach for induc-tion motor broken bar quantitative diagnostic analysis.   6. Conclusion  It has been shown that the current components at frequencies (1 ± 2s)f can be used for rotor fault diagno-sis of an induction machine. The characteristic fre-quencies are strongly dependent on the load level and fault extent. Following the physical phenomena caused by the failure, simplified relationships linking stator current, speed and torque ripples components have been derived. These relationships allow to recognise the machine reaction on the speed ripple as stator cur-rent and fault extent. Therefore, the ratio of the ripple components leads to the computation of the actual bro-ken bar number and can be referred as fault severity without complicated calculation.  7. References  [1] A. H. Bonnett, and C. Yung, “Increased efficiency ver-sus increased reliability,” IEEE Ind. Appl. Mag., vol. 14, no 1, pp. 29-36, 2008. [2] P. Zhang, Y. Du, T. G. Habetler, and B. Lu, “A survey of condition monitoring and protection methods for medium-voltage induction motors,” IEEE Trans. Ind. Appl., vol. 47, no 1, pp. 34-46, 2011. [3] S. H. Kia, H. Henao, and G. A. Capolino, “Diagnosis of broken-bar fault in induction machines using discrete wavelet transform without slip estimation,” IEEE Tran. Ind. Appl., vol. 45, no 4, pp. 1395-1404, 2009.  [4] A. Stefani, A. Bellini, and F. Filippetti, “Diagnosis of induction machines’ rotor faults in time-varying condi-tions,” IEEE Trans. Ind. Electron., vol. 56, no 11, pp. 4548-4556, 2009. [5] Z. Zhang, Z. Ren, and W. Huang, “Broken rotor bar detection in induction motors via wavelet ridge,” IEEE Trans. Energy Convers., vol. 18, pp. 417-423, 2003. [6] A. Ordaz-Moreno, R. de Jesus Romero-Troncoso, J. A. Vite-Frias, and J. R. Rivera-Gillen, “Automatic online diagnosis algorithm for broken-bar detection on induc-tion motors based on discrete wavelet transform for FPGA implementation,” IEEE Trans. Ind. Electron., vol. 55, no 5, pp. 2193-2202, 2008.  [7] J. Cusido, L. Romeral, J. A. Ortega, J. A. Rosero, and A. Garcia Espinosa, “Fault detection in induction machines using power spectral density in wavelet decomposition,” IEEE Trans. Ind. Electron., vol. 55, pp. 633-643, 2008.  [8] A. R. Munoz, and T. A. Lipo, “Complex vector model of the squirrel-cage induction machine including instan-taneous rotor bar currents,” IEEE Trans. Ind. Appl., vol. 35, no 6, pp. 1332-1340, 1999. [9] J. A. Antonino-Daviu, M. Riera-Guasp, J. Roger-Folch, F. Martinez-Gimenez, and A. Peris, “Application and optimization of the discrete wavelet transform for the detection of broken rotor bars in induction machines,” Applied and Computational Harmonic Analysis, vol. 21, no 2, pp. 268-279, 2006.  0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10-50510Signal and Approximation at level 6Time [s]Stator currents [A]0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10-50510Signal and Approximation at level 6Time [s]Stator currents [A]0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-15-10-5051015Signal and Approximation at level 6Time [s]Stator currents [A]Fig. 3. Experimental results of motor stator current under different load conditions. 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10-50510Signal and Approximation at level 6Time [s]Stator currents [A]a) Healthy motor b) One broken bar c) Two broken bars d) Three broken bars 

Broken bar fault diagnosis for induction machines under load variation condition using discrete Wavelet transform

https://glyndwr.repository.guildhe.ac.uk/17524/1/GURO_420_ewdts2014_submission_15.pdf

Broken bar fault diagnosis for induction machines under load variation condition using discrete Wavelet transform

Abstract

Similar works

Full text

Available Versions

Glyndŵr University Research Online