field computation with finite element method...
TRANSCRIPT
Field computation with finite element method applied
for diagnosis eccentricity fault in induction machine
Moufid Mohammedi, Tahar Bahi
1Electrical Department, Faculty of Science Engineering, Annaba University, Annaba, Algeria
Laboratory of Automatic and Signal Annaba (LASA)
[email protected]; [email protected]
Abstract— This paper deals with analysis of the
magnetic field by using FEM and numerical
computation of the electromagnetic characteristics of
Induction machine. The knowledge of
electromagnetic characteristics is very important in
performance analysis of electrical machines. The
purpose of this investigation is to use the field
computation by finite element model to evaluate,
detect and diagnosis fault of the static eccentricity
effect on the vector potential and field magnetic.
The result of simulation of our model allows us to
clearly see the effect of the eccentricity on the
electromagnetic quantities of the induction squirrel
machine.
Keywords—Induction machine, modelisation, finite
element methode, eccentricity, diagnosis, simulation.
I. INTRODUCTION
The sudden damage of the induction motors, which are
generally used as part of the product line in the industry,
can lead to stop the whole process. Therefore, the
diagnosis of the lack of time is important to prevent the
spread of the fault on the product range.
Energy conversion in an induction motor (converting
electrical energy into mechanical energy) is through the
magnetic energy in the air gap. However, the
displacement effect of the rotor (eccentricity) directly
affects the course of the magnetic flux (magnetic
reluctance) [1,2].
According to the model developed in this work, we
could introduce and study the consequences of the
eccentricity phenomenon on the magnetic quantities of
the machine through the magnetic vector potential. The
complexity related to the spatial distribution of local
forces [3,4] to calculate a resultant force has been
surmounted due to the flexibility of our program allows
us to consider the effect of changing the rotor position
by adjusting its coordinates in the program.In the following sections, we propose the problematic
will be resolved by our proposed model in this paper.
In the third section, we consider the development of the model using the formulation of magnetic vector potential. Next, we present the simulation results and their interpretations.
II. STATEMENT OF THE PROBLEM
Our study is to see the evolution of magnetic variable
(magnetic field and vector potential) along the axis of
movement (x) of the rotor for 25% of the value of the
airgap. Comparing the simulation results in the default
case (with eccentricity) with those of the healthy case,
we can see the impact of eccentricity on the magnetic
quantity of the asynchronous machine.
Figure.1 Balanced of the rotor along x axis.
y
x
Stator
Rotor
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Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016
ISBN: 978-9938-14-953-1 (196) Editors: Tarek Bouktir & Rafik Neji
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III. MODEL OF INDUCTION MACHINE
To determine the field distribution at each time-step, a two dimensional transverse section of the induction motor is represented, in reducing the problem to two dimensions [5,6]. The transient magnetic field in terms of magnetic vector potential (A); The permeability of airis defined by µ0 = 4.p.10-7
H/m; Conductivity (σ) and current density (Js), can be expressed as:
The constitutive linear relationship of ferromagnetic
material is:
(2)
Where,
B: flux density;
H: magnetic field;
µr: permeability relative.
To solve the general diffusion equation (1) a classical weighted residual method with first order shape functions we obtain the following integral form [7,8]:
(3)
ωi : ponduration function.
With the following linear approximation for the vector potential:
(4)
Then, we obtain the following algebraic form:
(5)
(6)
IV. SIMULATIONS AND DISCUTION
The finite element model described above to evaluate the
effects of rotor eccentricity in the air gap on the vector
potential magnetic and the magnetic field [9,10].
The figure 2 shows the geometry of the induction
machine with four poles, 36 slots in the stator and 32
rotor bars.
The discretization of the geometry with finite element is
shown in figure 3.
The equipotential of potential vector magnetic is shown
by the figure 4.
Figure 2 Induction machine geometry
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-0.2
-0.15
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0.05
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Figure 4 Equipotentiel of potential vector magnetic
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Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016
ISBN: 978-9938-14-953-1 (197) Editors: Tarek Bouktir & Rafik Neji
-0.2
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x(m)
spatial distribution of potentiel magnetic
y(m)
A(A
.m)
Figure.5 Spatial distribution of potential vector
V. EFFECT OF THE ECCENTRICITY
A) Potential vector magnetic
The figure.5 shows the spatial distribution of the
potential vector magnetic for each element of the
geometry.
The projection of the spatial distribution of magnetic
vector potential presented in Figure.5 on the plane “zx”
allows us to obtain the potential vector magnetic in the
healthy case (figure6.a) and with fault, that is to say that
the rotor is balanced along the “x” axis (figure 6.b) is
illustrated by figure 6.
In the healthy cases (Figure 6.a) we find that the shape of
the spatial distribution of the magnetic vector potential is
symmetrical. Furthermore, the same figure shows that we
have the same absolute amplitude on the four poles of the
induction machine.
Against by, in the case with defect (Figure 6.b), the
thickness of the air gap is not uniform, then the shape of
the magnetic potential is not symmetrical and the
absolute value of magnetic potential is not uniform in the
four poles.The change in the position of the rotor (eccentricity)
occurs with the change of magnetic reluctance. Indeed,when the air gap reduces, so, the magnetic reluctance also reduces, therefore the amplitude of the magneticvector potential increases.
By against, when the air gap increases we see the opposite effect.
North poles
South poles
North poles
South poles
a. healthy case
b. With fault
Figure.6 Effect of the eccentricity on the potential
vector magnetic
Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016
ISBN: 978-9938-14-953-1 (198) Editors: Tarek Bouktir & Rafik Neji
Figure.7 Spatial distribution of magnetic field
B) Magnetic field
The figure.7 shows the spatial distribution of the
magnetic field (absolute values) for each element of the
geometry.
The projection of the spatial distribution of magnetic
field presented in Figure.7 on the plane “zx” allows us to
obtain the magnetic field in the healthy case (figure 8.a)
and with fault, where the rotor is balanced along the “x”
axis (figure 8.b), is illustrated by figure 8.
In healthy cases, the air gap is healthy, therefore uniform along the contour of the air gap. This is expressed by the symmetry of the shape of the magnetic field distribution observed in Figure 8.a.
By against, the figure 8.b (with eccentricity case), there is no symmetry in the evolution plane of the magnetic field.
The effect of the eccentricity of the magnetic field is
opposite with respect to their effect on the potential
vector, when the reduced air gap, therefore, the magnetic
reluctance also therefore reduces the amplitude of the
magnetic field decreases. For against, , when the air gap
increases the magnetic reluctance also increases,
therefore. the amplitude of the magnetic field increases.
VI. CONCLUSION
The results of simulations enables us to introduce and
clearly see the impact of eccentricity on the magnetic
behavior of the machine (magnetic field and vector
potential) for the rotor position change of 25% from its
initial position, it is found that the effect of the
eccentricity influences first places on the magnetic
reluctance (the course of the field in the air gap), the
Figure.8 Effect of the eccentricity on the magnetic field
a. healthy case
b. With fault
Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016
ISBN: 978-9938-14-953-1 (199) Editors: Tarek Bouktir & Rafik Neji
variation of the latter, causes a variation of the
magnetic properties (magnetic quantities), mechanics
(mechanical quantities ) and electrical (electrical
quantities).
VII. REFERENCES
[1] M. Rigoni, N. Sadowski*, N. J. Batistela, J.P.A.Bastos, ” Detection and
Analysis of Rotor Faults in Induction Motors by the Measurement of the
Stray Magnetic Flux ”, Journal of Microwaves, Optoelectronics and
Electromagnetic Applications, Vol. 11, No. 1, June 2012
[2] Jawad Faiz, Hamid Toliyat, “Finite-Element Transient Analysis of Induction Motors Under Mixed Eccentricity Fault “,IEEE
TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 1, JANUARY
2008
[3] Sang Bin Lee, Member, IEEE, Gerald B. Kliman, Life Fellow, IEEE, Manoj R. Shah, W. Tony Mall, N. Kutty Nair, Life Senior Member,
IEEE, and R. Mark Lusted, “An Advanced Technique for Detecting
Inter-Laminar Stator Core Faults in Large Electric Machines,” IEEE
TRANS. ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5,
SEPTEMBER/OCTOBER 2005
[4] M. J. DeBortoli, S. J. Salon, D. W. Burow, C. J. Slavik “Effects of Rotor
Eccentricity and Parallel Windings on Induction Machine Behavior: A
Study Using Finite Element,”
IEEE TRANSACTIONS ON MAGNETICS, VOL. 29, NO. 2, MARCH
1993
[5] T W Preston, A B J Reece, P S Sangha“Induction motor analysis by time-stepping techniques,” IEEE
TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 1, JANUARY
1988.
[6] J. Shen and A. Kost, “Modeling of the Idealized Exciting Current Sources in the FEM,” IEEE TRANSACTIONS ON MAGNETICS.
VOL. 31, NO. 3, MAY 1995
[7] Chang-Chou Hwang* , S.J. Salon, R. Palma
“A finite element pre-processor for induction motor including motion
and circuit constraints,” IEEE TRANSACTIONS ON MAGNETICS,
VOL. 24, NO. 6, NOVEMBER 1988.
[8] M. Mohammedi , T. Bahi, Y. Soufi “Finite Element Modeling Under Stress by the Nonlinearity of a Material Ferromagnetic,”
Journal of Electrical Engineering (JEE), 2012.
[9] M. Mohammedi , T. Bahi, Y. Soufi “Integration of the eccentricity effect in the field computation by FE,” EVER, Monaco,2012.
[10] M. Mohammedi , T. Bahi, Y. Soufi “Integration of the eccentricity effect
in the field computation of reluctance machine,” Journal of Electrical
Engineering (JEE), 2014.
Proceedings of the International Conference on Recent Advances in Electrical Systems, Tunisia, 2016
ISBN: 978-9938-14-953-1 (200) Editors: Tarek Bouktir & Rafik Neji