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ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.20,NO.7,2014
1Abstract—This paper presents the finite element modelling
of three-phase squirrel-cage induction motor with broken rotor
bar faults. Finite element model based on a real machine is
constructed, propagation of broken rotor bar fault and its
influence on the magnetic flux density distribution of the
machine cage is observed. As the propagation of the fault will
result in total breakdown of the induction machine rotor, if the
fault is not detected and solved, necessity of condition
monitoring is pointed out. Analysis of the fault and its affect to
the magnetic field in the rotor cage as well as changes in the
phase voltage spectrum are presented.
Index Terms—Electric machines, induction motors, fault
diagnosis, electromagnetic fields, rotors, finite element analysis.
I. INTRODUCTION
Broken rotor bars of squirrel-cage induction machines
have been the subject of interest in numerous scientific
studies. A comprehensive yet ever growing list of the
researches dealing with diagnostic problems of electrical
machines is presented in [1]. As the given fault is one of the
more usual types of failures, condition monitoring to predict
the possible fault and detection of broken bars can be
considered an important issue in the field of induction
machine diagnostics.
Squirrel-cage induction machines are one of the most used
machine types in the industry nowadays. They are preferred
due to their rugged build, reliability and cost efficiency. This
also means that induction machines are used in such
applications, where sudden failures result with high
economic loss and also possible threat to the surrounding
environment as well as people manipulating them.
Induction machines are also often used as generators in
small hydro and wind power plants. Failures of the machines
used in such applications means a sudden drop of supply
reliability and power quality to the customers using
electricity produced in those units. With the world moving
Manuscript received December 16, 2013; accepted May 11, 2014.
This research has been supported by Estonian Ministry of Education
and Science base financing fund (project „Design and Optimization
Methodology for Electrical Machine-Drives“).
towards distributed generation, number of such small
generation units is expected to rise [2]. Due to that, rise in
the use of induction machines can also be expected.
Induction machine rotor faults usually start from a fracture
or a high resistivity spot in the rotor bar [3]. The fractured or
cracked rotor bar starts to overheat around the crack until the
bar breaks [4], [5]. This means that at the same time the
resistance of such bars is rising and becomes significantly
higher than the resistance of healthy bars in the rotor cage.
As there is a lack of induced current in those bars, the
magnetic field will become gradually more asymmetrical,
which will lead to local saturation in stator and rotor teeth
near the broken bar and disproportional distribution of
magnetic field in the air-gap [6].
Breaking of the consecutive rotor bars is the most
probable case in practice [7]. This happens, because currents
that are unable to flow in the broken bars are flowing
through the adjacent bars, which means that those bars
situated next to the broken ones are under higher thermal
stress due to higher current density. This means that if the
fault is not treated, it will propagate in time resulting in the
destruction of the whole rotor cage [8].
The aim of this paper is to show through a series of finite
element modelling how the magnetic field in the machine is
changing due to the presence of broken bars. Changes in the
field are expected to be growing as the severity of the fault is
rising and the fault propagates.
II. MODELLINGOF THE INDUCTION MACHINE
Experiments of the induction machine’s behavior were
performed on a three-phase squirrel-cage induction motor
with a healthy rotor and a rotor with up to three consecutive
broken bars. These tests, where the same machine is fed
through frequency converter supply are described in [9].
For the modelling of magnetic flux density distribution in
case of broken rotor bar fault of an induction machine, the
same motor as in previously mentioned experiments was
used. Data of the machine is presented in Table I.
Using the listed data and the machine layout, two
dimensional finite element model of the induction machine
Changing of Magnetic Flux Density
Distribution in a Squirrel-Cage Induction Motor
with Broken Rotor Bars
T. Vaimann1, A. Belahcen1, 2, A. Kallaste1
1Department of Electrical Engineering, Tallinn University of Technology,
Ehitajate tee 5, 19086 Tallinn, Estonia
2Department of Electrical Engineering, Aalto University,
P.O. Box 13000, 0076 Espoo, Finland
toomas.vaimann@ttu.ee
http://dx.doi.org/10.5755/j01.eee.20.7.8018
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ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.20,NO.7,2014
was constructed. The model of the machine showing the
magnetic flux density distribution in case of healthy rotor
cage is presented in Fig. 1.
TABLE I. DATA OF THE INDUCTION MACHINE.
Parameter
Symbol
Value
Rated voltage
Un
400V@60 Hz;
333V@50 Hz
Rated current
In
41 A
Rated speed
nn
1680 rpm@60 Hz;
1400 rpm@50 Hz
Rated power
Pn
22 kW@60 Hz;
18 kW@50 Hz
Frequency
f
50-60 Hz
Power factor
cosφ
0.86
Number of poles
p
4
Number of rotor bars
Qr
40
Number of stator slots
Qs
48
Fig. 1. Magnetic flux density distribution of a healthy induction motor.
III. EFFECT OF BROKEN BARS TO THE MAGNETIC FIELD
The necessity to detect the fault in an early stage, to
prevent further damage of the equipment due to fault
propagation, is one of the most important features of any
condition monitoring or diagnostic techniques. At the same
time, minor faults and early stages of the propagating fault
are less obvious to detect and are significantly harder to
grasp [10].
Based on this, the fault propagation in the given paper is
modelled from healthy rotor cage up to three consecutive
broken bars (which is 7.5 % of all the rotor bars of the
machine). The broken bars were modelled as areas with
significantly higher resistance and low conductivity, so they
would not contribute to the cage circuit [11], [12]. Figure 2
presents the flux density distribution of the induction motor
in case of one broken rotor bar.
As previously said, minor faults are very difficult to
detect. Comparing Fig. 1 and Fig. 2, the difference between
the flux density distributions is visible to some extent but not
clearly detectable for the naked eye. The difference becomes
easier to observe when one field distribution is subtracted
from another and only the difference in the two presented
flux density distributions remain. This difference of the flux
density distributions of the healthy cage and the machine
with one broken rotor bar is shown on Fig. 3.
It can be seen from Fig. 3 that already in case of one broken
rotor bar in the cage, the magnetic field distribution is
becoming distorted. Higher amount of magnetic saturation
can be seen around the broken bar in the rotor as a lack of
frequency-induced current in these rotor bars. Magnetic flux
density in the studied machine is increasing by 0.15 T
around the broken bar.
Fig. 2. Magnetic flux density distribution of an induction motor with one
broken rotor bar.
Fig. 3. Magnetic flux density distribution difference between the healthy
induction motor cage and the cage with one broken rotor bar.
Additionally, as the rotor magnetic field distribution is
distorted, this effect also influences the stator. In the stator
higher saturation can be seen in the teeth facing the broken
rotor bar and in stator yoke, where the magnetic flux density
is also increasing by approximately 0.15 T.
Further study was made with two broken rotor bars. The
simulation results of flux density distribution of this fault are
given in the Fig 4. Figure 5 presents a comparison of
magnetic field distribution difference between healthy cage
machine and an induction machine with two broken rotor
bars.
It can be seen that in case of two broken rotor bars the
magnetic field flux density is increasing around the broken
rotor bars and also in the stator facing the broken rotor bar
0.2 T. The phenomenon can be described similarly to the
one broken bar case, although the value of the magnetic flux
density is rising even more. Also it can be seen that the
magnetic flux density is increasing both in the stator and
rotor yoke opposite to the broken rotor bars. It should be
noted, that difference in the magnetic flux density
distribution between the healthy machine and the one with
broken bars corresponds to an asymmetric field inducing
eddy-currents in the shaft of the machine. Such current if
free to circulate, will cause bearing currents that usually
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ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.20,NO.7,2014
result in damaging the bearings.
Fig. 4. Magnetic flux density distribution of an induction motor with two
broken bars.
Fig. 5. Magnetic flux density distribution difference between the healthy
induction motor cage and the cage with two broken bars.
Magnetic field distribution simulation results in case of
three broken rotor bars are given in Fig. 6 and the
comparison with healthy induction machine cage is
presented in Fig. 7. It can be seen from Fig. 7 that three
broken rotor bars lead to relatively high saturation of the
iron around the broken rotor bars and opposite to the broken
bars. Flux density is increasing up to 0.4 T compared to
healthy machine and even more in the tooth between the
broken bars as well as the shaft of the machine.
It can be said that due to the increased magnetic flux
density, degradation in the mechanical performance of the
induction machine can be expected. In the regions where the
flux density is rising (around the broken bars and opposite to
the broken bars), the core loss density is higher compared to
other regions of the machine. These adjacent bars become
more susceptible to thermal stress due to overheating and
will lead to further breaking of rotor bar [13].
Although no currents pass through the broken bars and no
heat losses are generated, it becomes obvious from the
presented figures, that the currents passing through the bars
adjacent to the broken ones are dramatically increased and
the heat losses in the bars are increased in a large scale [14].
The air-gap field becomes asymmetrical due to the
presence of broken bars in the rotor cage and the harmonic
components of air-gap magnetic flux density vary
significantly. As the flux density is fluctuating, it was
assumed that it can also be traceable in the machine phase
voltage due to the presence of counter-electromotive force.
To visualize that effect, simulations were carried out and
machine phase voltages were found. A comparison was
made using the differences between healthy and faulty
machine phase voltages. These results are presented in
Fig. 8.
Fig. 6. Magnetic flux density distribution of an induction motor with three
broken bars.
Fig. 7. Magnetic flux density distribution difference between the healthy
induction motor cage and the cage with three broken bars.
(a)
(b)
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ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.20,NO.7,2014
(c)
Fig. 8. Phase voltage difference: upper – phase voltage difference between
healthy cage and one broken rotor bar case; middle – phase voltage
difference between healthy cage and three broken rotor bars case; bottom –
phase voltage difference between one broken bar case and three broken
rotor bars case.
From Fig. 8 it can be seen that compared to healthy
machine, the faulty machine phase voltage is fluctuating.
The fluctuation is increasing with the amount of broken bars.
In the studied machine, one broken bar in the cage leads to
voltage difference up to ±10 V and three broken bars raise
that difference up to ±15 V. It can also be seen that the third
harmonic component is dominating the voltage spectrum but
also higher harmonic presence up to 21st and higher can be
noted in the spectrum of the machine. The higher harmonic
presence can also be detected on the bottom graph of Fig. 8,
which shows phase voltage difference between one broken
bar case and three broken rotor bars case.
IV. CONCLUSIONS
Magnetic field modelling regarding the magnetic flux
distribution of the induction machine in case of healthy
machine and propagating severity of the broken rotor bars
fault was made and analyzed. It was found that presence of
broken rotor bars results in uneven distribution of magnetic
field in the rotor cage and the whole machine.
Magnetic field strength is increasing around the broken
bar in rotor and also in stator facing the broken bar. In
addition to that, the magnetic field strength is also increasing
on the opposite side of the broken rotor bar as well as the
shaft of the machine. The latter can be explained by the
asymmetric field that induces eddy-currents in the shaft and
will most likely cause bearing currents, which in time will
result in bearings damage.
When the fault propagates and the number of broken bars
in the rotor cage increases, the magnetic field asymmetry is
rising, resulting in higher local saturation in both rotor and
stator teeth. Uneven magnetic field distribution starts
affecting the machine phase voltage, resulting in the
presence of higher harmonic components in the voltage
spectrum. With increase of the number of consecutive
broken bars, higher harmonic amplitude in phase voltage is
also increasing, which means that various disturbances and
undesired phenomena (i.e. increase of noise, increase of
mechanical vibrations etc.) can be expected.
Based on the acquired magnetic field distribution figures,
it can be estimated that broken rotor bars fault can lead to
severe consequences if the fault is not dealt with in an early
stage. The propagation of the fault will not only result in the
destruction of the rotor cage but can also lead to various
stator failures (i.e. stator winding turn to turn short circuits,
lamination short circuits etc.) due to the broken rotor bar
influenced local saturation in and around stator teeth.
Additionally, such fault propagation can lead to bearings
problems as mentioned previously.
To prevent the possible economic losses, danger to
surrounding environment and people operating the
machines, condition monitoring of the machines should be
considered. This would grant the possibility of detecting the
faults during the stage where repairing of the machine would
still be reasonable and possible. Usage of sufficient
diagnostic measures would also mean lower down-time for
the industries where such machines are used.
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