ANALYSIS OF ECCENTRICITY AND BROKEN ROTOR BAR FAULTS EFFECT ON THE INDUCTION MOTOR
SPECTRUMS OF CURRENT AND STRAY FLUX
Ielyzaveta Ishkova
Doctoral Degree Programme (2), FEEC BUT E-mail: xishko00@stud.feec.vutbr.cz
Supervised by: Ondřej Vítek
E-mail: viteko@feec.vutbr.cz
Abstract: In this paper the analysis of effect of eccentricity and broken rotor bar faults on the spectrums of current and magnetic flux density outside the motor are presented. The behavior and origination of characteristic frequencies is presented and analysed. The results are presented in the form of figures illustrating the advantages of analysed diagnosis methods.
Keywords: induction motor, MCSA, stray flux, eccentricity, broken rotor bars
1. INTRODUCTION
There are a number of faults that can occur during the motor operation and they can be classified as: stator faults that result in the opening or shortening of a stator phase windings, abnormal con- nection of the stator windings, broken rotor bars or cracked rotor end-rings, static, dynamic, or mi- xed air-gap irregularities, bent shaft, shorted rotor field winding, bearing and gearbox failures.
Of the above types of faults the most prevalent ones are the eccentricity and the broken rotor bar faults. The result of presence of these faults in the induction motor can be the changes and unbalan- ces in the voltages and line currents, increased torque pulsations, decreased average torque, overhe- ating, etc.
In the present research the presence of the broken rotor bars in the motor as well as the presence of all of the eccentricity types (static, dynamic, mixed) were investigated. The condition monitoring of investigated motors was carried out using the motor current signature analysis (MCSA) as well as the monitoring of the magnetic flux density outside the motor [1, 2].
For clear understanding of the occurrence and presence of characteristic frequencies and other peaks in the spectrums, the behavior of the magnetic flux density depending on the time, together with spatial variation in the air-gap were considered.
2. FAULT EFFECT ON FREQUENCY CONTENT
It is well known that stator current spectrum of squirrel cage induction motors contains a wide ran- ge of harmonic components of different magnitudes and frequencies caused by the winding distri- bution, stator and rotor slot permeance, pole pair numbers, saturation, air-gap eccentricity, etc.
Among these components the characteristic frequencies as well as rotor slot harmonics or principal slot harmonics are used as the indicators of the fault in the motor.
2.1. ECCENTRICITY FAULT EFFECT ON THE CURRENT AND MAGNETIC FLUX DENSITY SPECTRUMS OF MOTOR
The harmonic content in the spectrum of magnetic flux density may be described using analysis of the magnetic flux density in the airgap of the motor as a function of time and angle in the same ti-
me [3]. Such consideration allows to see the direct dependence of the principal slot harmonics (PSH) as well as fundamental frequency and its multiples on the fundamental number of pole pairs as well as the number of stator or rotor slots.
Considering the length of the motor airgap, its change due to the presence of the fault and its inver- se function the value of the magnetic flux density in the motor with dynamic eccentricity is expres- sed as
0 m 1
1 1
( , t) cos( p t)
cos ( 1) ( ) t
2
cos ( 1) ( ) t
m m
d m
m r
m r
B F
k F
p p
(1)
where kεd – is the level of dynamic eccentricity, p - is the number of pole pairs.
Magnetic flux density for the case of static eccentricity is:
0 m 1
1 1
( , t) cos( p t)
cos ( 1) t
2
cos ( 1) t
m m
s m
m m
B F
k F
p p
(2)
where kεs – is the level of static eccentricity.
For the consideration of current harmonic content there exist two methods of detection of air-gap eccentricity. In most cases it may be detected with the help of certain high frequency components in the stator line current. The first method allows to monitor behavior of the current at the side- bands of the slot frequencies. The sideband frequencies associated with an eccentricity are
( ) 1
slot ecc s r d
f f kQ n s n
p
(3)
where nd = 0 in case of static eccentricity, and nd = 1,2,3… in case of dynamic eccentricity (nd is known as eccentricity order), fs is the fundamental supply frequency, Qr is the number of rotor slots, s is the slip, k is any integer, and nω is the order of stator time harmonics that are present in the power supply driving the motor (nω = 1,3,5, etc).
The second method is based on the monitoring of the behavior of the current at the sidebands of the supply frequency and its odd multiples. These frequencies of interest are given by
1
1
ecc s s
f k f m f s p
(4)
where m – is any integer.
2.2. BROKEN ROTOR BAR FAULT EFFECT ON THE SPECTRUMS OF THE MOTOR
Generation and presence of frequencies related to the presence of broken rotor bar faults can be described as follows. Due to the asymmetry in the rotor circuit, the rotor currents will produce posi- tive- and negative-sequence rotor MMFs. Since the angular frequency of the rotor currents is sω1, where ω1 is the angular stator supply frequency and s is the slip, the angular speed of the positive- sequence rotor MMF with respect to the stator is
1 1 1 1 1
r s s s
(5)
and the negative-sequence rotor MMF with respect to the stator is
1 1 1 1 1 2 1
r s s s s
(6)
If the symmetrical three-phase stator winding of a symmetrical three-phase A.C. machine with smooth airgap is supplied by a symmetrical three-phase voltage system, due to the effects of space- harmonics, the airgap flux density distribution around the periphery is not sinusoidal, but can be described by
1 1 1 1 5 1 1
7 1 1 11 1 1
, cos cos 5
cos 7 cos 11 ...
B t B t p B t p
B t p B t p
(7)
Where 1 is an angle around the periphery (1=0 is in the direct-axis of the stator), t is the time.
The frequencies of the induced rotor currents can be obtained by expressing (4) in the reference frame fixed to the rotor and thus by considering that
1 rt 2
(8)
where ris the angular rotor speed and 2is the initial position of the rotor at t=0,
2 1 1 2
5 1 2
7 1 2
11 1 2
, cos
cos 6 5 5
cos 7 6 7
cos 12 11 11
B t B s t p
B s t p
B s t p
B s t p
(9)
is obtained, where s is the slip. It follows that even in a symmetrical three-phase machine, due to space harmonics, the induced rotor currents will have slip-dependent frequencies.
The fundamental airgap flux density wave can be resolved into two counter-rotating waves. The positive-sequence wave has the normal amplitude of magnetic flux density, and the amplitude of negative-sequence one is changed due to the level of asymmetry.
In the case of asymmetries on rotor of an induction machine, when there is a broken rotor bar and only the fundamental space harmonic is considered, rotor currents will produce positive- and nega- tive-sequence rotor MMFs, and their frequencies are s1.
Magnetic flux density in the case of asymmetry with relation to rotor is
2 1 1 2
1 1 2
, cos
Fcos
B t B s t p
B s t p
(10)
So the magnetic flux density formula considering the presence of rotor asymmetry in the stator ref- erence frame is
1 1 1 1
1 1 1
1 1 1
1 1 1
, cos
cos 1 2
cos 1
cos 1
F
F
B t B t p
B s t p
B s s p
B s s p
(11)
From stated above expression of the magnetic flux density the presence of the fundamental fre- quency can be clearly seen, as well as the presence of the sideband at frequency 2sω1. This is twice the slip frequency modulation of the supply current. Such a cyclic variation in the current reacts back onto the rotor to produce a torque variation at twice the slip frequency that, if the rotor does not have an infinitely high inertia, gives rise to 2sω1 variation on mechanical vibration that can be used for fault detection. This speed effect reduces the lower sideband current swing and produces an upper sideband at (1+2s)ω1, enhanced by modulation of the third harmonic flux in the stator and it can be seen that other sidebands at (1±2s)ω are also found [4].
3. EXPERIMENTAL RESULTS
a) b)
Figure 1: Measured spectrums of current (a) and magnetic flux density (b) of the healthy motor (black) compared to the motor with dynamic eccentricity (red)
a) b)
Figure 2: Measured spectrums of current (a) and magnetic flux density (b) of the healthy motor (black) compared to the motor with mixed eccentricity (red)
a) b)
Figure 3: Measured spectrums of current (a) and magnetic flux density (b) of the healthy motor (black) compa- red to the motor with 2 adjacent broken rotor bars(red)
Frequency Frequency
Frequency Frequency
Frequency Frequency
The current of motor as well as its stray flux were monitored and analyzed using the experimental installation with F.W. Bell 7030 Gauss/Teslameter and the magnetic flux sensor.
There were measured the 4-pole squirrel cage induction motors with static, dynamic and mixed ec- centricities as well as the motors with different ammount and position of broken rotor bars. Mea- sured results were supported by the data obtained from the somulation models. All obtained data were processed using the LabView Software, Ansys Maxwell and MatLab software.
From the obtained results it can be seen that the monitoring of the current spectrum of the motor is useful for the detection of the presence of eccentricity and broken rotor bar faults. Analysis of magnetic flux density in the case of these faults show that the monitoring of spectrum of stray flux of motor is useful in the case of eccentricity fault, that can be seen from the Figure 1(b) and Figure 2(b). But in the case of the broken rotor bar fault magnetic flux density is not useful, that is proved by the Figure 3 (b) as well as by the presented formulas.
4. CONCLUSIONS
In this paper the effects of eccentricity and broken rotor bar faults in induction motor were analy- sed. Data obtained from the measurement of real motors as well as from simulation in Ansys Ma- xwell was used for the analysis. The paper is focused on the effect of fault on the spectrums of current and magnetic flux density outside the motor. Methods used for the analysis of these effects are the MCSA with the monitoring of the stray flux of motor. The paper consist of the theoretical part where the formulas of magnetic flux density and there changes due to the presence of the fault are presented, as well as the experimental part. Obtained results are presented in the form of fi- gures.
From the obtained results it is clearly seen that for the detection of presence of eccentricity fault monitoring of current spectrum is useful as well as the analysis of the magnetic flux density spectrums. Characteristic frequencies for this type of fault can be clearly destinguished in the spectrums, that allows to recognize the fault in the motor. For the diagnosis of broken rotor bar fault it is better to use the monitoring of the current spectrum, spectrum of magnetic flux density is not useful in this case.
ACKNOWLEDGEMENT
This research work has been carried out in the Centre for Research and Utilization of Renewable Energy (CVVOZE). Authors gratefully acknowledge financial support from the Ministry of Educa- tion, Youth and Sports of the Czech Republic under NPU I programme (project No. LO1210).
REFERENCES
[1] Romary, R., Pusca, R., Lecointe, J.P., Electrical Machines Fault Diagnosis by Stray Flux Analysis. In: IEEE Workshop on Electrical Machines Design, Control and Diagnosis, Paris, France, 2013, pp.247-256
[2] Ishkova, I., Vitek, O., Diagnosis of Eccentricity and Broken Rotor Bar Related Faults of In- duction Motor by Means of Motor Current Signature Analysis. In: 16th International Scienti- fic Conference on Electric Power Engineering, Kouty nad Desnou, Czeck Republic, 2015, pp.682-686
[3] Boldea, I., Nasar, S., The Induction Machine Handbook. Boca Raton: CRC Press, 2002 [4] Tavner, P., Ran, L., Penman, J., Sedding, H., Condition Monitoring of Rotating Electrical
Machines. Stevenage: Institution of Engineering and Technology, 2008, ISBN 978-0-86341- 739-9
