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Electrical Induction Motor Higher Harmonics
Analysis based on Instantaneous Angular Speed
Measurement
CONFERENCE PAPER · DECEMBER 2014 CITATION1
READS172
3 AUTHORS, INCLUDING: Marco Spagnol Università degli Studi di Trieste 1 PUBLICATION 1 CITATION SEE PROFILE Luigi Bregant Università degli Studi di Trieste 21 PUBLICATIONS 44 CITATIONS SEE PROFILE Available from: Luigi Bregant Retrieved on: 09 April 2016Electrical Induction Motor Higher Harmonics
Analysis based on Instantaneous Angular Speed
Measurement
Marco Spagnol1, Luigi Bregant1, Alessandro Boscarol2
1
Universit´a degli Studi di Trieste, Trieste, Italy {mspagnol,bregant}@units.it
2
Nidec ASI S.p.A, Monfalcone, Italy
Abstract. This paper proposes the measurement of Instantaneous An-gular Speed (IAS) as a condition monitoring tool for Induction Motors. The main advantages with respect to vibration and Motor Current Signa-ture Analysis (MCSA) are the high resolution of the result obtained com-bined with small data storage. The hi-quality information shows many hi-order harmonics that are not easy to interprete and correlate with the machine construction. In this paper a review of the analytic charac-teristics frequencies due to electromagnetic effects is reported and, fur-thermore, theoretical results and experiments are compared. From the comparison obtained, the authors conclude that IAS has the potential of extract information due to the rotor’s skewness.
Keywords: Instantaneous Angular Speed · Induction Motor · Electro-magnetic Noise · Frequency Analysis · Condition monitoring
1
Introduction
Induction motors are frequently used in industries and can be one of the most important components of a system. The maintenance of this equipment is very important from a business and a safety point of view, so the electrical machine reliability has been an hot topic in industry for decades. Three mayor surveys were done in order to classify the major damages:
• 1983 by the Electric Power Research Institute (EPRI), project performed by General Electric (GE)
• 1985 by the Institute of Electrical and Electronics Engineers, Inc.(IEEE) • 1995 by the Institute of Electrical and Electronics Engineers, Inc.(IEEE) These surveys are published in [1]. Other recent studies confirm the results of former surveys, such as [2–4]. Bearings and stators are the components where improvement of maintenance and redesign programs may most significantly in-crease motor reliability. Note that the most frequently failing components are ground insulation (18.5%) and sleeve bearings (9.7%), followed by ball bearings (4.9%), [5].
Table 1. Main faults in Electrical Machines
Failure Percentage %
Bearings Damaged (lubrication, misalignment, unbalance) 41
Stator Faults 37
Rotor Faults 10
Other faults 12
The previous studies showed that inadequate maintenance and poor installa-tion/testing are significant causes of failures. On-line condition monitoring tech-nologies and Precision Maintenance ([6, 7]) are proved to improve the motor reliability. For instance, motor bearing failures would be significantly reduced if the driven equipment is properly aligned through the operative life regardless of the loading conditions.
Thanks to the collaboration between Nidec ASI S.p.A and Universit´a degli Studi
di Trieste, a confirmation of this failure distribution was obtained.
1.1 Fault Diagnosis Techniques
This section introduces recent developments in fault diagnostics of induction motors (IMs), by providing theoretical guidelines and practical considerations. Reference [8] reports a complete bibliography on Induction Motors Faults De-tection and Diagnosis up to December 1999. Measurement techniques for fault detection are based on different measurement approaches: stator current mea-surement, vibration measurements (acceleration, velocity, displacement) as well as the method proposed in this work, the Instantaneous Angular Speed Analysis. MCSA - Motor Current Signature Analysis the stator current is used as diagnostic signal; ”stator current is the most used diagnostic signal in the in-dustrial applications” [9], since it enables for non invasive diagnostic and does not require the use of additional probes. A related problem during field mea-surements is the exposure to live parts. This may result in exposing the persons involved in the test set-up to electrical shock or arc-flash hazards, [10]. A review of MCSA diagnostic techniques is reported in [11, 12]. MCSA is not always re-liable for bearing fault detection [13], since the amplitude of fault signatures in the current signal is very low, except in some dedicated operating conditions. In [9] the most common algorithms applied to MCSA are reported. There is an inverse relationship between the fault detection ease and the importance to the user of that fault detection. In fact, there are dozens of papers published on broken rotor bars and only two or three on the use of MCSA for bearing faults detection, in spite of several studies that show bearing faults to account for almost 50% of induction motor failures as opposed to around 10% for rotor cage problems, [12].
Vibrations Many faults can be detected using acceleration, velocity or displace-ment sensors. Many books explain how to impledisplace-ment a condition monitoring
system [14, 15]. Angular Resampling, Envelope Analysis and Cyclostationarity are the common techniques used in order to remove the speed fluctuations, em-phasize the presence of a fault and find a signal that vary cyclically with time. Sometimes the main problem is the transfer path of the vibration signal through the machine walls.
IAS - Instantaneous Angular Speed Some work has been done recently in order to show the capability of Instantaneous Angular Speed (IAS) to detect bearing faults [16, 17] and broken rotor bars [18–20]. The IAS measurements is very informative for low speed and high radial load situations, but can also be applied for higher speed motors with a counter with high counting frequencies [21]. A common method used to acquire the IAS is through an incremental optical encoder and a counter board in order to measure the time elapsed between rising edge of the encoder’s signal. In this way, the angular information is directly acquired. In a previous research, acceleration and IAS were compared [22] and the slip effect due to Induction motor behaviour was detected. In this work, the behaviour of the electrical motor is explained from the IAS point of view. The aim is to perform condition monitoring tasks using only the encoder connected to the rotor.
1.2 Mechanical-Electrical Interaction
In an electric motor, noise and vibration are related to the excitation forces produced by the electromagnetic field present in the stator and rotor of the motor. The behaviour of a motor can be affected by the variation of these fields due, for example, to the presence of an inverter (eg. the switching frequency can be seen in the vibration spectrum), by a grid variation [23, 24] or by the motor’s design. Thus, the healthy induction motor also has a specific spectrum signature when there are no faults [25, 26]. In bibliography [27–31], different analytical formulas of the electromagnetic forces are reported. In the next section these main frequencies are summarized. These can be found in the current, vibration and IAS spectra.
2
Characteristic Frequencies
Rotor and stator excite magnetic flux density waves in the air gap. The slots, the distribution of windings in slot, the input current waveform distribution, the air gap permeance fluctuation, the rotor eccentricity and the phase unbalance give rise to mechanical deformations and vibrations. Magnetomotive force (MMF) space harmonics, time harmonics, slot harmonics, eccentricity harmonics and saturation harmonics, produce parasitic higher harmonic forces and torques. In order to explain peaks found in IAS spectrum, a review of the analytical formulas of electromagnetic fields generation in IM is done. In this paper only Magnetomotive force (MMF) space harmonics in IAS spectrum are reported. In Table 2 the main parameters for an IM are reported.
Table 2. Induction Machine main parameters f Fundamental frequency s Slip
p Pole pair number m Number of phases k, g Ordinal numbers ν Harmonic order
ν+ Harmonic order (forward) ν−Harmonic order (backward)
R Rotor slot (bars) S Stator slot Fmν MMF Amplitude θs Angle (stator ref)
oν Order in IAS spectrum fr Frequency in current spectrum
sk Skewness
P = 2p Poles
ω = 2πf Angular frequency ns= f /p Synchronous speed
nsν = ∓f /(νp) Synchronous speed for νth harmonic nm= (1 − s)ns Mechanical speed
τs= 1/ns Synchronous speed period
τm= 1/nm Mechanical speed period
nsl= ns− nm Slip speed
s = nsl/ns Slip definition
sf = psns Slip frequency
sν= 1 − ν(1 − s) Slip for νth harmonic
f sν= f [1 − ν(1 − s)] Slip frequency for νth harmonic
2.1 Magneto-motive force (MMF) space harmonics in IAS spectrum
The current flowing into the stator of an IM generates an MMF which consists in an infinite number of harmonic MMFs changing in time according to cos(ωt)
and in space according to cos(νpθs). A three-phase (m = 3) ideal motor with
balanced sinusoidal currents is considered. Three windings are shifted in space by 2π/3 electrical degrees. Three input currents are injected into the stator with theoretically the same amplitude and the same phase shift equal to 2π/3 electrical degrees. This generates a total MMF of:
F1(θs, t) = Σν∞Fmνcos[(2πf )t ∓ (νp)θs] = Σν∞Fmνcos[(νp)θs∓ (2πf )t] (1)
with:
ν+= 2km + 1 ν− = 2km − 1 ν = 2km ± 1 (2)
or using another notation [25],
ν = 2gm + 1 g = 0, ±1, ±2, . . . ν = 1, −5, 7, −11, 13, . . . (3)
F1(θs, t) = Σν∞Fmνcos[(2πf )t − (νp)θs] = Σν∞Fmνcos[(νp)θs− (2πf )t] (4)
In this specific case (three-phase stator winding), the harmonics present in the spectrum ν = mk with k = 1, 3, 5, . . . do not exist. The forward-rotating
harmon-ics ν+= 1, 7, 13, 19, . . . are the arithmetic sum of waves in all three phases, while
the backward-rotating harmonics ν− = 5, 11, 17, 23, . . . are zero, [29]. ν = 5, 7
Table 3. Current harmonic frequencies, (p = 2,s = 0.03417) ν 1 2 3 4 5 6 7 8 9 10 oν 0 2.0708 4.1415 6.2123 8.2830 10.3538 12.4245 14.4953 16.5661 18.6368 ν 11 12 13 14 15 16 17 18 19 20 oν 20.7076 22.7783 24.8491 26.9199 28.9906 31.0614 33.1321 35.2029 37.2736 39.3444 ν -1 −2 −3 −4 -5 −6 −7 −8 −9 −10 oν -4.1415 −6.2123 −8.2830 −10.3538 -12.4245 −14.4953 −16.5661 −18.6368 −20.7076 −22.7783 ν −11 −12 −13 −14 −15 −16 −17 −18 −19 −20 oν −24.8490 −26.9199 −28.9906 −31.0614 −33.1321 −35.2029 −37.2736 −39.3444 −41.4152 −43.4859
the presence of the slip s. This parameter is correlated to the load/speed of the machine. At the motor’s startup the slip is 1, at no load is 0, with load 1 < s < 0. Other slip-dependent parameters are defined in Table 2. The magnetic flux in
the rotor and in the stator are running with the same synchronous speed ns,
since ns= ns(1 − s) + sns. Considering a constant fundamental frequency, the
current in the stator completes a revolution in θs, while the rotor does it in
θm (with τs6= τm) owing to the slip. The encoder senses this latter speed. The
equation 4 describes the MMF with a periodicity of
wν = 0, 12, 12, 24, 24, 36, 36 . . . for ν = 1, −5, 7, −11, 13, −17, 19, . . . (5)
while in the IAS spectrum these orders can be found at oν, Eq.6. This equation
does not take into account the fundamental frequency because it does not have an influence on the generated periodicity.
oν= p
ν − 1
1 − s (6)
In Table 3 the harmonics generated in IAS spectrum by the MMF space
harmon-ics are reported. Note that ν = −5, 7 have the same absolute value oν= 12.425,
ν = 3, 9, 15, . . . can be correlated to stator eccentricity, while even space har-monics are due to mechanical unbalance. These harhar-monics exactly excite the frequencies found calculating stator and rotor combinations [30]
oν= 0, 4.142, 8.283, 12.425, 16.566, 20.708, 24.849, 28.991, 33.132, . . . (7)
2.2 Time harmonics and other frequencies
In bibliography, analysing the second time harmonic of the frequency in order to detect the current supply unbalance is suggested [15, 22, 29, 32]:
fr= 2f (8)
this could also be due to by the presence of ν = 3. In IAS spectrum an extra order can be found at 4.1415 for a four-poles motor with 50Hz supply frequency
and slip s = 0.03417. Instead, the harmonic fr = 3f is related to the motor’s
Table 4. IAS current harmonic frequencies oν, (p = 2)
s 0.00088 0.00175 0.01466 0.03417 ν = 11, −9 ±20.0176 ±20.0351 ±20.2976 ±20.7076
2.3 Slip effect
Figure 1 shows the same motor in two different experimental configurations: • TR motor only (no load)
• EL torquemeter, magnetic brake (three loads) [21, 22]
In the EL case, there is a strong 100Hz component, owing to unbalanced currents or stator eccentricity. In this specific case it was probably due to eccentricity because a new experimental setup was built with the same motor and a stiffer coupling that fixed the rotor in a better position and amplitudes of orders due to ν = 3 were decreased. The Order 3 keeps the same amplitude trough the various measurements. Sidebands are present around these orders at 2ps. The IAS spectrum of the induction motor can be divided into two zones:
• orders 0-16: current space and time harmonics effect
• orders 16-40: rotor/stator slotting, skewness effect, saturation
In Table 4, the calculation of oν (Eq. 6) is extended to the four different
config-urations of slip (s = 0.00088, 0.00175, 0.01466, 0.03417). In Figure 2 these orders are highlighted.
2.4 Rotor influence
In Figure 3, a phenomenon correlated to the rotor skewness is present. This effect can be seen in those orders integer order + 2ps with sidebands. The latter can be calculated with Eq. 9. In Table 5 these sidebands are calculated for two different motors. The first involved in the experiment has a skew of 1 bar. The
value of oν is very close to the experimental value 0.282. Considering geometric
tollerances, the value 1.033 can be assigned to the sk parameter. Sidebands are present also in the second motor, but further investigation is necessary because
it has R = 32 and sk = 1.5, so the result is osk= 0.2813, Table 5.
The physical explanation of these sidebands is very simple: at every integer order, the rotor feels the electromagnetic pull (main order correlated with 2ps) and owing to the presence of skewness, the number of pole pairs, the number of phases and the number of rotor bars, a modulation around the main order appears. If confirmed, it may be a very interesting result because this effect cannot probably be seen in MCSA owing to the smearing of the peaks. IAS spectrum, being fixed with the rotor, allows this kind of information extraction.
osk=
p m sk
Table 5. Sidebands in IAS spectrum due to skewness (p = 2,m = 3) R 22 22 32 sk 1 1.033 1.5 osk0.2727 0.2817 0.2813 0 5 10 15 20 25 30 35 40 45 50 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Amp [rad/s] Orders TR no load EL 0.00Nm − 2.17A EL 2.60Nm − 2.27A EL 6.16Nm − 2.75A 0 2 4 6 8 10 12 14 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Amp [rad/s] Orders TR no load EL 0.00Nm − 2.17A EL 2.60Nm − 2.27A EL 6.16Nm − 2.75A 24 25 26 27 28 29 30 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Amp [rad/s] Orders TR no load EL 0.00Nm − 2.17A EL 2.60Nm − 2.27A EL 6.16Nm − 2.75A
Fig. 1. Harmonics in IAS spectrum, TR (only motor) and EL configuration (s1 =
20 20.2 20.4 20.6 20.8 21 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 Amp [rad/s] Orders
Order: 20.018 Order: 20.035 Order: 20.298 Order: 20.708
Fig. 2. MMF Harmonics in IAS spectrum, TR (only motor) and EL configuration (s1= 0.00088, s2= 0.00175, s3= 0.01466, s4= 0.03417) 20.7 20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 Amp [rad/s] Orders Order: 21.140Sideband: 0.282 Order: 21.060Sideband: 0.282 Order: 21.007Sideband: 0.282
Fig. 3. Skew Harmonics in IAS spectrum, TR (only motor) and EL configuration (s1= 0.00088, s2= 0.00175, s3= 0.01466, s4= 0.03417)
3
Conclusions
This research shows the influence of current supply effect in the IAS measure-ment. Motor noise and vibrations can be predicted using analytical formulas found in bibliography. Nevertheless, further work must be done in order to iden-tify all the harmonics and sidebands present in the spectrum. From the exper-iments it is clear that the saturation harmonics are very strong in induction machines. Sidebands were found probably correlated to the rotor skewness.
Acknowledgements. This research is supported by Universit´a degli Studi di
Trieste, Nidec ASI S.p.A. and ”Programma Operativo del Fondo Sociale Europeo 2007/2013 della Regione Autonoma Friuli Venezia Giulia”.
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