Finite Element Diagnosis of Rotor Faults in Induction Motors based on Low Frequency Harmonics of the Near-Magnetic Field A. Ceban(1), V. Fireteanu(2), R. Romary(1), R. Pusca(1) and P. Taras(2)
Φ Abstract -- The influence of different faults of squirrel-cage rotor in induction motors on the near-magnetic field are studied in this paper. The 2D finite element analysis of electromagnetic field is used to investigate the detection of broken rotor bars and rotor eccentricity faults. This analysis is focused on the low frequency harmonics of the near-magnetic field, which are much modified under faulty conditions and less attenuated by the motor frame.
Index Terms--Broken bars, fault diagnosis, finite element analysis, rotor eccentricity.
I. INTRODUCTION OR many industrial applications it is interesting to use the noninvasive measurement methods to detect the faults in induction motors without stopping the motor operation. A diagnostic technique which can predict a failure and to prevent the total damage is therefore of great importance [1], [2]. Fault detection has been already largely investigated, using different techniques such as those based on the motor vibrations or motor current signature analysis [3]-[7]. Recently, methods based on the analysis of external magnetic field have been developed; their advantages are the noninvasive investigation and simplicity of implementation [8], [9]. The noninvasive evaluation of a motor healthy state takes into account the reality that any fault is more or less reflected in the near vicinity of the machine [8]-[11]. In this context, this paper studies the influence of different faults in the squirrel-cage induction motors on the near-magnetic field, such as broken rotor bars and eccentricity. The interest is focused on the low frequency harmonics of this field, which are less attenuated during their penetration through the stator magnetic core and the frame of the machine. The study considers the interaction of the broken bar fault with rotor eccentricity and allow to analyze the influence of each or both faults in the modification of the external magnetic field. The 2D finite element models of the motor are used to compute the electromagnetic field inside and
F
(1) A. Ceban, R. Romary and R. Pusca are with the Univ. Lille de Nord France, F-5900 Lille, France and UArtois, LSEE, F-62400 Béthune, France (e-mails:
[email protected],
[email protected],
[email protected]). (2) V. Fireteanu and P. Taras are with POLITEHNICA University of Bucharest, Electrical Engineering Faculty, EPM_NM-Lab, 313 Splaiul Independentei, 060042 Bucharest, Romania (e-mails:
[email protected],
[email protected]).
outside the motor and the harmonics of the near-magnetic field. Section II of this paper is devoted to the presentation of some experimental results with the coil sensor technique [8] related to the influence of a broken rotor bar on the magnetic field outside the motor. Section III describes the finite element model of a squirrel cage induction motor able to investigate the near-magnetic field and the section IV analyzes the time variation and the harmonics of the output voltages in the coil sensors of this model. Results related the lines of the near-magnetic field for the healthy and faulty motors, the time variation of the magnetic flux density in a point and the low frequency harmonics of the magnetic field are presented in the Section V. II.
EXPERIMENTAL ASCERTAINMENTS
The flux signature analysis is very simple and completely noninvasive; also it is more efficient than the classical motor current analysis to detect the stator and rotor faults in induction machines [12], [13].The tests were performed on a healthy and a faulty motors with one broken rotor bar (Fig. 1). A coil sensor has been used to investigate the magnetic field outside the motors. It is circular of 10 cm2 area with the coil constituted of 1200 turns. The sensor output voltage is transmitted to a PULSE Brüel&Kjær analyzer (Fig. 1), which performs signal processing and provides its spectrum.
Fig. 1. Test-bed used for experimental analysis.
In case of the Ox sensor position (see Fig. 1), the coil turns are vertical and for the Oy position they are horizontal.
The spectra of the output voltage for the Ox sensor position are presented in Fig. 2 for the healthy motor and in Fig. 3 for the faulty motor. In this position, the output voltage is the image of the radial component of the magnetic field outside the motor. It can be noticed that spectrum components less than 50 Hz increase in amplitude when one rotor bar breaks.
As shown in Figs. 2-5 the harmonic at 26.25 Hz increases in the ratio 9.43/1.49 = 6.33 in case of the Ox sensor position and in the ratio 4.10/0.76 = 5.38 in case of the Oy position. III. DESCRIPTION OF THE FINITE ELEMENT MODELS FOR NONINVASIVE DIAGNOSIS OF INDUCTION MOTOR The FLUX2D circuit, geometry and mesh presented in Fig. 6(a)-(c) correspond to the same 4 poles induction motor, 4 kW, 3 x 380 V, fn = 50 Hz used in the experimental tests. The 2D computation domain, infinitely extended, contains the stator and the rotor cores - magnetic and nonconductive regions, the 48 stator slots - nonconductive, nonmagnetic and source regions, the airgap of 0.5 mm thickness and regions of solid conductor type - the rotor slots, the rotor shaft and the motor frame of 6 mm thickness [Fig. 6(a)].
Fig. 2. FFT spectrum of the coil sensor voltage in position Ox – case of the healthy motor.
Fig. 3. FFT spectrum of the coil sensor voltage in position Ox – case of one broken rotor bar.
(a)
Figs. 4-5 show the corresponding spectra for the Oy position of the coil sensor. In this case, the output voltage is the image of the azimuth component of the magnetic field outside the motor.
(b)
Fig. 4. FFT spectrum of the coil sensor voltage in position Oy – case of the healthy motor.
(c) Fig. 6. The finite element model: (a) geometry; (b) electric circuit; (c) mesh zoom. Fig. 5. FFT spectrum of the coil sensor voltage in position Oy – case of one broken rotor bar.
The state variable of the electromagnetic field - the
IV. LOW FREQUENCY HARMONICS OF COIL SENSORS VOLTAGE OUTPUT The time variation and the harmonics of the output voltage of Ox coil sensor are presented in Fig. 7 for the healthy motor and constant speed, in Fig. 8 for one broken
1 Voltage (V)
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where μ is the magnetic permeability, ρ is the resistivity and Js is the current density in the stator slots. The term (∂A/∂t)/ρ is the density of the induced current that is different from zero only in the solid conductor regions of the rotor slots. In the field model considered in this paper the source current density has the structure Js[0,0,Js(x,y,t)]. As consequence, the vector potential As[0,0,As(x,y,t)] is oriented along the Oz axis and not depends on the coordinate z and the second equation (1) is implicitly satisfied. The electric circuit [Fig. 6(b)] attached to the field model contains twelve components of stranded coil type, which correspond to the four zones of each of three phases of the stator winding. The inductances Lσ1f correspond to the part of the stator winding outside the stator magnetic core and the voltage sources UU, UV, UW are phase-to-null voltages of the symmetric three phase motor supply. Four components of stranded coil type, correspond to the two coil sensors and two resistors are considered for sensor voltage measurement. The macro-component squirrel-cage reflects the 28 rotor bars and the electric parameters of the squirrel cage outside the rotor slots. Since the main interest of the finite element model is the non-invasive fault diagnosis based on magnetic field outside the motor, the mesh of the computation domain [Fig. 6(c)] is fine enough inside and outside the motor and it is also fine enough in the regions of solid conductor type, in order to have a good accuracy of the numerical solution. The nonlinear magnetic cores are characterised by the saturation at 2 T, the initial relative magnetic permeability is 4000 and the curvature coefficient is 0.3. The squirrel-cage is aluminium made of resistivity 0.027 μΩm and the frame of the motor is Al-Si alloy made of resistivity 0.045 μΩm. The rotor shaft is magnetic steel made of resistivity 0.2 μΩm, saturation 1.8 T and initial relative permeability 1800. The step-by-step type in time domain analysis of the electromagnetic field considers the time step values 1 ms. The steady state motor operation is reached in about 0.6 s, so that the time interval (0.6…1.4) s is considered for the results analysis. As further explained, 0.8 s is the period of the electromagnetic field outside the motor when the rotor has the speed 1425 rpm. The field-circuit-motion model of the motor takes into account two variants of motor operation: constant rotor speed 1425 rpm, respectively the slip value s = 0.05 and constant mechanical load 26 Nm.
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Fig. 7. Voltage time variation (up) and FFT spectrum (down) of Sensor Ox for the healthy motor and constant speed.
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curl [1 μ ⋅ curl A] + ( ∂A ∂t ) ρ = J s ( x, y, z , t ) ; div A = 0
rotor bar and constant speed and in Fig. 9 for one broken bar and constant load torque. The corresponding rms values are 421.3 mV, 427.2 mV and 428.1 mV. The same very small differences characterise the amplitude of the 50 Hz voltage harmonic [Figs. 7-9 (down)]. Contrariwise, the spectra and the amplitudes of the harmonics with very low frequency, 1.25 Hz, 2.5 Hz, 3.75 Hz, ... , 12.5 Hz, are completely different for the healthy motor and for the motor with one broken bar.
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magnetic vector potential A(x,y,z,t), satisfies the following differential equations [14]-[17]:
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Fig. 8. Voltage time variation (up) and FFT spectrum (down) of Sensor Ox for one broken rotor bar and constant speed.
In the case of the healthy motor, Fig. 10, the lines of the near-magnetic field around the motor are identical for all four poles. For all other cases, Figs. 11-13, the symmetry of the four poles of the near-magnetic field is more or less affected by the rotor faults.
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Fig. 10. Lines of the near-magnetic field for the healthy motor.
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Fig. 9. Voltage time variation (up) and FFT spectrum (down) of Sensor Ox for one broken rotor bar and constant load.
The harmonic with the frequency sfn = 2.5 Hz, which is practically inexistent in the case of healthy motor (Fig. 7) has around 0.6 mV amplitude for one broken bar and constant speed (Fig. 8) and around 0.7 mV for of one broken bar and constant load (Fig. 9).
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Fig. 11. Lines of the near-magnetic field for motor with one broken bar.
V.
STUDY OF MAGNETIC FIELD OUTSIDE THE MOTOR – THE NEAR-MAGNETIC FIELD In order to show why the electromagnetic field finite element computation is important for faults identification, this section presents the results of motor operation at constant mechanical load, for the healthy motor, for one broken bar, for 0.2 mm static eccentricity of the rotor and for both motor faults – one broken bar and eccentricity. In the case of the heathy motor, the speed has very small oscilations, in the range (1428.4…1428.8) rpm. For a broken bar the speed oscilates in the range (1423.8…1428.5) rpm, for rotor eccentricity in the range (1428.3…1428.9) rpm and for both faults in the range (1424.0…1429.2) rpm. This variation has been experimentaly proved by the appearance of the harmonic 3sfn of the external magnetic field [9]. The Field Lines of the Near-Magnetic Field The charts of the magnetic field lines outside the motor for the time steps 600 ms, 1000 ms and 1400 ms are presented in Fig. 10 for the healthy motor, in Fig. 11 for one broken rotor bar, in Fig. 12 for rotor eccentricity and in Fig. 13 for both faults – broken bar and eccentricity. For the value 1425 rpm of the rotor speed, the corresponding period of the rotor currents is T = 1000 / (sfn) = 400 ms. Thus, as Figs. 10-13 show, the approximate period of the near-magnetic field is the double 2T = 800 ms of the period of rotor currents. This explains the choice for the time steps 600 ms, 1000 ms and 1400 ms for the magnetic field lines representation. A.
600 ms
1000 ms
1400 ms
Fig. 12. Lines of the near-magnetic field for the motor with rotor eccentricity.
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1000 ms
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Fig. 13. Lines of the near-magnetic field – one broken bar and eccentricity.
B. Low Frequency Harmonics of the Magnetic Flux Density The time variation radial component Bx of magnetic flux density in the center of the Ox sensor and azymuthal component By in the center of the Oy sensor are studied in order to diagnose the motor faults based of the magnetic field low frequency harmonics. These curves are presented in Fig. 14 for the healthy motor, in Fig. 15 for one broken bar, in Fig. 16 for rotor eccentricity and in Fig. 17 for both faults: one broken bar and 0.2 mm rotor eccentricity.
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Fig. 14. Time variation of the magnetic flux density for the healthy motor. -4
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Fig. 17. Time variation of the magnetic flux density for one broken rotor bar and rotor eccentricity.
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The comparison of all under 10 Hz harmonics for the healthy motor (0BC) and for one broken rotor bar (1BC) in Fig. 18 states the choice for the 1.25 Hz and 6.25 Hz harmonics to characterize the broken bar fault.
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Fig. 15. Time variation of the magnetic flux density for one broken rotor bar. -4
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(b) Fig. 18. Amplitudes of low frequency harmonics for the healthy motor and the motor with one broken bar: (a) Bx harmonics; (b) By harmonics.
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Fig. 16. Time variation of the magnetic flux density for rotor eccentricity.
As shown in Fig. 19 the increase of the all harmonics amplitudes with frequency under 10 Hz of the two components of the magnetic flux density it is also evident when a rotor excentricity exists (Ecc + 0BC) or in the case of both motor faults (Ecc + 1BC). Related to the Bx component in Fig. 19(a) the most important increase characterises the 6.25 Hz harmonic when one rotor bar is broken or when both faults are present. In case of eccentricity the harmonic at 7.50 Hz is the most important for such a fault diagnostic.
different from one harmonic to another and from a motor fault to another. Consequently, the first step in the diagnosis strategy implementation for motors in operation or during the new motors design it is the choice based on finite element models of the most appropriate harmonic which should be used for fault detection. VII. [1] (a)
[2] [3] [4] [5] [6]
(b) Fig. 19. Amplitudes of low frequency harmonics for healthy and faulty motors: (a) Bx harmonics; (b) By harmonics.
In case of the By component, since the amplitudes of the 2.5 Hz are higher than those of the Bx component, it is this low frequency harmonic to be considered for motor faults diagnosis. Two harmonics with the frequency 21.25 Hz and 26.25 Hz (Fig. 20) have much higher amplitudes than the under 10 Hz harmonics. The first harmonic is not so affected by the eccentricity fault, but the second is very efficient for diagnosis of all three motor faults considered in this study: 1BC, Ecc + 0BC, Ecc + 1BC.
[7] [8]
[9] [10] [11]
[12]
[13]
[14] [15] [16] Fig. 20. Amplitudes of two Bx harmonics over 10 Hz for healthy and faulty motors.
VI. CONCLUSIONS This paper studies a very simple and efficient method for the noninvasive diagnosis of broken bars and rotor eccentricity faults in squirrel-cage induction motors, based on the evaluation of low frequency harmonics of the nearmagnetic field. The increase of the amplitudes of the magnetic field harmonics for faulty motor with respect the healthy motor is
[17]
REFERENCES
D. Pouliezos and G. S. Stavrakakis, Real Time Fault Monitoring of Industrial Processes. Norwell, MA: Kluwer, 1994. P. Tavner, L. Ran, J. Penman, and H. Sedding, Condition Monitoring of Rotating Electrical Machines, 2nd ed. Stevenage, U.K.: IET, 2008. S. Nandi, H. A. Toliyat, and L. Xiaodong, “Condition monitoring and fault diagnosis of electrical motors—A review,” IEEE Trans. Energy Convers., vol. 20, no. 4, pp. 719–729, Dec. 2005. W. T. Thomson and M. Fenger, “Current signature analysis to detect induction motor faults,” IEEE Ind. Appl. Mag., vol. 7, no. 4, pp. 26– 34, Jul./Aug. 2001. M. Benbouzid and G. B. Kliman, “What stator current processingbased technique to use for induction motor rotor faults diagnosis?” IEEE Trans. Energy Convers., vol. 18, no. 2, pp. 238–244, Jun. 2003. H. Henao, H. Razik, and G. A. Capolino, “Analytical approach of the stator current frequency harmonics computation for detection of induction machine rotor faults,” IEEE Trans. Ind. Appl., vol. 41, no. 3, pp. 801–807, May/Jun. 2005. F. Filippetti, G. Franceschini, C. Tassoni, and P. Vas, “AI techniques in induction machines diagnosis including the speed ripple effect,” IEEE Trans. Ind. Appl., vol. 34, no. 1, pp. 98–108, Jan./Feb. 1998. R. Pusca, R. Romary, A. Ceban, and J.F. Brudny, “An online universal diagnosis procedure using two external flux sensors applied to the ac electrical rotating machines,” Sensors 2010, vol. 10, pp. 10448-10466, Nov. 2010. A. Ceban, R.Pusca, R. Romary, “Eccentricity and broken rotor bars faults – Effects on the external axial field”, in Proc. ICEM Conf., Roma, Italy, Sep. 6-8, 2010, pp.1-6. R. Fišer and S. Ferkolj, “Magnetic field analysis of induction motor with rotor faults,” COMPEL vol. 17, no. 1–3, pp. 206–211, 1998. A. Bellini, A. Yazidi, F. Filippetti, C. Rossi, and G.-A. Capolino, “High frequency resolution techniques for rotor fault detection of induction machines,” IEEE Trans. Ind. Electron., vol. 55, no. 12, pp. 4200–4209, Dec. 2008. A. Yazidi, H. Henao, G.A. Capolino, M. Artioli, F. Filippetti, D. Casadei, “Flux signature analysis: an alternative method for the fault diagnosis of induction machines,” in Proc. IEEE PowerTech, St. Petersburg, Russia, 2005, pp. 1–6. K. Bacha, H. Henao, M. Gossa, and G.-A. Capolino, "Induction machine fault detection using stray flux EMF measurement and neural network-based decision," Electric Power Systems Research, vol. 78, pp. 1247-1255, 2008. V. Fireteanu, T. Tudorache, P. Taras, “Finite element diagnosis of squirrel cage induction motors with rotor bar faults”, in Proc. OPTIM Conf., Brasov, Romania, 2006, pp.1-6. V. Fireteanu, P. Taras, “Teaching induction machine through finite element models”, in Proc. ICEM Conf., Vilamoura, Portugual, Sep. 69, 2008, pp.1-6. A.B.J. Reece and T.W. Preston, Finite Element. Methods in Electrical Power Engineering. Oxford University Press, 2000. J. Kappatou, C. Marchand, A. Razek, "Finite element analysis for the diagnosis of broken bars in 3-phase induction machines", Studies in Applied Electromagnetics and Mechanics, vol. 27, pp. 348-353, 2006.
VIII.
BIOGRAPHIES
Andrian Ceban was born in Leova, Moldova, in 1982. He received the Master’s degree in electrical engineering from the Technical University of Moldova, Chisinau, Moldova, in 2008. He is currently Ph.D. student in electrical engineering at the Laboratory of Electrical Systems and Environment (LSEE), Artois University, Béthune, France. His research interests include diagnosis and numerical modeling of electrical machines.
Virgiliu Fireţeanu was born Runcu-Dambovita, Romania, on November 7, 1947. He graduated in 1970 the former Polytechnic Institute of Bucharest, Electrotechnical Faculty. From 1994 he is Full Professor of POLITEHNICA University of Bucharest, Electrical Engineering Faculty. His actual field of interest it is the finite element analysis of electro-mechanical and electrothermal energy conversion systems. He animates the activity in higher education and research and the EPM_NM Laboratory (http://www.amotion.pub.ro/~epm). Raphaël Romary received the Ph.D. from Lille University in 1995 and the D. SC degree from Artois University in 2007. He is currently Full Professor in that University and researcher at the Laboratory of Electrical Systems and Environment (LSEE). His research interest concerns the analytical modeling of electrical machines with applications to noise and vibration, losses, electromagnetic emissions, diagnosis.
Remus Pusca was born in Medias, Romania, in 1972. He received in 1995 the electrical engineering degree from Technical University of Cluj-Napoca, Romania. He obtained in 2002 Ph.D. degree in electrical engineering, from the University of Franche-Comté, France. Since 2003 he has joined the Laboratory of Electrical Systems and Environment (LSEE). He is Associate Professor at the Artois University. His research interest is control of electrical systems and diagnosis of electrical machines. Petrică Taraş was born in Călăraşi, Romania, on June 22, 1983. He graduated from the POLITEHNICA University of Bucharest, Romania. His main interest resides in applied finite element modeling. He is a member in the EPM_NM laboratory team. He is currently pursuing a Ph.D. degree in the area of rails induction heating before hardening.
