effects of rotor faults on operation parameters and the low frequency ...

ISEF 2011 - XV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering Funchal, Madeira, September 1-3, 2011

EFFECTS OF ROTOR FAULTS ON OPERATION PARAMETERS AND THE LOW FREQUENCY HARMONICS OF THE MAGNETIC FIELD OUTSIDE INDUCTION MOTORS Virgiliu FIRETEANU(1), Petrica TARAS(1), Raphael ROMARY(2), Remus PUSCA(2), Andrian CEBAN(2) (1)

POLITEHNICA University of Bucharest, EPM_NM-Lab, 060042 Bucharest, ROMANIA (2) University of Artois, LSEE - Lab, 62400 Bethune, FRANCE

Abstract – This paper analyses the effects of the abnormal induction motor operation in case of one broken rotor bar and rotor static eccentricity faults for two different machines, with two and eight poles respectively. The electromagnetic field outside the motor steel casings is studied in order to see the changes in the spectrum of low frequency harmonics of this field in case of only one, or of both faults.

Introduction The electrical machines diagnosis [1 - 4] is more and more based on finite element models [5, 6] that give more information of the machine operating parameters than the analytical approaches. The induction motor operation in case of rotor broken bars or/and rotor static eccentricity is studied in this paper for two machines with two and eight poles with nonlinear magnetic steel casing. The finite element analysis is focused on the electromagnetic field outside the motors in order to study, like in the reference [6] where a four poles induction motor with silumin casing was considered, the effect of faults on the amplitude of low frequency harmonics of this field. The geometry and the circuit model of the machine I, Fig. 1, characterizes the two poles induction motor of 7.5 kW, 3 x 380 V, 50 Hz and 2898 rpm rated speed. The 2D computation domain of the electromagnetic field, infinitely extended, contains the stator and the rotor magnetic cores, 24 stator slots, the air gap of 0.5 mm thickness and 20 rotor bars, aluminum made - resistivity 0.048 m. The steel casing of the motor has the outer diameter 222 mm and the thickness 5 mm. y

SensorOx

O

x

SensorOy

a) Fig.1. Geometry and circuit model of the machine I

b)

The machine II of 500 kW, 3 x 6000 V, 50 Hz and 743 rpm rated speed, has 72 stator slots, the air gap thickness 1.5 mm, 58 rotor bars in copper - resistivity 0.0296 m with cross-section 6.2 x 60.2 mm and steel casing with the diameter 1006 mm and thickness 16 mm. The rotor eccentricity has the values 0.1 mm for the machine I and 0.3 mm for the machine II. The magnetic field outside the machine is investigated through the output voltage of two coil sensors, SensorOx and SensorOy, Fig. 1a). The circuit model, Figs 1b), contains the coils of the stator winding, three inductances corresponding to the part of this winding outside the magnetic core, the voltage sources of the symmetric three phase electric power supply, four coils corresponding to the two sensors, two resistors for sensor output voltage measurement and the squirrel-cage, defined by the number of bars and the electrical parameters of the short-circuit rings between two successive rotor slots. The magnetic cores are magnetic nonlinear and nonconductive regions. The casing of the two machines and the shaft of the two-pole machine are characterized by the resistivity 0.2 m, the saturation 1.8 T and the initial relative magnetic permeability 1800. The time step of step by step in the time domain finite element computation has the value 1 ms. The rotor motion model in the applications analyzed in the following two sections of the paper is of constant rotor speed type - 2898 rpm for the machine I and 743 rpm for the machine II. The machine II is studied in the last section taking into account a motion model with constant load.

Time variation of the electromagnetic torque and force acting on the rotor The influence of one broken bar (brb), of rotor eccentricity (ecc) and of the both fault (brb+ecc) on the motor operation parameters is analyzed in this section. The time variation and the amplitude of the stator currents are practically non affected by the bar interruption or by the rotor eccentricity. Contrarily, the time variation of the electromagnetic torque (a) and of the module of the force on the rotor (b), Figs. 3 – 6, are different in all faulty cases in comparison with the healthy cases (her). Taking as reference the healthy machine I-(her), Fig. 3, the low frequency oscillations of the electromagnetic torque around the mean value are not so evident in the I-(ecc) case, Fig. 5, but they increase in cases I-(brb), Fig. 4 and I-(brb+ecc), Fig. 6. The mean value of the force acting on the rotor, 0.0407 N, is completely negligible in the I-(her) case, Fig. 3, in comparison with 207.7 N for I-(brb) case, Fig. 4, 324.4 N for I-(ecc) case, Fig. 5 and 432.6 N for I-(brb+ecc) case, Fig. 6. The low frequency oscillations of this force are very important in all faulty cases.

(a)-I-(her)

(b)-I-(her)

Fig. 3. Time variation of the rotor torque and force for the healthy machine I-(her)

(a)-I-(brb)

(b)-I-(brb)

Fig. 4. Time variation of the rotor torque and force for the machine I with one broken bar (brb)

(a)-I-(ecc)

(b)-I-(ecc)

Fig. 5. Time variation of the rotor torque and force for the machine I with rotor eccentricity (ecc)

(a)-I-(brb+ecc)

(b)-I-(brb+ecc)

Fig. 6. Time variation of the rotor torque and force for machine I with broken bar and eccentricity (brb+ecc)

For the machine II, the mean value of the force acting on the rotor, 0.0170 N, it is also completely negligible for the II-(her) case in comparison with the values 5335 N for the II-(brb) case, Fig. 7, 9909 N for the II-(ecc) case and 15171 N for the II-(brb+ecc) case, Fig. 8.

(a)-II-(brb)

(b)-II-(brb)

Fig. 7. Time variation of the rotor torque and force for the machine II with one broken bar (brb)

(a)-II-(brb&ecc)

(b)-II-(brb&ecc)

Fig. 8. Time variation of rotor torque and force for the machine II with broken bar and eccentricity (brb+ecc)

Magnetic Field Outside the Motors The lines of the magnetic field outside the two poles healthy machine I, Fig. 9, are practically the same for the time steps 900 ms, in the image (her)-900, and 1400 ms, in the image (her)-1400. These lines correspond to the range [-5e-8 …. 5e-8] Wb of the magnetic flux. The two-poles symmetry and the periodicity of the magnetic field lines disappears when one bar of the machine I is broken, as the images (brb) – 900 and (brb) – 1400, Fig. 9, show. The lines are now in the range [6e-8…. 14e-8] Wb for the time step 900 ms and in the range [-25e-8 …. -1.5e-8] Wb for the time step 1400 ms. Some bounds of the ranges of magnetic flux lines in the (brb) case are out of the range corresponding to the (her) case; therefore, the magnetic field intensity outside the motor increases when the broken bar fault appears.

(her) - 900

(brb) - 900

(her) - 1400

(brb) - 1400

Fig. 9. Lines of the magnetic field for two time steps, machine I, (her) and (brb) cases

For the machine II, time step 2700 ms, the image (her), Fig. 10, reflects the eight poles of the field outside the motor, property which disappears in case of faults; these lines correspond to the range [-9e-10 . 9e-10] Wb of the magnetic flux. The lines are in the ranges [65e-10 ... 165e-10] Wb for the (brb) case, [-6e-10 ... 8e-10] Wb for the (ecc) case and [148e-10 …. 250e-10] Wb for the (brb+ecc) case. Therefore, the change of the magnetic field intensity outside the machine II is much more important in case of broken bar fault than in case of rotor static eccentricity.

(her)

(brb)

(ecc)

(brb+ecc)

Fig. 10. Lines of the magnetic field outside the machine II - (her), (brb), (ecc), (brb+ecc) cases

Low Frequency Harmonics of the Coil Sensor Output Voltages A simple way to investigate the magnetic field outside the motor consists in the use of coil sensors. The time variation and the harmonics of the SensorOx output voltage are presented in Fig 11 a) for the healthy machine I - (her) case, in Fig 11 b) for the (brb) case, in Fig. 11 c) for the (ecc) case and in Fig. 11 d) for both faults – the (brb+ecc) case.

a) - (her) case

c) – (ecc) case

b) – (brb) case

d) – (brb+ecc) case

Fig. 11. Time variation and harmonics of the SensorOx output voltage – machine I

The results of the machine I, in which the rotor currents have the rated frequency 1.7 Hz, show: (aI) there are non significant differences between healthy and faulty states related the values of the amplitude of the 50 Hz harmonic, Table 1 (last column) of the SensorOx output voltage. The rms value of this voltage has also no significant differences from one case to another; Table 1. Amplitude in [mV] of the harmonics of the SensorOx output voltage – machine I Case (her) (brb) (ecc) (brb+ecc)

1 0.0197 2.94 0.46 2.99

2 0.0103 4.63 1.61 5.08

Harmonic Frequency [Hz] 3 4 5 6 0.014 0.0117 0.0070 0.0088 0.638 0.314 6.47 1.24 0.47 0.30 0.21 0.18 0.93 0.58 6.98 1.19

8 0.0045 2.63 0.13 2.56

10 0.0056 0.87 0.10 0.94

50 31.5 31.8 31.5 31.8

(bI) when a bar is broken, the amplitude of the harmonics of 2 Hz and 5 Hz increases 4.63/0.0103 = 449.5 times and respectively 6.47/0.007 = 924.3 times with respect the healthy state; (cI) when the rotor has 0.1 mm static eccentricity, the amplitude of the harmonics of 2 Hz and 3 Hz increases 1.61/0.0103 = 156.3 times and respectively 0.47/0.0142 = 33.1 times; (dI) when both faults are present, the amplitude of the harmonics of 2 Hz and 5 Hz increases 5.08/0.0103 = 493.2 times and respectively 6.98/0.007 = 997.1 times. For the machine II, the time variation and the harmonics of the SensorOx voltage are presented in Fig. 12 a) for the (her) case, in Fig. 12 b) for the (brb) case, in Fig 12 c) for the (ecc) case and in Fig. 12 d) for both faults – the (brb+ecc) case. The comparison of the results shows a completely different time variation and amplitude of the sensor voltage in the (brb) and ((brb+ecc) faulty cases Figs. 12 b), d), with respect the healthy case, Fig. 12 a).

a) - (her) case

c) – (ecc) case

b) – (brb) case

d) – (brb+ecc) case

Fig. 12. Time variation and harmonics of the SensorOx output voltage – machine II

For the eight-poles machine II, in which the rotor currents have the rated frequency 0.467 Hz, the analysis of the results shows: (aII) there are no significant differences between the healthy and faulty states related the values of the amplitude of the 50 Hz harmonic only, Table 2 (last column). As shown in the next section of the paper, the rms values of the sensor output voltages are different; (bII) when a bar is broken, the amplitude of the harmonics of 1 Hz, 12 Hz, 13 Hz and 25 Hz of the sensor output voltage increases 564/0.37 = 1524.3 times, 3522/0.08 = 44025 times, 2817/0.55 = 5121.8 times and 530.2/0.34 = 1559.4 times with respect the healthy state;

(cII) when the rotor has 0.3 mm static eccentricity, the amplitude of the harmonics of 12 Hz, 13 Hz and 25 Hz of the sensor voltage increases 2.04/0.08 = 25.5 times, 2.50/0.55 = 4.55 times and 10.1/0.34 = 29.7 times; Table 2. Amplitude in [µV] of the harmonics of the SensorOx output voltage – machine II Case (her) (brb) (ecc) (brb+ecc)

1 0.37 564 0.52 761.4

5 2.56 40.5 2.23 46.1

Harmonic Frequency [Hz] 12 13 25 0.08 0.55 0.34 3522 2817 530.2 2.04 2.50 10.1 3857 3090 599.5

50 399 403.2 399.8 405.8

(dII) the amplitude of the harmonics of 1 Hz, 12 Hz, 13 Hz and 25 Hz of the sensor voltage increases 761.4/0.37 = 2057.8 times, 3857/0.08 = 48213 times, 3090/0.55 = 5618.2 times and 599.5/0.34 = 1763.2 times when both faults are present. There are important differences between the two-poles machines I and the eight-poles machine II related the harmonics which are efficient in fault diagnosis. In case of the first machine, the rotor faults determines important increases of the amplitude of harmonics under 6 Hz, while in case of the second machine, the increase of the amplitude of harmonics over 10 Hz is much more important.

Influence of the Motor Load on the Coil Sensor Output Voltage The influence of the motor load is analyzed in this section for the machine II through a motion model of constant load type. The full_load application considers the rated value 6500 Nm of the load torque, half_load the value 3250 Nm and no_load the value 200 Nm. The constant value 0.014 Nms/degree characterizes the friction torque proportional with the rotor speed. The results of the rotor speed mean value for the healthy machine, 743.7 , 747.1 and 749.7 rpm, correspond to the frequency 0.42 Hz, 0.19 Hz and 0.0004 Hz of the rotor currents. When a bar is broken, the rotor speed oscillations increase (see the curve brb in Fig. 13). The first harmonic of the speed time variation in (brb) case has the frequency 0.85 Hz and the amplitude 0.164 rpm.

Fig. 13. Time variation of motor speed, (her) and (brb) cases, full_load application

The rms values of SensorOx output voltage, Table 3, are practically not affected by the motor load when the motor is healthy. But, there is an important increase of this voltage when one bar is broken and this increase grows when the load of the motor increases. Table 3. Rms value in [V] of the SensorOx output voltage Motor load Healthy motor (her) One broken bar (brb) Ratio (brb)/(her)

No_load 288.3 881.3 3.06

Half_load 286.5 2538.6 8.86

Full_load 284.8 3158.4 11.1

The time variation of the SensorOx output voltage of the healthy motor – image (her) in Fig. 14, is practically independent on the motor load. But when one bar is broken, Fig. 14 – (brb) images, the amplitude and the frequency of this voltage change in time. In case of no_load motor operation only the harmonic of 12.5 Hz, Table 4, reflects the one broken bar fault. The amplitude of this harmonic has a very low value in case of healthy motor and when one bar is broken this amplitude increases very much. This amplitude is more than two times higher than the amplitude of the 50 Hz harmonic.

(her)

(brb) – no_load

(brb) – half_load

(brb) – full_load

Fig. 14. Dependence of time variation of SensorOx output voltage on the motor load – (her) and (brb) cases

Table 4. Amplitude in [V] of the harmonics of the SensorOx output voltage - no_load operation Harmonic frequency [Hz] Healthy motor (her) One broken bar (brb) Ratio (brb)/(her)

0.4 3.30 2.59 0.785

2.0 2.32 2.37 1.02

6.0 0.40 0.50 1.25

12.5 0.004 880 220000

25.0 4.16 88.0 25.15

50.0 404.27 404.31 1.000

When the load of the motor increases, Tables 5 and 6, the amplitude of the 12.5 Hz harmonic increases in both cases, healthy and faulty motor. The ratio of the two values, for motor with one broken bar and for the healthy motor, decreases when the load of the motor increases. This criterion for (brb) fault characterization rests greater than 2500 even for rated load motor operation. Table 5. Amplitude in [V] of the harmonics of the SensorOx output voltage - half_load operation Harmonic frequency [Hz] Healthy motor (her) One broken bar (brb) Ratio (brb)/(her)

0.2 0.136 112.7 828.7

0.6 0.107 73.67 688.5

1.0 0.166 15.64 94.2

1.9 0.528 3.16 5.98

12.7 26.5 0.067 3.71 2508 347.3 37433 93.6

50.0 401.8 403.7 1.005

Table 6. Amplitude in [V] of the harmonics of the SensorOx output voltage - full_load operation Harmonic frequency [Hz] Healthy motor (her) One broken bar (brb) Ratio (brb)/(her)

0.43 0.187 364.6 1954.7

1.28 0.355 350.0 985.6

2.14 0.943 28.5 30.2

3.00 0.109 10.96 100.6

12.4 25.2 1.163 0.159 3024.7 436.5 2605.1 2745.1

50.0 399.4 402.7 1.008

Another important finding for one broken bar fault diagnostic concerns the amplitude of the harmonics with frequency equal or lower than the frequency of the rotor currents. The results in Tables 5 and 6 show the increase of the amplitude of these harmonics when the bar is broken, respectively the increase of the ratio (brb)/(her) when the motor load increases. Conclusions Huge values characterize the mean value and the amplitude of the oscillations of the electromagnetic force acting on the rotor in case of motor operation with one broken bar and rotor static eccentricity. The space structure of the magnetic field outside the motor, which in case of healthy motors reflects the number of identical poles of the rotating magnetic field - space and time dependent, drastically changes when the faults one broken bar or/and rotor eccentricity are present. It was proved that the component of the magnetic field generated by the faults has a higher intensity than the rotating field. All harmonics with high efficiency in fault diagnosis can be evaluated through the finite element models of the investigated motor. Taking also into account the results of the four-poles machine analyzed in the reference [6], it should be stated two categories of harmonics of interest for one broken bar and rotor eccentricity diagnosis: (a) – the harmonics of very low frequency, equal or lower then three times the rated frequency of the rotor currents and (b) harmonics with frequency equal or multiple of the ratio between the rated supply frequency and the couple of poles. The very low frequencies (a) in this paper are lower than 3 x 1.7 = 5.1 Hz for the machine I and lower than 3 x 0.467 = 1.4 Hz for the machine II. The low frequency harmonics (b) for the machine II are of 50/4 = 12.5 Hz and 2 x 12.5 = 25 Hz. The consistency of the information related the broken bar fault based on the amplitude of very low frequency harmonics increases when the load of the motor grows. References [1] 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 2005 IEEE Russia Power Tech, 2005. [2] R. Romary, R. Corton, D. Thailly, and J. F. Brudny, "Induction machine fault diagnosis using an external radial flux sensor," The European Physical Journal - Applied Physics, vol. 32, pp. 125-132, 2005. [3] A. Ceban, R. Pusca, and R. Romary, "Eccentricity and broken rotor bars faults - Effects on the external axial field," in XIX International Conference on Electrical Machines - ICEM 2010, Rome, Italy, 2010. [4] M. D. Negrea, "Electromagnetic flux monitoring for detecting faults in electrical machines" doctoral dissertation, Helsinki University of Technology, Laboratory of Electromechanics, November, 2006. [5] B. Vaseghi, N. Takorabet, and F. Meibody-Tabar, "Transient finite element analysis of induction machines with stator winding turn fault," Progress In Electromagnetics Research (PIER) Journals, vol. 95, pp. 1-18, 2009. [6] A. Ceban, V. Fireteanu, R. Romary, R. Pusca, and P. Taras, "Finite element diagnosis of rotor faults in induction motors based on low frequency harmonics of the near-magnetic field," in 8th IEEE International Symposium on Diagnostics for Electrical Machines, Power Electronics & Drives - SDEMPED 2011, Bologna, Italy, 2011.