Fault Type Detection using Frequency pattern of Stator Current in IPM-type BLDC Motor under Stator InterTurn, Dynamic Eccentricity, and Coupled Faults Jun-Kyu Park, Il-Man Seo, and Jin Hur School of Electrical Engineering, University of Ulsan, Ulsan, South Korea [email protected] Abstract— This paper considered the frequency pattern of the stator input current to detect the fault types for stator interturn fault and dynamic eccentricity fault as well as coupled fault of stator inter-turn fault and dynamic eccentricity fault in a permanent magnet brushless DC motor by monitoring the stator current. In the present study, the additional side-band frequencies of the stator current were analyzed to classify the fault types. As a result, each type of the fault appears the different additional frequency patterns. Therefore, we propose the coupled fault modeling method and the fault type detecting algorithm to efficient fault response.

I.

INTRODUCTION

An interior permanent magnet (IPM)-type BLDC motors are widely used in industrial and home applications as well as electric vehicles. However, its lifetime and reliability are sharply reduced by mechanical and electrical faults. These problems not only lead to high repair expense but also cause financial losses in the field where they are used [1]. The generation of stator inter-turn fault (SITF), which is a type of electrical fault, and dynamic eccentricity fault (DEF), which is a type of mechanical fault, lead to the simultaneous distortions in the magnetic field and the stator input current [2]. If coupled fault (CF) at mixed failure of between SITF and DEF occur, it could result in broken down of the motors, and damage to the systems which is use the motors. For this reason, the determination of the fault type is necessary to obtain an efficiency fault response, and prevent the losses from the faults. In [3], an offline technique for the stator faults diagnosis by measuring the odd multiples of third harmonic at the induction motor (IM) terminal voltage right after switch-off has been proposed. In [4], the inter-turn short circuit fault detection in permanent magnet synchronous machines (PMSM) using an open-loop physics-based back electromotive force (BEMF) estimator is presented. In [5], the positive- and negative-sequence third harmonics (±3f) of line current under stator inter-turn faults for IM have been explored by combining space and time harmonics. In [6], a novel diagnosis method for detection and discrimination of two typical mechanical failures such as load torque

978-1-4799-0336-8/13/$31.00 ©2013 IEEE

oscillations and eccentricity in induction motor by current analysis. In [7], the static eccentricity fault has been detected through the BEMF of an axial-flux PM machines. In [8], the eccentricity faults such as the static eccentricity (SE), dynamic eccentricity (DE) faults, as well as mixed eccentricity fault; combination of SE and DE faults has been detected using the spectrum analysis of the stator current. Generally, stator input current and harmonic analysis has been widely studied to detect and diagnosis the fault for the PMSMs and IMs. In this study, we proposed the algorithm to detect the fault types, and the modeling method of CF for the IPM-type BLDC motors. In the case of SITF, frequency patterns of input current are computed by taking into account the effects of circulating current. In case of the DEF, frequency patterns of input current taking into account the air-gap permeance are computed. II.

DETERMINATION OF THE FUNDAMENTAL FREQUENCY

The calculation of a fundamental frequency is required to analyze the frequency pattern of the stator current in the BLDC motors. In case of the PMSMs and IMs, the supply frequency (50 or 60Hz) is used as the fundamental frequency [8]. On the other hands, rotating frequency is used as the fundamental frequency instead of the supplied frequency because the BLDC motor is driven by a square-wave voltage source. Here, the rotating frequency is calculated as RPM (1) f = ×P f

III.

60 [ Hz ]

ANALYSIS OF THE SITF FREQUENCY PATTERNS

Fig. 1 (a) shows a schematic of the three-phase windings with the SITF in the A-phase. Here, as1 is the healthy windings, as2 is the shorted windings, ia is the stator input current, if is circulating current, Rf is the resistance of shorted windings. SITF, which is known as insulation failure, leads to not only the distortion of the stator input current but also the generation of the shorted windings separated with healthy windings. In the shorted windings, a huge circulating current is generated and it causes an inverse air-gap flux density [9].

2516

Using (4), if is represented as vas

if =

Rf

r +

u

(5)

+ jwe ( Lls + u( L1 − 3L2 ))

Here, the A-phase voltage equatiion is represented as

Hence, the frequency patterns of the sstator current are determined taking into account the if. Generrally, if is induced by the flux of PM as well as healthy windinngs in the shorted windings as shown in Fig. 1 (b). Howevver, because the fundamental frequency of the BLDC motorr is determined as the rotating frequency, the frequency pattterns only taking into account the flux by the PM. In this studdy, we have used voltage equation of A-phase for the SITF ccondition that has been calculated in [10], and can be representted in (2). A. d-q axis voltage equation. Generally, d-q axis voltage equation of an IPM-type BLDC motor can be represented as

⎡vq ⎤ ⎡ R iq + ωe ( Lq id + λPM )⎤ ⎥ ⎢ ⎥=⎢ ⎥⎦ ⎢⎣vd ⎥⎦ ⎢⎣ R id − ωe Lq iq

[R if =

3P [λPM iq + ( Ld − Lq )id iq ] 22

3P [λPM 22

λsr =

vas =

u

i f + {Rs i f + [ Lls + uLam (θ r )]

di f dt

+ uωe

dLam (θ r ) if } dθ r

) + we [(Lls + u( L1 − 3L2 ))]

∞

∑λ

2 k − 1 cos (( 2 k

G

if =

S1

(8) (9)

− 1 )ωt )

+ we ⋅λ Gl

= c + αλ

sr

+ G

S 2

(10)

sr

in which GS1, GS2, Gl, c, and α are integer i and are calculated using (10)-(14). C1

(11)

C2 + id

Gs 2 = − R ⋅ id + ωe ⋅ Lq ⋅

Gl = ( R +

where vas is A-phase voltage, Rs and Rf is the resistance of ween the shorted healthy windings, and the resistance betw windings, respectively. if is circulating curreent, μ is the turnfault fraction, Lls and is the leakage inductannce, Lam(θr) is the self-magnetizing inductance of the A-phasee, ωe is electrical rotating velocity.

(7)

2

Thus,

(4)

(4)

)]2

k =1

α=

C. Calculation of the circulating current (if) Voltage equation of A-phase for the SITF condition, which has been calculated in [2], is used to calculate the circulating current. Rf

u

2

2

λsr = ( Ld ⋅ id + λPM )

Gs1 = R +

C1 = + ( Ld − Lq )id ] C2 + id

Rf

C1 C2 + id

f by stator and rotor is From equation (7), the linkage flux represented as (8), and it can be exp pressed as in (9) by using fast Fourier transform (FFT) [4].

(3)

Te

+ we( Ld ⋅ id + λPM )]2 + [(−RS ⋅ id + we ⋅ Lq ⋅

where L1 is the inductance of the heealthy windings, L2 is the inductance of the faulty windings, Ld·id is the linkage flux by the stator, remainder parameters aree represented as constant coefficient values.

where C1 and C2 are integer dependeent on machine parameters. As a result, if is represented as iq =

C1 C2 + id

(R+

(2)

B. Calculation of the Torque. Using (2), torque equation of the IPM-tyype BLDC motor can be calculated as in (3), and iq can be reprresented as in (4)

(6)

By inserting (1), (3) and (6) into (5), the following equations can be obtained.

where λPM is the linkage flux by the PM M, R is the stator resistance, Ld and Lq are the d-q axis inducctance, Vd and Vq are the d-q axis voltages, id and iq are the d-qq axis currents.

Te =

v q2 + v d2

v as =

(a) Stator inter-turn fault (b) Linkage fluxx of shorted windings Figure. 1. Schematic representation off SIFT

Rf u

C1 C2 + id

) + ωe ( Lls + u( L1 − 3L2 ))

ωe Gl

(12) (13) (14)

G + Gs 2 c = s1 = Gl

C1 C1 + ( − Rs ⋅ id + ωe ⋅ Lq ⋅ ) C2 + id C2 + id Rf (R + ) + ωe ( Lls + u( L1 − 3L2 )) u

R +

(15)

From (6)-(9), we can identify th hat harmonic component of if is affected by λsr. As a resullt, if can be rewritten by using FFT as ∞

i f (t ) = c + k ∑ I fk cos((2k − 1)) ωt ± φ fk ) k =0

where k is integer (k = 0, 1, 2, 3…)

2517

(16)

D. Fault Frequency Pattern of the SITF Therefore, because harmonic components of if directly affect the stator input current, the pattern off SITF frequency can be determined as

f SITF = (2k − 1) f f IV.

(16)

ANALYSIS OF THE DEF FREQUENC CY PATTERNS Figure. 3. Distribution of the air-gap flux density under DEF condition

C. DEF frequency pattern Using (9) and (10), the stator currrent can be calculated by applying FFT as ∞

ia , DE (t ) = ∑ I fk cos((1 ± (2k − 1))ωt ± φ fk )

(10)

k =0

(a) Position of rotor and stator (b) Scheematic diagram Figure. 2. Schematic representation off DEF.

Therefore, the frequency pattern of DEF is calculated as

As shown in Fig. 1 (b), OA is the cennter of the stator symmetry, OB is the rotor rotation center, annd OR is the rotor symmetrical axis. Further, x: 0.4 mm represeents the distances by which the rotor symmetrical axis is separrated by the DEF. In the DEF, the symmetry axis of thhe stator and the rotation axis of the rotor are identical, but thhe rotor symmetry axis is not located with the rotation axis of tthe rotor. In such a case, the air-gap around the rotor is not uuniform with time varying.

f DE = [1 ± ( 2k − 1)] f f

(11)

ANALYSIS THE CFS FRE EQUENCY PATTERNS

V.

CFs is the combination faults of o the SITF and DEF as shown in Fig. 3. Therefore, the freq quency pattern of CFs is a combination of the frequency pattern ns of both SITF and DEF. As a result, the frequency pattern off CFs can be calculated as fCFs = f SITF + f DE

(12)

A. Air-gap permeance In [8], the air-gap permeance is calculatted by taking into account the effect of the stator slots, saturatiion, as well as the DEF of the permanent magnet synchronouss motor (PMSM). In case of the BLDC motors, the numberr of pole pairs is considered in calculation of the fundamentall frequency. Thus, the total permeance can be computed withoout consideration of the number of pole pairs as PTotal =

∞

∞

∞

∞

∑ ∑ ∑ ∑P

k SS =0 k SAT =0 kSE =0 kDE =0

k SS

⋅ PkSAT ⋅ PkDE

(17)

× cos(±(2k SAT + k DE )ωt + (k SS S ± 2k SATT ± k DE )θ

Figure. 4. Algorithm for detectting the fault types

where Pkss, PkSAT, PkDE are the permeances calculated by taking into account the effect of stator slots, saturation, and dynamic eccentricity, respectively. KSAT, kDEE, and kSS are the integers. B. Magnetic flux density Because the magnetic flux density under the DEF condition is not uniform, maximum air-gaap and minimum air-gap are generated during the rotating as shown in Fig. 3. Thus, magnetic flux density in the air-gap ccan be calculated as (18) using (17). B (t ) = Pair − gap (t ) ∫ μ 0 ⋅ Hdθ = PTotal (t ) ∫ μ 0 ⋅ j S (θ , t )dθ

18)

where Pair-gap is permeance of the air-gap, H is magnetic field in the air-gap, μ0 is magnetic permeability off the air-gap, jS(θ, t) is current density of the stator inner surfacce.

VI.

FAULT TYPE DETECT TION ALGORITHM

Following the calculation for th he frequency patterns of the stator current, different frequenccy patterns are confirmed according to the fault types. On the basis of these calcullations, we propose an algorithm to detect the fault types for SITF, DEF, and CFs conditions, as shown in Fig. 5. Here, a calculation of the fundamental frequency is required for fault detection by the he BLDC motor. input current spectrum analysis of th Consequently, the SITF and DEF F generates the frequency patterns at (2k - 1)ff, and [1 ± (2kk - 1)]ff, respectively. In addition, the CF generates the SIITF and DEF frequency patterns such as (2k - 1)ff and [1 ± (2k ( - 1)]ff. Thus, the fault detection and development of an efficient e response against fault types are possible using this alg gorithm.

2518

F Figure. 5. Algorithm for detecting the fault types

VII. SIMULATION RESULTTS A. Simulation Models

(a) Healthy frequency pattern of the stator current (2500 rpm)

(a) Simulation model (b) Modeling uunder CFs conditions Figure. 6. Simulation model under healthy and CFs conditions

(b) if frequency pattern (2500 ( rpm)

TABLE I. SPECIFICATION OF THE ANALYSIIS MODELS Rated Rated Rated Input Pole/ Magnet Division Power Speed Torque Current Slot [T] [rpm] [Nm] [A] No. [W] IPM 400 3600 1.06 14 6/9 1.23 SPM 400 3600 1.06 14 6/9 1.23

In this study, we have simulated the BLDC motor at 3500 rpm under a 1.1 mN·m load. Because tthe SITF changes the rotating speed, the value of the fundam mental frequency varied. Hence, the BLDC motor was also ssimulated at 2500 rpm to validate the fault frequency patterns according to the variation in the rotating speed. Here, tthe fundamental frequencies at 2500 and 3500 rpm were 125 and 175Hz, respectively. Meanwhile, the sampling frequency was determined by the Nyquist Law to be 200Hzz [10]. Figs. 7 and 8 show the frequency patterrns under healthy and SITF conditions at 2500 and 3500 rpm, respectively, by the FEM analysis. Here, the frequency pattern for if is identical to that of the stator current at (2k - 1)ff although the rotating speed is changed. In addition, we confirm that the amplitude of the if frequency is larger than that of the stator current frequency. Hence, we confirm thatt the if frequency affects the stator current frequency. The frequency patterns for DEF condittion at 3500 rpm are shown in Fig. 9. The generation of the sppecific frequency patterns of [1 + (2k - 1)]ff is confirmeed. The specific frequency patterns for CFs at 3500 rpm are sshown in Fig. 10. For CFs conditions, generation of the SITF and DEF frequencies is confirmed.

2519

(c) SITF frequency pattern n (2500 rpm) Figure. 7. Frequency patterns for SIT TF condition at 2500 rpm

(a) Healthy frequency pattern of the stator current (3500 rpm)

(b) if frequency pattern (3500 ( rpm)

(c) SITF frequency pattern n (3500 rpm) Figure. 8. Frequency patterns for SIT TF condition at 3500 rpm

The frequency patterns for each fault condition are shown in Figs. 13–16. Because thee BLDC driver by pulse width modulation control is ussed in experiment, the amplitude of the frequency is differeent compared with that of the simulation results. However, the identical frequency patterns for each fault type are vaalidated by the proposed algorithm.

Figure. 9. Frequency patterns for DEF conditioon at 3500 rpm

(a) Healthy frequency patterrn at 2500 rpm Figure. 10. Frequency patterns for CFs conditionns at 3500 rpm

VIII. EXPERIMEMTAL RESULLTS A BLDC motor driver, a dynamo set, a B BLDC motor and, an oscilloscope were used in the experim ment as shown in Figs. 11 and 12. In the SITF experiment, the winding taps are applied to the IPM-type BLDC motor oowing to generate the short and if. In the DEF experimeent, the shaft is fabricated to realize and experiment of the D DEF. In the experiment, the BLDC motor is loaded with 1.1[Nm] load using the dynamo set. The frrequency patterns are verified using the FFT function of the osscilloscope.

(b) if frequency pattern at a 2500 rpm

(c) SITF frequency pattern n at 2500 rpm Figure. 14. Frequency pattern for SIT TF condition at 2500rpm

(a) Healthy frequency patterrn at 3500 rpm

(b) if frequency pattern at a 3500 rpm

Figure. 11. Experimental setup (c) SITF frequency pattern n at 3500 rpm Figure. 15. Frequency pattern for SIT TF condition at 3500 rpm

Figure. 16. Frequency patterns for DE EF condition at 3500 rpm

Figure. 12. Experimental motor desiign

Figure. 17. Frequency patterns for CF Fs condition at 3500 rpm

Figure. 13. Shaft design for DEF experriment

2520

Table I shows the order of the frequency patterns from the proposed algorithm, simulation and experiment. From these results, we can verify the accuracy of the proposed algorithm. TABLE II. THE FREQUENCIES ORDER UNDER EACH CONDITION. (○ : The generation of the additional frequency) Order

1

Healthy

○

SITF

○

DEF

○

○

CF

○

○

2

3

4

○

5

○

IX.

7

○

○

○

○

○ ○

6

○ ○

○

8

9

11 ○

○ ○

○

10

○

○ ○

○

○

[8]

B. M. Ebrahimi, J. Faiz, and M. Javan-Roshtkhari, “Static-, dynamic-, and mixed-eccentricity fault diagnosis in permanent-magnet synchronous motors,” IEEE Trans. Ind. Electron., vol. 56, pp. 47274739, Nov. 2009. [9] B. W. Kim, K. T. Kim, and J. Hur, “Simplified impedance modeling and analysis for inter-turn fault of IPM-type BLDC motor,” Journal of Power Electronics, vol. 12, pp. 10–18, Jan. 2012. [10] Y. K. Lee, “A stator turn fault detection method and a fault-tolerant operating strategy for interior PM synchronous motor drives in safety-critical application, Ph.D. dissertation, Georgia Inst. Tech., U.S.A, 2007, unpublished. [11] B. Vaseghi, B. N. mobarakh, N. Takorabet, and F. M. Tabar, “Inductance identification and study of PM motor with winding turn short circuit fault,” IEEE Trans. Magn. vol. 47, pp. 978-982, 2011.

○

CONCLUSION

We proposed an algorithm to detect the fault type and a modeling method for a SITF, DEF, and CFs of the BLDC motor. Here, the rotating frequency was determined as the fundamental frequency for the frequency pattern analysis because the BLDC motor is driven by square-wave voltage source. In the SITF frequency pattern analysis, the effect of if is considered. In the DEF frequency pattern analysis, the characteristics of the air-gap magnetic field were considered. In conclusion, fault detection and efficient response against faults were possible because all the SITF and DEF frequency patterns appear under the CFs condition. This research was supported by the MSIP(Ministry of Science, ICT&Future Planning), Korea, under the C-ITRC(Convergence Information Technology Research Center) support program (NIPA2013-H0401-13-1008) supervised by the NIPA(National IT Industry Promotion Agency)

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

Z. Q. Zue, D. Ishak, D. Howe and J. Chen, “Unbalanced magnetic forces in permanent magnet brushless machines with diametrically asymmetric phase windings,” IEEE Trans. Ind. Appl., vol. 43, no. 6, pp. 1544-1553, Nov/Dec. 2007. J. Hur, J. W. Reu, B. W. Kim, and G. H. Kang, “Vibration reduction of IPM-type BLDC motor using negative third harmonic elimination method of air-gap flux density,” IEEE Trans. Ind. Appl., vol. 47, pp. 1300–1309, May. 2011. S. Nandi, “Detection of stator faults in induction machines using residual saturation harmonics,” IEEE Trans. Ind. Appl., vol. 42, pp. 1201-1208, Sep./Oct. 2006 A. Sarikhani, and O. Mohammed, “Inter-turn fault detection in PM synchronous machines by physics-based back electromotive force estimation,” IEEE Trans. Ind. Appl., vol. 60, pp. 3472-3484, Aug. 2013. Q. Wu, S. Nandi, “Fast single-turn sensitive stator interturn fault detection of induction machines based on positive- and negativesequence third harmonic components of line currents,” IEEE Trans. Ind. Appl., vol. 46, pp. 974-983, May/June 2010. S.Andreas, H. G. Sedding and P. James, “Current monitoring for detecting inter-trun short circuits in induction motor,” IEEE Trans. Energy Convers., vol. 16, pp. 32-37, Mar. 2001. S. M. Mirimani, A. Vahedi, F. Mirignetti, and E. D. Santis, “Stitic eceitricity fault detection in single-stator-single-rotor axial-flux permanent-magnet machines,” IEEE Trans. Ind. Appl., vol. 48, no. 6, Nov./Dec. 2012

2521

I.

INTRODUCTION

An interior permanent magnet (IPM)-type BLDC motors are widely used in industrial and home applications as well as electric vehicles. However, its lifetime and reliability are sharply reduced by mechanical and electrical faults. These problems not only lead to high repair expense but also cause financial losses in the field where they are used [1]. The generation of stator inter-turn fault (SITF), which is a type of electrical fault, and dynamic eccentricity fault (DEF), which is a type of mechanical fault, lead to the simultaneous distortions in the magnetic field and the stator input current [2]. If coupled fault (CF) at mixed failure of between SITF and DEF occur, it could result in broken down of the motors, and damage to the systems which is use the motors. For this reason, the determination of the fault type is necessary to obtain an efficiency fault response, and prevent the losses from the faults. In [3], an offline technique for the stator faults diagnosis by measuring the odd multiples of third harmonic at the induction motor (IM) terminal voltage right after switch-off has been proposed. In [4], the inter-turn short circuit fault detection in permanent magnet synchronous machines (PMSM) using an open-loop physics-based back electromotive force (BEMF) estimator is presented. In [5], the positive- and negative-sequence third harmonics (±3f) of line current under stator inter-turn faults for IM have been explored by combining space and time harmonics. In [6], a novel diagnosis method for detection and discrimination of two typical mechanical failures such as load torque

978-1-4799-0336-8/13/$31.00 ©2013 IEEE

oscillations and eccentricity in induction motor by current analysis. In [7], the static eccentricity fault has been detected through the BEMF of an axial-flux PM machines. In [8], the eccentricity faults such as the static eccentricity (SE), dynamic eccentricity (DE) faults, as well as mixed eccentricity fault; combination of SE and DE faults has been detected using the spectrum analysis of the stator current. Generally, stator input current and harmonic analysis has been widely studied to detect and diagnosis the fault for the PMSMs and IMs. In this study, we proposed the algorithm to detect the fault types, and the modeling method of CF for the IPM-type BLDC motors. In the case of SITF, frequency patterns of input current are computed by taking into account the effects of circulating current. In case of the DEF, frequency patterns of input current taking into account the air-gap permeance are computed. II.

DETERMINATION OF THE FUNDAMENTAL FREQUENCY

The calculation of a fundamental frequency is required to analyze the frequency pattern of the stator current in the BLDC motors. In case of the PMSMs and IMs, the supply frequency (50 or 60Hz) is used as the fundamental frequency [8]. On the other hands, rotating frequency is used as the fundamental frequency instead of the supplied frequency because the BLDC motor is driven by a square-wave voltage source. Here, the rotating frequency is calculated as RPM (1) f = ×P f

III.

60 [ Hz ]

ANALYSIS OF THE SITF FREQUENCY PATTERNS

Fig. 1 (a) shows a schematic of the three-phase windings with the SITF in the A-phase. Here, as1 is the healthy windings, as2 is the shorted windings, ia is the stator input current, if is circulating current, Rf is the resistance of shorted windings. SITF, which is known as insulation failure, leads to not only the distortion of the stator input current but also the generation of the shorted windings separated with healthy windings. In the shorted windings, a huge circulating current is generated and it causes an inverse air-gap flux density [9].

2516

Using (4), if is represented as vas

if =

Rf

r +

u

(5)

+ jwe ( Lls + u( L1 − 3L2 ))

Here, the A-phase voltage equatiion is represented as

Hence, the frequency patterns of the sstator current are determined taking into account the if. Generrally, if is induced by the flux of PM as well as healthy windinngs in the shorted windings as shown in Fig. 1 (b). Howevver, because the fundamental frequency of the BLDC motorr is determined as the rotating frequency, the frequency pattterns only taking into account the flux by the PM. In this studdy, we have used voltage equation of A-phase for the SITF ccondition that has been calculated in [10], and can be representted in (2). A. d-q axis voltage equation. Generally, d-q axis voltage equation of an IPM-type BLDC motor can be represented as

⎡vq ⎤ ⎡ R iq + ωe ( Lq id + λPM )⎤ ⎥ ⎢ ⎥=⎢ ⎥⎦ ⎢⎣vd ⎥⎦ ⎢⎣ R id − ωe Lq iq

[R if =

3P [λPM iq + ( Ld − Lq )id iq ] 22

3P [λPM 22

λsr =

vas =

u

i f + {Rs i f + [ Lls + uLam (θ r )]

di f dt

+ uωe

dLam (θ r ) if } dθ r

) + we [(Lls + u( L1 − 3L2 ))]

∞

∑λ

2 k − 1 cos (( 2 k

G

if =

S1

(8) (9)

− 1 )ωt )

+ we ⋅λ Gl

= c + αλ

sr

+ G

S 2

(10)

sr

in which GS1, GS2, Gl, c, and α are integer i and are calculated using (10)-(14). C1

(11)

C2 + id

Gs 2 = − R ⋅ id + ωe ⋅ Lq ⋅

Gl = ( R +

where vas is A-phase voltage, Rs and Rf is the resistance of ween the shorted healthy windings, and the resistance betw windings, respectively. if is circulating curreent, μ is the turnfault fraction, Lls and is the leakage inductannce, Lam(θr) is the self-magnetizing inductance of the A-phasee, ωe is electrical rotating velocity.

(7)

2

Thus,

(4)

(4)

)]2

k =1

α=

C. Calculation of the circulating current (if) Voltage equation of A-phase for the SITF condition, which has been calculated in [2], is used to calculate the circulating current. Rf

u

2

2

λsr = ( Ld ⋅ id + λPM )

Gs1 = R +

C1 = + ( Ld − Lq )id ] C2 + id

Rf

C1 C2 + id

f by stator and rotor is From equation (7), the linkage flux represented as (8), and it can be exp pressed as in (9) by using fast Fourier transform (FFT) [4].

(3)

Te

+ we( Ld ⋅ id + λPM )]2 + [(−RS ⋅ id + we ⋅ Lq ⋅

where L1 is the inductance of the heealthy windings, L2 is the inductance of the faulty windings, Ld·id is the linkage flux by the stator, remainder parameters aree represented as constant coefficient values.

where C1 and C2 are integer dependeent on machine parameters. As a result, if is represented as iq =

C1 C2 + id

(R+

(2)

B. Calculation of the Torque. Using (2), torque equation of the IPM-tyype BLDC motor can be calculated as in (3), and iq can be reprresented as in (4)

(6)

By inserting (1), (3) and (6) into (5), the following equations can be obtained.

where λPM is the linkage flux by the PM M, R is the stator resistance, Ld and Lq are the d-q axis inducctance, Vd and Vq are the d-q axis voltages, id and iq are the d-qq axis currents.

Te =

v q2 + v d2

v as =

(a) Stator inter-turn fault (b) Linkage fluxx of shorted windings Figure. 1. Schematic representation off SIFT

Rf u

C1 C2 + id

) + ωe ( Lls + u( L1 − 3L2 ))

ωe Gl

(12) (13) (14)

G + Gs 2 c = s1 = Gl

C1 C1 + ( − Rs ⋅ id + ωe ⋅ Lq ⋅ ) C2 + id C2 + id Rf (R + ) + ωe ( Lls + u( L1 − 3L2 )) u

R +

(15)

From (6)-(9), we can identify th hat harmonic component of if is affected by λsr. As a resullt, if can be rewritten by using FFT as ∞

i f (t ) = c + k ∑ I fk cos((2k − 1)) ωt ± φ fk ) k =0

where k is integer (k = 0, 1, 2, 3…)

2517

(16)

D. Fault Frequency Pattern of the SITF Therefore, because harmonic components of if directly affect the stator input current, the pattern off SITF frequency can be determined as

f SITF = (2k − 1) f f IV.

(16)

ANALYSIS OF THE DEF FREQUENC CY PATTERNS Figure. 3. Distribution of the air-gap flux density under DEF condition

C. DEF frequency pattern Using (9) and (10), the stator currrent can be calculated by applying FFT as ∞

ia , DE (t ) = ∑ I fk cos((1 ± (2k − 1))ωt ± φ fk )

(10)

k =0

(a) Position of rotor and stator (b) Scheematic diagram Figure. 2. Schematic representation off DEF.

Therefore, the frequency pattern of DEF is calculated as

As shown in Fig. 1 (b), OA is the cennter of the stator symmetry, OB is the rotor rotation center, annd OR is the rotor symmetrical axis. Further, x: 0.4 mm represeents the distances by which the rotor symmetrical axis is separrated by the DEF. In the DEF, the symmetry axis of thhe stator and the rotation axis of the rotor are identical, but thhe rotor symmetry axis is not located with the rotation axis of tthe rotor. In such a case, the air-gap around the rotor is not uuniform with time varying.

f DE = [1 ± ( 2k − 1)] f f

(11)

ANALYSIS THE CFS FRE EQUENCY PATTERNS

V.

CFs is the combination faults of o the SITF and DEF as shown in Fig. 3. Therefore, the freq quency pattern of CFs is a combination of the frequency pattern ns of both SITF and DEF. As a result, the frequency pattern off CFs can be calculated as fCFs = f SITF + f DE

(12)

A. Air-gap permeance In [8], the air-gap permeance is calculatted by taking into account the effect of the stator slots, saturatiion, as well as the DEF of the permanent magnet synchronouss motor (PMSM). In case of the BLDC motors, the numberr of pole pairs is considered in calculation of the fundamentall frequency. Thus, the total permeance can be computed withoout consideration of the number of pole pairs as PTotal =

∞

∞

∞

∞

∑ ∑ ∑ ∑P

k SS =0 k SAT =0 kSE =0 kDE =0

k SS

⋅ PkSAT ⋅ PkDE

(17)

× cos(±(2k SAT + k DE )ωt + (k SS S ± 2k SATT ± k DE )θ

Figure. 4. Algorithm for detectting the fault types

where Pkss, PkSAT, PkDE are the permeances calculated by taking into account the effect of stator slots, saturation, and dynamic eccentricity, respectively. KSAT, kDEE, and kSS are the integers. B. Magnetic flux density Because the magnetic flux density under the DEF condition is not uniform, maximum air-gaap and minimum air-gap are generated during the rotating as shown in Fig. 3. Thus, magnetic flux density in the air-gap ccan be calculated as (18) using (17). B (t ) = Pair − gap (t ) ∫ μ 0 ⋅ Hdθ = PTotal (t ) ∫ μ 0 ⋅ j S (θ , t )dθ

18)

where Pair-gap is permeance of the air-gap, H is magnetic field in the air-gap, μ0 is magnetic permeability off the air-gap, jS(θ, t) is current density of the stator inner surfacce.

VI.

FAULT TYPE DETECT TION ALGORITHM

Following the calculation for th he frequency patterns of the stator current, different frequenccy patterns are confirmed according to the fault types. On the basis of these calcullations, we propose an algorithm to detect the fault types for SITF, DEF, and CFs conditions, as shown in Fig. 5. Here, a calculation of the fundamental frequency is required for fault detection by the he BLDC motor. input current spectrum analysis of th Consequently, the SITF and DEF F generates the frequency patterns at (2k - 1)ff, and [1 ± (2kk - 1)]ff, respectively. In addition, the CF generates the SIITF and DEF frequency patterns such as (2k - 1)ff and [1 ± (2k ( - 1)]ff. Thus, the fault detection and development of an efficient e response against fault types are possible using this alg gorithm.

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F Figure. 5. Algorithm for detecting the fault types

VII. SIMULATION RESULTTS A. Simulation Models

(a) Healthy frequency pattern of the stator current (2500 rpm)

(a) Simulation model (b) Modeling uunder CFs conditions Figure. 6. Simulation model under healthy and CFs conditions

(b) if frequency pattern (2500 ( rpm)

TABLE I. SPECIFICATION OF THE ANALYSIIS MODELS Rated Rated Rated Input Pole/ Magnet Division Power Speed Torque Current Slot [T] [rpm] [Nm] [A] No. [W] IPM 400 3600 1.06 14 6/9 1.23 SPM 400 3600 1.06 14 6/9 1.23

In this study, we have simulated the BLDC motor at 3500 rpm under a 1.1 mN·m load. Because tthe SITF changes the rotating speed, the value of the fundam mental frequency varied. Hence, the BLDC motor was also ssimulated at 2500 rpm to validate the fault frequency patterns according to the variation in the rotating speed. Here, tthe fundamental frequencies at 2500 and 3500 rpm were 125 and 175Hz, respectively. Meanwhile, the sampling frequency was determined by the Nyquist Law to be 200Hzz [10]. Figs. 7 and 8 show the frequency patterrns under healthy and SITF conditions at 2500 and 3500 rpm, respectively, by the FEM analysis. Here, the frequency pattern for if is identical to that of the stator current at (2k - 1)ff although the rotating speed is changed. In addition, we confirm that the amplitude of the if frequency is larger than that of the stator current frequency. Hence, we confirm thatt the if frequency affects the stator current frequency. The frequency patterns for DEF condittion at 3500 rpm are shown in Fig. 9. The generation of the sppecific frequency patterns of [1 + (2k - 1)]ff is confirmeed. The specific frequency patterns for CFs at 3500 rpm are sshown in Fig. 10. For CFs conditions, generation of the SITF and DEF frequencies is confirmed.

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(c) SITF frequency pattern n (2500 rpm) Figure. 7. Frequency patterns for SIT TF condition at 2500 rpm

(a) Healthy frequency pattern of the stator current (3500 rpm)

(b) if frequency pattern (3500 ( rpm)

(c) SITF frequency pattern n (3500 rpm) Figure. 8. Frequency patterns for SIT TF condition at 3500 rpm

The frequency patterns for each fault condition are shown in Figs. 13–16. Because thee BLDC driver by pulse width modulation control is ussed in experiment, the amplitude of the frequency is differeent compared with that of the simulation results. However, the identical frequency patterns for each fault type are vaalidated by the proposed algorithm.

Figure. 9. Frequency patterns for DEF conditioon at 3500 rpm

(a) Healthy frequency patterrn at 2500 rpm Figure. 10. Frequency patterns for CFs conditionns at 3500 rpm

VIII. EXPERIMEMTAL RESULLTS A BLDC motor driver, a dynamo set, a B BLDC motor and, an oscilloscope were used in the experim ment as shown in Figs. 11 and 12. In the SITF experiment, the winding taps are applied to the IPM-type BLDC motor oowing to generate the short and if. In the DEF experimeent, the shaft is fabricated to realize and experiment of the D DEF. In the experiment, the BLDC motor is loaded with 1.1[Nm] load using the dynamo set. The frrequency patterns are verified using the FFT function of the osscilloscope.

(b) if frequency pattern at a 2500 rpm

(c) SITF frequency pattern n at 2500 rpm Figure. 14. Frequency pattern for SIT TF condition at 2500rpm

(a) Healthy frequency patterrn at 3500 rpm

(b) if frequency pattern at a 3500 rpm

Figure. 11. Experimental setup (c) SITF frequency pattern n at 3500 rpm Figure. 15. Frequency pattern for SIT TF condition at 3500 rpm

Figure. 16. Frequency patterns for DE EF condition at 3500 rpm

Figure. 12. Experimental motor desiign

Figure. 17. Frequency patterns for CF Fs condition at 3500 rpm

Figure. 13. Shaft design for DEF experriment

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Table I shows the order of the frequency patterns from the proposed algorithm, simulation and experiment. From these results, we can verify the accuracy of the proposed algorithm. TABLE II. THE FREQUENCIES ORDER UNDER EACH CONDITION. (○ : The generation of the additional frequency) Order

1

Healthy

○

SITF

○

DEF

○

○

CF

○

○

2

3

4

○

5

○

IX.

7

○

○

○

○

○ ○

6

○ ○

○

8

9

11 ○

○ ○

○

10

○

○ ○

○

○

[8]

B. M. Ebrahimi, J. Faiz, and M. Javan-Roshtkhari, “Static-, dynamic-, and mixed-eccentricity fault diagnosis in permanent-magnet synchronous motors,” IEEE Trans. Ind. Electron., vol. 56, pp. 47274739, Nov. 2009. [9] B. W. Kim, K. T. Kim, and J. Hur, “Simplified impedance modeling and analysis for inter-turn fault of IPM-type BLDC motor,” Journal of Power Electronics, vol. 12, pp. 10–18, Jan. 2012. [10] Y. K. Lee, “A stator turn fault detection method and a fault-tolerant operating strategy for interior PM synchronous motor drives in safety-critical application, Ph.D. dissertation, Georgia Inst. Tech., U.S.A, 2007, unpublished. [11] B. Vaseghi, B. N. mobarakh, N. Takorabet, and F. M. Tabar, “Inductance identification and study of PM motor with winding turn short circuit fault,” IEEE Trans. Magn. vol. 47, pp. 978-982, 2011.

○

CONCLUSION

We proposed an algorithm to detect the fault type and a modeling method for a SITF, DEF, and CFs of the BLDC motor. Here, the rotating frequency was determined as the fundamental frequency for the frequency pattern analysis because the BLDC motor is driven by square-wave voltage source. In the SITF frequency pattern analysis, the effect of if is considered. In the DEF frequency pattern analysis, the characteristics of the air-gap magnetic field were considered. In conclusion, fault detection and efficient response against faults were possible because all the SITF and DEF frequency patterns appear under the CFs condition. This research was supported by the MSIP(Ministry of Science, ICT&Future Planning), Korea, under the C-ITRC(Convergence Information Technology Research Center) support program (NIPA2013-H0401-13-1008) supervised by the NIPA(National IT Industry Promotion Agency)

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