Journal of Signal and Information Processing, 2013, 4, 72-79
doi:10.4236/jsip.201343B013 Published Online August 2013 (http://www.scirp.org/journal/jsip)
A Study of Motor Bearing Fault D i ag nosis using
Modulation Signal Bispectrum Analysis of Motor
Current Signals
Ahmed Alwodai1, Tie Wang2, Zhi Chen2, Fengshou Gu1, Robert Cattley1, Andrew Ball1
1Centre for Efficiency and Performance Engineering, University of Huddersfield, Queensgate, Huddersfield HD1 3DH, UK;
2Department of Vehicle Engineering, Taiyuan University of Technology Taiyuan, Shanxi Province, China
Received April, 2013.
ABSTRACT
Failure of induction motors are a large concern due to its influence over industrial production. Motor current signature
analysis (MCSA) is common practice in industry to find motor faults. This paper presents a new approach to detection
and diagnosis of motor bearing faults based on induction motor stator current analysis. Tests were performed with three
bearing conditions: baseline, outer race fault and inner race fault. Because the signals associated with faults produce
small modulations to supply component and high nose levels, a modulation signal bispectrum (MSB) is used in this
paper to detect and diagnose different motor bearing defects. The results show that bearing faults can induced a detest-
able amplitude increases at its characteristic frequencies. MSB peaks show a clear difference at these frequencies whe-
reas conventional power spectrum provides change evidences only at some of the frequencies. This shows that MSB has
a better and reliable performance in extract small changes from the faulty bearing for fault detection and diagnosis. In
addition, the study also show that current signals from motors with variable frequency drive controller have too much
noise and it is unlikely to discriminate the small bearing fault component.
Keywords: Induction Motor; Motor Current Signature; Power Spectrum Bispectrum; Motor Bearing
1. Introduction
A general review of monitoring and fault diagnosis tech-
niques are studied in [1, 2]. The different faults in an
electrical machine can be classified as follows [3]:
Figure 1. Components of the rolling ball bearing.
 Stator faults, for example, short circuit, loss of a sup-
ply phase.
 Rotor faults, for example, broken bar, broken end-
ring.
 Static and dynamic eccentricities.
 Bearing faults.
Studies have shown that the common faults in induc-
tion motors (about 40%–50%) happen in rolling bearings,
depending on the type of installation, the motor size, and
the supply voltage [4]. In general it is due to manufac-
turing faults, lack of lubrication, installation errors and
wear and tear. According to the affected elements, shown
in Figure 1, bearing faults can be classified as inner ring,
outer ring, ball element and cage faults.
The inner ring is mounted on the shaft of the machine
and is usually the rotating part whereas the outer ring is
fixed in the housing of the machine and in most cases it
does not rotate. The rolling elements may be balls, cylin-
drical rollers, spherical rollers, tapered rollers or needle
rollers. They rotate against the inner and outer ring race-
ways and transmit the load acting on the bearing via
small surface contacts separated by a thin lubricating
film. The cage separates the rolling elements to prevent
metal-to-metal contact between them during operation.
Seals are important for protection of bearing from con-
tamination and keep the lubricant inside the bearing sur-

A Studyof Motor Bearing Fault Diagnosis using Modulation Signal Bispectrum Analysis of Motor Current Signals 73
roundings.
2. Bearing Fault Modes
This paper considers rolling-element bearings with a
geometry shown in Figure 2. The bearing consist essen-
tially of the outer and inner raceways, the balls, and the
cage, which keeps the distances between the balls equals.
The number of balls is Nb, their diameter is Db, and the
pitch diameter is Dp. The point of contact between a ball
and the raceway is characterized by the contact angle β.
Bearing faults can be classified into distributed and
localized defects [5]. Distributed defects affect a whole
region and are difficult to characterize by distinct fre-
quencies. On the other hand, single-point defects are lo-
calized and can be classified according to the following
affected element:
 Outer raceway defect
 Inner raceway defect
 Ball defect
 Cage defect
With each type of bearing fault, a characteristic fre-
quency can be associated. This frequency is correspond-
ing to the periodicity by which an irregularity appears
due to the existence of the fault. The characteristic fre-
quencies are functions of the bearing geometry and the
mechanical rotor frequency fr. For the four considered
fault types, the characteristic frequency takes the follow-
ing expressions[3, 5]:
Figure 2. Geometry of a rolling-element bearing.
bb
r
p
ND
f(1 cosβ)
2D
o
f (1)
(1cos )
2
bb
ir
p
ND
ff
D

 (2)
2
2
2
(1cos )
pb
br
bp
DD
ff
DD

 (3)
1(1cos )
2
b
cr p
D
ff
D

 (4)
where fo is the outer race fault frequency, fi is the inner
race fault frequency, fb is the ball fault frequency and fc is
cage fault frequency.
The characteristic fault frequencies are the result of the
absolute motion (vibration) of the machine. The stator
current is not affected by the absolute motion of the ma-
chine, but rather by a relative motion between the stator
and rotor (i.e., changes in the air gap). In the instance of
a bearing fault, the characteristic fault frequencies are
essentially modulated by the electrical supply frequency.
3. Bearing Fault Detection by Stator Current
Analysis
The most often mentioned model studying the influence
of bearing damage on the induction machine stator cur-
rent was presented by Schoen etal [6]. The author con-
siders the generation of rotating eccentricities at bearing
fault characteristic frequencies fv, which leads to peri-
odical changes in the machine inductances. This should
produce additional frequencies fbfin the stator current,
which can be predicted by:
bfs v
f
fkf (5)
where fs is the electrical supply frequency, fv is one of the
four characteristic fault frequencies defined by Equation
1 through Equation 4 .and k = 1, 2, 3...
This model has been used in several recent works [6-8].
In [6], two types of faults were tested, namely a hole
drilled through the outer race and indentation produced
in both the inner and outer surfaces. For both faults, the
vibration and current spectra are analyzed in both loaded
and unloaded motor cases. The first faulty condition
(outer race defect)is characterized by fo and 2fo compo-
nents in the vibration spectrum and |fs ± fo| and |fs ± 2fo|
com- ponents in the current spectrum. The second fault
(inner race defect) is highlighted byfo, 2fo, and fi compo-
nents in the vibration spectrum and |fs ± fo|, |fs± 2fo|, and
|fs ± fi| components in the current spectrum. The authors
claim that the characteristic fault frequency components
are relatively small when compared to the rest of the
current spectrum. The largest components occur at mul-
tiples of the supply frequency and are caused by satura-
tion, winding error distribution, and supply voltage
changes. However, an evaluation of the amplitude of
these largest components in different cases (healthy and
two types of fault condition) is not shown. In [7], two
inner race faults (spalls and drilled hole) are analyzed,
and the authors point out a problem related to the ex-
perimental simula- tion of bearing faults: The act of dis-
assembling, re- mounting, and realigning the test motor
can significantly alter the vibration and current spectra.
The results show that, for both defects, the characteristic
fault-frequency components are clearly visible only in
the vibration spec- trum and not in the current spectrum.
Both inner and outer raceway defects are analyzed in [8].
They show some differences in the amplitudes of the

A Studyof Motor Bearing Fault Diagnosis using Modulation Signal Bispectrum Analysis of Motor Current Signals
74
current spec- trum of a 1.5 kW induction motor at full
load, but the characteristic fault-frequency components
do not stand out clearly.
A new analytical model was suggested by [3] to take
into account the load-torque variations caused by bearing
faults in addition to the effect of relative motion between
rotor and stator. In this way, new frequencies in the
current spectrum are identified for the defects in the inner
raceway.
isri
f
ffkf
 (6)
In [9] a three-phase 2.2-kW two-pole induction motor
was used and the motor is equipped with two rolling ball
bearings, type 6205Z, with nine balls, lubricated with
grease. The research presents four different types of
bearing defects namely, crack in the outer race, hole in
the outer race, deformation of the seal, and corrosion.
The tests are performed under no-load and full-load.
The faults in the outer race have noticeable effects on
the current spectrum, both in load and no-load conditions;
the result shows a considerable increase of the third and
seventh harmonic components at no load, and an increase
of the even harmonics at high frequencies in the load
condition. In case of no-load the second harmonic (k=2)
of the predicted frequency obtained by Equation. 5 exist
on the other hand it does not appear under the load con-
ditions studied.
In general previous studies have demonstrated the ca-
pability of current power spectrum based bearing fault
signatures to detect bearing faults and produced diagnos-
tic features of different bearing faults. However, because
of high background noise levels of the current signals,
especially when the motor is supplied by a variable speed
drive (VFD), the features are often very weak.
This paper will examine the motor current spectra of
healthy, outer race faults and inner race faults of an un-
loaded machine supplied with and without a VFD. To
confirm the existences of the bearing characteristic fre-
quencies, the motor is disconnected from the test rig and
connected to an independent power supply directly to
reduce the noise which is caused by the inverter and
drive couplings. The current signals are analyzed by both
power spectrum (PS) and modulation signal bispectrum
(MSB), The latter analysis technique is a modified bis-
pectrum analysis and has been demonstrated in previous
studies to have good performance in noise reduction [13,
14] and is expected to produce more reliable bearing
fault detection than that of power spectrum.
4. Analysis Techniques
4.1. Power Spectrum
The power spectrum method is generally used to describe
the power distribution of the current signal in the fre-
quency domain. Usually it is calculated using Fourier
transform (FT) by:



*()

P
fEXfXf (7)
Where


Xf and its conjugate are the
Fourier transform of the signal sequence
*()Xf


,
x
nand E{.} is
the expectation operator.
4.2. Conventional Bispectrum
The bispectrum analysis is a type of higher order spectra,
which is used by a large number of researchers since the
1980s [10] in different fields such as communications
and medicine. Given a discrete time current signal x(n),
its discrete Fourier transform (DFT), X(f) is defined to be

2
()
j
fn
k
Xf xne



 (8)
According to [11] the conventional bispectrum can be
defined as








*
12121 2
,(BffEXfXf Xff) (10)
Wheref1, f2 and f1+ f2 indicate the individual frequency
components achieved from Fourier series integral.
Bispectrum analysis has a number of unique properties
such as nonlinear system identification, phase informa-
tion retention and Gaussian noise elimination when
compared with power spectrum analysis. Especially,
bispectrum is an effective tool for detecting quadratic
phase coupling which occurs when two waves interact
non-linearly and generate a third wave with a frequency
and phase equal to the sum (or difference) of the first two
waves.
A summary of the various bicoherence estimators can
be found in [12]. The definition of squared bicoherence
used in Equation 11 is chosen because it is bounded be-
tween 0 and 1 which is useful for comparing the degree
of nonlinearity or coupling effect between different sig-
nals.






2
1, 2
2
12 22
12 12
,
()
Bff
bff EXfXfEXf f  (11)
A normalized form of the bispectrum or bicoherence is
usually used to measure the degree of coupling between
coupled components. The bicoherence is close to 1 if
there are nonlinear interactions among frequency combi-
nations f1, f2 and f1+ f2. On the other hand, a value of
near 0 means an absence of interactions between the
components.
4.3. Modulation Signal Bispectrum (MSB)
Equation 10 includes only the presence of nonlinearity
from the harmonically related frequency components: f1,

A Studyof Motor Bearing Fault Diagnosis using Modulation Signal Bispectrum Analysis of Motor Current Signals 75
f2 and f1+f2. It overlooks the possibility that the occur-
rence of f1-f2 might be due to the nonlinearity between f1
and f2as well. Because of this, it is not adequate to de-
scribe amplitude modulation (AM) signals such as motor
current signals.
Figure 3. Outer race fault.
Figure 4. Inner race fault.
To improve the performance of the conventional bis-
pectrum in characterizing the motor current signals, a
new variant of the conventional bispectrum, named as a
modulation signal bispectrum (MSB) is examined in [13,
14] as in Equation 12







**
1, 2212122MS
Bff EXffXffXfXf

(12)
Furthermore, to make a direct comparison with power
spectrum in Equation 7 a normalized version of Equation
12 is introduced as:







1, 2
**
22
21 21
22
MSN
Bff
X
fXf
EXff XffXfXf











(13)
In Equation 13 the amplitude of
*
2
2
()
|()|
X
f
X
f which re-
lates to carrier component f2 is unity. Thus the amplitude
of the modulation signals bispectral peaks are determined
purely by the magnitude of the sideband components. In
other words the resultant modulation signal bispectral
magnitudes are independent of the amplitude of the car-
rier component at supply frequency and hence can be
directly compared with that of power spectrum.
4.4. Bearing Faults and Test Setup
Two types of common bearing faults have been tested in
this study. The first one, an abrasive wear in the outer
race has been considered; which models that caused by
friction between ball and outer race surfaces due to lack
of lubrication as shown in Figure 3, while the second
case of fault is an inner race defect as shown in Figure 4.
To analyze the current signals, a dataset is acquired in
a motor rig under different simulated fault cases and
operating conditions. Figure 5 shows the schematic
diagram of the test facility employed to examine motor
stator faults. The system consists of an induction motor,
variable speed controller, supporting bearings, couplings
and DC generator as a load. The test motor is a three-
phase induction motor with rated output power of 4 kW
at 1420 rpm (two-pole pairs). The motor has 28 rotor
bars and 36 stator slots. Two rolling ball bearings, type
6206ZZ deep groove ball bearing measuring 30x62x16
mm, with nine balls (Nb=9),Db=9.52 mm and Dp=46.0
mm, are used to support the rotor . To change the speed
of the test motor, a digital variable speed controller is
attached to the test rig between the power line source and
the motor. The controller can be programmed to any
specific shaft rotation speed between 0 and 1500rpm.
The induction motor is directly coupled with a DC
generator. The field of the generator is connected to a DC
source through a controller while the generated power
was fed back to the mains electrical grid via an inverter
and the load on the induction motor can be adjusted by
changing the field resistance of the DC generator. The
operating load can be varied from no load to full load via
the control panel.
A power supply measurement unit was designed to
measure the instantaneous AC voltages, currents and
power, using hall-effect voltage and current transducers
and a universal power cell by the University staff. A
shaft encoder, mounted on the shaft end produces 100
pulses per revolution for measuring the motor speed. A
piezoelectric accelerometer, mounted on the bearing
end-caps, is used to measure vibration of the motor. The
accelerometer has a sensitivity of 5.0 mV/ms2 with a
frequency range from 0.5 to 5000Hz, the current
transducer has a sensitivity of 0.1A/V and a measurement
range of 50A which allows the small changes of current
and vibration to be measured with adequate accuracy.
During the tests the data was acquired using a GST
YE6232B high speed data acquisition system. This
system has 16 channels, each with 24 bit resolution, a
maximum sampling frequency of 96 kHz, which allows
the details of the 50Hz component, the high order supply
harmonics, rotor bar pass frequency, stator bar pass
frequency and motor bearing frequency to be recorded
for further analysis.

A Studyof Motor Bearing Fault Diagnosis using Modulation Signal Bispectrum Analysis of Motor Current Signals
76
Figure 5. Schematic of induction motor te st rig.
To evaluate the performance of PS and MSB analysis,
current signals were collected under three different motor
conditions: healthy motor, outer race fault and inner race
fault and under four successive load conditions: zero,
25%, 50% and 75% of full load, which allows the
diagnostic performance to be examined at different loads
and avoid any possible damage to the test system at the
full load when the faults are simulated. However,
because of noises which are caused by controller, the
characteristic bearing fault frequencies were difficult to
differentiate from complex spectrum patterns. The motor
was then disconnected from the loading system and the
test was carried out with and without the controller and
the results will be discussed in next section.
In the meantime vibration signals were also measured
under healthy and two bearing faults to confirm the ef-
fectiveness of fault induced based on the vibration fre-
quencies values which calculated by Equation 1 to Equa-
tion 4.
5. Results and Discussions
The dataset is processed off-line using a Matlab program
which implements PS and MSB calculations simultane-
ously with a 4-term Blackman-Harris window and 100
times of average. In this way they can be compared di-
rectly in the performance of identifying the characteristic
frequencies and quantifying their spectral peaks.
5.1. Effect of Controller
The phase current signal is firstly examined under dif-
ferent supply cases (with and without controller). Before
exploring the current spectrum, vibration signals are
examined to confirm the introduction of the faults.
Figure 6 shows the vibration spectrum for both the
outer race and inner race faults. The characteristic fre-
quency and their harmonics are clearly shown. In addi-
tion, the amplitude at the fundamental frequency fi is
higher than that of fo, indicating that the fault from inner
race may be higher than that of the outer race. These then
shows that the two types of faults have been induced
with sufficient severity so that the vibration based me-
thod can detect them.
Figure 7 shows a comparison of current spectrum be-
tween a healthy case and two faulty bearings under four
different loads with the VFD controller. To highlight the
small components, the Y-scale is fixed to 0.4A. It is dif-
ficult to find the spectrum components at the characteris-
tic frequencies suggested in Equation 5 due to bearing
faults for all load conditions. Instead there are clear
peaks at frequencies (fs±fr) which become higher with
faults. In addition the peak values decreases with the
increase of load. These changes show that there is no-
ticeable eccentricity which may be induced to the rotor
system when refitting the faulty bearings. It may indicate
that the eccentricity induced changes mask the changes
due to bearing faults. In addition, the controller will
cause high level of noise because VFD provides a pulse
width modulated signal source, which may also mask the
small component at bearing characteristic frequencies.
050100 150 200 250300 350 400 450 500
0
0. 2
0. 4
(a) Vi brati on Si gnal Wit hout Control l er
Frequency (Hz)
A m plit ude (m/ s
2
) Oute r Race
050100 150 200 250300 350 400 450 500
0
0. 2
0. 4
(b) Vi brati on Si gnal Wit hout Control l er
Frequency (Hz)
A m plit ude (m / s
2
) Inner Race
fo=89.5
2*fo=179 3*fo= 268.6
4*fo=35 8.1
fi= 1 35.4
2*fi=270.7
5*fo= 447.6
fi+50=185.4 3*fi=406.1
2*fi-50=220.7
Figure 6. Spectrum of vibration for faulty be ar ings.
0100 200 300 400500 600 700 800 900 1000
0
0.2
0.4 (a) Curre nt S pe ct ru m und er Loa d=0(%)
Frequency(Hz)
Ampli tude(A)
Healthy
Outer Race
Inne r Ra ce
0100 200 300 400500 600 700 800 900 1000
0
0.2
0.4 (b ) Current Spectrum u nder L oad=25(%)
Frequency(Hz)
Amplitude(A)
0100 200 300 400500 600 700 800 900 1000
0
0.2
0.4 (c) Current Spe ct ru m und er Loa d=50(%)
Frequency(Hz)
Amplitude(A)
0100 200 300 400500 600 700 800 900 1000
0
0.2
0.4 (d ) Current Spectrum u nder L oad=75(%)
Frequency(Hz)
Ampli tude(A)
fs±fr
fs±fr
fs± fr
fs±fr
3*fs 5*fs 7*fs
3*fs
3*fs
3*fs
7*fs
7*fs
7*fs
5*fs
5*fs
5*fs
Figure 7. Current spectra with controller.

A Studyof Motor Bearing Fault Diagnosis using Modulation Signal Bispectrum Analysis of Motor Current Signals 77
To eliminate these two types of noise and other possi-
ble influences caused by downstream components such
as generators and couplings, the motor was disconnected
from the control system and connected directly to main
power supply. The unloaded machine was then tested
under three corresponding conditions, namely, healthy,
outer race and inner race faults. Figure 8 presents the
spectrum of the phase current from the unloaded motor
with and without the controller.
The spectrum with controller shown in Figure 8(a)
has very rich frequency components which include not
only the harmonics of supply frequency but also distinc-
tive components at 100Hz, 200Hz etc. The later indi-
cates certain degree of the imbalance of the supply sys-
tem. Moreover, the background noise level is more than
40dB higher than that of the case without controller. This
shows that it is likely the bearing fault frequency is
masked by the background noise. Therefore, further
study of current signature analysis is carried out under
the condition of no-controller and no-load. Considering
the small components and complicated spectrum pattern
due to bearing faults and high order harmonics, more
advanced MSB analysis along with PS analysis will be
used to process the measured signals.
5.2. Outer Race Fault Detection and Diagnosis
Figure 9 shows the results of MSB and PS analysis for
both the healthy and faulty outer race cases in the fre-
quency ranges around the first two harmonics of bearing
fault frequency. For the healthy case both types of spec-
tra do not show significant peaks at the characteristic
frequencies of fs± fo and fs± 2fo forPS orfo and 2fo for
MSB. For the faulty case clear peaks can be observed at
some of these frequencies. MSB shows distinctive peaks
at both fo and 2fo. However, from PS spectra only one
spectral peak at fs-2fo can be discriminated in Figure 9(b2)
and the rest of three peaks cannot be determined due to
high background noise level. This shows that MSB have
better capability to separate the small bearing features
from noisy measurement.
To show more details of the spectrum changes, Table
1 summarizes the peak values at the characteristic fre-
quencies of interest. For comparison the peak values at
corresponding frequency are also listed even if they are
not very distinctive in the spectrum. The table shows the
peaks for the faulty one are higher than that of the
healthy one, showing that faulty bearings cause more
fluctuation in the current signal, which is consistent with
that predicted in theory.
Moreover, MSB peaks show higher percentage in-
creases at both of the peaks compared with that of PS.
This demonstrates that MSB has a better diagnosis capa-
bility. Especially, it shows that the peak increase at 2fo is
higher than atfo, which shows is agree with the the spec-
trum results of vibration shown in Figure 6(a) in that the
fault induce higher amplitude in the second harmonic
component.
100 200 300400 500600 700800 9001000
-100
-80
-60
-40
-20
0
20 (a) Phase Current Wit hout Cont rol l e
r
Frequency (Hz )
Amplitude (dB)
Baseline
Outer Rac e
Inner Rac e
100 200 300400 500600 700800 9001000
-100
-80
-60
-40
-20
0
20 (b) Phase Current Wi t h Control l er
Frequency (Hz )
Amplitude (dB)
Baseline
Outer Rac e
Inner Rac e
Figure 8. Current spectra with controller and without con-
troller.
Table 1. Comparison of spectral peaks for outer race fault.
Spectral PeakHealthy[1E-6] Faulty[1E-6] [1E-6] [%]
MSB at fo 0.0007 0.0072 0.0065 916
PS at fs-fo 0.0182 0.1191 0.1009 553
PS at fs+fo 0.0032 0.0106 0.0074 231
MSB at 2fo 0.00015 0.00345 0.003302154
PS at fs-2fo 0.00342 0.02254 0.01912559
PS at fs+2fo 0.00082 0.00804 0.00722877
5.3. Inner Race Fault Detection and Diagnosis
Figure 10 shows the results of MSB and PS analysis for
both the healthy and faulty inner race cases in the fre-
quency ranges around the first two harmonics of bearing
fault frequency. For the healthy case both types of spec-
tra do not show significant peaks at the characteristic
frequencies of fs± fi and fs± 2fi for PS or fi and 2fi for
MSB. For the faulty case clear peaks can be observed at
most of these frequencies. MSB shows distinctive peaks
at both fi and 2fi,. Especially, the peak at 2fi is quite dis-
tinctive as shown in Figure 10(b1). Without double, the
presence of the inner race fault can be detected by MSB
analysis. From PS spectra, three peaks can be determined
at Figure 10 (a2), (b2) and (b3). However, the peak at
fs+fiin Figure10 (a3) cannot be resolved properly and
has higher amplitude than that of healthy case. Because
at least one set of sideband can be found it is possible
now to detect the inner race fault by SP analysis. This

A Studyof Motor Bearing Fault Diagnosis using Modulation Signal Bispectrum Analysis of Motor Current Signals
78
also shows that PS is capable to detect the fault when the
se- verity is higher which is confirmed by the vibration
spectrum shown in Figure 6. In other words, PS is less
reliable in detecting this inner race compared with MSB
analysis.
86 88 90 92 94
0
1
2
3
x 10
-8

89.51
7.22e-00
(a1) MS B c los e t o
fo
Frequency(Hz)
C urrent(A
4)
9
Healthy
Faulty
176 178180 182
0
0.5
1
1.5
x 10
-8

179
3.45e-00
( b1) MSB close to
2fo
Frequency(Hz)
C urrent(A
4)
9
36 38 40 42 44
0
2
4
x 10
-7

39.56
1.19e-00
(a 2) PS close to
fo-fs
Frequency(Hz)
C urrent(A
2)
7
126 128130 132
0
0.5
1
x 10
-7

129.1
2.25e-00
(b2) PS close to
2fo-fs
Frequency(Hz)
C urrent(A
2)
8
136138140 142 144
0
2
4
x 10
-8

139.5
1.06e-00
(a3) PS close to
fo+fs
Frequency(Hz)
C urrent(A
2)
8
226 228230 232
0
2
4x 10
-8

229
8.04e-00
(b 3) PS close to
2fo+fs
Frequency(Hz)
C urrent(A
2)
9
Figure 9. Spectrum in the frequency range close to fo and
2fo.
To show more details of the spectrum changes, the
peak values at characteristic frequencies of interest are
also summarized, shown in Table 2. For comparison the
peak value at fs+fiis also listed even though it is not dis-
tinctive and has higher amplitude than the healthy case in
the spectrum. The table shows that the peak values for
the faulty one are higher than that of the healthy one ex-
cept for the peak at fs+fi, showing that faulty bearings
cause more fluctuation in the current signal, which is
consistent with that predicted in theory.
Moreover, MSB peaks show higher percentage in-
creases at both of the peaks compared with that of PS.
This demonstrates that MSB has a better diagnosis capa-
bility. Especially, it shows that the peak increase at 2fi is
higher than at fi, which is agree with the spectrum results
of vibration shown in Figure6(b) in that the fault induce
higher amplitude in the second harmonic component.
However, comparing the amplitude increases between
Table 1 and Ta bl e 2 has found that the amplitudes of the
inner race fault are smaller than that of outer race fault.
This is not very consistent with that of vibration results
show in Figure 6. However, this less amplitude changes
may be due to the higher attenuation in the high fre-
quency range of the induction motor, which can be un-
derstood in the spectra of Figure 8 in which the spectral
amplitude has a monotonic decrease trend with the in-
creasing of frequency. Based on this frequency response
characteristics the amplitude changes at fi, and its har-
monics will be lower because fi, is higher than fo.
Table 2 Comparison of spectral peaks for inner race fault.
Spectral PeakHealthy[1E-6]Faulty[1E-6] [1E-6] [%]
MSB at fi 0.0058 0.0174 0.0116 200
PS at fs- fi 0.1075 0.6741 0.5666 527
PS at fs+ fi0.0036 0.0021 -0.0016-43
MSB at 2fi0.000294 0.001578 0.001284437
PS at fs- 2fi0.000901 0.003153 0.002252249
PS at fs+ 2fi0.000309 0.001685 0.001376445
132 134 136138
0
2
4
6
8
x 10
-8

135.1
1.74e-00
Frequency(Hz)
Current(A
4)
(a1) MSB cl os e t o
fi
8
Healthy
Faulty
266 268270 272
6
x 10
-9
274
0
2 
270.5
1.58e-0
4
0
Frequency(Hz)
Current(A
4)
(b1) MSB cl os e t o
2fi
9
82 84 86 88
0
1
2
3
x 10
-6

85
6.74e-00
Frequency(Hz)
Current(A
2)
(a 2) PS clos e to
fi-fs
7
216 218220 222
1.5 x 10
-8
224
0
0.5
1

220.5
3.15e-00
Frequency(Hz)
Current(A
2)
(b2) PS clos e to
2fi-fs
9
182 184 186188
0
0.5
1x 10
-8

185
2.07e-00
Frequency(Hz)
Curr ent(A
2)
(a3) PS clos e to
fi+fs
9
316 318320 322
8x 10
-9
324
0
2
4
6

320.5
1.69e-00
Frequency(Hz)
Curr ent(A
2)
(b3) PS close to
2fi+fs
9
Figure 10. Spectrum in the frequency range close to fi and 2
fi.
6. Conclusions
MSB analysis is evaluated using motor current signals to
detect and diagnosis motor bearing faults. From its spec-
trum presentations, it can be found that MSB show a
simpler spectrum structure compared with the power
spectrum. It means that MSB shows peaks only at kfo and
kfi for outer race and inner race faults respectively whe-
reas power spectrum shows peaks at (fs±kfo) and (fs±kfi)
which cause difficulty to be identified them when the
spectrum components are rich. Moreover MSB pro- duc-
es more accurate amplitude estimate due to its ca- pabil-
ity of noise reduction and non-modulation compo- nent
removal.
With MSB analysis the motor current can be used to
detect and diagnosis bearing faults when the motor oper-
ates without VFD controller under no-load condition.
The VFD induces too much noise into the system and it
is not possible to discriminate the small bearing compo-

A Studyof Motor Bearing Fault Diagnosis using Modulation Signal Bispectrum Analysis of Motor Current Signals
79
nent for condition monitoring.
The bearing fault causes amplitude increases at the
characteristic frequencies corresponding to outer race
and inner race faults. MSB produces a reliable difference
at these frequencies whereas PS only provides change
evidences at some of the frequencies. This shows that
MSB has a better performance in extract small changes
from the faulty bearing for fault detection and diagnosis.
REFERENCES
[1] D. Basak, A. Tiwari and S. P. Das, “Fault Diagnosis and
Condition Monitoring of Electrical Machines—A Re-
view,” in Proc. IEEE ICIT, 2006, pp. 3061–3066.
[2] M. E. H. Benbouzid, “A Review of Induction Motors
Signature Analysis as a Medium for Faults Detection,”
IEEE Transactions Industrial Electron, Vol. 47, No. 5,
2000, pp. 984–993.doi:10.1109/41.873206
[3] M. Blödt, P. Granjon, B. Raison and G. Rostaing, “Mod-
els for Bearing Damage Detection in Induction Motors
Using Stator Current Monitoring,” IEEE Transactions On
Industrial Electronics Vol. 55, No. 4, 2008, pp.
1813-1822.doi:10.1109/TIE.2008.917108
[4] A. Shrivastava and S. Wadhwani, “Condition Monitoring
for Inner Raceway Fault of Induction Motor Ball Bear-
ings,”International Journal of Electrical Engineering,
Vol. 5, 2012, pp. 239-244.
[5] J. Stack, T. G. Habetler and R. G. Harley, “Fault Classi-
Fication and Fault Signature Production for Rolling Ele-
ment Bearings in Electric Machines,” IEEE Transactions
Industrial Applications, Vol. 40, 2004, PP. 735–739.
[6] R. R. Schoen, T. G. Habetler, F. Kamran and R. Bartheld,
“Motor Bearing Damage Detection Using Stator Current
Monitoring,” IEEE Transactions Industrial Applications,
Vol. 31, No. 6, 1995, pp. 1274–1279.
doi:10.1109/28.475697
[7] R. R. Obaid, T. G. Habetler and J. R. Stack, “Stator Cur-
rent Analysis for Bearing Damage Detection in Induction
Motors,”in Proc. SDEMPED,Atlanta, 2003, pp. 182–187.
[8] I. Rodríguez and R. Alves, “Bearing Damage Detection
of the Induction Motors Using Current Analysis,”in Proc.
TDC IEEE/PES Transmiss.Distrib. Conf. Expo.: Latin
America, August 2006, pp. 1–5.
[9] L. Frosini and E. Bassi, “Stator Current and Motor Effi-
ciency as Indicators for Different Types of Bearing Faults
in Induction Motors,” IEEE Transactions on Industrial
electronics, Vol. 57, No. 1, 2010, pp. 244-251.
doi:10.1109/TIE.2009.2026770
[10] G. C. Zhang, M. G. e, H. Tong, Y. Xu and R. Du, “Bis-
pectral Analysis for on-line Monitoring of Stamping Op-
eration,”Engineering Applications of Artificial Intelli-
gence, Vol. 15, No. 1, 2002, pp. 97–104.
doi:10.1016/S0952-1976(02)00007-6
[11] W. B. Collis, P. R. White and J. K. Hammond,
“Higher-order Spectra: The Bispectrum and Trispec-
trum,” Mechanical Systems and Signal Processing, Vol.
12, No. 3, 1998, pp. 375-394.
doi:10.1006/mssp.1997.0145
[12] J. W. A. Fackrell, S. McLaughlin and P. R. White, “Bi-
coherence Estimation Using the Direct Method. Part 1:
Theoretical considerations,”Applications. Signal Proc-
ess,Vol. 3,1995, pp. 155-168.
[13] F. Gu, Y. Shao, N. Hu and A. D. Ball, “Electrical Motor
Current Signal Analysis Using a Modified Bispectrum for
Ault Diagnosis of Downstream Mechanical Equipment,”
Mechanical Systems and Signal Processing,” Vol. 25, No.
1,2011, pp. 360–372. doi:10.1016/j.ymssp.2010.07.004
[14] A. Alwodai, X. Yuan, Y. Shao, F. Gu, and A. D. Ball,
“Modulation Signal Bispectrum Analysis of Motor Cur-
rent Signals for Stator Fault Diagnosis,” Proceedings of
the 18th ICAC, September 2012.