Study of Rotor Faults in Induction Motors Using ... - Semantic Scholar

2082

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 5, MAY 2012

Study of Rotor Faults in Induction Motors Using External Magnetic Field Analysis Andrian Ceban, Remus Pusca, and Raphaël Romary, Member, IEEE

Abstract—This paper presents a new signature for detection of rotor faults in induction motors, such as eccentricity and broken rotor bars, that uses the external magnetic field analysis. The proposed method is based on the variations of axial flux density in the presence of these faults. The low frequency part of the magnetic field spectrum is particularly analyzed. The analysis is realized through a machine modeling based on permeance circuit under eccentricity fault and also by machine modeling based on coupled magnetic circuit theory under broken rotor bars fault. Analytical relations which describe the machine operation under broken bars fault highlight the influence of speed variation to modify the low frequency components of the external magnetic field. The theoretical results have been validated by experimental measurements. In particular, an inverse stator cage induction machine have been used to measure the bar currents under healthy and faulty cases. Index Terms—Broken rotor bar, eccentricity, fault diagnosis, field analysis, induction motors, low frequency, magnetic flux density, magnetic spectral analysis.

N OMENCLATURE Symbol Explanation α Position of an air-gap point in a stator reference frame, m. β Position of the minimum air-gap thickness. δ Value of the rotor off-centering. Total torque, N · m. Ce_tot Mean torque due to the interaction of the stator and Ce_srp the rotor fields in the clockwise direction, N · m. Torque corresponding to pulsation 2sω, N · m. Ce_srn Load torque, N · m. Cr em Average value of the air-gap thickness, m. Emf provided by coil sensor, V. esensor Mmf between the stator and the rotor along the airε1 gap inside the coil. Mmf between the stator and the rotor along the airε2 gap outside the coil. f Frequency, Hz. Axial flux, Wb. ΦA Flux generated only by the end coil (axial-radial). ΦA

Manuscript received December 10, 2010; revised March 24, 2011 and June 20, 2011; accepted July 8, 2011. Date of publication July 29, 2011; date of current version February 3, 2012. The authors are with the University Lille Nord de France, 59000 Lille, France, and also with the Laboratory of Electrical Systems and Environment (LSEE), Artois University, 62400 Béthune, France (e-mail: apceban@ gmail.com; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2011.2163285

Φe1 , Φe2 Φext ΦAT ϕB s ϕBrp ϕBrn [I] Is Irn Irp ie ibn irn is J kr ks L [L] Lb Le Lmr Lms [Ls ] Lsf Ls1 Mrr Ms Msr μ0 n nt nc n Ωr Ω0 Ωs ω Pe1 , Pe2 p R [R]

Air-gap fluxes, Wb. Linked flux, Wb. Total axial flux, Wb. Phase relative to the stator phase current of the stator flux density. Phase relative to the rotor flux density in the clockwise direction. Phase relative to the rotor flux density in anticlockwise direction. Current vector, A. Stator rms current, A. Amplitude of negative-sequence current system, A. Amplitude of positive-sequence current system, A. End ring current, A. Current crossing the bar n of the rotor cage, A. Current crossing the loop n, A. Stator instantaneous current, A. Total moment of inertia, kg · m2 . Coefficient that depends on the rotor cage constitution. Coefficient that depends on the stator winding arrangement. Active length of the magnetic circuit (of a core), m. Global inductance matrix, H. Rotor bar leakage inductance, H. Rotor end ring leakage inductance, H. Magnetizing inductance for each rotor loop, H. Inductance for each stator coil, H. Stator inductance matrix, H. Leakage inductance, H. Total inductance of the stator coil 1, H. Mutual inductance between two rotor loops, H. Mutual inductance between the stator phases, H. Mutual inductance between stator coils and rotor loops, H. Magnetic permeability of the air. Number of rotor bars or rotor loops. Number of turns per pole pair and per phase. Number of coil sensor turns. Number of elementary coil turns. Angular velocity, rad/s. Mean value of Ωr , rad/s. Synchronous speed, rad/s. Angular frequency, rad/s. Air-gap permeances. Number of pole pairs. Average radius of the air-gap, m. Global resistance matrix, Ω.

0278-0046/$26.00 © 2011 IEEE

CEBAN et al.: STUDY OF ROTOR FAULTS IN INDUCTION MOTORS USING EXTERNAL MAGNETIC FIELD ANALYSIS

Re Rb [Rr ] [Rs ] S s t [V ]

End ring resistance, Ω. Rotor bar resistance, Ω. Rotor resistance matrix, Ω. Stator resistance matrix, Ω. Coil sensor area, cm2 . Slip, between 0 and 1. Time, s. Voltage vector, V. I. I NTRODUCTION

O

NE OF THE most important objectives in the maintenance of wide industrial systems is the detection of incipient faults in induction motor drive as soon as possible to realize the repairs during the maintenance period, without stopping the working process. Induction motors are widely used in industrial applications, and among the defects which may appear, broken rotor bars represent 10% to 20% of the whole faults [1]–[3]. This kind of failure does not cause immediate break down, but deteriorates the operation of the machine, decreasing its performances. During the last two decades, there have been many papers dealing with the detection of the broken rotor bar fault. A wide part of these studies published in the ’90th can be found in [4]. In 1988, Kliman shows that the component at (1 − 2s)f (where s represents the rotor slip and f is the supply frequency) in the current spectrum was an indicator of this fault [5], and most of the further studies were based on the current signature analysis [2], [3], [6]–[12]. The development of efficient methods of signal processing has improved the detection procedures [13]. For example, time frequency analysis enables to exploit the data measurement during a start-up transient [14], [15]. Other methods exploit the slot harmonics [16], [17] or are based on parameter estimation [18]. On the other hand, the development of artificial intelligence techniques [19], [20] has improved the automatic discrimination of the fault. Other methods based on mechanical analysis by means of vibrations, noise measurement [21]–[23], voltage analysis technique [24], or real-time signal analysis [25], [26] also exist. There are many papers which deal also with the eccentricity in induction machines [27], [28]. Each method has its advantages and disadvantages, but it is essential that the used method should be able to detect incipient faults and to prevent the total damage (unexpected shutdowns). More recently, methods based on the external magnetic field analysis have been developed; their advantage lays in the aspect of noninvasive measurement and the simplicity of implementation [17], [29], [30]. The magnetic field existing outside the electrical machines is an inherent phenomenon in the functioning of these machines. It is an image of the air-gap flux density, and consequently, it contains information concerning the presence of a defect [17], [29]–[35]. In [29], it is shown that 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. The study presented in this paper shows a signature in the low frequency spectrum of the external axial magnetic field in the case of broken rotor bar fault. The originality is that one

2083

Fig. 1. Coil sensor in different measurement positions.

considers the interaction of the broken rotor bar fault with the effect of eccentricity on the low frequency spectrum. Initially, a study concerning the influence of the dynamic eccentricity on the axial flux of a three-phase induction machine, more particularly on the very low frequency component of the spectrum at sf , is presented. Then, the paper shows the results issue from modeling by coupled electric magnetic circuit, proposed for a machine with broken rotor bars. That allows one to highlight the rotation speed variation of the machine, caused by a broken bar fault. It is then shown the presence in the axial flux of the low frequency component at 3sf under broken rotor bars. Finally, a special machine, designed to measure the bar currents is used to validate the theoretical current distribution in each bar under healthy and faulty cases; that is rarely presented in literature. Then, the experimental measurements based on spectral analysis of the stray field allow verifying qualitatively and quantitatively the results of the theoretical study. II. E XTERNAL M AGNETIC F IELD M EASUREMENT The modeling of the external magnetic field is based on its axial-radial decomposition [17], [30]. The axial field is in a plan which includes the machine axis; it is generated by currents in the stator end windings or rotor cage end ring. The radial field is located in a plane perpendicular to the machine axis, it is an image of the air-gap flux density which is attenuated by the stator magnetic circuit (package of laminations) and by the external machine frame. The both fields can be measured separately by a convenient location of the sensor. Fig. 1 shows the different positions of a coil sensor, derived from the presumed circulation of the field lines. It enables to measure, respectively, the axial (Pos. 2) or radial field (Pos. 3). Indeed, in Pos. 3, the coil sensor is parallel with the longitudinal plan of the machine, and the linked flux of the sensor concerned by the axial field is null. In Pos. 1, the sensor measures the radial field and also a part of the axial field. The pure axial field measurement can be done in Pos. 2, but this position is not always accessible in an industrial environment. Pos. 1 will be preferred for axial measurement. Analyzing the magnetic field spectrum, emitted by an induction motor, the appearance of a component at sf can be observed. This component presents the characteristic that it exists only in the axial field. Under healthy conditions, the magnitude can be relatively low. The theoretical explanation for the emergence of this component can be done through a modeling using the permeance circuit that takes the eccentricity into account.

2084


Analytical developments show that Fk = fk

Fig. 2. Circuit of axial permeances. (a) Section of the machine. (b) Permeance circuit.

III. M ODELING OF E CCENTRICITY IN AN I NDUCTION M ACHINE The modeling through permeance circuit requires to determine the flux path permeance of the various field lines. For the modeling of the axial field, it is necessary to consider the field lines existing at the machine extremities. The distribution of these ones strongly depends on the geometry and the mechanical components that exist at the machine extremities [35]. However, a simplified geometry which allows one to identify and to classify the different fluxes can be considered (Fig. 2). Fig. 2(a) shows a longitudinal half section of the machine, which represents the end coil of n elementary coil turns supplied by a is current. In this section, the external frame of the machine and the end bells are not represented. The considered machine has a smooth air-gap. Fig. 2(b) gives the permeance circuit, relating to the half of the machine. The flux path permeances in the iron parts are neglected. In this circuit, n is is the total magnetomotive force (mmf) generated by the coil. ε1 and ε2 are the mmf between the stator and the rotor along the air-gap: ε1 inside the coil and ε2 outside, with n is = ε1 − ε2 . In this circuit, two kinds of fluxes can be distinguished according to the direction of the magnetic field. 1) Radial fluxes, which are mainly the air-gap semifluxes Φe1 /2 and Φe2 /2, associated with air-gap permeances Pe1 and Pe2 . The permeances Pe1 and Pe2 depend, among other things, on the air-gap thickness e which can take the eccentricity into account [35] e = em + δ cos(α + β)

(1)

where em is the average value of the air-gap thickness, δ is the value of the rotor off-centering, α locates the position of a point of the air-gap in a stator reference frame, and β indicates the position of the minimum airgap thickness. It allows one to define the kind of eccentricity (static or dynamic). Considering p the number of pole pairs, Pe1 and Pe2 can be expressed as follows: π/2p

Pe1 =RL −π/2p

μ0 dα = μ0 RL F0 + e

2π−π/2p

Pe2 =RL π/2p

p

(2)

k=1

p μ0 dα = μ0 RL F0 − Fk cos kβ . e k=1

k = 0;

π π F0 = f0 ; F0 = f0 2π − ; p p 2j p δ (2j)! . f0 = em (j!)2 2j j=0 R is the average radius of the air-gap, L is the active length of the magnetic circuit, and μ0 is the magnetic permeability of the air. 2) Axial fluxes, principally ΦA which can be decomposed into ΦA1 and ΦA2 : ΦA = ΦA1 + ΦA2 . These fluxes go out from the rotor in an axial way and can be associated with permeances PA1 and PA2 . Regarding ΦA , the flux generated only by the end coil, it presents an axial part, but also a radial part. The decomposition between these two parts depends on the coil geometry; it comes from the decomposition along two axes of the current in the coil ends. The permeance circuit given in Fig. 2(b) allows one to calculate the air-gap mmfs (ε1 , ε2 ) and thus the distribution of air-gap flux density by taking into account the axial flux. This circuit also enables to calculate the axial flux ΦA going out from the rotor. By summing the axial fluxes of all coils that constitute the machine, when it is supplied by a three phase sine balanced current system at ω angular frequency, one obtains the total axial flux ΦAT which originates from the eccentricity [35] p √ (−1)p δ 3 ΦAT = − nt Is 2 PA cos(ωt − pβ) (4) 2 πf0 2p−1 em where PA = PA1 + PA2 , nt is the number of turns per pole pair and per phase, Is is the stator rms current, and β defines the type of eccentricity. 1) Case of a static eccentricity: β is constant, there is a component of angular frequency ω. The eccentricity therefore generates an axial flux component at the supply frequency. This component is combined with this coming from ΦA at the same frequency. 2) Case of dynamic eccentricity: β depends on the angular velocity Ωr of the rotor; β = β0 + Ωr t = β0 + (1 − s)(ωt/p). Relation (4) then leads to ˆ cos(sωt − pβ0 ) ΦAT = Φ

(5)

with

Fk cos kβ

kπ 2 sin , k 2p

(3)

p √ ˆ = − 3 nt Is 2 (−1) PA Φ p−1 2 πf0 2

δ em

p .

(6)

In this case, the appearance of an axial flux component at angular frequency sω can be seen which is proportional to (δ/em )p .


Fig. 3.

Operation schema. (a) Healthy motor. (b) Faulty motor.

Although in theory, this component exists only in the case of a machine with dynamic eccentricity [35], [36], but in reality other machines regarded as perfect also present a component sf with a low value, because the manufacturing techniques of machines are not perfect. IV. BASIS ON B ROKEN ROTOR BAR E FFECT The presentation of the phenomenon will consider only the flux density component of p pole pairs. Under healthy operating conditions, the balanced three-phase current system creates a fundamental clockwise rotating magnetic field in the air-gap. This field induces a current in the rotor bars with a frequency proportional to the rotor slip s. The rotor bars then generate a clockwise field rotating at sΩs in a rotor referential [Fig. 3(a)]. For a symmetrical motor (healthy machine), there is not any anticlockwise field in the air-gap [19], [37], [38]. Under rotor faults, in addition to the clockwise field, an anticlockwise field appears, created by the imbalance of rotor bar currents and which rotates at an angular velocity −sΩs shown in Fig. 3(b). It is possible to associate with this anticlockwise field a negative-sequence current system with amplitude Irn , which is added to the positive-sequence current system with amplitude Irp . Fig. 3(b) shows the phenomenon due to the appearance of rotor failure. A flux density component rotating at Ωf ault appears in the stator referential Ωf ault = Ωr − sΩs = Ωs (1 − 2s)

(7)

which leads to the well-known frequency in literature ff ault , appearing in the radial external magnetic field and in the line current ff ault = (1 − 2s)f.

(8)

The interaction of the rotor currents with the clockwise stator field produces the electromagnetic torque. In case of broken rotor bar fault, the total torque can be expressed as follows [37]: Ce_tot =Ce_srp +Ce_srn =π

RLem ks Is kr Irp sin ϕBs +ϕBrp μ0 +kr Irn sin (2sωt+ϕBs −ϕBrn )] (9)

2085

where Ce_srp represents the mean torque due to the interaction of the stator and the rotor fields in the clockwise direction, Ce_srn is the pulsating torque of pulsation 2sω due to the interaction of the stator clockwise field with the anticlockwise rotor field; ϕBs , ϕBrp , and ϕBrn are respectively the phases relative to the stator phase one current of the stator flux density, the rotor flux densities in the clockwise direction and in the anticlockwise direction; ks is a coefficient that depends on the stator winding arrangement, and kr is a coefficient that depends on the rotor cage constitution. The torque oscillation at frequency 2sf , also presented in [19], [39]–[41], generates a speed oscillation at this frequency whose amplitude depends on the rotor asymmetry, the motor load level [19], [41], and the total moment of inertia J. The speed is calculated with the relation J

dΩr = Ce_tot − Cr = Ce_srn dt

where Cr is the load torque 1 Ce_srn dt + Ω0 . Ωr = J

(10)

(11)

By calculating the integral (11), one obtains Ωr = Ω0 + ΔΩr · cos(2sωt + ϕ)

(12)

where ΔΩr = −πks Ikrn Irn (1/2sJ) · (RLem /μ0 ) is the magnitude of the speed oscillation, Ω0 is the mean value of Ωr which changes in the dependence on the number of broken bars at given load torque, and ϕ = ϕBs − ϕBrn . It is well known that the speed oscillation also generates an additional air-gap flux density component at (1 + 2s)f [19], [37], [38], [41]. V. I NFLUENCE OF S PEED VARIATION IN THE A XIAL F LUX As mentioned in (4), the total axial flux outside the induction machine with an eccentricity fault can be written in the following form: ˆ cos(ωt − pβ) ΦAT = Φ

(13)

with β = β0 + Ωr t. Under broken rotor bar fault, a speed variation appears and will influence the external axial flux. In this case (13) can be written as follows: ˆ cos [ωt − p(β0 + Ωr t)] . ΦAT = Φ

(14)

Developing the argument of the cosine, using (12), one obtains ˆ cos [sωt − ΔΩr pt cos(2sωt + ϕ) − pβ0 ] . ΦAT = Φ

(15)

A frequency modulation appears in ΦAT . ˆ = 1 Wb, ΔΩr = 1 rad/s, The time variation of (15) for Φ and s = 2.5% is presented in Fig. 4(a). A direct analysis of the signal is difficult; hence the change in the frequency domain is performed by fast Fourier transform (FFT). The obtained spectrum is given in Fig. 4(b).

2086


Fig. 5. Equivalent circuit of squirrel-cage rotor showing rotor loop currents and circulating end ring current.

rotor cage ibj = irj − ir(j+1) .

(17)

The mathematical model of squirrel cage induction motor can be written as follows: [V ] = [R][I] + Fig. 4. Simulation of axial flux variation. (a) Axial flux signal. (b) FFT for the axial flux.

In the spectrum, the appearance of the harmonic 3sf due to the speed variation can be observed. One can notice that a small speed variation can produce an important component at frequency 3sf . With the considering speed variation that corresponds approximately to two broken bars, the component 3sf is higher than the initial component sf . VI. Q UANTITATIVE D ESCRIPTION AND N UMERICAL S IMULATION The simulation of the machine in faulty conditions is done by a modeling method that used the coupled magnetic-electric circuits. Many papers [42], [43] give a detailed description of this model. In this paper, one uses the well-known model described in [43]. The model is based on coupled magnetic approach by considering that the current in each bar is an independent variable. The effects of nonsinusoidal air-gap mmf produced by both the stator and the rotor currents have been incorporated into the model. Let us consider a 3 − n winding machine with the following assumptions: three identical stator windings with axes of symmetry such that even harmonics of the resulting spatial winding distribution are zero; uniform air-gap; negligible saturation; insulated rotor bars; eddy current, friction, and windage losses are neglected. The cage rotor can be viewed as n identical and equally spaced rotor loops (Fig. 5). The electrical equation of the rotor loop j (1 < j ≤ n) is given by

d ([L][I]) dt

where [V ] is the voltage vector [Vs ] = [vs1 vs2 T [V ] = [[Vs ] [Vr ]] ⇔ [Vr ] = [0 0 0 where n is the number of rotor bars. [I] is the current vector [Is ] = [is1 is2 T [I] = [[Is ] [Ir ]] ⇔ [Ir ] = [ir1 ir2

(18)

vs3 ] · · · 0]1×(n+1) (19)

is3 ] ir3 · · ·

[R] is the global resistance matrix

[Rs ] [0]3×(n+1) [R] = [0](n+1)×3 [Rr ] with [Rs ] is the stator resistance matrix given by ⎤ ⎡ Rs1 0 0 0 ⎦ Rs2 [Rs ] = ⎣ 0 0 0 Rs3

irn

. ie ] (20)

(21)

(22)

dΦrj =0 dt (16)

where Rs1 = Rs2 = Rs3 are the resistances of a stator phase winding. The matrix [Rr ] is n + 1 by n + 1 symmetric, expressed as ⎤ ⎡ Rrr −Rb 0 ··· 0 −Rb −Re ⎢ −Rb Rrr −Rb · · · 0 0 −Re ⎥ ⎢ . .. .. .. .. .. ⎥ ⎥ ⎢ . ⎢ . . . ··· . . . ⎥ ⎥ ⎢ . . . . . . [Rr ] = ⎢ .. .. .. .. .. .. ⎥ ··· ⎥ ⎢ ⎢ 0 0 0 · · · Rrr −Rb −Re ⎥ ⎥ ⎢ ⎣ −R 0 0 · · · −Rb Rrr −Re ⎦ b −Re −Re −Re · · · −Re −Re nRe (23)

where irj is the current crossing the loop j, ie is the end ring current, and ibj is the current crossing the bar j of the

where Rrr = 2(Re + Rb ), Re is the end ring resistance and Rb is the rotor bar resistance.

Re irj + Rbj ibj + Re (ibj − ie ) − Rb(j−1) ib(j−1) +


2087

The global matrix inductance can be presented by [L] =

Ls Mrs

Msr . Lr

(24)

The stator inductance matrix [Ls ] is symmetric with constant elements; its expression is written as ⎡

Ls1 [Ls ] = ⎣ Ms Ms

Ms Ls2 Ms

⎤ Ms Ms ⎦ Ls3

(25)

where Ms is the mutual inductance between the stator phases, and Ls1 , Ls2 , Ls3 are the total inductances of the stator coil which represent the sum of the magnetizing inductance for each stator coil Lms and the leakage inductance Lsf Ls1 = Ls2 = Ls3 = Lms + Lsf .

(26)

The inductance matrix of rotor loops is given by (27) as shown at the bottom of the page where Lrr = Lmr + 2(Lb + Le ), Lmr is the magnetizing inductance for each rotor loop, Lb is the rotor bar leakage inductance, Le is the rotor end ring leakage inductance and the mutual inductance between two rotor loops Mrr . The mutual inductance Msr is a 3 × n matrix consisting of mutual inductances between stator coils and rotor loops ⎡

Ms1r1 [Msr ] = ⎣ Ms2r1 Ms3r1

Ms1r2 Ms2r2 Ms3r2

··· ··· ···

⎤ Ms1rn Ms2rn ⎦ Ms3rn

(28)

where Msr is the mutual inductance between stator coils and rotor loops. The electromagnetic torque is given by Ce =

1 T d[L] [I] [I]. 2 dθ

(29)

To solve the system of differential equations (18), the Euler’s integration method is used. The simulation is performed using MATLAB software. Depending on the simulated events, the break of the bar is modeled by a strong increase of the bar resistance (Rb × 200). The machine considered in this study is a three-phase squirrel-cage induction motor with four poles 4 kW/50 Hz,

⎡

Lrr ⎢ Mrr − Lb ⎢ .. ⎢ ⎢ . ⎢ .. [Lr ] = ⎢ . ⎢ ⎢ M rr ⎢ ⎣M − L rr b −Le

Mrr − Lb Lrr .. . .. . Mrr Mrr −Le

Fig. 6. Rotor bar rms current distribution. (a) Healthy motor. (b) Faulty motor with one broken bar.

220/380 V, J = 0.0131 kg · m2 . The machine has 28 rotor bars and 48 stator slots. Other parameters of this machine are presented in Table I of the Appendix (Machine I). The simulation is done with 220 V sine voltage supply (star connected) and with constant load torque Cr = 14.2 N · m. The rotor bar rms current distributions under healthy and faulty conditions are given in Fig. 6. Fig. 6(a) shows the uniform distribution of the current in each bar under healthy running. The magnitudes of rms currents are approximately the same in each bar. The results obtained when the rotor is defective are shown in Fig. 6(b). The faulty bar has been chosen as the fourteenth. When one bar is broken, it can be observed that the amplitudes of bar currents in adjacent bars increase and change significantly compared with that in the healthy state. The larger currents imply extra stresses on the adjacent bars, potentially propagating the fault [44]. Fig. 7 shows the electromagnetic torque for a healthy and faulty machine with any broken rotor bars (fault starts at t = 0.8 s). It can be observed very well the torque oscillations that increase with the number of broken bars. Under healthy running conditions, the slip is 2.5%, but under faulty operating

Mrr Mrr − Lb .. . .. . Mrr Mrr −Le

··· ··· ··· ··· ··· ··· ···

Mrr Mrr .. . .. . Lrr Mrr − Lb −Le

Mrr − Lb Mrr .. . .. . Mrr − Lb Lrr −Le

⎤ −Le −Le ⎥ .. ⎥ ⎥ . ⎥ .. ⎥ . ⎥ ⎥ −Le ⎥ ⎥ −Le ⎦ nLe

(27)

2088


Fig. 7. Electromagnetic torque in the case of a healthy motor and a motor with broken rotor bars (t = 0.8 s) (a) and its zoom (b).

conditions with the same load, the slip slightly increases leading to a torque oscillation slightly higher than 2.5 Hz. Fig. 8 shows the rotor speed for a healthy and a faulty machine with 1, 2, and 3 broken rotor bars. The reported results in Fig. 8(b) show a low speed variation at frequency 2sf , which increases with the number of broken rotor bars. Let us notice that the practical difficulty will be the direct measurement of this speed variation particularly in the case of one broken bar, where ΔΩr < 0.5 rad/s.

Fig. 8. Rotor speed in the case of a healthy motor and a motor with broken rotor bars (t = 0.8 s) (a) and its zoom (b).

A. Experimental Validation of Rotor Bar Current Distribution

machine with 48 stator slots that has been transformed in a stator squirrel-cage induction machine (Fig. 9). The stator winding was changed and replaced by a copper bar in each slot. These bars are in short circuit through the copper rings used to obtain a motor stator cage. The bars are accessible outside the machine to perform the current bar measurements [Fig. 9(b)]. This motor is energized through the wound rotor instead of being fed by the stator. On the electromagnetic point of view, the rotor winding will create a three-phase rotating field as would the stator and generate the induced currents in the stator to the creation of a torque. In this case, the induced currents which appear in the stator cage can be measured; they are equivalent to the rotor current in a normal machine. To avoid confusion, the stator and rotor elements will be called, respectively, primary and secondary elements. The practical problems for this kind of machine are as follows:

The rotor bar current distributions are verified by a special modified machine. This is a three-phase wound-rotor induction

• The fundamental rotor current is 50 Hz instead of low frequency sf , the iron losses are more important than

VII. E XPERIMENTAL R ESULTS Two test-beds are used to perform the experimental validations of the proposed method: the first is used to validate the rotor bar current distribution and the second is used to highlight the appearance of the low frequency components sf and 3sf .


2089

Fig. 10. Simulated rotor bar rms current distribution. (a) Healthy motor. (b) Faulty motor with one broken bar.

Fig. 9. Test-bed used for experimental measurement of bar currents. (a) Test-bed. (b) Stator cage induction machine. (c) Rogowski coil.

usual, where a risk of overheating that requires a motor ventilation at all times. • The rotor is fed by a reduced voltage, depending on the rotor number of turns. For measurements, one cannot exceed 80 V because a higher voltage level induces a destructive current for the machine, hence the need to monitor the current rise. The machine parameters were, before the modifications: 7.5 kW/50 Hz, stator: 220/380 V, 21/12 A, rotor: 80 V, 41 A, Nts = 48, Ntr = 36, p = 2. The new parameters are: nominal supplying voltage: V pri = 80 V; number of turns per pole pairs in the primary windings: z pri = 12; Ntpri = 36; Ntsec = 48. More parameters of this machine are presented in Table I of the Appendix (Machine II). The measurements are performed in load case (s = 6%). A Rogowski coil is used to measure the current in each stator bar [Fig. 9(b) and (c)]. The simulation results for this machine are given in Fig. 10. Similar results than those presented in Section VI are obtained. The experimental measurements of the currents in 39 bars under healthy and faulty states are shown in Fig. 11(a) and Fig. 11(b), respectively. In the healthy case, the uniform distribution of the current in each bar can be observed [Fig. 11(a)]. The measurements, when the rotor is defective, are shown in Fig. 11(b). The fault has been chosen in the 21st bar. The current distributions in both cases are in agreement with the simulation results presented in Fig. 10. In Fig. 11(b), it can be observed that on the broken bar, it is measured a current with a small value, whereas ideally the broken bar current should be zero. This is due to the measurement error of the Rogowski coil

Fig. 11. Experimental rotor bar rms current distribution. (a) Healthy motor. (b) Faulty motor with one broken bar.

which can be slowly influenced by the magnetic field generated by the other bars. B. Experimental Validation of the Low Frequency Components sf and 3sf The measurements are performed on a healthy motor and a faulty motor with one broken rotor bar (Fig. 12). To test the suggested diagnostic method, two identical machines which have the same settings (corresponding to Machine I) and placed on the same benchwork are used. The load is assured by

2090


Fig. 12. Test-bed used for experimental validation of proposed signature.

a synchronous generator connected to a resistive bed. The running conditions are the same than these of the simulations (s ≈ 2.5%, Cr = 14.2 N · m). To perform the experimental validation, an external coil sensor, manufactured in our laboratory, is used (Fig. 12). This sensor is noninvasive, adaptable to any electrical machines. It is circular of S area (S = 12 cm2 ) and the coil is constituted of nc turns (nc = 1200). The sensor provides an electromotive force (emf) esensor related to the linked flux Φext , such that esensor = nc dΦext /dt. To highlight the appearance of the low frequency components, it is important to realize the machine test in the load case when the measured signals are more visible. The emf signal delivered by the coil sensor is transmitted to the analyzer PULSE Brüel&Kjær (Fig. 12). This device performs signal processing and provides its spectrum. The analyzed results are transmitted to a computer for viewing and recording. The collected information is focused on the amplitude of the specific components at frequencies sf and 3sf . Let us point out that to distinguish these components in the spectrum, a high frequency resolution is necessary (< 0.1 Hz), what leads to a long acquisition time (≈10 s). When the sensor is placed in Pos. 3 (see Fig. 1), one measures only the radial field. The corresponding spectra of esensor for a healthy machine and a faulty machine are given, respectively, in Fig. 13(a) and (b). It can be noticed that the components at frequencies sf and 3sf have small values and are negligible. Fig. 14(a) and (b) give the spectra of esensor when the sensor is placed in the Pos. 1 (Fig. 1) in a healthy state and with broken rotor bar fault. The Pos. 1 is sensitive to the axial field and one can notice the presence of harmonics sf and 3sf that confirms the axial origin of these components. In a healthy state [Fig. 14(a)], both harmonics have low magnitudes; they are a consequence of the imperfections obtained in practical realization of the machine. The spectrum under fault condition given in Fig. 14(b) indicates that the fault caused on the rotor has a great influence on the harmonic 3sf . It may be noted that the amplitude of this harmonic is higher in comparison with the component sf . The component 3sf denotes the speed variation

Fig. 13. Frequency spectrum of the external magnetic field (pure radial— Pos. 3) for Machine I (1460 rpm). (a) Healthy motor. (b) Motor with one broken rotor bar.

Fig. 14. Frequency spectrum of the external magnetic field (Pos. 1) for Machine I (1460 rpm). (a) Healthy motor. (b) Motor with one broken rotor bar.

at frequency 2sf , caused by a broken rotor bar. The experiments confirm the simulation results: only one broken bar is able to generate a high component 3sf coming from the frequency


Fig. 15. Frequency spectrum of the external magnetic field (pure radial— Pos. 3) for Machine III (1465 rpm). (a) Healthy motor. (b) Motor with one broken rotor bar.

modulation of the component sf at 2sf . It should also be noted that the derivative effect of the measurement requires to divide by 3 the magnitude of the 3sf component, to compare the results with the theoretical spectrum of Fig. 4(b), as far as only the variations are concerned. To test the effectiveness of the proposed method, another machine called Machine III has been used. It is squirrel-cage induction motor with four poles 4 kW/50 Hz, 230/400 V, In = 8.2 A, Ωn = 1440 rpm, 28 rotor bars, and 36 stator slots. The measures are realized for one broken bar in Pos. 1 and Pos. 3 (Fig. 1) at the slip s ≈ 2.3%. The results are given in the Figs. 15 and 16. The comparison of experimental results shown in Figs. 15 and 16 confirms again the axial origin of the components sf and 3sf . The diagram presented in Fig. 17 shows the advantages of proposed method (easy implementation, simple coil sensor, low cost). It can be concluded that the proposed method is characterized by the simplicity of its implementation and analysis of experimental results. The appearance of the 3sf frequency component is a good indicator which announces the presence of the fault. VIII. C ONCLUSION The paper presents a new signature of rotor faults in induction machines. This signature concerns the external magnetic field, particularly the axial components, measured by a simple coil sensor and the analysis is oriented to the low frequency components of the FFT spectrum at sf and 3sf .

2091

Fig. 16. Frequency spectrum of the external magnetic field (Pos. 1) for Machine III (1465 rpm). (a) Healthy motor. (b) Motor with one broken rotor bar.

Fig. 17. Advantages of diagnostic technique based on external magnetic field analysis.

The description of component sf is done by the permeance circuit model that considers the permeances related to axial fluxes on the machine extremities and by taking into account the eccentricity. The diagnosis method consists in checking the magnitude of the component 3sf generated by the speed variation that can be compared to that of the component sf . The broken rotor bar fault produces a low speed variation at 2sf that is able to generate a high magnitude component 3sf . The advantage of this noninvasive method compared to other existing methods is its simplicity to implement and a lowcost set-up. Also, it does not require the knowledge of the healthy signature, and it is weakly influenced by the magnetic shield of machine frame because the observed phenomena are in very low frequency. Moreover, the frequencies of the observed components depend on the machine running (the slip); consequently, the analysis is not disturbed by other sources of magnetic field presented in an industrial environment. An experimental validation realized using two induction motors of different realization and power confirms the validation of used model and proposed method for detection of rotor faults. A stator squirrel-cage induction machine was also manufactured

2092


TABLE I PARAMETERS OF M ACHINES U SED IN T ESTS AND IN S IMULATION

to measure the bar currents. The simulation and experimental analyses confirm the models and used approaches. A PPENDIX The machines’ parameters used for simulation and experimental measurements are given in Table I. R EFERENCES [1] 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. [2] P. Tavner, L. Ran, J. Penman, and H. Sedding, Condition Monitoring of Rotating Electrical Machines, 2nd ed. Stevenage, U.K.: IET, 2008. [3] 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. [4] M. E. H. Benbouzid, “Bibliography on induction motors faults detection and diagnosis,” IEEE Trans. Energy Convers., vol. 14, no. 4, pp. 1065– 1074, Dec. 1999. [5] G. B. Kliman, R. A. Koegl, J. Stein, R. D. Endicott, and M. W. Madden, “Noninvasive detection of broken rotor bars in operating induction motors,” IEEE Trans. Energy Convers., vol. 3, no. 4, pp. 873–879, Dec. 1988. [6] A. Bellini, F. Filippetti, C. Tassoni, and G.-A. Capolino, “Advances in diagnostic techniques for induction machines,” IEEE Trans. Ind. Electron., vol. 55, no. 12, pp. 4109–4126, Dec. 2008. [7] G. B. Kliman and J. Stein, “Methods of motor current signature analysis,” Elect. Mach. Power Syst., vol. 20, no. 5, pp. 463–474, Sep. 1992. [8] M. E. H. Benbouzid, “A review of induction motors signature analysis as a medium for faults detection,” IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 984–993, Oct. 2000. [9] A. M. da Silva, R. J. Povinelli, and N. A. O. Demerdash, “Induction machine broken bar and stator short-circuit fault diagnostics based on three-phase stator current envelopes,” IEEE Trans. Ind. Electron., vol. 55, no. 3, pp. 1310–1318, Mar. 2008.

[10] G. R. Bossio, C. H. De Angelo, J. M. Bossio, C. M. Pezzani, and G. O. García, “Separating broken rotor bars and load oscillations on im fault diagnosis through the instantaneous active and reactive currents,” IEEE Trans. Ind. Electron., vol. 56, no. 11, pp. 4571–4580, Nov. 2009. [11] M. Pineda-Sanchez, M. Riera-Guasp, J. Roger-Folch, J. A. AntoninoDaviu, J. Perez-Cruz, and R. Puche-Panadero, “Diagnosis of induction motor faults in time-varying conditions using the polynomial-phase transform of the current,” IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 1428– 1439, Apr. 2011. [12] J. Pons-Llinares, J. A. Antonino-Daviu, M. Riera-Guasp, M. PinedaSanchez, and V. Climente-Alarcon, “Induction motor diagnosis based on a transient current analytic wavelet transform via frequency b-splines,” IEEE Trans. Ind. Electron., vol. 58, no. 5, pp. 1530–1544, May 2011. [13] G. Didier, E. Ternisien, O. Caspary, and H. Razik, “Fault detection of broken rotor bars in induction motor using a global fault index,” IEEE Trans. Ind. Appl., vol. 42, no. 1, pp. 79–88, Jan./Feb. 2006. [14] F. Briz, M. W. Degner, P. Garcia, and D. Bragado, “Broken rotor bar detection in line-field induction machines using complex wavelet analysis of startup transients,” IEEE Trans. Ind. Appl., vol. 44, no. 3, pp. 760–768, May/Jun. 2008. [15] M. Pineda-Sanchez, M. Riera-Guasp, J. A. Antonio-Daviu, J. RogerFolch, J. Perez-Cruz, and R. Puche-Panadero, “Instantaneous frequency of the left sideband harmonic during the start-sp transient: A new method for diagnosis of broken bars,” IEEE Trans. Ind. Electron., vol. 56, no. 11, pp. 4557–4570, Nov. 2009. [16] A. Khezzar, M. Y. Kaikaa, M. El Kamel Oumaamar, M. Boucherma, and H. Razik, “On the use of slot harmonics as a potential indicator of rotor bar breakage in the induction machine,” IEEE Trans. Ind. Electron., vol. 56, no. 11, pp. 4592–4605, Nov. 2009. [17] R. Romary, R. Corton, D. Thailly, and J. F. Brudny, “Induction machine fault diagnosis using an external radial flux sensor,” EPJ. Appl. Phys., vol. 32, no. 2, pp. 125–132, Nov. 2005. [18] M. S. N. Said, M. E. H. Benbouzid, and A. Benchaib, “Detection of broken bars in induction motors using an extended Kalman filter for rotor resistance sensorless estimation,” IEEE Trans. Energy Convers., vol. 15, no. 1, pp. 66–70, Mar. 2000. [19] 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. [20] O. Ondel, E. Boutleux, and G. Clerc, “A method to detect broken bars in induction machine using pattern recognition techniques,” IEEE Trans. Ind. Appl., vol. 42, no. 4, pp. 916–923, Jul./Aug. 2006. [21] N. Arthur and J. Penman, “Induction machine condition monitoring with higher order spectra,” IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 1031– 1041, Oct. 2000. [22] A. Menacer, M. S. Nat-Said, A. H. Benakcha, and S. Drid, “Stator current analysis of incipient fault into induction machine rotor bars,” J. Elect. Eng., vol. 55, no. 5/6, pp. 122–130, Jul. 2004. [23] W. D. Li and C. K. Mechefske, “Detection of induction motor faults: A comparison of stator currentvibration and acoustic methods,” J. Vibration Control, vol. 12, no. 2, pp. 165–188, Feb. 2006. [24] M. Nemec, K. Drobnic, D. Nedeljkovic, R. Fiser, and V. Ambrozic, “Detection of broken bars in induction motor through the analysis of supply voltage modulation,” IEEE Trans. Ind. Electron., vol. 57, no. 8, pp. 2879– 2888, Aug. 2010. [25] B. Akin, C. Seungdeog, U. Orguner, and H. A. Toliyat, “A simple realtime fault signature monitoring tool for motor-drive-embedded fault diagnosis systems,” IEEE Trans. Ind. Electron., vol. 58, no. 5, pp. 1990–2001, May 2011. [26] C. Seungdeog, B. Akin, M. M. Rahimian, and H. A. Toliyat, “Implementation of a fault-diagnosis algorithm for induction machines based on advanced digital-signal-processing techniques,” IEEE Trans. Ind. Electron., vol. 58, no. 3, pp. 937–948, Mar. 2011. [27] S. Nandi, T. C. Ilamparithi, L. Sang Bin, and H. Doosoo, “Detection of eccentricity faults in induction machines based on nameplate parameters,” IEEE Trans. Ind. Electron., vol. 58, no. 5, pp. 1673–1683, May 2011. [28] C. Bruzzese and G. Joksimovic, “Harmonic signatures of static eccentricities in the stator voltages and in the rotor current of no-load salientpole synchronous generators,” IEEE Trans. Ind. Electron., vol. 58, no. 5, pp. 1606–1624, May 2011. [29] A. Yazidi, H. Henao, G. A. Capolino, M. Artioli, F. Filippetti, and 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. [30] 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, vol. 10, no. 11, pp. 10 448–10 466, Nov. 2010.


[31] H. Henao, C. Demian, and G. A. Capolino, “A frequency-domain detection of stator winding faults in induction machines using an external flux sensor,” IEEE Trans. Ind. Appl., vol. 39, no. 5, pp. 1272–1279, Sep./Oct. 2003. [32] O. Chabedec, V. P. Bui, P. Granjon, L. L. Rouve, N. Le Bihan, and J. L. Coulomb, “Rotor fault detection of electrical machines by low frequency magnetic stray field analysis,” in Proc. IEEE SDEMPED Conf., Vienna, Austria, Sep. 7–9, 2005, pp. 1–6. [33] R. Fišer and S. Ferkolj, “Magnetic field analysis of induction motor with rotor faults,” COMPEL, vol. 17, no. 1–3, pp. 206–211, 1998. [34] 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. [35] A. Ceban, R. Pusca, and 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. [36] D. G. Dorrell, W. T. Thomson, and S. Roach, “Analysis of airgap flux, current, and vibration signals as a function of the combination of static and dynamic airgap eccentricity in 3-phase induction motors,” IEEE Trans. Ind. Appl., vol. 33, no. 1, pp. 24–34, Jan./Feb. 1997. [37] G. Didier, “Modeling and diagnosis of induction machine in presence of failures,” Ph.D. dissertation, Dept. Elect. Eng., Univ. Henri Poincaré, Nancy-I, Nancy, France, 2004. [38] G. Didier, H. Razik, and A. Rezzoug, “An induction motor model including the first space harmonics for broken rotor bar diagnosis,” Euro. Trans. Electr. Power, vol. 15, no. 3, pp. 229–243, May/Jun. 2005. [39] A. M. Trzynadlowski, M. Ghassemzadeh, and S. F. Legowski, “Diagnostics of mechanical abnormalities in induction motors using instantaneous electric power,” IEEE Trans. Energy Convers., vol. 14, no. 4, pp. 1417– 1423, Dec. 1999. [40] S. M. A. Cruz and A. J. M. Cardoso, “Rotor cage fault diagnosis in three-phase induction motors by the total instantaneous power spectral analysis,” in Conf. Rec. IEEE IAS Annu. Meeting, 1999, vol. 3, pp. 1929–1934. [41] A. Bellini, F. Filippetti, G. Franceschini, and C. Tassoni, “Quantitative evaluation of induction motor broken bars by means of electrical signature analysis,” IEEE Trans. Ind. Appl., vol. 37, no. 5, pp. 1248–1255, Sep./Oct. 2001. [42] P. Vas, F. Filippetti, G. Franceschini, and C. Tassoni, “Transient modeling oriented to diagnostics of induction machines with rotor asymmetries,” in Proc. ICEM Conf., Paris, France, 1994, pp. 62–66. [43] H. A. Toliyat and T. A. Lipo, “Transient analysis of cage induction machines under stator, rotor bar and end ring faults,” IEEE Trans. Ind. Appl., vol. 10, no. 2, pp. 241–247, Jun. 1995. [44] C. C. M. Cunha, R. O. C. Lyra, and B. C. Filho, “Simulation and analysis of induction machines with rotor asymmetries,” IEEE Trans. Ind. Appl., vol. 41, no. 1, pp. 18–24, Jan./Feb. 2005.

2093

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 working toward the Ph.D. degree in electrical engineering at the Laboratory of Electrical Systems and Environment, Artois University, Béthune, France. His research interests include diagnosis and numerical modeling of electrical machines.

Remus Pusca was born in Medias, Romania, in 1972. He received the electrical engineering degree from Technical University of Cluj-Napoca, ClujNapoca, Romania, in 1995, and the Ph.D. degree in electrical engineering, from the University of Franche-Comté, Besançon, France, in 2002. In 2003, he joined the Laboratory of Electrical Systems and Environment, Artois University, Béthune, France, as an Associate Professor and Researcher. His research interest is control of electrical systems and diagnosis of electrical machines.

Raphaël Romary (M’10) received the Ph.D. degree from Lille University, Lille, France, in 1995 and the D.Sc. degree from Artois University, Béthune, France, in 2007. He is currently a Full Professor in Artois University, and a Researcher at the Laboratory of Electrical Systems and Environment. His research interest concerns the analytical modeling of electrical machines with applications to noise and vibration, losses, electromagnetic emissions, diagnosis.