An Overview On Induction Machine's Diagnosis Methods

An Overview on Induction Machine's Diagnosis Methods Szabó L.*, Tóth F.**, Kovács E.** and Fekete G.**

*

Department of Electrical Machines, Marketing and Management Technical University of Cluj RO-400750 Cluj, P.O. Box 358, Romania e-mail: [email protected] **

Department of Electrical and Electronic Engineering University of Miskolc H-3515 Miskolc-Egyetemváros, Hungary e-mail: [email protected]

Abstract – Several methods for diagnosing the faults of the squirrel-cage induction motors are cited in the literature. The authors focused their researches on the rotor faults of the squirrel cage induction machines. The aim of the paper is to compare these fault diagnosis methods by means of data processing in LabVIEW the results obtained by measurements. It will be emphasized that beside the current signature analysis also the threephase current vector, the instantaneous torque, respectively the outer magnetic filed can be used for diagnosing the rotor faults.

Since the 80's the most widely used diagnosis method was based on the vibration analysis. In the 90's the motor current signature based fault detection methods (MCSA – Motor Current Signature Analysis) got more widespread. In this paper the main methods used for the broken rotor bars detection will de overviewed. The measurements were performed by using advanced data acquisition boards and methods. The measured data were processed using the LabView program.

Keywords: induction machine, rotor faults, electrical machine's faults detections and monitoring

During the startup of the squirrel cage induction motors their current is 5-8 times greater than the rated current. Due to this a great quantity of heat is produced in the rotor. The temperature of the bars is rapidly increasing and the bars are suspected to significant mechanical stresses. In steady-state regime the strong thermal and mechanical stresses are diminished. If the induction machine is rather old or is frequently started the connection between the bars and the end rings can be damaged. Hence the resistance of the of a part of the rotor circuit is increased, which leads to an asymmetry in the machine's field.

I. INTRODUCTION Due to their reliability, robustness and low price the squirrel cage induction motors are widely used as energy converters. But also these reliable electrical machines can get faulty. The statistical data show that 10% of the induction machine's faults are the rotor faults [1]. The typical rotor faults are the damaged rotor bars, discontinuities in between the bars and the end rings, rotor eccentricity, etc. In order to prevent more serious damages, and due to this long time plant shutdowns, it is recommended to detect these faults as soon as possible. The electrical machines can be diagnosed via several methods. The rotor bar faults can be detected using the following methods: • Sensing the machine's vibrations and using frequency analysis of the vibrations [2, 3] • Measuring the line currents and analysing its harmonic content [3, 4, 5] • Studying the three-phase current vector (Park vector) [6, 7, 8] • Sensing the torque's variation and applying its frequency analysis [9, 10] • Maesuring the machine's external magnetic fields and analysisng its harmonic content [11, 12, 13]

II. THE EFFECTS AND DIAGNOSIS OF BROKEN ROTOR BARS

A. The line current's spectrum analysis In the three-phase induction motor under perfectly balanced conditions (healthy motor) only a forward rotating (direct sequence) magnetic field is produced, which rotates at synchronous speed, n1 = f1 p , where f1 is the supply frequency and p the pole-pairs of the stator windings. The rotor of the induction motor always rotates at a speed (n) less than the synchronous speed. The slip, s = (n1 − n) n1 , is the measure of the slipping back of the rotor regarding to the rotating field. The slip speed ( n2 = n1 − n = s n1 ) is the actual difference between the speed of the rotating magnetic field and the actual speed of the rotor. The frequency of the rotor currents is called the slip frequency and is given by f 2 = n2 p = s n1 p . The speed of the rotating magnetic field produced by the current carrying

rotor conductors with respect to the stationary stator winding is n + n2 = n + n1 − n = n1 . With respect to a stationary observer on the fixed stator winding, the speed of the rotating magnetic field from the rotor equals the speed of the stator rotating magnetic field, namely, the synchronous speed. Both fields are locked together to give a steady torque production by the induction motor. With broken rotor bars in the motor there is an additional, backward rotating magnetic field produced. This is rotating at the slip speed with respect to the rotor. The backward rotating magnetic field speed produced by the rotor due to broken bars and with respect to the rotor is: nb = n − n2 = n1 (1 − s ) − s n1 = n1 − 2sn1 = n1 (1 − 2 s )

(2)

where k = 1,2,3… An estimate of the number of the broken rotor bars can be analytically determined [4]. The ratio of the linear magnitude of the lower sideband at (1 − 2 s ) f1 to the magnitude of the supply current f1 .

Rs ≈

sin α `, 2 p(2π − α )

f p = 2 p ⋅ f slip

(7)

From (6)÷(7) results the pole frequency: f p = 2 ⋅ s ⋅ f1

(8)

The spectrum of the vibration's amplitude versus the frequency is given in Fig. 1.

(1)

The stationary stator winding now sees a rotating field at nb = n1 (1 − 2s ) or f b = f1 (1 − 2s ) (expressed in terms of frequency). This means that a rotating magnetic field at that frequency cuts the stator windings and induces a current at that frequency (fb). This in fact means that fb is a twice slip frequency component spaced 2 s f1 down from f1 . Thus speed and torque oscillations occur at 2 s f1 , and this induces an upper sideband at 2 s f1 above f1 . Classical twice slip frequency sidebands therefore occur around the supply frequency: fb = f1 (1 ± 2ks)

• pole pass frequency:

Fig. 1. The vibration's spectrum of amplitude

C. Plotting the three-phase current vector It is known that the m.m.f. generated by the symmetrical induction machines stator winding is given by: Θ s (ϑ , t ) =

2 ξ s ⋅ N1 ⋅ p

π

2π 2π ⎤ ⎡ ⋅ ⎢isa (t ) cos ϑ + isb (t ) cos(ϑ − ) + isc (t ) cos(ϑ + ) 3 3 ⎥⎦ ⎣

(9)

using the complex versor a = e j 2π / 3 equation (9) can be written as: Θ s (ϑ , t ) =

3 ξ s ⋅ N1 ⋅ p π

2 ⎧2 ⎫ ⋅ Re⎨ ⎡⎢isa (t ) + a ⋅ isb (t ) + a isc (t )⎤⎥ e − jϑ ⎬ 3 ⎣ ⎦ ⎩ ⎭

(3)

(10)

where

where:

α=

2π n p , R

(4)

and n is the number of the broken bars, p the number of pole pairs, respectively R the rotor's slot number. B. The spectrum analysis of the vibrations In electrical machines the torque is produced upon the interaction of the stator and rotor fields. The radial (vibration generating) forces are balanced by the specific design of the induction machines (pair number of slots and uniform air-gap). If one or more rotor bars are broken, the force balance inside the machine is damaged, hence the unbalanced forces generate significant vibrations. These vibrations can be measured with adequate sensors and analyzed. The specific terms used in vibration analysis are: n • rotational frequency: f f = [Hz]; (5) 60 n − n f1 = • slip frequency: f slip = 0 s; (6) 60 p

i s (t ) =

2 2⎡ isa (t ) + a ⋅ isb (t ) + a isc (t )⎤⎥ 3 ⎢⎣ ⎦

(11)

is the so-called three-phased current vector (Park vector, or space vector). If the stator current varies in a sinusoid way, isa (t ) = Iˆs cos(ωt + ϕi ) , then the three-phase current vector can be given as: i s (t ) = Iˆs e j (ωt +ϕ i )

(12)

where Iˆs is the peak value of the line current. Relation (12) shows that the symmetric three-phase winding and the sinusoidally varying three-phase currents generate a vector rotating at constant frequency ω. If the currents in the windings are not equal, this change will be observed also in the three-phase vector (12). The former circular shape will be modified in an elliptical shape. The difference from the circular shape indicate the fault's rate. The stator current (12) has two (a real and an imaginary) component:

{}

i x = Re i s =

2 1 ⋅ isa − (isb + isc ) 3 3

{}

1

i y = Im i s =

3

(isb − isc )

(13) (14)

The voltage signals proportional to these two components, ix and iy, can be plotted.

The external magnetic flux is due to the unbalance between the m.m.f. of the stator and the rotor, which are not in equilibrium neither in the case of a healthy machine. When faults occur in the spectrum of the external flux, typical harmonic components can be detected. The voltages induced by the radial external fluxes are given in Fig. 3 (measured at no-load condition).

D. Potting the torque during startup The flux vector of the three-phase windings can be expressed in a similar way as the current vector [14]: Ψs =

2 2 (Ψa + a ⋅ Ψb + a Ψc ) 3

(15)

Knowing the flux and current vectors the torque can be computed as [15]: m=

{

3 Im Ψ s ∗ ⋅ i s 2

}

a) healthy machine

(16)

When asymmetry occurs the torque will be compound of a direct and an inverse component and a balancing component. The last component has double frequency and generates noises and vibrations [14].

E. Sensing the external magnetic flux The external magnetic filed of an electrical machine can be sensed by a coils with great number of turns. The so-called search coil can be placed at the end of the machine (see Fig. 2a). In this case the axial components of the flux will be detected. Also it can be placed in a radial direction for detecting the radial external magnetic flux of the machine (see Fig. 2b). The e.m.f in the coil depends on the distance from the machine, but as we observed the waveform is not influenced by the distance.

b) machine with broken rotor bars Fig. 3. The voltage induced by the external radial flux

III. THE SAMPLED VALUES The measurements were performed using an induction machine with the following nameplate data: Pn = 1.5 kW, Un = 400/230 V (Y/Δ), f1 = 50 Hz, In = 4.2/7.3 A, n = 1361 1/min, cos φn=0.69. The slot numbers were: Zs = 24, Zr =18. The pictures of the stator and the rotor of the sample machine are given in Fig. 4. In Fig. 4.b. both the healthy and the damaged (right side) rotor can be seen.

a)

b)

b) Fig. 2. Laboratory setup for mesuring the external flux

a) Fig. 4. The stator and rotor of the sample machine

A. The time plots of the sampled values

B. The spectrum of the sampled values

The data acquisition was performed using the LabVIEW program. The time plots of the sampled values are shown in the next figures: in Fig. 5 the plots for the healthy machine, respectively in Fig. 6 those for the machine having broken rotor bars: • in figures a) the torque; • in figures b) the phase current; • in figures c) the voltage induced by the external radial flux; • in figures d) the vibrations of the machine mesured by a sensor placed on the macine's housing

The Fourier analysis was performed using the same LabVIEW program. The spectrum of the signals plotted in Fig. 5 and 6 are given in Fig. 7 and 8 (those corresponding to the healthy machine in Fig. 7, respectively those for the faulty machine in Fig. 8). The plots correspond for: • in figures a) the spectrum of the torque; • in figures b) the phase current's spectrum; • in figures c) the spectrum of the voltage induced by the external radial flux; • in figures d) the spectrum of the machine's vibrations

Fig. 5. Plots versus time of the sampled values (healthy machine)

Fig. 6. Plots versus time of the sampled values (machine having broken rotor bars)

Fig. 7. The spectrum of the sampled values (healthy machine

C. The time plots of the sampled values during startup During startup the differences between a healthy and faulty machine can be observed much easy. These differences are highlighted in Fig. 9 and 10. In a same manner as in the previous figures the plotted values are:

Fig. 9. Plots versus time of the sampled values during startup (healthy machine)

Fig. 8. The spectrum of the sampled values (machine having broken rotor bars)

• in figures a) the torque; • in figures b) the phase current; • in figures c) the voltage induced by the external radial flux; • in figures d) the vibrations of the machine

Fig. 10. Plots versus time of the sampled values during startup (machine having broken rotor bars)

D. The plots versus time of the phase currents and the three-phase current vectors The rotor bar faults of a squirrel cage induction machine can be also diagnosed by plotting the three-phase current vector. A suggestive example is given in Fig. 11 (Fig 11a for the healthy machine, respectively Fig. 11b for that having broken rotor bars). As it can be seen very clearly in Fig. 11b the pulsations of the phase current are highlighted also in the plot of the current vector.

a) healthy machine

b) machine with broken bars Fig. 11. The phase current's plots versus time and the plots of the three-phase current vector

IV. CONCLUSIONS As it could be observed the broken bars of a squirrel cage induction machine can be diagnosed with all of the method above described. In the last time, due to its simplicity the motor current signature analysis (MCSA) method was the mostly used in industrial environment. It can be predicted that in the near future diagnosis methods based on the detection of the external magnetic fields of the electric machines, a more simple and cheap method, could be more widespread.

ACKNOWLEDGMENT The work was possible due to the support given by the Romanian Ministry of Education and Research, National Authority for Scientific Research (CNCSIS) and the Hungarian National Office for Research and Technology (NKTH) in the framework of the "Romanian-Hungarian Intergovernmental S&T Cooperation Program 2008-2009". The authors should like to sincerely thank this way for the financial support. REFERENCES [1] Tian Han, Bo-Suk Yang, Won-Ho choi and Jae-Sik Kim, "Fault Diagnosis System of Induction Motor Based on Neutral Network and Genetic Algorithm Using Stator Current Signal", International Journal of Rotating Machinery, Vol. 2006, pp. 1-13. [2] Mori D., Ishikawa T., Force and vibration analysis of induction motors", IEEE Transaction on Magnetics, vol. 41, no. 5 (May 2005), pp. 1948-1951. [3] Weidong Li: "Detection of Induction Motor Faults: A Comparison of Stator Current, Vibration and Acoustic Methods," Journal of Vibration and Control, Vol. 12, No. 2, pp. 165-188 (2006). [4] Ming Xu, Tom Alfod, "Motor current analysis and its applications in induction motor fault diagnostics", ENTERACT, 98, pp. 1-21. [5] Mark Fenger, Blake A., "Case histories of current signature analysis to detect fault in induction motor drives", Electric Machines and Drives Conference, IEMD '2003, vol. 3, pp. 1459-1465. [6] Cruz S. M. A.; Cardoso A.J.M., "Rotor Cage Fault Diagnosis in Three-Phase Induction Motors by Extended Park"s Vector Approach", Electric Machines and Power Systems, Volume 28, Number 4, pp. 289-299. [7] M. Arkan, H. Calis, M.E. Taguk "Bearing and misalignment fault detection in induction motors by using the space vector angular fluctuation signal", Electrical Engineering (2005), no. 87, pp. 197-206. [8] Izzet y Önel, K Burak Dalci and Ibrahim Senol, "Detection of bearing defects in three-phase induction motors using Park's transform and radial basis function neutral networks", Sadhana, Vol. 31, Part 3, pp. 235-244. [9] Rastko Fiser, Stanislav Ferkolj, "Development of Steady-State Mathematical Model of Induction Motor with Rotor Cage Faults", Proceeings of the ICEM '1998, Vol. 3, pp. 2188-2191. [10] P. Bajec, R. Fiser, J. Nastran, "Detection of Induction Motor Squirrel Cage Asymmetry Using Run-Up Test", Proceedings of the ICEM '2004, pp. 837-838. [11] Voitto Kokko, "Conditiom Monitoring of Squirrel-Cage Motors by Axial Magnetic Flux Measurements", Dissertation, Oulu, 2003. [12] R. Romary, R Corton,D. Thailly, and J.F. Brudny, "Induction machine fault diagnosis using an external radial flux sensor", The European Physical Journal, Applied Physics, 32 (2005), pp. 125-132. [13] Negrea, M.D. "Electromagnetic flux monitoring for detecting fault in electrical machines", TKK Dissertations 51, Espoo, 2006. [14] K.P. Kovács, "Symmetrische Komponenten in Wechsel strommaschinen", Birkhäuser Verlag Basel und Stutgart, 1962. [15] Dr. Retter Gyula: "Villamosenergia átalakítók" 2. kötet, MK, Bp.1987.