Download SIMULTANEOUSLY FULFILLMENT OF STUDIES FOR MAGNETIC

TEMPERATURE AND MAGNETIC FIELD ANALYSIS ON AN
ACTUATOR BY USING FINITE ELEMENT METHOD
N.Füsun SERTELLER
M.Ü. Teknik Eğitim fakültesi Elektrik eğitimi Bölümü 34722 Ziverbey / İstanbul [email protected]
Abstract:
In this research FL 150 D Type contactor's
dimensions is used as an actuator. Three types of
material, which commonly used in industry, are
examined. These studies are executed seperatly two
main groups. First study: Immediately before
contactor was switched off, magnetic field and force
analysis of contactor is carried out using finite
element method (FEM) software program. The other
studies, immediately after contactor was switched off.
Temperature analysis is obtained by a developed
program and their comparative results are issued. In
this study, Ferro magnetic and joule losses are so
lower, they are neglected, and the study is carried out
at a certain time interval that plays most significant
role in operation of contactor.
Keywords  Actuator, Electromagnetic Field,
Magnetic Material, Finite Element Element, Heat
transfer
I-INTRODUCTION
Contactors play an important role in Electrical
Industry and Electrical Devices. The contactors are
not only used as switches, they are also used for
controlling and supporting measurement. Their
effects on electrical circuits are highly important;
both magnetic and thermal operation performances
have to be known in detail.
The attributes of this study done here, computing
and analyzing the electromagnetic field and force
and temperature distributions, constituting two
indispensable researches not only on an actuator but
also all electrical equipments. This study brings
together magnetic and temperature analysis together
in the same structure. However the analyses are
studied separately. The complex processes are
strictly tried to avoid, and clear expressions brought
in the study to make the problems understandable.
II- NUMERICAL PROPERTIES BY USING
FINITE ELEMENT METHOD
a- Magnetic Field and Force
Electromechanical energy conversion is possible
when the amount of energy stored in the coupling
field depends on the relative positions of the
mechanical system.
The magnetic field density and magnetic field in an
actuator system necessitates of the governing
electromagnetic equations to predict accurately the
system performance.
M
2
Bn
Sn
n 1 2  0
F 
(1)
B is called magnetic force field, n refers to different
air gaps in the contactor, M is the total number of
air gap, 0 is the permebility of air gap.
Finite Element Method (FEM) allowed the problem
discretised in the x-y plane by using magnetic
vector potential. Drichlet Boundary conditions are
entered to solve the problem [1-2].
b-Thermal Equations
The problem inherits symmetry with respect to xaxis; it is considered only ( y  0 ) part of the
device. The formulation of the problem is given
such
2
 T ( x, y )
x
2
2

 T ( x, y )
y
2

1
s ( x, y )
(2)
k
Where T is temperature, s , heat source and k
thermal conduction coefficient of contactor metal.
FEM scheme based on Galerkin method. Linear
triangle elements are chosen. In each triangular
element, a field function may be approximated by
the first order polynomial, application of the
weighted residual method we eventually obtain the
discretised FEM form of the heat conduction
equation in the contactor.
III –SIMULATION AND PROGRAMMING
RESULTS
a- Simulation and Analytical Results for Magnetic
force
The numerical method is used to solve magnetic
force problems in industrial frequency applications,
in
magnetic vector potential (A=B)
formulation. J current density (A/mm2) as a
magnetic field source and dirichlet boundary
conditions are used for problem to analyze. The
problem structure is shown in Fig.1.
Fig. 1 (E Type) Contactor with airgap
Problem is analyzed for three materials; cast steel,
silicon sheet iron and cast iron.
After analyzing the problem, equations are built to
obtain the force values numerically. The numerical
results are given in Fig2.
Casting Steel
F-B Curves
y axis. The algorithm incorporates linear triangular
elements that facilitate proper modeling of problem
geometry and can represent the field variables in
heat conduction problems very accurately.
Silicon Sheet Iron
Casting Iron
4,50000E+01
4,00000E+01
3,50000E+01
3,00000E+01
F
2,50000E+01
2,00000E+01
1,50000E+01
1,00000E+01
5,00000E+00
3,06361E-01
2,77650E-01
2,52311E-01
2,31452E-01
2,30770E-01
2,47809E-01
2,84674E-01
3,25940E-01
3,70137E-01
0,00000E+00
B
Fig 2. F-B relationship curves
Fig. 2 shows that the various materials play an
important role for contactor’s performance and
magnet design [2].
Mathematica program is developed to analyze
temperature distribution on contactor. In the FEM
analysis, 204 nodes and 320 triangular elements are
chosen. This indicates relatively fine meshing
structure for this work. The linear system
constructed according to Eq.(2) is solved by the
preconditioned conjugate gradient algorithm [3].
The numerical results are tested by the Finite
Difference Method (FDM) that based on the same
number of nodes. This means that in both methods,
the temperature is evaluated in the same spatial
points.
Fig. 3 Temperature distribution in the contactor
The test solutions are performed for different
contactor materials. It is presented in Fig.3. At first
glance, this graph seems to sketch the temperature
distribution as a function of only x spatial variable.
Actually, it must be interpreted that each adjacent
curve also represents the thermal variation along the
IV- CONCLUSION
This research study examined how relationship
between force and magnetic flux is and how this
relationship varies as per temperature values. In
some operating conditions, to know this
information can be highly important. Beside this
high thermal state of a contactor affects its
magnetic properties. The other point is the using of
both analyzing in the same problem is the specialty
of the study. Additionally, the study will have been
adapted easily on different subjects. Essential ones
are magnet design, coupled problems, temperature
distribution problems etc.
ACKNOWLEDGE
The author would like to thank İ. Taşçı and his
company Federal Electric for his technical support.
REFERENCES
[1] K. Miyoshi, H. Shimizu, S.I. Megura, H. Ueteka, N. Hirota,
K. Kitazawa” Development of Compact Magnet for High
Magnetic
Force”
IEEE
Transaction
on
Applied
Superconductivity, vol 12, no.1, March 2002.
[2] A. Benhama, A.C. Williamson, A.B.J. Reece," Virtual work
Approach to the computation of Magnetic Force Distribution
from Finite Element Method" IEEE ,Proc-Electro. Power Appl.
Vol. 147,No. 6, November 2001.
[3] D. S. Burnett, “Finite Element Analysis”, Reading,
Massachusetts, Addison-Wesley, 1987.