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What Stator Current Processing Based Technique to
Use for Induction Motor Rotor Faults Diagnosis?
Mohamed Benbouzid, Gerald Kliman
To cite this version:
Mohamed Benbouzid, Gerald Kliman. What Stator Current Processing Based Technique to Use for
Induction Motor Rotor Faults Diagnosis?. IEEE Transactions on Energy Conversion, Institute of
Electrical and Electronics Engineers, 2003, 18 (2), pp.238-244. �hal-01052444�
What Stator Current Processing Based Technique
to Use for Induction Motor Rotor Faults Diagnosis?
Mohamed Benbouzid, Senior Member, IEEE and Gerald B. Kliman, Life Fellow, IEEE
Abstract—In recent years, marked improvement has been
achieved in the design and manufacture of stator winding.
However, motors driven by solid-state inverters undergo severe
voltage stresses due to rapid switch-on and switch-off of
semiconductor switches. Also, induction motors are required to
operate in highly corrosive and dusty environments.
Requirements such as these have spurred the development of
vastly improved insulation material and treatment processes. But
cage rotor design has undergone little change. As a result, rotor
failures now account for a larger percentage of total induction
motor failures. Broken cage bars and bearing deterioration are
now the main cause of rotor failures. Moreover, with advances in
digital technology over the last years, adequate data processing
capability is now available on cost-effective hardware platforms,
to monitor motors for a variety of abnormalities on a real time
basis in addition to the normal motor protection functions. Such
multifunction monitors are now starting to displace the
multiplicity of electromechanical devices commonly applied for
many years. For such reasons, this paper is devoted to a
comparison of signal processing based techniques for the
detection of broken bars and bearing deterioration in induction
motors. Features of these techniques which are relevant to fault
detection are presented. These features are then analyzed and
compared to deduce the most appropriate technique for
induction motor rotor fault detection.
Index Terms—Induction motor, rotor fault diagnosis, stator
current.
I. INTRODUCTION
It is well known that induction motors dominate the field
of electromechanical energy conversion. These machines find
a wide role in most industries in particular in the electric
utility industry as auxiliary drives in central power plants of
power systems, as well as restricted role in low MVA power
supply systems as induction generators, mining industries,
petrochemical industries, as well as in aerospace and military
equipment. Therefore, assessments of the running conditions
and reliability of these drive systems is crucial to avoid
unexpected and catastrophic failures. Consequently, the issue
of preventive maintenance and noninvasive diagnosis of the
condition of these induction motors drives is of great concern,
and is becoming increasingly important [1-2].
M.E.H. Benbouzid is with the Centre de Robotique, d’Electrotechnique
et d’Automatique (CREA) of the University of Picardie – Jules Verne at
Amiens, 7, Rue du Moulin Neuf, 80000 Amiens, France (e-mail:
m.benbouzid@ieee.org).
G.B. Kliman is with the Electrical, Computer & Systems Engineering
Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590 USA
(klimag@rpi.edu).
In recent years, marked improvement has been achieved in
the design and manufacture of stator winding. However,
motors driven by solid-state inverters undergo severe voltage
stresses due to rapid switch-on and switch-off of
semiconductor switches. Also, induction motors are required
to operate in highly corrosive and dusty environments.
Requirements such as these have spurred the development of
vastly improved insulation material and treatment processes.
But cage rotor design has undergone little change [3]. As a
result, rotor failures now account for a larger percentage of
total induction motor failures (Fig. 1) [4]. Broken cage bars
and bearing deterioration are now the main cause of rotor
failures (Fig. 2).
In general, condition-monitoring schemes have
concentrated on sensing specific failures modes in one of
three induction motor components: the stator, the rotor, or the
bearings. Even though thermal and vibration monitoring have
been utilized for decades, most of the recent research has been
directed toward electrical monitoring of the motor with
emphasis on inspecting the stator current of the motor [5].
Fault detection based on motor current relies on
interpretation of the frequency components in the current
spectrum that are related to rotor or bearing asymmetries.
However, the current spectrum is influenced by many factors,
including electric supply, static and dynamic load conditions,
noise, motor geometry, and fault conditions. These conditions
may lead to errors in fault detection.
With advances in digital technology in recent years,
adequate data processing capability is now available on cost-
effective hardware platforms, to monitor motors for a variety of
abnormalities on a real time basis in addition to the normal
motor protection functions. Such multifunction monitors are
now starting to displace the multiplicity of electromechanical
devices commonly applied for many years. For such reasons,
this paper is devoted to a comparison of signal processing based
techniques for the detection of broken bars and bearing
deterioration in induction motors. Features of these techniques
which are relevant to fault detection are presented. These
features are then analyzed and compared to deduce the most
appropriate technique for induction motor rotor fault detection.
II. MOTOR CURRENT SPECTRAL COMPONENTS
A. Broken Bars
The broken rotor bar frequencies in the motor current are
given by [6]
s
p
s
kff
sbrb
1
(1)
Where f
s
is the electrical supply frequency, k/p = 1, 5, 7, 11,
13,
...
(due to the normal winding configuration), s is the per
unit slip, and p is the number of pole pairs.
Even though the predicted frequencies are the same for
both airgap dynamic eccentricity [5] and broken bars, the
sideband amplitudes corresponding to a particular harmonic
number are different allowing the two faults to be
distinguished. The amplitude of the sideband frequency
component is roughly proportional to the number of broken
rotor bars. In fact, the amplitude I
brb
of frequency component
f
s
(1 – 2s) can be approximated by [7]
22p
sin
I
I
s
brb
(2)
Where I
s
is the stator current fundamental frequency
component,
R
pR
b
2
(3)
R
b
is the number of broken bars.
By analyzing the stator current, it is possible to evaluate the
general condition of the rotor. If there are broken bars in various
parts of the rotor, the current analysis is not capable of
providing information on the configuration of noncontiguous
broken bars. For example, the frequency component f
s
(1 – 2s)
does not exist if broken bars are electrically /2 radians away
from each other. It should be noted that some experimental
studies have demonstrated that both skewing and noninsulation
of rotor bars lead to reduce the broken rotor bar harmonic
components. It has been demonstrated experimentally that when
the amplitude of these harmonics is over 50 dB smaller than the
fundamental frequency component amplitude, the rotor may be
considered healthy [7].
B. Bearings Fault
Bearing problems are often caused by improperly forcing
the bearing onto the shaft or into the housing. This produces
physical damage in the form of brinelling or false brinelling of
the raceways, which leads to premature failure. Misalignment
of the bearing, which occurs in the four ways depicted in Fig.
3, is also a common result of defective bearing installation.
The relationship of the bearing vibration to the stator
current spectra can be determined by recalling that any air gap
eccentricity produces anomalies in the air gap flux density.
Since ball bearings support the rotor, any bearing defect will
produce a radial motion between the rotor and stator of the
machine. The mechanical displacement resulting from
damaged bearings causes the machine airgap to vary in a
manner that can be described by a combination of rotating
eccentricities moving in both directions. As with the airgap
eccentricity, these variations generate stator currents at
frequencies given by
o,isbng
fmff
(4)
Where m = 1, 2, 3,
...
and f
i,o
is one of the characteristic
vibration frequencies which are based upon the bearing
dimensions shown in Fig. 4.
cos
pd
bd
f
n
f
ro,i
1
2
(5)
Where n is the number of bearing balls, f
r
is the mechanical
rotor speed in Hz, bd is the ball diameter, pd is the bearing
pitch diameter, and is the contact angle of the balls on the
races [5]. It should be noted from (5) that specific information
concerning the bearing construction is required to calculate
the exact characteristic frequencies. However, these
characteristic race frequencies can be approximated for most
bearings with between six and twelve balls [8].
ri
ro
fn.f
fn.f
60
40
(6)
This generalization allows for the definition of frequency
bands where the bearing race frequencies are likely to show
up without requiring explicit knowledge of the bearing
construction.
C. Load Effects
If the load torque does vary with rotor position, the current
will contain spectral components, which coincide with those
caused by a fault condition. In an ideal machine where the
stator flux linkage is purely sinusoidal, any oscillation in the
load torque at a multiple of the rotational speed mf
r
will
produce stator currents at frequencies of [9]
p
s
mffmff
srsload
1
1
(7)
Where m = 1, 2, 3,
...
. Since the same frequencies are given by
(2) and (3), it is clear that when the induction machine
operates with a typical time-varying load, the torque
oscillation results in stator currents that can obscure, and often
overwhelm, those produced by the fault condition as
illustrated by Fig. 5 [10]. Therefore, any stator current single-
phase spectrum based fault detection scheme must rely on
monitoring those spectral components, which are not affected
by the load torque oscillations [10]. However, broken bars
detection is still possible since the current typically contains
higher order harmonics than those induced by the load.
III. ROTOR FAULT DETECTION TECHNIQUES
A. Fast Fourier Transform (FFT)
For this method, the stator current monitoring system is
sketched in Fig. 6. Generally, not denying the diagnostic value
of classical spectral analysis techniques, induction motor
faults detection, via FFT-based stator current signature
analysis, could be improved by decreasing the current
waveform distortions as is illustrated by Figs. 7 and 8 [11].
Moreover, it is well known that motor current is a
nonstationary signal, the properties of which vary with the
time-varying normal operating conditions of the motor. As a
result, it is difficult to differentiate fault conditions from the
normal operating conditions of the motor using Fourier
analysis.
B. Instantaneous Power FFT
In this case, in place of the stator current, the
instantaneous power is used as a medium for motor signature
analysis [12]. It was shown that the amount of information
carried by the instantaneous power, which is the product of
the supply voltage and the motor current, is higher than that
deducible from the current alone. In fact, besides the
fundamental and the two classical sideband components, the
instantaneous power spectrum contains an additional
component directly at the modulation frequency as shown by
the following equation.
tcoscostcos
tcos
IMV
tptp
oscosc
osc
LLL
6
2
6
2
6
2
2
0
(8)
Where p is the instantaneous power, M is the modulation
index, V
LL
is the rms value of the line-to-line voltage, and I
L
is
that of the line current, while and denote the supply
radian frequency and motor load angle, respectively, and
osc
is the radian oscillation frequency.
As an illustration, Fig. 9 shows clearly the differences with
Fig. 7b. In fact, all the fault harmonics are translated into the
frequency band 0–100 Hz. This constitutes a great advantage
because the fault harmonics domain is well bounded.
However, the power spectra are still quite noisy. Even adding
filters has not brought significant improvement. Moreover,
even though the power spectrum is particularly adapted to
mechanical abnormality detection (worn or damaged bearing),
it still has the same principal drawback as the classical motor
current FFT (nonstationary signal).
C. Bispectrum
Bispectrum, also called third-order spectrum, derives from
higher order statistics. The bispectrum is defined in terms of
the two-dimensional Fourier transform of the third-order
moment sequence of a process [13]. The bispectrum is
periodic with a period of 2, and preserves both magnitude
and phase information. It is then capable of revealing both the
amplitude and phase information of the signals. With these
additional dimensions, fault detection and diagnostic
processes can be enriched.
Very promising results were obtained, as illustrated by
Fig. 10. In fact, experimental results indicate that the
bispectrum magnitude of the dominant component, caused by
the machine rotation, increased with the fault level increase.
These results clearly indicate that stator current bispectrum is
capable of providing adequate and essential spectral
information for induction motors condition monitoring and
fault detection. However, this technique is more appropriate
for the detection of electrical based faults, such as stator
voltage unbalance, because those faults do not have a well-
identified harmonic frequency component [11].
D. High Resolution Spectral Analysis
A main disadvantage of the classical spectral estimation is
the impact of side lobe leakage due to the inherent windowing
of finite data sets. Window weighting allows mitigation of the
effects of side lobes at the expense of decreasing the spectral
resolution that can be no better than the inverse of acquisition
time. In order to improve the statistical stability of the spectral
estimate, i.e. to minimize the estimate variance, pseudo
ensemble averaging by segmenting the data was introduced at
the price of further decreasing the resolution. A class of
spectral techniques based on an eigenanalysis of the
autocorrelation matrix has been promoted in the digital signal
processing research literature [14].
As an illustration, two well known eigenanalysis-based
frequency estimators have been used: MUSIC (Multiple
Signal Classification) and ROOT-MUSIC for stator voltage
unbalance underscoring [11]. In this case, one of the principal
spectral components modified by the electric fault is the
supply frequency third harmonic (i.e. 150 Hz) whose
amplitude increases in a significant way whatever the load.
The two principal spectral components of the stator current
spectrum are the first and the fifth harmonics (50 Hz - 250
Hz) for a healthy motor, and the first and third harmonics (50
Hz - 150 Hz) for a stator voltage unbalance. The MUSIC
algorithm has been applied for each case and results are given
in Fig. 11. With regard to these results, MUSIC and ROOT-
MUSIC methods allow keeping only the main frequencies
without other spectral information. Moreover, stator current
high-resolution spectral analysis used as a medium for
induction motors faults detection will be useful for all faults
modifying main spectral components.
E. Wavelet Analysis
Fourier analysis is very useful for many applications where
the signals are stationary. The Fourier transform is however
not appropriate to analyze a signal that has transitory
characteristics such as drifts, abrupt changes and frequency
trends. To overcome this problem it has been useful to
analyze small sections of the signal at various times. This
technique is known as Short-Time Fourier Transform (STFT)
or windowing technique. The technique maps a signal into a
two-dimensional function of time and frequency. The STFT
represents a sort of compromise between time and frequency
based views of a signal and it provides some information
about both. However, we can only obtain this information
with limited precision, and that precision is determined by the
size of the window. The fixed size of the window is the main
drawback of the STFT [15].
The wavelet transform was introduced with the idea of
overcoming the difficulties mentioned above. A windowing
technique with variable-size region is used to perform the
signal analysis, which can be the stator current. Wavelet
analysis allows the use of long time intervals where we want
more precise low frequency information, and shorter regions
where we want high frequency information. The ability to
perform local analysis is one of the most interesting features
of the wavelet transform. The advantages of using wavelet
techniques for fault monitoring and diagnosis of induction
motors is increasing because these techniques allow us to
perform stator current signal analysis during transients. The
wavelet technique can be used for a localized analysis in the
time-frequency or time scale domain. It is then a powerful tool
for condition monitoring and fault diagnosis.
As an illustration, Fig. 12 provides the result where STFT
and the wavelet technique are combined. These results show
the improvements introduced by the wavelet technique for the
signal frequency monitoring [16].
F. The Park’s Vector Approach
A two dimensional representation can be used for
describing three-phase induction motor phenomena. A
suitable one being based on the stator current Park’s vector
[17]. As a function of mains phase variables (i
a
, i
b
, i
c
) the
current Park’s vector components (i
d
, i
q
) are
cbq
cbad
iii
iiii
2
1
2
1
6
1
6
1
3
2
(9)
Under ideal conditions, three-phase currents lead to a
Park’s vector with the following components
22
6
2
6
tsinii
tsinii
Mq
Md
(10)
Where i
M
is the supply phase current maximum value and
s
is
the supply frequency. Its representation is a circular pattern
centered at the origin of the coordinates. This is a very simple
reference figure that allows the detection of faulty conditions
by monitoring the deviations of the acquired patterns as
illustrated by Fig. 13. The healthy pattern differs slightly from
the expected circular one, because supply voltage is generally
not exactly sinusoidal.
Recently, a new implementation of the Park’s vector
approach has been proposed [18]. Under abnormal conditions,
for example in the presence of rotor cage faults such as broken
bars, (9) and (10) are no longer valid, because the induction
motor supply current will contain sideband components at
frequencies differing from the fundamental by the double slip
frequency. These additional components at frequencies of (1 –
2s)f
s
and (1 + 2s)f
s
will also be present in both motor current
Park’s vector components (i
d
, i
q
). In these conditions, it can be
shown that the spectrum of the stator current Park’s vector
modulus is the sum of a dc level, generated mainly by the
fundamental component of the induction motor supply current,
plus two additional terms, at frequencies of 2sf
s
and 4sf
s
. In this
way, the spectrum of the stator current Park’s vector modulus ac
level is clear from any component at the fundamental supply
frequency, making it more useful to detect the components
directly related to the induction motor fault. This new
implementation of the Park’s vector approach is intended to
eliminate some of the technical limitations of the conventional
FFT technique. In fact, Fig. 14a shows that, in the absence of
faults, the behavior of the induction motor is mostly
characterized by the absence of any relevant spectral
component. Moreover, results obtained by the extended Park’s
vector approach are more discriminating than those obtained by
the traditional FFT technique (Fig. 14b).
G. Adaptive Statistical Time-Frequency Method
The motor current can be modeled as a nonstationary
random signal. However, as previously mentioned, Fourier
transform techniques are not sufficient to represent
nonstationary signals. Moreover, the uncertainty involved in
the system requires an adaptive statistical framework to
address the problem in an efficient way. In recent years,
advancement of statistical signal processing methods has
provided efficient and optimal tools to process nonstationary
signals. In particular, time-frequency and time-scale
transformations provide an optimal mathematical framework
for the analysis of time-varying, nonstationary signals [19].
Recently, an adaptive statistical time-frequency method to
detect broken bars and bearing faults has been proposed. The
key idea in this method is to transform the motor current into
a time-frequency spectrum to capture the time variation of the
frequency components and to analyze the spectrum
statistically to distinguish fault conditions from the normal
operating conditions of the motor. Since each motor has a
distinct geometry, a supervised approach is adapted. In this
approach, the algorithm is trained to recognize the normal
