10th International Symposium
„Topical Problems in the Field of Electrical and Power Engineering“
Pärnu, Estonia, January 10-15, 2011
Detection of broken rotor bars in three-phase squirrel-cage
induction motor using fast Fourier transform
Toomas Vaimann, Ants Kallaste
Tallinn University of Technology
toomas.vaimann@ttu.ee
Abstract
Induction motors have become the most used
electrical motors in the world. They are rugged,
easy to maintain, low in cost and good in performance. Those benefits have made induction motors
very popular among users. During their exploitation period induction motors are exposed to various
stresses that can become fatal to their performance
and bring with them huge economic losses and
safety risks for the people and companies using the
motors. This has been the reason why there has
been increasing interest in different condition
monitoring and diagnostic systems in the past two
decades. This paper analyses the diagnostic
possibilities of three-phase squirrel-cage induction
motor rotor faults through the implementation of
fast Fourier transform.
Keywords
Induction motor, rotor faults, diagnostics, stator
current, broken rotor bars, fast Fourier transform,
FFT
Introduction
Induction motors are critical for many industrial
processes because they are cost effective and robust
in the sense of performance. They are also critical
components in many commercially available equipment and industrial processes [1]. Furthermore,
induction motors are often used in critical duty
drives where a sudden failure can cause safety risks
and economic expenses. Different failures can occur
in electrical drives and one of the most common
faults is the breaking of the rotor bars.
The rotor failures are caused by a combination of
various stresses that act in the rotor. These stresses
can be electromagnetic, thermal, residual, dynamic,
environmental and mechanical [2]. However, the
induction motor rotor faults usually start from a
small fracture or a high resistivity spot in the rotor
bar [3]. When a fault like this increases the magnetic
field becomes more and more asymmetrical due to
the lack of induced currents in faulty rotor bars. This
leads to local saturation in stator and rotor teeth near
broken bars and unproportional distribution of magnetic field in the air gap. It can trigger several
electromagnetic phenomena like increase of higher
harmonic components, development of inverse mag52
netic field, torque pulsation, unbalanced magnetic
pull etc. All these phenomena are undesired because
they decrease the reliability of the induction motor
and the whole drive. [4]
Not only the number of the broken bars is important,
but their position in the rotor cage has a very big role
as well.
As calculations have shown, the worst case of
asymmetry is, when faulty bars are concentrated
close together one by one under the same magnetic
pole. Researches have verified that such case is also
most probable in practice, because the increase of
current is the highest in the bars near the broken one
and so under highest thermal stress. When the same
number of broken bars is situated under different
poles the asymmetry is less expected. [4]
Asymmetry of rotor cage winding due to some
broken or cracked bars represents a significant part
among several possible faults and must be detailed,
considered and taken into account [5]. Another
phenomenon that cannot be looked over is the
induced rotor current.
Resistance of broken bars is very high in comparison
with the value of healthy rotor bars. This is very
likely to cause unproportional distribution of rotor
currents. Parts of the rotor currents, which are not
able to flow in broken bars due to the high
resistance, are flowing in bars, situated next to the
broken ones. This leads to the increase of the current
value in those bars. Although the currents of broken
bars are flowing in adjacent bars, the entire sum of
rotor currents is lower than in the case of healthy
rotor. Too high current density leads to overheating
in these bars and the fault propagates until the rotor
cage is destroyed [4].
The main reasons for such faults is poor manufacturing, such as defective casting and poor jointing
(Fig. 1). Another common reason is over current e.g.
due to jam condition of the rotor [3], but there can
be various reasons that will lead to cracking or
broken rotor bars [6]:
1) Thermal stress due to over-load, non-uniform
heat distribution, hot spot and arc.
2) Magnetic stresses due to electromagnetic forces,
magnetic asymmetry forces, noises and electromagnetic vibrations.
over a sampling period that is sufficient to achieve
the required fast Fourier transform. [9]
Calculation of the fast Fourier algorithm was performed with MATLAB-software where computing
of this transform can be done in a simple way. The
MATLAB functions Y = fft(x) and y = ifft(X) implement the transform and inverse transform pair given
for vectors of length N by:
N
j −1 k −1
X ( k ) = ∑ x ( j ) ω N( )( )
(1)
j =1
x( j) =
Fig. 1. Defective casting of the rotor bar of an
induction machine [3]
5) Circumferential stress due to wearing and pollution of rotor material by chemical materials and
humidity.
6) Mechanical stress due to mechanical fatigue
of different parts, bearing damage, loosened
laminations etc.
The biggest problem of those faults is that it is often
not worth or possible to repair the rotor. However all
of this can be avoided, when the motor is supervised
by an appropriate condition monitoring or diagnostic
system.
1 Fast Fourier Transform
During the past twenty years there has been a
continually increasing interest and investigation into
induction motors fault detection and diagnosis. As
this interest has grown, the literature has also
grown. [7] Many different techniques can be found
for the fault diagnostics of an induction motor rotor.
All of them have their own benefits and drawbacks.
In this case, fast Fourier transform was chosen to be
a sufficient diagnostic method for induction motor
broken rotor bars detection.
Fourier analysis is very useful for many applications
where the signals are stationary, as in diagnostic
faults of electrical machines [8]. Its purpose is to
monitor a single-phase stator current. This is accomplished by removing the 50 Hz excitation component
through low-pass filtering and sampling the resulting
signal. The single-phase current is sensed by a
current transformer and sent to a 50 Hz notch filter
where the fundamental component is reduced. The
analog signal is then amplified and low-pass filtered.
The filtering removes the undesirable high-frequency components that produce aliasing of the
sampled signal while the amplification maximizes
the use of the analog-to-digital converter input range.
The analog-to-digital converter samples the filtered
current signal at a predetermined sampling rate that
is an integer multiple of 50 Hz. This is continued
N
∑ X ( k ) ω N(
− j −1)( k −1)
(2)
k =1
where
3) Residual stress from the fabrication process.
4) Dynamic stress due to rotor axial torque and
centrifugal forces.
1
N
ωN = e
2π i
N
(3)
is an Nth root of unity [10]. Equations 1 and 2 are
known as fast Fourier transform algorithms, which
have been developed from the discrete Fourier
transform to reduce the amount of computations
involved [11].
Induction motor faults detection, via fast Fourier
transform based stator current signature analysis,
could be improved by decreasing the current
waveform distortions. After all, it is well known that
motor current is a non-stationary 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. [8]
The differentiation of faulty conditions of the motor
will be easier, if the figures of healthy motor state
are used as comparison material for the faulty rotor
figures and peculiarities of local electrical network
are noted.
2 Experimental setup and measurements
Technical data of the tested induction motor (Fig. 2):
Un = 177 V
In = 14.8 A
nn = 1456 rpm
Tn = 20 Nm
f = 50 Hz
cosφ = 0.785
Fig. 2. Experimental setup for testing purposes
Two different motor states were used for the measurements. First series of measurements were done with
53
a healthy rotor and the second series with a faulty
rotor, containing seven broken bars, situated under
the same magnetic pole next to each other (Fig. 3).
Thus, the measurements provided two sets of results:
one healthy set and one set with a faulty rotor in a
very bad shape.
Fig. 3. Magnetic field distribution in the cross section
of a 3 kW induction motor at nominal load operating
condition: left – healthy rotor cage, right – faulty
rotor cage with seven broken bars (shaded) [12]
To apply torque to the motor, an electromagnetic
brake was used. As the nominal moment of the
motor is 20 Nm and the length of the handle of the
magnetic brake is 0.5 m, the measurements were
taken from 0…40 N, when measured by the force
sensor at the furthest point of the handle from the
motor.
The measurements were performed in two different
series. In the first, a healthy rotor and in the second,
a rotor with seven broken bars was used. During all
these tests four different values were measured:
Ua – first phase voltage,
Ub – second phase voltage,
Ia – first phase current,
Ib – second phase current.
Measurements were done while applying different
torques. Torque values were chosen so that the torque
would rise step by step: starting from 0 Nm, continuing with 5; 10; 15 and ending at 20 Nm, being the
nominal moment of the motor. All of those measurements were performed in two different time bases
(10 and 100 ms). Two different time bases were
chosen in order to have more data before starting the
analysis. This gave the opportunity to make the
transforms in that time base, which is visually more
traceable. A four-channel oscilloscope was used to
obtain the oscillations of current and voltage at all
the values mentioned before and results were saved
as MATLAB files. All together 80 files were produced using all four channels of the oscilloscope,
two different time bases, two different motor states
and five different torque values.
3 Analysis
According to the literature, fast Fourier transform
should provide a good technique for finding out
whether a rotor is healthy or not. The graph shows
peaks of current in different frequencies and
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harmonics, so there should be a difference between
the graphs of a healthy rotor current and the current
of the rotor with seven broken bars. In addition, the
amplitude of the current should be different according to the torque applied to the motor. Figures that
were plotted result from the measurements done
with the time base of 100 ms, considering more
periods of the measured signal available for the
analysis. That yields better results. For better
comparison graphs of both rotor states and different
torques were plotted (Figs. 4 and 5).
First observation from these graphs would be that
the amplitude rises as more torque is applied to the
motor. This can be particularly well observed at the
peak of the first harmonic (50 Hz). At the beginning
of the test when torque is set to 0 Nm, it can be
noted that the current amplitude stays at 0.55 units in
the case of healthy rotor, whereas at 20 Nm the
amplitude has risen to almost 0.9 units. It can also be
seen that in the case of the faulty rotor, the amplitude is always higher than in the healthy motor state,
whichever the applied torque to the motor is.
Second biggest change in those graphs is the development of peaks at different frequencies. Some unexpected peaks can be seen even on the healthy rotor
graphs, but these should not be considered relevant
as they are not significantly big and are most likely
arising as a result of the non-ideal sine waves that
occur in the line voltage. On the other hand, on the
faulty rotor figures, some of the peaks are significantly larger and are certainly caused by the broken
bars in the squirrel-cage rotor of the induction motor
that was tested. There are different peaks that vary in
size and shape at 75 Hz and 100 Hz margins. The
largest and the most viewable is the peak at the third
harmonic (150 Hz) which changes substantially in
shape when more torque is applied to the motor.
According to the plotted graphs and literature about
using fast Fourier transform to analyze the state of
induction motors, it can be stated that in the case that
is shown on Fig. 5 there is obviously some problems
in the motor and it can indeed be faulty. All of the
described factors can be considered a proof that the
fast Fourier transform can be used as an indicator for
a possibly faulty motor and broken rotor bars for
diagnostic purposes.
Conclusion
All the measurements and analyses were done in
laboratory conditions but it should be taken into
account that the voltage supply during the measurements was not ideal in view that it was not perfectly
sinusoidal. This provides an explanation to the
figures that appear not exactly the same as in the
literature describing the methods and not always
quite the same as expected. Non-ideal sine waves
have an effect on the outcomes of the current figures
and some unexpected peaks and curves in the
graphs.
Fig. 4. Stator current spectra of a healthy squirrelcage rotor with applied torque values of 0 Nm;
5 Nm; 10 Nm; 15 Nm; 20 Nm
Fig. 5. Stator current spectra of a faulty squirrelcage rotor (seven broken bars) with applied torque
values of 0 Nm; 5 Nm; 10 Nm; 15 Nm; 20 Nm
55
There are some drawbacks for the stator current
spectral analysis of three-phased squirrel-cage
motors in order to detect broken rotor bars when
using the fast Fourier transform. One of them is that
the resolution of the obtained figure of fast Fourier
transform is directly related to the length of the
sampling time. In order to get fine and correctly
readable figures, the motor has to be in steady-state
during the sampling of the signal. It is however often
not possible to keep the motor in a steady state
during a prolonged sampling time.
References
Attention should be paid to the fact that it is difficult
to differentiate fault conditions from the normal
operating conditions of the motor using only fast
Fourier transform, due to variability of properties of
the non-stationary motor current signal. It is essential to know the characteristics of the tested motor
under normal operating conditions, as well as the
peculiarities of the local electrical network where the
motor is being tested.
Another drawback of this kind of diagnosis is that
the computational power required for the analysis is
rather large. Without appropriate knowledge and
software it is not possible to make all the transformations and graphs so easily.
The benefit is that on-line monitoring makes the
detection of a fault easy. If all the procedures are
done correctly, then the faults will appear on the
graphs. Also, when the drive is monitored, the faults
of the rotor will be detected on an early stage. When
using that kind of monitoring it will not be necessary
to stop the motor of running in its stage of work. All
the needed procedures can be done without changing
the working cycle.
However, in general it is certainly possible to decide
on the motor rotor state using only the signals of the
stator current and analyzing them through fast
Fourier transform. The differences are very clearly
shown in the figures and the faulty motor is
noticeable. Still it would be the best if the fast
Fourier transform figures could be proved by some
other diagnostic method that is used simultaneously
or in cooperation with the fast Fourier transform.
These tests and analysis that are presented in this
paper are based on the measurements performed on
a healthy motor and a motor in a very bad shape. For
future tests it is necessary to analyse similar
diagnostic possibilities on motors with smaller faults
as well. This would show if such diagnosis is
relevant in cases not as severe as described here.
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Acknowledgement
11. Ingle V., Proakis J., Digital Signal Processing
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This paper is based on the measurements and
analysis of induction motor rotor faults performed
in Ljubljana University, Faculty of Electrical
Engineering, under supervision and help of
Prof. Dr. Vanja Ambrožič, Dr. Mitja Nemec and
Mr. Klemen Drobnič.
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