Broken Bearings and Eccentricity Fault Detection for a ... - IEEE Xplore

Broken Bearings and Eccentricity Fault Detection for a Permanent Magnet Synchronous Motor J. A. Rosero, J. Cusido, A. Garcia, J.A. Ortega, L. Romeral Dept. d'Enginyeria Electrònica Universitat Politècnica de Catalunya C. Colom 1. 08222 Terrassa Catalunya. Spain [email protected] robotics and military power drive applications. In many of the critical drive applications, it is required that the drive comprising the motor and the converter under fault, be able to operate stable and meet base drive needs for a period of time before the system can be repaired [2].

Abstract – The paper presents an experimental study of the broken bearings and eccentricity faults detection for a permanent magnet synchronous motor (PMSM). Conclusions are obtained from the analysis of the stator current harmonic spectrum. The analysis is spread to a zero component and q axis component of the stator current, for the whole range of rotor speeds.

Among the PMSM, the interior permanent synchronous motor is becoming popular in high performance applications where require high-speed operation and precise torque control due to some its advantageous features which include high torque to current ratio as well as high power to weight ratio, high efficiency, low noise and robustness [3].

Index Terms – PMSM drives, fault detection, eccentricity, bearing damage.

I. INTRODUCTION The failure of a drive has usually a serious impact on the operation of a system. In some cases the failure results in lost production, whilst in others it may jeopardize human safety. In such applications it is advantageous to use a drive capable of continuing to operate in the presence of any single point failure. Such a drive is termed fault tolerant [1] and the development of a fault tolerant drive is the final aim of the research presented here.

The major faults of electrical machines, and hence of PMSM, can broadly be classified as the following [4] [5]: • •

The general requirements for a fault tolerant drive system are summarized below:

Almost 50 % of all motor failures are related to mechanical faults, and they lead to a noise and vibrations, and even to the total damage of the machine and the mechanics coupled to it if the failure is not detected and isolated.

•

Higher efficiency design over the operating speed range to better utilise the power supply, • Electrically and physically isolated phases to prevent phase to phase short-circuit, propagation of the fault into the neighbouring phases and reduce inverter faults, • Higher winding inductance to limit the winding shortcircuit current, • Effective cooling to allow about 25% overloading capacity to be utilised during take off and climb. It is a requirement that the fault does not indirectly compromise the operation of healthy phases by unduly disturbing the common input (the dc link) or the common output (net shaft torque). Thus in the event of any fault, rapid action must be taken to prevent the faulted phase from drawing excessive current or applying significant braking torque to the shaft. Rapid fault detection is also important in the fault tolerant drive system, to enable appropriate post fault action to be taken.

A. Bearing Faults. Even under normal operating conditions with balanced load and good alignment, fatigue failures may take place. Flaking or spalling of bearings might occur when fatigue causes small pieces to break loose from the bearing. Other than the normal internal operating stresses caused by vibration, inherent eccentricity, and bearing currents [6] due to solid state drives, bearings can be also spoiled by many other external causes, like abnormal mounting. Sometimes bearing faults might manifest themselves as rotor asymmetry faults, which are usually covered under the category of eccentricity-related faults. Otherwise, the ball bearing related defects can be categorized as [7] outer bearing race defect, inner bearing race defect, ball defect, and train defect.

Permanent Magnet Synchronous Motor (PMSM) drives are now extensively used in many industrial as applications requiring high system reliability, high efficiency and extended high-speed operation. Such applications include power steering in automotive vehicles, aerospace/aircrafts,

1-4244-0136-4/06/$20.00 '2006 IEEE

Mechanical faults, like static and/or dynamic air-gap irregularities, Bent shaft (akin to dynamic eccentricity), and bearing and gearbox failures Electromagnetic faults, like stator faults resulting in the opening or shorting of one or more of a stator phase winding, abnormal connections and demagnetization of the permanent magnet.

It should be noted that specific information concerning the bearing construction is required to calculate the exact characteristic frequencies.

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B. Eccentricity-Related Faults

[R] = diag[rs

Machine eccentricity is the condition of unequal air gap that exists between the stator and rotor [8]. When eccentricity becomes large, the resulting unbalanced radial forces (also known as unbalanced magnetic pull or UMP) can cause stator to rotor rub, which result in a serious damage to stator core and windings. There are two types of air-gap eccentricity: the static air-gap eccentricity and the dynamic air gap eccentricity. In the case of the static air-gap eccentricity, the position of the minimal radial air-gap length is fixed in space. If the rotor-shaft assembly is sufficiently stiff, the level of static eccentricity is not significant.

[λ ] = [λ T

qd

d

rs

rs ]

− λq

0

]

[λ ] = [M ][i ] + [Φ ] T

qdo

[Φ PM ]

T

qdo

qdo

= [0 Φ PM

[M ] = Diag [L qdo

q

PM

0] L d Lo

]

(2)

where index this v, i, L, λ, are voltages, stator currents, inductances and stator flux linkages. Subindex d, q and 0 represent values in dq0 frame. rs and ω are the stator resistance and inverter frequency, respectively, and ΦPM is the flux linkage due to the rotor magnets linking the stator.

In case of dynamic eccentricity, the center of the rotor is not at the center of the rotation and the position of minimum air-gap rotates with the rotor. This misalignment may be caused due to several factors such as a bent rotor shaft, bearing wear or misalignment, mechanical resonance at critical speed, etc.

The electric torque is

Te =

[

3 p Φ PM iq + (Ld − Lq )iq .id 22

]

and the equation for the motor dynamics is

It has been shown [9] that only a particular combination of machine pole pairs and rotor slot number will give rise to significant only static or only dynamic eccentricity-related components in the stator current.

J

∂ω = Te − Tl − Bω ∂t

∂θ =ω ∂t

If id is forced to be zero, then the torque is directly proportional to the q axis current. Additionally, the introduction of a negative id will weaken the airgap flux. Vector control for PMSM drives provides the de-coupling control between the torque and flux components, and is able to obtain good performance characteristics similar to that of a DC motor, so vector control is a popular control method for PMSM [11]. But owing to the construction property of PMSM, its vector control drive is only equivalent to a DC motor with no-compensation winding, its transient performance is affected, thus some other control strategies are also developed. Otherwise, in the most papers, whether the maximum torque control for PMSM exists and its maximum torque control is the same concept with vector control has not been proposed and analyze.

This paper deals with mechanical fault detection in the PMSM, especially eccentricities and broken bearings, by using MCSA method applied to composed stator currents in the frame dq0. II. VECTOR CONTROL OF THE PMSM. The permanent magnets used in the PMSM are of a modern rare-earth variety with high resistivity, so induced currents in the rotor are negligible. In addition, there is no difference between the back EMF produced by a permanent magnet and that produced by an excited coil. Hence the mathematical model of a PMSM is similar to that of the wound rotor SM. The following assumptions are made in the derivation [10]:

Fig.1 shows a general scheme for a vectorial control of a PMSM, including position and speed closed loops.

1) Saturation is neglected although it can be taken into account by parameter changes. 2) The induced EMF is sinusoidal. 3) Eddy currents and hysteresis losses are negligible. 4) There are no field current dynamics. With these assumptions, the stator d, q equations of the PMSM in the rotor reference frame are: qdo

qdo

[v ] = [v [i ] = [i T

qdo

T

qdo

q

q

qdo

vd id

vo

io

]

qd

(4)

p is the number of poles, Tl is the load torque, B is the damping coefficient, ω is the rotor speed and J is the moment of inertia.

Among the methods to detect motor failures, Motor Current Signature Analysis (MCSA) has become one of the most popular. MCSA is based on the analysis of the specific current harmonic components that appear in the stator current due to unbalance of the magnetic fields inside the motor in case of fault.

[v ] = [R][i ]+ ∂∂t [λ ]+ ωλ

(3)

(1)

]

Fig. 1. Scheme of vectorial control of PMSM.

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III. EXPERIMENTAL RESULTS

Fig. 4 to Fig. 7 show the i0 and iq stator currents measured under eccentricity and bearing fault in the motor. It is evident a reduction of the iq current amplitude, as well as an increment in the current oscillations due to the faults.

Some experiments have been carried out for different two motors with broken bearing and rotor eccentricity, respectively. The motors were driven at nominal, medium and low speed. Stator currents were acquired and their harmonics in abc and dq0 frames have been obtained and represented in the paper.

Oscillations present a period of about 10ms, which correspond to rotor frequency of 100 Hz at 6000 rpm, and they are especially clear in case of rotor eccentricity. On the other hand, zero sequence current presents also a strong variation, with oscillations twice (bearing fault) to four times (eccentricity) greater than in case of healthy motor.

For a three pair of poles, power supply from the inverter is three times the rotor frequency in Hz, which is obtained as rotor speed in rpm divided by sixty. All the following harmonic representations have been related to this rotor frequency, which changes for every rotor speed.

0.6

For the firs motor, one ball among the eight of the bearing was artificially damaged, while for the second motor a dynamic eccentricity was produced by changing the center of gravity of the rotor.

Amplitude (pu)

0.4

Table I shows the parameters of the motors, which was controlled by a power converter running the control scheme shown in Fig. 1. For the proposal of this paper, id reference was fixed to zero, then controlling torque with iq. Fig. 2 and Fig. 3 depict q and d axes stator current for a nominal torque and rotor speed in a healthy motor.

0.2 0 -0.2 -0.4 -0.6 2

Time (S)

2.015

2.02

2.025

1

V rpm N.m

Amplitude (pu)

380 6000 2.3 3 2.9 2.6 9.6 0.000235 57.6 20 42 8

2.01

Fig. 4. Zero sequence current of PMSM under eccentricity. 6000 rpm.

Table 1. PMSM Nominal Data Voltage Speed Torque Pair of poles Current Resistance Inductance Moment of Inertia Back EMF Constant Inner bearing diameter, Di Outer bearing diameter, Do Rolling elements number, Nb

2.005

A Ω mH kgm² Vrms/krpm mm mm

0.8 0.6 0.4 2

2.005

2.01

Time (S)

2.015

2.02

2.025

Fig. 5. iq axis stator current of PMSM under eccentricity. 6000 rpm. 0.2 Amplitude (pu)

0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 6

6.005

6.01

Time (S)

6.015

6.02

6.025

Fig. 6. Zero sequence stator current of PMSM with bearing fault. 6000 rpm.

Fig.2. iq axis stator current. 6000 rpm. iq rms =1.05 pu

Amplitude (pu)

1 0.8 0.6 0.4 2

Fig. 3. id axis stator current. 6000 rpm. id rms =0.01 pu.

2.005

2.01

Time (S)

2.015

2.02

2.025

Fig. 7. iq axis stator current of PMSM with bearing fault. 6000 rpm.

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Amplitude (pu)

0.2

1.28 w=6000 rpm 1.05 0.98

0.15

M Healthy M Bearing M Eccentricity


2

1.5

1

0.5 0

200

400

600 Frequency (Hz)

800

1000

1200

Fig, 12. Stator current spectrum for PMSM. 6000 rpm.

This mechanical frequency, which is 258.20 Hz for the bearing considered, will induce on the stator current (due to flux unbalance) harmonics at a frequency difference between them and the supply frequency. For the experiment carried out, with the motor running at 6000 rpm, the new current harmonics are at 300 Hz minus fORF_B, i.e., 41.80 Hz. If subsequent rotor and fault harmonics are considered, the complete list of current harmonics in Table II due to mechanical unbalance by bearing damaged are obtained.

0.05

The rest of the harmonic spectrum in Fig. 8 to Fig. 12 does not give useful information for fault detection, because of the presence of numerous harmonics due to motor and power converter, even for a healthy motor.

1.28 0.98 w=3000 rpm 0.96

0.1

Amplitude (pu)

2.5

Also, Fig, 12 shows these specific harmonics along the stator current spectrum for a motor running at 6000 rpm.

Fig, 8 . Stator current harmonics for a PMSM. 6000 rpm.

0.08


0.06

0.04

0.02

0 0 1 2

3 4

5 6

7 8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 Harmonics

Fig. 9. Stator current harmonics for PMSM. 3000 rpm. 0.08

1.15 0.93 0.90

0.07

0.06 Amplitude (pu)

x 10 w=6000 rpm

0.1

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Harmonics

w=1500 rpm M Healthy M Bearing M Eccentricity

0.05

0.04

0.03

0.02

0.01

0 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 Harmonics

Fig. 10. Stator current harmonics for a PMSM. 1500 rpm. 0.06

1.05 0.86 0.85

0.05 Amplitude (pu)

-3

3 Amplitude (pu)

Fig. 8 to Fig. 11 show the harmonic content of the stator current for a healthy and faulty motors. The curves have been normalized to a rotor frequency for every case. For the bearing damaged the harmonics first and fifth around the main one, i.e., the third harmonic from the rotor point of view, could be used to detect the failure, because they present in case of fault an increment of at least 30% over the corresponding one of the healthy motor. Of course, the higher the speed, the greater the harmonic increment, making easier the fault detection. Moreover, it is well known [7] that damaged ball in the internal ring produces specific fault mechanical frequencies given by Di (5) f ORF _ B = Nb fr Do + Di where: Di : inner diameter, Do: outer diameter, Nb: number of rolling elements, and fr: rotor frequency.

w=300 rpm

0.04


0.03

0.02

0.01

0 0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 Harmonics

Fig. 11. Stator current harmonics for a PMSM. 300 rpm.

It can be concluded that bearing damage causing an eccentricity in the rotor movement produces specific fault harmonics at frequencies of rotor and its third and fifth harmonics, plus additional frequencies due to mechanical unbalances. The harmonics due to rotor eccentricity can not be clearly discriminated from the general harmonic content except in the main harmonic sidebands. However, the low amplitude of these fault harmonics regarding those of the healthy motor invalidates the stator current spectrum harmonic analysis method to detect eccentricities in the rotor. In fact, the motor used in the experiments was modified by adding an additional weight in the rotor axis of 50 g., which is quite small and not able to create a rotor eccentricity, except for a very high speed. Instead of using stator current spectrum, harmonic decomposition of zero component current in dq0 frame is proposed here to detect eccentricity harmonics in the faulty motor, despite its low amplitude. As zero component current collects the sum of the effects of thirds components, it is assumed that harmonics 3, 6, 9, 12, 15, 18,… of this i0 current component could show better than harmonics of the phase current the eccentricity fault. Fig. 13 to Fig. 16 show the i0 stator current harmonics, which have been related to rotor frequency. As expected, the third harmonics of the rotor frequency show the effects of the eccentricities for every speed, and could be used to detect this kind of fault, even in case of a small fault. Of course, the detection is much more easier at a high speed, because the mechanical unbalance becomes larger.

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Amplitude (pu)

0.04

w=6000 rpm

Table II. New frequencies for a mechanical bearing fault. A ball damaged among the nine balls of the bearing


0.03

6000 rpm Harmonic Frequency Amplitude (n) (Hz) (x10-3 pu) 1 141,75 1,1 2 241,75 2,06 3 341,75 2,02 4 441,75 1,3 5 541,75 2,06 6 641,75 1,2 7 741,75 1,4 8 841,75 2,51 9 941,75 1,6 10 1041,75 2,42 11 1141,75 2,6 16 --27 ---

0.02 0.01 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Harmonics

Fig. 13. Current harmonics of zero sequence i0 current for the PMSM running at 6000 rpm. 0.05

w=3000 rpm

Amplitude (pu)

0.04


0.03 0.02 0.01 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Harmonics

spectrum of the composed currents in frame dq0. By this way, specific faults such as rotor eccentricities become easier to detect. Besides, the harmonic frequencies appearing for the mechanical unbalance due to damaged internal ring can help for proper eccentricity detection.


w=1500 rpm


Amplitude (pu)

0.03 0.025

3000 rpm Frequency Amplitude (Hz) (x10-3 pu) 70,75 1,41 120,75 1,24 170,75 1,16 220,75 0,94 270,75 0,95 320,75 1,1 370,75 1,3 420,75 1,3 470,75 1,3 ----820,75 1,2 1370,75 1,1

The experimental results showed in the paper demonstrate the possibility of using these methods to detect rotor eccentricities and broken bearings in a PMSM.

0.02 0.015 0.01 0.005 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Harmonics

V. ACKNOWLEDGMENT


w=300 rpm


0.025 Amplitude (pu)

The authors would like to acknowledge the economic support received from the Spanish Ministry of Science and Technology for realizing this work under the DPI 200403180 Research Project. Also, the work was supported by the Programme Alban, the European Union Programme of High Level Scholarships for Latin America, scholarship No.E04D027632CO, Mr. J.A. Rosero.

0.02 0.015 0.01 0.005

REFERENCES

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Harmonics

[1]

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[2]

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[3]

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Fig. 16. Current harmonics of zero sequence i0 current for the PMSM running at 300 rpm

IV. CONCLUSIONS The different types of faults, together harmonic’s amplitudes variation for the full speed range, suggest us to consider not a specific harmonic to detect fault conditions in the PMSM, but a combination of them. Moreover, it is suggested in the paper to use not only the stator current spectrum, like in classical MCSA method, but also the

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[4]

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[5]

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[6]

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[7]

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[8]

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[9]

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[10] P. Pillay, R. Krishnan, ”Modeling, simulation, and analysis of permanent-magnet motor drives. I. The permanent-magnet synchronous motor drive,” IEEE Transactions on Industry Applications, vol. 5, Issue 2, pp. 265-273, March-April 1989. [11] B. Zhang, M. H. Pong, “Maximum torque control and vector control of permanent magnet synchronous motor,” International Conference on Power Electronics and Drive Systems, 1997, vol. 2, pp. 548-552, 26-29 May 1997.

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