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ELECTRIC POWER ENGINEERING 2011
Overview of Sensorless Diagnostic Possibilities of Induction
Motors with Broken Rotor Bars
Toomas Vaimann
1)
, Ants Kallaste
2)
, Aleksander Kilk
3)
Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia, http://www.ttu.ee
1)
tel: +372 620 3800, email: toomas.vaimann@ttu.ee,
2)
tel: +372 620 3800, email: ants.kallaste@ttu.ee
3)
tel: +372 620 3800, email: kilk@cc.ttu.ee
A
BSTRACT
During the past few decades there has been a continu-
ally increasing interest and investigation into fault detection
and diagnostics of induction motors. There are various
different diagnostic approaches and methods to detect faults
in induction motors. Attention should be paid to the fact that
as induction motors are often used in critical duty drives, it
is essential not to disturb the working cycle of the motor in
any way while performing the needed diagnostic proce-
dures. The needed measurements have to be carried out
with the motor remaining in its normal operating mode, as
changing of the working cycle can mean safety risks and
economic losses in some applications where induction mo-
tors are used. This paper gives an overview of the sensor-
less diagnostic possibilities of three-phase squirrel-cage
induction motors with broken rotor bars via the analysis of
stator current.
Keywords: Induction motor, Rotor faults, Diagnostics,
Stator current, Broken rotor bars, FFT, Clarke transforma-
tion, Current vector amplitude oscillation, Wavelet analysis,
Finite element method
1 I
NTRODUCTION
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 proc-
esses [1]. In developed countries today there are more than
3 kW of electric motors per person and most of it is from
induction motors [2]. Furthermore, induction motors are often
used in critical duty drives where sudden failures can cause
high safety risks and unnecessary economic expenses. Differ-
ent failures can occur in electrical drives and one of the most
common faults is the breaking of the rotor bars.
The majority of all stator and rotor faults are caused by a
combination of various stresses, which can be thermal, elec-
tromagnetic, residual, dynamic, mechanical or environ-
mental [3]. Broken rotor bars are not only one of the most
common faults but also one of the most uncomfortable
ones [4].
The worst case of such fault is when the broken rotor bars
are situated closely one after another. This case is also most
probable in practice as broken rotor bars are usually not de-
tected at early stage. As the resistance of the broken bar is
very high in comparison with the healthy ones, currents start
to distribute unproportionally in the rotor cage. Parts of the
rotor currents, which are unable to flow in broken bars, are
flowing in adjacent bars. This increases the rms value of
currents in the bars next to the broken ones [4]. As the
healthy bars next to the broken one have too high current
density, they will start to overheat, so these bars are under
severe thermal stress. Those bars start cracking and breaking
and when attention to the problem is not paid, the fault will
continue to cascade, until the rotor cage is destroyed.
Broken rotors bars can lead to vibration problems, but
more likely, in severe cases, the bar pounds out of the slot
and makes contact with the stator core or winding [3]. 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.
2 S
ENSORLESS
D
IAGNOSTIC
M
ETHODS
The biggest advantage that sensorless diagnostic of induc-
tion motors provides is that testing and diagnostics can be
done without any disturbances to the motor’s normal working
cycle. It means that in case of motors which are used in criti-
cal duty drives or perform on high risk conditions, no addi-
tional changes have to be made in order to perform the tests.
There are different possibilities to perform sensorless di-
agnostics on induction motors. One of the ways is to measure
stator currents of the motor and analysing the measured sig-
nals. Some diagnostic methods for performing this analysis
are described in this paper.
2.1 Fast Fourier Transform (FFT)
Fourier analysis is very useful for many applications
where the signals are stationary, as in diagnostic faults of
electrical machines [5].
Its purpose is to monitor a single-phase stator current.
This is accomplished by removing the 50 Hz excitation com-
ponent through low-pass filtering and sampling the resulting
signal. Single-phase current is sensed by a current trans-
former and sent to a 50 Hz notch filter where the fundamental
component is reduced. Analog signal is then amplified and
low-pass filtered. Filtering removes the undesirable high-fre-
quency components that produce aliasing of the sampled
signal while the amplification maximizes the use of the ana-
log-to-digital converter input range. Analog-to-digital con-
verter samples the filtered current signal at a predetermined
sampling rate that is an integer multiple of 50 Hz. This is
continued over a sampling period that is sufficient to achieve
the required fast Fourier transform. [6]
Calculation of the fast Fourier algorithm can be per-
formed with MATLAB-software where computing of this
transform can be done in a simple way. The MATLAB func-
tions Y = fft(x) and y = ifft(X) implement the transform and
inverse transform pair given for vectors of length N by:
( ) ( )
( )( )
1 1
1
1
Nj k
N
k
x j X k
N
ω
− − −
=
=
∑
(1)
( ) ( )
( )( )
1 1
1
1
Nj k
N
k
x j X k
N
ω
− − −
=
=
∑ (2)
where
2
i
N
N
e
π
ω
=
(3)
is an Nth root of unity [7]. Equations 1 and 2 are known as
fast Fourier transform algorithms, which have been devel-
oped from the discrete Fourier transform to reduce the
amount of computations involved [8].
Induction motor faults detection, via fast Fourier trans-
form based stator current signature analysis could be im-
proved 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. [5]
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 peculiari-
ties of local grid are noted. Differences between healthy and
faulty rotor conditions are traceable as seen on Figs. 1 and 2.
Fig. 1 Stator current spectrum of healthy motor on nominal
torque
Fig. 2 Stator current spectrum of faulty motor with seven
broken rotor bars on nominal torque
2.2 Clarke Vector Approach
As fault detection based only on the fast Fourier trans-
form can be quite difficult, other diagnostic methods should
also be taken in consideration in order to make appropriate
decisions on the state of the tested motor.
A two-dimensional representation can be used for de-
scribing three-phase induction motor phenomena. This trans-
formation can be made using Clarke vector (or Park’s vector)
( )
2 3
a
b c
i i
i i i
α
β
=
= +
(4)
where i
a
, i
b
, and i
c
are phase currents, i
α
and i
β
are alpha and
beta components of the current.
Its representation is a circular pattern centered at the ori-
gin of the coordinates. This is a very simple reference figure,
which allows the detection of an abnormal condition due to
any fault of the machine by observing the deviations of the
acquired picture from the reference pattern [9].
The healthy pattern differs slightly from the expected cir-
cular one, because supply voltage is generally not exactly
sinusoidal [10]. Pattern of the rotor with broken bars is how-
ever more like an ellipse shaped one. Patterns of healthy and
faulty motors are shown on Figs. 3 and 4.
Fig. 3 Stator current Clarke vector pattern of healthy motor
on nominal torque
Fig. 4 Stator current Clarke vector pattern of faulty motor
with seven broken rotor bars on nominal torque
2.3 Current Vector Amplitude Oscillation
Clarke transformation can be followed by monitoring the
current vector amplitude oscillation. This method is not
commonly described in the literature concerning induction
motor rotor fault diagnostics, but it can prove to be a good
indicator for the state of the rotor. The aim is primarily to find
out whether there are changes in the figures according to the
state of the motor and torque applied to it or not. This is also
a simple procedure if the Clarke transformation is already
performed or in other words, the three-dimensional system is
transformed into a two-dimensional system. After the Clarke
transformation only one simple formula is required to acquire
the graph of the current vector amplitude oscillation:
2 2
Cvao i i
α β
= +
(5)
After completing this calculation, Figs. 5 and 6 can be
plotted.
Fig. 5 Current vector amplitude oscillation of healthy motor
on nominal torque
Fig. 6 Current vector amplitude oscillation of faulty motor
with seven broken rotor bars on nominal torque
Difference is clear. The amplitude of a faulty rotor current
vector is much higher, especially when the nominal torque is
applied. It should be mentioned that the rise of the amplitude
results also from the torque applied. This leads to a rise in
current. Nevertheless, this method allows deciding on the
state of the motor based on the analysis of the stator current
measurements.
2.4 Other Possible Methods
In addition to the described methods that have been used
by the authors for induction motor diagnostics there are vari-
ous other methods for analyzing the measured stator current.
Hereby a brief overview of some other existing analyzing
methods is given.
Wavelet Analysis
As it was said before it can be difficult to differentiate
fault conditions from the normal operating conditions of the
motor using FFT. To overcome this problem wavelet analysis
can be used.
Wavelet is a time frequency analysis tool originated from
seismic signal analysis, which uses narrow windows for high
frequency component [11]. Continuous wavelet transforms
(CWTs) have constant frequency to bandwidth ratio
analysis and therefore, CWTs provide powerful multi-
resolution in time-frequency analysis for characterizing the
transitory features of non-stationary signals [12]. Wavelet
analysis can be used for localized analysis in the time-
frequency or time scale domain, which makes it a powerful
tool for condition monitoring and fault diagnosis [5].
Examples of the stator current spectra of healthy and
faulty motors which are gained using wavelet theory are
shown on Figs. 7 and 8.
Fig. 7 Stator current spectrum of healthy motor [13]
Fig. 8 Stator current spectrum of healthy motor with three
broken rotor bars [13]
Finite Element Method
The finite element method, which is well established for
induction motors modeling, could be used to provide an accu-
rate evaluation of the magnetic field distribution inside the
motor [6]. To assess the magnetic saturation effect on faults
detection, the time-stepping finite-element method is recom-
mended [14]. Faults in the rotor can be simulated using the
finite element method and this would give an opportunity to
estimate the magnetic field anomalies, based on the motor
simulation. One example of the results of such simulation is
shown on Fig 9.
Fig. 9 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) [15]
3 C
ONCLUSION
In general, it is certainly possible to decide upon the state
of the rotor, and the whole induction motor respectively,
using only the signals of stator currents and analyzing them.
All of the methods described can be used as indicators of the
motor state. However, there are some aspects that should be
considered when such methods of sensorless diagnostics are
used.
Firstly, it is essential to know the characteristics of the
tested motor under normal operating conditions, as well as
the peculiarities of the local grid where the motor is being
tested. Deviations such as not perfectly sinusoidal supply
voltage can have an effect on the outcomes of the current
figures and can produce some unexpected peaks and curves
in the graphs.
Secondly, to prove that the performed measurements and
analyses are correct, the tests should not be performed using
only one of the methods. For example the resolution of the
obtained figure of FFT 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 sam-
pling of the signal. It is however often not possible to keep
the motor in a steady state during a prolonged sampling time.
As a result it can be difficult to differentiate fault conditions
from the normal operating conditions of the motor using only
FFT, due to variability of properties of the non-stationary
motor current signal. This problem can be solved when fig-
ures are proved by some other diagnostic method that is used
simultaneously or in cooperation with the chosen one.
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 possi-
ble to make all the transformations and graphs so easily.
Interpretation of the figures require the operator or the user to
have some degree of expertise and experience as well, be-
cause the deviations on the graphs can result from a number
of sources, including the normal operating conditions for
number of reasons, some of which have been described.
On the other hand, online monitoring makes the detection
of a fault easy. If all the procedures are done correctly, 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 this kind of monitoring it will not be nec-
essary to stop the motor of running in its stage of work. All
the needed procedures can be done without changing the
working cycle of the tested motor.
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