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Trajin, Baptiste and Regnier, Jérémi and Faucher, Jean Comparison between vibration and stator current analysis for the detection of bearing faults in asynchronous drives. (2010) IET Electric Power Applications, 4 (2). 90-100. ISSN 1751-8660

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https://doi.org/10.1049/iet-epa.2009.0040

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Comparison between vibration and statorcurrent analysis for the detection of bearingfaults in asynchronous drivesB. Trajin1,2 J. Regnier1,2 J. Faucher1,2

1LAPLACE (Laboratoire Plasma et Conversion d’Energie), Universite de Toulouse; INP, UPS; ENSEEIHT, 2 rue Camichel, BP7122,F-31071 Toulouse Cedex 7, France2CNRS; LAPLACE; F-31071 Toulouse, FranceE-mail: baptiste.trajin@laplace.univ-tlse.fr

Abstract: This study deals with the application of vibration and motor current spectral analysis for themonitoring of rolling bearings damage in asynchronous drives. Vibration measurement is widely used todetect faulty bearings operations. However, this approach is expensive and cannot always be performed,while electrical quantities such as the machine stator current are often already measured for control anddetection purposes. Signal processing methods and global indicators associated with bearing fault detectionof vibration measurements are recalled. Compared to these methods, an automatic detector based onvibration spectral energy extraction is then proposed and its performances are discussed. Moreover, loadtorque measurements underlines that bearing faults also induce mechanical load torque oscillations.Therefore a theoretical stator current model in case of load torque oscillations is used to demonstrate thepresence of phase modulation (PM) on stator currents. Frequency behaviour of the related sidebandcomponents is strongly investigated for monitoring purposes. Thus, a fault detector using the extraction ofspectral energy of stator current is proposed to detect damaged bearings. This detector is then compared tothe one defined on vibration signals.

1 IntroductionElectrical drives using induction motors are widely used inmany industrial applications because of their low cost andhigh robustness. However, many types of faulty operationscould appear during the lifetime of the system. A largeoverview of electrical machines failures and monitoringtechnics can be found in [1]. A classification of the mostfrequently encountered faults can be found in [2]. Toimprove the availability and reliability of the drive, acondition monitoring could be implemented to favour thepredictive maintenance. Traditionally, motor condition issupervised using vibration analysis [3] but measuring suchmechanical quantities is often expensive. Indeed vibrationsensors such as piezoelectric accelerometers and associatedload amplifier are often expensive. Moreover, the ability ofa clear detection of bearing faults by vibrationmeasurements lies in the sensor locations. Indeed,

accelerometers need to be mounted near to each possiblefaulty bearing of the machine.

To overcome this problem, the detection could be based onthe measurement of stator currents which are often available forcontrol purposes. A general review of monitoring and faultdiagnosis schemes using stator current is available in [4]. Asshown in [2], the major faults come from faulty bearings. Inthis case, several studies demonstrate that specific signaturesappear on stator current spectrum [5]. A comparison betweenvibration and stator current monitoring has been presented in[6]. A model for bearing fault detection has been proposedin [5, 7], based on the assumption that bearing defects leadto a particular airgap eccentricity and thus induce thecharacteristic signatures on stator current spectrum. Otherstudies consider that bearing faults induce load torqueoscillations [8]. Then, spectral techniques are often applied todetect and classify such phenomena. Therefore the definition

of an indicator performing an automatic extraction of relevantinformation from the current spectrum is rarely of concern [9].This work presents the design and validation of a novelautomatic indicator for bearing faults detection based onenergy extraction from stator current spectrum. Theefficiency of such a detector is compared to a similarmechanical automatic detector based on vibration analysis.

In this paper, an overview of methods for the detection anddiagnosis of defects in ball bearings is firstly recalled inSection 2. A basic automatic detector based on vibrationspectral energy extraction is proposed to detect bearingfaults with a good confidence rate and its performances arecompared with other methods. Section 3 studies the effectsof bearing faults on mechanical quantities such aseccentricity and load torque. It is demonstrated that airgapvariation and thus eccentricity induced by bearing defectsmay be considered as negligible. Consequently, the paperfocuses on load torque variations due to bearings faults. InSection 4, a stator current model that demonstrates thatsideband components due to load torque oscillations existin the current spectrum is recalled. A gain diagram isestablished to study the amplitude of these specificsidebands related to the load torque oscillation frequency.In Section 5, an automatic detection based on currentspectral energy estimation is proposed to detect faultybearings. Restrictions of the proposed indicator regardingits definition and the use of the gain diagram are thendiscussed as well as a general comparison between vibrationand stator current detectors. Finally, some suggestions areproposed to choose a detection method regarding to thesystem that has to be monitored.

2 Vibration analysis for bearingfaultsIn this paper, three different types of bearings are studied.Bearings are mounted in a 5.5 kW, two pole-pairsinduction machine supplied by a variable frequencyinverter. An acquisition board is used to sample vibrations,load torque and stator currents. First of all, two 6208-typebearings are modified using electro-erosion to create a3 mm-large hole in the full width of the outer or innerraceway. A photograph of an inner race artificial fault isgiven in Fig. 1. These single point defects are comparableto the worst case of the effect of spalling due to a severeineffective lubrication [10]. The third bearing is a healthyone used as a reference.

2.1 Characteristic bearing faultfrequencies

Faulty bearings characteristic frequencies are theoreticallywell known. Moreover, frequency harmonics due to defectscould appear as combinations of characteristic frequencies,cage and mechanical rotational frequencies. These

characteristic frequencies can be expressed using (1) [11].

forf ¼fr2

Nb 1�Db cos u

Dp

!

firf ¼fr2

Nb 1þDb cos u

Dp

!

fc ¼fr2

1�Db cos u

Dp

!(1)

where:

† forf is the outer race fault frequency;

† firf is the inner race fault frequency;

† fc is the cage frequency;

† fr is the mechanical rotational frequency;

† Nb is the number of balls;

† Db is the ball diameter;

† Dp is the pitch diameter;

† u is the contact angle.

2.2 Bearing effects on vibration signals

For localised defects on one of the elements of the bearing,frequencies previously given in (1) appear in the vibrationspectrum. Moreover, the outer ring natural frequencies will

Figure 1 Photograph of 6208-type bearing with artificialinner race fault

also be excited and modulated with the characteristicfrequencies [10–12]. Consequently, the knowledge ofnatural frequencies of the outer ring of the consideredbearing is of strong interest for vibration analysis. Thesenatural frequencies can be obtained by measurements, finiteelement modal analysis or approximate formulas where theouter ring is considered as a cylinder. The formula (2)given in [13] allows to calculate the natural modes of loworder for a cylinder with a good confidence rate.

fn ¼1

2p

n(n2� 1)

n2 þ 1p

Elh3

12mR4

s(2)

where:

† n is the mode order;

† E is the Young’s modulus of elasticity;

† m is the mass per unit length;

† R is the mean radius of the ring;

† l is the width of the ring;

† h is the thickness of the ring;

Considering the physical and geometrical parameters ofour 6208-type bearing, the approximate frequencies of thenatural modes of the bearing are given in Table 1. Anexample of the vibration spectrum from an accelerometerpositioned near the housing of a 6208-type bearing is givenin Fig. 2. It can be noticed that the frequency values givenby (2) allow to have a good approximation of natural modefrequencies. Moreover, considering the parameters of thebearing, natural modes have high frequencies. It impliesthat the spectral study of vibrations considering the modefrequencies requires a high frequency acquisition system.

2.3 Scalar indicators for the detectionof bearing faults

Many wear processes can lead to bearing failure, includingmechanical damage, lubricant deficiency and corrosion[11]. Generally, the first step of wear is the appearance ofgeneralised fluting or spalling for instance, leading tonumerous pitting points and consequently high-frequency

Table 1 Natural mode frequencies for 6208-type bearing

Mode order Frequency, Hz

2 2309

3 6531

4 12 522

5 20 251

vibrations that can excite natural modes. Thus, the peakamplitude of the vibration signal increases. The last step ofbearing wear often lies in the appearance of severeindentation, considered as localised defects leading toharmonics on the vibration spectrum at combination ofcharacteristic fault frequencies related to the defect location.Thus, the RMS value of the vibration signal increases.

For a discrete signal x of length N and mean x, three majorscalar indicators are thus defined: the Crest factor (3), the Kfactor (4) and the Kurtosis (5) [14]

Crest ¼max(jxj)

ð1=N ÞPN

i¼1 x2i

q (3)

K ¼ max(jxj)1

N

XN

i¼1

x2i

vuut (4)

kurt ¼(1=N )

PNi¼1 (xi � �x)4

(1=N )PN

i¼1 (xi � �x)2h i2

(5)

The evolution of the Crest factor indicates the presence of abearing fault. As a contrary, K factor and kurtosis have to becompared to determined thresholds to detect the presence ofa fault. However, these indicators have to be applied onsignals with a high sampling frequency to take the naturalmodes into account.

2.4 Advanced signal processing methodsfor the detection of bearing faults

Various signal processing methods are used to detect bearingfaults on vibration signals. Three major techniques are oftenpresented. The analytic signal resulting from the vibrationsignal can be computed using the Hilbert transform [15,16]. The spectrum of the corresponding complex envelopeor intrinsic mode functions (IMF) resulting from the

Figure 2 Power spectral density of vibration of a 6208-typebearing

complex envelope allows to detect amplitude modulations atcharacteristic fault frequencies. However, considering thatthe Hilbert transform is obtained through the Fouriertransform (FT), the Hilbert frequency filtering and theinverse FT, this technique induces a high computationcomplexity. In order to detect the appearance of modulationsor multiples of harmonics at characteristic fault frequenciesin vibration spectrum, the cepstrum can be used [17]. Thismethod lies in the computation of twice the FT of thevibration signal, leading to the detection of periodicalphenomena into the spectrum. However, this method alsoinduces a high computation complexity. The third detectionscheme is the computation of the wavelet or wavelet packettransform [18–20]. The difficulty lies in the choice of theappropriated wavelet, regarding the quality of results and thecomputation complexity depending on the wavelet filterlength K and the analysis level J. Finally, although advancedsignal processing techniques are efficient, the resultingcomputation complexities of previous signal processingmethods are given in Table 2 and can be considered as toohigh to use them in low cost industrial applications.

2.5 Vibration spectral energy detector

These observations concerning scalar indicators andadvanced signal processing methods lead us to define amechanical detector based on spectral energy extraction invibration spectrum. Consequently, the computation of thedetector is only based on the acquisition and the achievingof the FT of the vibration signal. The related computationcomplexity is recalled in Table 2. The fault detector isdefined by extracting energies on frequency ranges relatedto the frequency components at multiples of fdef , where fdef

is either the inner or the outer race theoretical characteristicfrequency. Moreover, the frequency ranges are extended toinclude modulations linked to the mechanical speed andcage frequencies. The chosen frequency ranges are given in(6). The proposed indicator uses the relative error of energyin the specified frequency ranges between a faulty andhealthy reference vibration spectrum. A cumulative sum isthen applied on the energy differences extracted from thefrequency ranges. Finally, cumulative sums related to outerand inner race frequency ranges are added. The detectorvalue is then defined as the last value of the cumulative sum.

[nfdef � fc; nfdef þ fc]

[nfdef � fr � fc; nfdef � fr þ fc]

[nfdef þ fr � fc; nfdef þ fr þ fc]

(6)

where n [ [1; 3].

As an example of the detector results, Fig. 3 presents thisindicator for the detection of localised outer race fault with asupply frequency fs ¼ 50 Hz. Notice that Fig. 3 is doublescaled with a factor of 1000 between the two vertical axis.The distinction between healthy and faulty cases can thusbe clearly done. This approach certifies that bearing faultdetection is possible using the energy in the spectrum ofvibration signal. As numerous harmonics due to inner racedefect exist in frequency ranges corresponding to outer racefault and reciprocally, setting fdef ¼ forf or fdef ¼ firf doesnot guarantee the distinction between inner and outer racefaults. Thus, this indicator is built to detect bearing faultswhatever these locations on the bearing, by consideringouter and inner race fault characteristic frequenciesappearance in vibration spectrum.

Comparing to scalar indicators, this indicator needs a lowsampling frequency of vibration signals. As a matter of fact,the frequency ranges used in the detection scheme do notexceed 500 Hz, thus the sampling frequency can be limitedto 1 kHz, comparing to scalar indicators taking intoaccount the natural modes of the outer ring that need asampling frequency often higher than 10 kHz.

3 Mechanical effects in case ofbearing faultBefore studying the detection of bearing faults on statorcurrents of the asynchronous machine, it has to bedemonstrated that bearing defects induce effects onmechanical quantities. Except vibration appearance, twomajor effects of bearing faults on mechanical quantities

Figure 3 Mechanical indicator for outer race fault

Table 2 Computation complexity of vibration signal processing methods for the detection of bearing faults

IMF of Hilbert transform Cepstrum Wavelet transform Wavelet packet transform Spectral energy detector

3 N log2(N ) 2 N log2(N ) 4KN JN (2K 1) N log2(N )

4.5 � 106 3 � 106 5.12 � 106 12.16 � 106 1.5 � 106

Example with N 128 000, K 10, J 5

have to be studied. Firstly, a radial eccentricity can be inducedby the hole on raceways [7]; then, load torque oscillations canbe considered [8].

3.1 Eccentricity due to artificialbearing faults

Artificial bearing faults, considered as severe damagedbearings, may produce a radial displacement of balls whenrolling through the hole. According to the geometricalparameters of the 6208-type bearing and the faultdimensions, the radial displacement of a ball e is expressedas (7).

e ¼ RB 1� 1�R2

h

R2B

s0@

1A (7)

where:

† RB ’ 6.3 mm is the ball radius;

† Rh ’ 1.05 mm is the apparent half-width of the hole onthe surface of the raceway.

Then, the radial displacement of a ball due to the defect isabout 90 mm. It has to be noticed that the other balls are notaffected by the defect.

In normal conditions, when no balls are affected by thedefect, the radial load applied on the bearing, by the weightof the shaft for instance, is distributed on each ball in theload zone of the bearing. When a ball in the load zone isaffected by the defect, it does not support any load.Consequently, other balls in the load zone are subjected toan over-load, inducing an indentation of these balls in theraceways depending on the hardness of materials. In thiscase, according to simulations, the radial displacement ofthe rotor is about 0.3 mm.

Considering the average airgap length of the machine,namely 800 mm, the relative eccentricity induced by thebearing defects equals 0.0375%. According to the literature,using stator current monitoring, a clear detection of at least20% of dynamic eccentricity is ensured [21]. Consequently,the eccentricity induced by bearing defects is considered asnegligible and non-detectable on stator currents.

3.2 Load torque oscillations due tobearing faults

When a ball rolls through a defect, an impact occurs thatinduces vibrations and a resistance to the rotation of thebearing and thus a torque disturbance. The experimentalspectrum of load torque demonstrates the presence ofharmonics at frequencies related to bearing faults. Here, thesupply frequency is chosen equal to the nominal onenamely 50 Hz. Thus, the mechanical speed equals to about

half the supply frequency due to the number of pole pairs(p 2) and the slip of the machine fr ’ fs=p ¼ 25 Hz.The outer race fault frequency is around 89 Hz and theinner race frequency is about 136 Hz. Hence, as anexample, Fig. 4 shows a part of the mechanical load torquespectra around twice the characteristic fault frequency forinner race fault compared to the healthy case. As forvibration analysis, the load torque oscillation frequencies arecombinations of characteristic frequencies of the bearingand rotational frequency. All theoretical combinations donot appear in load torque spectrum and the frequencycontent cannot be theoretically predicted.

Moreover, for many industrial applications, theimplementation of a torque sensor may be a too expensivespending. Consequently, a detector based on load torquespectral analysis has not been yet investigated.

4 Stator current model in caseof bearing faults4.1 Stator current model with loadtorque oscillations

Previous studies on mechanical failures in induction motorshave shown that load torque oscillations induce phasemodulations (PM) on stator current [8, 22, 23].Considering that load torque oscillations are composed of asum of n harmonics of frequencies fn and amplitudes Gn,the load torque on the shaft of the machine can beexpressed using (8). The average load torque is equal to theelectromagnetic motor torque that is considered as aconstant G0.

Gload(t) ¼ G0 þX

n

Gn cos(2pfnt) (8)

In case of slight load torque oscillations, the FT of the statorcurrent expression can be approximated by a phase modulated

Figure 4 Spectrum of mechanical load torque –comparison between healthy and inner race fault cases

signal (9) along the frequency n [22]. In (9), Is is theamplitude of stator current, Ir is the amplitude of rotorcurrent and p is the number of pole pairs of theasynchronous machine. Moreover, one can notice that incase of faulty bearings, the frequencies of load torqueoscillations fn may equal any combination of characteristicfault frequencies underlined by the load torque spectrum.

jFT {i(t)}j ¼ (Isþ Ir)d(n� fs)þ Ir

Xn

bn

2d(n� ( fs + fn)) (9)

where:

bn¼ f (Gn, fn) (10)

In (10), f is an unknown function that has to be characterised.

4.2 Amplitude variation law of sidebandcomponents

The knowledge of the amplitude variation of stator currentsideband components related to the fault frequency, is ofstrong interest for the detection of bearing faults. Thus, thestator current sideband amplitudes at fs + fn are studiedregarding the load torque oscillation frequency. Thecorresponding function bn(fn, fs)=Gn is then studiedregarding fn and fs.

Consider the general model of an electrical drive. On theone hand, the model is composed of a mechanicalsubsystem with load and electromagnetic torques as entriesand rotational speed as output. On the other hand, themodel is composed of an electrical subsystem withrotational speed and stator voltages as entries,electromagnetic torque as output and stator currents asintermediate variables. It is understandable that both themechanical and electrical models must be taken intoaccount to establish the link between stator currents andload torque. In a general approach, mechanical andelectrical transfer functions are at least of first order. Thus,even if mechanical and electrical transfer functions are non-resonant, the corresponding transfer function resulting fromtheir association may present a resonant behaviour with anorder greater or equal to 2. The existence of this resonanceis related to electrical and mechanical parameters values ofthe models.

Due to the product of currents and fluxes to obtain theelectromechanical torque, a complete analytical approachcannot be performed to determine bn(fn, fs)=Gn. To obtainsuitable information concerning the variation law ofsideband components on the stator current with regard tothe load torque oscillation frequency, a simulation approachis proposed. Firstly, a state model of the motor is associatedwith a first-order mechanical model composed of an inertiaplus a friction. An oscillating load torque with variablefrequency fn is added to the mean load torque and

amplitude of sideband components at fs + fn in the statorcurrent are extracted from its spectrum. Using electrical andmechanical parameters of the set-up, the simulationdemonstrates that a natural resonance exists in the drive.Moreover, the resonance characteristics, in terms of gainand frequency, also depend on the motor operating point.Fig. 5 underlines this point by depicting the gain diagram20 log10(bn( fn, fs)=Gn) along the load torque oscillationfrequency fn and the supply frequency of the inductionmachine fs. The level of grey depicts the gain value. In asecond time, a more complete mechanical model isintroduced.

The physical set-up is composed of the asynchronousmotor coupled to a DC motor used as a load. Themechanical system is composed of inertias of the motorand the load, frictions and and a coupling stiffness.Parameters of the mechanical transfer function come fromthe manufacturer datasheets and a mechanical resonancearound 20 Hz can be pointed out. The whole drive model,including the previous mechanical model, is simulated andcompared to measurements achieved on the experimentalset-up. The DC machine is connected to a resistor througha DC/DC converter that controls the DC motor armaturecurrent. In order to obtain the experimental gain diagrambn( fn, fs)=Gn, the reference current of the DC/DCconverter is composed of an oscillating component plus anoffset in order to induce load torque oscillations around amean load torque value. Fig. 6 depicts the experimentalgain diagram for several supply frequencies ( fs 50 Hz,fs 13.3 Hz and fs 6.7 Hz) and the simulated one forfs 50 Hz. The main observation lies in the existence ofan experimental and simulated resonance point aroundfres ’ 20 Hz. It can be noticed that even if the resonanceamplitude varies, the resonance frequency is almostconstant whatever the considered supply frequency. Thisobservation is confirmed by simulation. Comparing to thesimulation results obtained with a first-order mechanical

Figure 5 Simulated 3D gain diagram 20 log10 [bn/Gn] witha non-resonant mechanical transfer function for 20 Hz � fs

� 50 Hz

model (Fig. 5), it can be said that accurately modelling themechanical part of the drive allows to be more realisticin order to predict the whole frequency behaviour of theset-up. According to the frequency response of theelectromechanical test bench and assuming that a bearingdefect creates slight load torque oscillations at one of thecharacteristic frequencies determined in (1), the resonancepoint may be used as a natural amplifier to obtain amplifiedPM harmonics on stator current. It has to be noticed thatgain diagrams depicted in Fig. 6 are deeply associated withthe considered test bench. However, using this simulationmethod, accurately modelling the mechanical system andidentifying electrical parameters of a machine, the gaindiagram of any induction drive may be established.

5 Stator current spectral detectorfor bearing faultsAs shown in Section 3.2, bearing defects induce load torqueoscillations and consequently, PM on stator current.However, the amplitude of these PM is quite slight andcould be buried in noise. Some techniques are used toreduce the stator current signal-to-noise ratio (SNR). Thefast Fourier transform (FFT) of two stator currents isperformed and resulting spectrums from the two phases aremultiplied to correlate signatures [24]. This method allowsimproving the efficiency of fault harmonics detection.

5.1 Definition of spectral indicator S

Similarly to the vibration analysis and according to the statorcurrent model (9), the detector S is defined by extractingenergies on frequency ranges corresponding to the sidebandcomponents at fs + nfdef where fdef is either the inner orthe outer theoretical mechanical fault frequency. Moreover,as for mechanical torque analysis, the frequency content ofstator current in case of bearing faults cannot be

Figure 6 Experimental and simulated gain diagrams ofsideband components on stator current for several supplyfrequencies

theoretically evaluated. Thus, as a contrary to other studiesthat generally focus on the detection of specific harmonics isstator current spectra, such as in [9], the proposed indicatortakes into account the probabilistic nature of stator currentharmonics due to bearing defects. This allows to considerthe possible appearance of numerous harmonics on statorcurrents related to bearing faults by analysing a global energyincrease in frequency ranges. Thus, the frequency ranges areextended to include modulations linked to the cage andmechanical rotational frequencies underlined by the vibrationand the mechanical load torque spectral analysis (see Fig. 4).Chosen frequency ranges are given in (11).

jfs + [nfdef � fc; nfdef þ fc]j

jfs + [nfdef � fr � fc; nfdef � fr þ fc]j

jfs + [nfdef þ fr � fc; nfdef þ fr þ fc]j

(11)

where n [ [1; 5].

Notice that in case of current spectral analysis, themechanical rotational frequency is estimated via slotharmonics on stator current [25]. Moreover, bearingsmanufacturer often provide characteristic frequencies for agiven rotational frequency. According to (1), using theproportionality between rotational speed and characteristicfrequencies, these ones are estimated for the computedrotational speed. For the induction machine under test, themaximum slot harmonic frequency is 750 Hz forthe maximum supply frequency. As a comparison, themaximum frequency analysed in the bearing fault detectionscheme is fs þ 5fi rf þ fr þ fc ’ 765 Hz. Consequently, thesampling frequency can be limited to 2 kHz and thedetection of slot harmonic does not change the samplingfrequency of stator current. In each frequency range, thespectral energy is estimated and normalised by themaximum value in the considered range.

Then, the proposed indicator uses the relative error ofenergy between the current spectrum in faulty and healthycases in the specified frequency ranges. Thus, the relativeerrors of energy extracted from frequency ranges related toouter and inner race fault are added in order to obtain asingle energy difference. Finally, a cumulative sum is usedto build the indicator. Only the last value of the cumulativesum is considered as the detector value.

5.2 Detection of localised faults using theresonance point

To illustrate the computation of the detector values, adetailed example is given for detector S in case of alocalised outer or inner race fault and healthy bearing. Acommon healthy energy reference is used for the threebearing cases. The figures show cumulative sumscorresponding to the computation of detector S. For thedetection of localised faults, three experimental conditionsare tested, corresponding to three different supply

frequencies. In Fig. 7a, the supply frequency fs is tuned to13.3 Hz in order to ensure forf ¼ fres. In Fig. 7b, the supplyfrequency fs is tuned to 6.7 Hz to ensure firf ¼ fres. InFig. 7c, the supply frequency fs is tuned to 50 Hz,corresponding to the nominal supply frequency of themachine. In this case, firf ¼ 136 Hz and forf ¼ 89 Hz andno characteristic fault frequency equals to the resonancepoint. The PM signatures are located in the attenuationpart of the electromechanical gain diagram (see Fig. 6).Fig. 7c underlines that distinction between healthy andfaulty cases is not possible with this detector when thesideband components are strongly attenuated. It emphasisesthe importance of properly tune the supply frequency toensure the detection of a possible bearing fault.

Moreover, as expected, properly tuning the frequencysupply leads to focus on inner or outer race fault. When fsis set to guarantee forf ¼ fres, the effects on stator currentsof load torque oscillations due to the outer race localisedfault are amplified by the resonance point and the detection

of the outer race fault is ensured. Reciprocally, using thesimilar amplification effects, the detection of the inner racefault is ensured when fs is set to guarantee firf ¼ fres.

5.3 Detection of naturally damagedbearing using the resonance point

The detector S is applied on stator currents to detect faults onnaturally damaged bearings that was rejected by a vibrationanalysis performed in the after-sales service of a motormanufacturer. The fault types or locations are unknown.According to the detection scheme and the exploitation ofthe resonance point, the detector S is computed in healthyand faulty cases for the two emphasised operating points(fs ¼ 6:7 Hz and fs ¼ 13:3 Hz). In case of the detection ofpossible inner race fault (fs ¼ 6:7 Hz), the faulty detector isclearly higher than the healthy one which is close to zero asit can be seen in Fig. 8. This result proves that inner racefaults affect the damaged bearing. A vibration spectrum isalso performed to reinforce the assumption of the presence

Figure 7 Cumulative sums of relative error in %

a forf ’ fres

b firf ’ fres

c fs ¼ 50 Hz

of inner race defects. Several fault harmonics related to innerrace characteristic frequency appear in the vibration spectrumaccording to Table 3.

5.4 Discussions on the proposed indicator

The proposed indicator is restricted by the electromechanicalbehaviour of the experimental set-up. This resonance allowsto amplify the effects of load torque oscillations on statorcurrent and consequently improve the detection efficiency.Consequently, the characteristic fault frequencies forf or firf ,depending on the rotational frequency and thus on the supplyfrequency of the induction machine, have to be close to theresonance frequency. This is achieved by tuning the supplyfrequency to ensure that one of the characteristic frequenciesequals the resonance point. Moreover, it means that thedetection of bearing defects by the proposed indicatorbecomes underachiever for any other supply frequency,especially for the nominal supply frequency where thecharacteristic fault harmonics are high frequency, filtered bythe electromechanical gain diagram depicted in Fig. 6.Consequently, the detection of bearing faults is necessarilydetermined by the electromechanical behaviour of the systemand the ability of tuning the supply frequency of the inductionmotor to take into account the possible resonance points.

It can be noticed that this indicator is less sensitive than theone based on vibration signals. However, the interest of thismethod lies especially in the cost of instrumentation.Vibration analysis needs well positioned accelerometers neareach bearing that has to be monitored. This instrumentationis often incompatible with low cost drives such as inductiondrives. As a comparison, the monitoring based on statorcurrent analysis only needs current sensors such as Halleffect sensor or current transformer such as Rogowski coilsensor [26]. These sensors are often already used for controland protection purposes. Moreover, as for the vibrationspectral detector, the stator current indicator needs a lowsampling frequency especially for low supply frequencies.

Figure 8 Cumulative sums of relative error in % for thedetection of naturally damaged bearing

5.5 Suggestions for the choice of adetection method

The choice of a detector depends on the monitored system.When the supply frequency is variable and can be set to alow value, depending on the electromechanical behaviour ofthe system, the stator current spectral indicator can be usedto detect faults due to wear on bearings. This method isparticularly appropriated for industrial systems where adiagnosis procedure can be operated periodically, forinstance before starts of the mission of the machine.

However, when the machine is running at a unique speedthat does not allow to use the resonance point, the vibrationanalysis has to be used. In this case, the automatic detectorcan be preferred to scalar indicators or advanced signalprocessing methods due to the high computationperformances required. In order to follow the wear processof bearings, the scalar indicators are well appropriated butthe acquisition system has to be of high frequency sampled.

6 ConclusionsIn this paper, some methods for the detection of bearingfaults in induction motors using vibration and statorcurrent monitoring have been presented. On artificiallydamaged bearings, a vibration spectrum analysis has beenproposed to detect and diagnose the faults. This methodhas been compared to classical techniques such as scalarindicators and advanced signal processing methods.Mechanical considerations have shown that bearing defectsinduce preferentially load torque oscillations comparing toeccentricity. Thus, the effects of load torque oscillations onstator current have been recalled. The amplitude variationlaw of the stator current components has been determinedby experimental measurements and simulation results. Theresonance point has been used to amplify slight load torqueoscillations and to allow detecting preferentially inner orouter race fault. An automatic detector based on statorcurrent spectral analysis has been presented and validatedon localised faults and naturally damaged bearing.

Comparison between vibration and stator current indicatorshas been presented. Restrictions of the detector concerning its

Table 3 Example of fault harmonics in vibration spectrum ofa naturally damaged bearing for fr 25 Hz

Harmonic frequency Energy variation, dB

firf þ fr �fc

2

þ21

2firf �fc

2

þ26.5

2firf þ31

3firfþ fr fc þ27

3firfþ fr þ18.8

definition and the consideration of the electromechanicalbehaviour of the test bench have been discussed. This hasled to indications concerning the choice of detectionmethods depending on the considered system. Compared tovibration analysis, the stator current detector needs lessexpensive instrumentation. However, the vibration indicatoris usable in several applications. To extend the application offault detection, condition monitoring on variable speeddrives could be studied by using time-frequency or timescale analysis to detect bearing faults at the start-up of themachine. Moreover, other faulty conditions such aslubricant contamination or grease wear could be investigatedon stator current along the lifetime of the bearing. Finally,other mechanical quantities such as mechanical speed ortorque can be studied by measurements or estimation.

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