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Detection of an End-Ring Fault in Asynchronous Machines by Spectrum Analysis of the Observed
Electromagnetic Torque
Hamed Yahoui, Guy Grellet
To cite this version:
Hamed Yahoui, Guy Grellet. Detection of an End-Ring Fault in Asynchronous Machines by Spectrum Analysis of the Observed Electromagnetic Torque. Journal de Physique III, EDP Sciences, 1996, 6 (4), pp.443-448. �10.1051/jp3:1996133�. �jpa-00249468�
Short Communication
Detection of an End-Ring Fault in Asynchronous Machines by
Spectrum Analysis of the Observed Electromagnetic Torque
Hamed Yahoui and Guy Grellet
Universit4 Claude Bernard Lyon 1, Laboratoire d'#lectrotechnique et d'#lectronique de Puissance, 43 Bd du it novembre 1918, 69622 Villeurbanne Cedex, France
(Received 9 October 1995, revised 8 January1996, accepted 14 February1996)
PACS.02.30.Nw Fourier Analysis
PACS.07.05.Tp Computer modeling and simulation
PACS.07.05.Kf Data analysis algorithms and implementation data management
Abstract. For asynchronous machines, 20% of the failures are due to the rotor [1] and
particularly the end-ring fault of cage motors. Studies [2,4] have shown that
a rotor fault generates flux harmonics which induce in term of harmonics in the stator currents. So, the
analysis of the torque which is the product of these two quantities, must give a better information
on the faults. In this paper a new technique is presented allowing the diagnostic of an end-ring fault of a cage threephase asynchronous machine. Previous researches by the authors [5j hm,e given the expression of the instantaneous electromagnetic torque with these defects influence.
It has been observed actually that the ruptures influence greatly this quadratic quantity. The torque was calculated from the line currents and the e-m-f across flux sensors placed in the stator
windings. In this method, the flux sensors are not essential to determine the electromagnetic torque. The i'otor flux can be directly estimated by using an observer. This study presents ho~v
a model of the asynchronous machine is used to build the observer.
1. Measurement of the Electromagnetic Torque
In the d- q model and in a fixed reference frame ~i~ith respect to the stator, the electromagnetic torque can be written as follows:
~em " Pj (~q~ ~ds ~dr?qs) (I)
where #dr, #q~ are the rotor flux with respect to the stator and Ids, Iq~ are the stator currents in the d q axis.
2. Modelling of an Asynchronous Machine and of a Corresponding Observer In a fixed reference frame with respect to the stator, the electrical and mechanical equation of the machine can be written as [6]:
" ~~ ~ ~ ~~~
© Les #ditions de Physique 1996
444 JOURNAL DE PHYSIQUE III N°4
Ids Iqs
~vhere ~ is the state variable vector Id~
Iq~
Q~
Id~, Iq~ are the rotor currents in the d q axis; Q~, the angular speed of rotation, and ~ is the
input matrix.
Vds Ls 0 Ms~ 0 0
1§s 0 Ls 0 illsr 0
i~ = 0
,
A = Ms~ 0 L~ 0 0
0 0 Ms~ 0 L~ 0
C~ 0 0 0 0 J0
Rs
0 0 0 00 l~ 0 o 0
j~ 0 -Ms~o~p Rr -L~orp 0
1I£srorp 0 Lrorp Rr 0
~
p illsrlqr ~ p MsiId< 0 0 0
where Ls, is the stator phase inductance; J£Is~ is the mutual inductance between a stator and
a rotor phase; Lr is the phase rotor inductance; p is the number of pole-pair; ll~ is the phase
stator resistance; Ri is the phase rotor resistance; Vds, Vq~ are the supply voltages in the d q axis; Cr is the load torque; Jo is the moment of inertia of the rotating part. Equation (2) is
then ,vritten in a canonical form as shown belo~v:
)
= Aijxjz + El U (3)
~vhere Al
" (A)~~(-B) et El
" (A)~~
In practice, in most of the cases, the internal state of a system is not directly measurable, only
the inputs and the outputs are known.
In fact. an observer is a dynamic system which allows to reconstitute the states of the system from the informations on the inputs and on the outputs of the system. For an asynchronous
motor, a control affine system is used.
The observer has the same form of equation as the model, but contains in addition, a
correctional term such as:
" Al+j fl + B U + C°t~ (4)
ivith cor~
=
~~ Sp~ C~(fi y), as presented in reference iii after a coordinates transfor- ox
mation 16 to obtain an observability canonical form of the system with a high gain 9, where fi is the observed variable vector of the outputs measured; y is the variable vector of the outputs
measured; C a matrix of the measured outputs of the system and I the observed state variable vector.
Practically, the observer reconstitutes the internal variable state by correction of the mea- surable external state variable. As shown in Figure 1.
Tem " Pj3 Ids #qr Iqs #dr
,
u~r = p Qr is the electrical speed of rotation, (~m is the electromagnetic torque.
Vd~
MODEL Id~ OBSERVED
(2~ TORQUE
I~~
OBSERVER(O)
ids 0h
Fig. 1. Determination of the torque with the observed rotor fluxes.
Spectrum analysis of staler current in the d-axis Spectrum analysis af staler current in the d-axis
)OS
(w
fl 0.4
oz
00 200 0 400.0 500.0 800.0 1000.0 0 0 200.0 400.0 600.0 500.0 1000 0
~) frequency (Hz) b) frequency (Hz)
Fig. 2, Spectral analysis of observed current.
3. Results
This method was applied to a 4 kW cage asynchronous motor with 6 poles, 36 stator slots and
44 rotor bars. Two identical rotors with 44 bars were put in the same stator frame one after
the other (in order to collect curents and voltages signals necessary to process the observer for these t~vo cases). One of them was a healthy rotor and the other has an end- ring fault (broken end-ring). On line measurement of these signals has been done at no-load (g = 0.06%) in a
steady state condition for this machine. Figures 2 a,b and 3 a,b give the spectrum analysis
of current and flux observed respectively at no-load in steady state condition. We can notive
that harmonic components are more significant for the flux signal than for the current signal.
Figures 4 a,b show the instantaneous torque obtained for the t~vo types of rotor after pro-
cessing the observer. Gain of the observer has been adjusted by simulation to obtain the best convergence of the obser,~ed flux in respect to those obtain by the simulation of Park's model with or without noise injected in the inputs. Park's paraineters hm+ been measured during
no-load and locked rotor tests.
A marked variation can be seen on the form of the torque with fault compared to that of a sound rotor.
446 JOURNAL DE PHYSIQUE III N°4
of rotor flux in the d-axis of rotor flux in the d-axis
1.0
OS
106
w
w u
~ (
~0.~ %04
02
o-o
0 0 200.0 400.O 600.0 800.O IOOO.0 O-O 200 400.0 600.O BOO.O lO00.0
~) frequency (Hz) b) frequency (Hz)
Fig. 3. Spectral analysis of observed flux.
mochine
i-e Broken
o-e
o-e
~ -OI
~ ~
h ~
-o.e -
°.3' 0.3
~~~ (4 [me lsi
a) b)
Fig. 4. Observed Torque.
4. Theorical Analysis of the Torque Spectrum Components
The harmonics of the airgap flux distribution [2] are present in the stator current and in the
airgap flux, so with repect to the relation (i), used to obtained the torque where the torque is the product of these t~vo quantities, we can write the expression of the electromagnetic torque:
C~m(b,t)
=
~j Cm,p cos(mb fit) (5)
m,P with:
m = n[~ NR + n~~, S + nip fl = (n[~NR)Qr+n)u~i
where NR, number of rotor slots; S, number of stator slots; u~i " 27rfi, fi, supply frequency;
A~~i~$ Healthy rotor ~~j~j($ End-ring fault
Level Level
O.1 0.
o.075 o.075
o.05
0.025
O-O
700.O 750.O 800.0 850.0 900.O 950.01000.0 700.0 750.0 800.0 850.0 900.0 950.01000.0
Frequency @h) Frequenn. @h)
a) b)
Fig. 5. Spectral analysis of observed torque.
n[~, n[~ sum or difference of any two integers. n[, nj, the space harmonic and the time harmonic order, respectively.
So the time component of this expression gives the harmonics included in the torque for a
healthy machine:
f)~ =
(»lt
AIR) ~~
~
~~ + »),j fi (6)
f), = (n[~ NR + n[, p) (~ ~) + n), j fi (7)
P where g is the per unit slip. n[
,
nj the space harmonic and the time harmonic order of the
stator, respectively, n[
,
nj
,
tie siace harmonic and the time harmonic order of the rotor,
respectively, fj
,
fj a~e th/ time frequencies.
For a rotor /th aiymmetry (broken bar, end-ring fault or excentricity) Thomson et al. have
shown that the slot harmonic frequencies become [2]:
fi AT~-(i g) + n) + 2gfi ivhere n = 1, 2, 3... (8)
P
This frequency will appear in the stator current and the airgap flux density. The torque is calculated with expression (i) as the product of these two quantities, so the slot harmonic
frequency components of the torque for a rotor with asymmetry are:
fi l~~(i g) + n' (9)
P
fi ~~ (l g) + n'j + 4g fi (10)
P
Where n' is a sum or difference of any two integers n' = 2, -1, 0, 1, 2,....
Figures 5 a,b show the existence and an increase of the spectra at 733, 750 and 900 Hz
respectively. The torque spectrum can highlight the change in the spectra for the t~vo types of
448 JOURNAL DE PHYSIQUE III N°4
rotor. The spectra at 733 Hz corresponds to harmonics due to the number of rotor bars (9).
It can be concluded that the evolution of the spectra at 733 and 900 Hz can fortell an end-ring
fault in the rotor.
Table I gives the magnitude for the high-order harmonics of the instantaneous torque.
Table I. Magniti~de of the high-order harmonics of the torqi~e.
Frequency (Hz) Sound Broken ring
733 1.0 x 10~~ 3.0
x 10~~
900 0.3 x 10~~ 6.2 x 10~~
5. Conclusion
The new on-line fault diagnostic technique described in this paper shows that there is no need for any flux coils to be placed on the stator. The detection of an end-ring fault in the rotor
can be discriminated by the high-order harmonics of the instantaneous torque. This can be identified by an increase of the principal slot harmonics. The observer can also reproduce
the instantaneous angular speed. In future work, we will improve the model of the motor to
take account of saturation and space harmonic componends to allow a best convergence of the
observer.
Acknowledgments
We would like to thank particulary the Laborde et Kupfer Repelec company for it's industrial collaboration and the french Agence Nationale de Valorisation de la Recherche for it's financial support.
References
ill Prevention des avaries, Machines Alectriques toumantes, Cahier de prAvention, CP2, Allianz
(1988).
[2] Thomson W-T-, Deans N-D-, Leonard R-A- and MiIne A-J-, Monitoring strategy for dis-
criminating bet,veen different types of defects in induction motors, 18 th. Universities Power
Engineering, Conference Proc. (University of Surrey, England, 12 April 1983).
[3] Deleroi W., Broken bar in squirrel cage rotor of an induction motor, Part i: Description by superimposed fault currents, Arch. Fir. Eiektrotechnik 67 (1984) 91-99.
[4] Jufer M. and Abdelaziz M., Influence d'une Rupture de Barre ou d'un Anneau sur les CaractAristiques Extemes d'un Moteur Asynchrone h Cage. Bull. SEV (1978) pp. 921-925.
[5] Thollon F., Grellet G. and Jammal A., Asynchronous Motor Cage Fault Detection through Electromagnetic Torque Measurement, ETEP 3 (Sep. /oct. 1993).
[6] Jammal A., DAmarrage d'un moteur asynchrone, Rapport interne (France 1984).
[7] Bomard G. and Hammouri H., A high gain observer for a class of uniformly observable systems, IEEE CDC (Brighton, GB, 1991).
