International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 5, May 2012)
Analysis of U-I and U-U Type Rail and Actuator Used in
Electromagnetic Levitation System Using FEM Software
P.K.Biswas1, S.Bannerjee2
1
Department of Electrical Engineering, Asansol Engineering College, Asansol, India.
2
Department of Electrical Engineering, NIT, Durgapur-9, India.
1
pabitra.biswas2009@gmail.com
2
bansub2004@rediffmail.com
The electrodynamics levitation system is inherently
stable, but at high speed it possess stability problem due to
negative damping. So some kind of passive damper is
required in elctrodynamically levitated vehicle to maintain
stability at high speed. In electromagnetic system, the
levitation is produced due to the attractive force between
electromagnets and ferromagnetic objects [3, 8].
Abstract— Electromagnetic levitated and guided system is
commonly used in the field of people transport, tool machines
frictionless bearing and conveyor system. In the case of low
speed people transport vehicles, the electromagnetic levitation
offers the advantage of a very salient motion and of a reduced
maintenance of the rail.In this work FEM based analysis and
design of different structure of rail (guide-way) and
electromagnetic levitation system (EMLS) has been
performed utilizing ANSYS software. Actuator and guide-way
are the most important part for magnetic levitation system. A
FEM analysis utilizing ANSYS software has done to find out
the flux pattern, working flux density, field intensity, force etc.
for different single actuator based levitation system at
different operating conditions. Different aspects of rail and
actuator have been described based on the ANSYS simulation
results. In this paper shows a simple magnetic model for the
study of the levitation and guidance forces produced by an
electromagnet and rail. The electromagnet shapes taken into
consideration in this paper U type and with I and U type rail.
Keywords—Electromagnetic Levitation,FEM analysis,
ANSYS software, Flux pattern, Guidance and Levitation
Force.
I. INTRODUCTION
T Electromagnetic levitated and guided systems are
commonly used in the field of people transport Vehicles,
tool machines frictionless bearings and conveyor systems.
In the case of low speed people transport vehicles, the
electromagnetic levitation offers the advantage of a very
silent motion and of a reduced maintenance of the rail.
Magnetic levitation trains are becoming a popular
transportation topic all round the globe [1,3]. Currently
MAGLEV trains have been created in Germany and Japan
for test runs only. Some other applications of electromagnetic levitation, apart from the application in
frictionless bearings and MAGLEV vehicles, are in the
fields of levitation of models in a wind tunnel, vibration
isolation of sensitive machinery, levitation of molten metal
in induction furnaces, levitation of metal slabs during
manufacture etc.
Figure.1. Simplified diagram of DC electromagnetic levitation system
(inverted model)
In case of DC electromagnetic levitation, electric current
in a wire wound coil produces the primary field while the
ferromagnetic object or guide-way creates a means of
shaping the magnetic flux. Generally the electromagnet is
kept fixed and the ferromagnetic object is made to remain
Suspended under the magnet as shown in Figure.1. The
electromagnet (actuator) and guide-way (rail) combination
along with associated closed loop control will make an
EMLS. In the Figure.2 the electromagnet is made to remain
suspended under the fixed ferromagnetic guide-way [1, 3].
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 5, May 2012)
At any particular point of the time the force of the
attraction between the electromagnet and the ferromagnetic
rail is given by,
F (i, z )  
d 1

L( z )i(t ) 2 

dz  2

(4)
Now substituting the value of the inductance from the
eq. (1.2) in the above equation we get,
F (i, z ) 
 0 N 2 A  i(t ) 
2
 z (t ) 


4
(5)
Figure.2. Block diagram of Electromagnetic Levitation System
At the equilibrium position (i0z0) the normalized force
eq.
This
configuration
is
normally
used
in
electromagnetically levitated vehicle and maglev train. The
electromagnet acts as an ‗actuator‘ which provides the
basic suspension force. When the electric current is passed
through a wire wrapped around a core of ferromagnetic
material, magnetic flux is generated. This flux produces an
attractive force on any nearby ferromagnetic material. With
reference to the Figure.1, the instantaneous coil inductances
can be expressed as [1, 3]
N
N Ni (t ) N 2
L( z ) 
T 

i(t )
i(t ) RT
RT
F0 (i0 , z 0 ) 

i(t) = instantaneous current of the coil
Фt = total flux in the magnetic circuit
RT = Reluctance of the entire magnetic circuit.
If the reluctance of the magnetic core is assumed to be
negligible with compared to the two air gaps then,
2 z (t )
2z 0
.
 0 N 2 A  i(t ) 
4
2
 z (t )   mg; (7)


II. DIFFERENT TYPES OF ELECTROMAGNET-RAIL SYSTEM
(2)
The mechanical action depends not only on the structure
of the electromagnet but also on the shape of the guide
way. In particular, the same electromagnet coupled to guide
ways of different shapes results in a change of intensity of
the two forces. The shape of the guide way is important,
first of all in order to get levitation and guidance force with
the same electromagnet [2].
Then the normalize inductance of the magnet-coil at any
equilibrium position (z0) is given by,
L 
(6)
The magnet configuration is selected on the basis of
required pole face area and the necessary window area to
house the excitation coils [3,4].The eddy current will
generate in the magnet core as well as in the solid guideways and it will be different for the different structures of
magnet and guide-way. This eddy current will reduce the
lift force. Laminated core structure is a better option as far
as eddy current losses and faster response time of the
magnet are concerned.
N = No of the turns of the coil
0 N 2 A
   mg
 z0 
mz(t )   F (i, z)  mg;
(1)
0 N 2 A
4
2
The dynamics of the electromagnet is the given by
Where
L( z ) 
 0 N 2 A  i0 
(3)
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 5, May 2012)
f LEV (i, z, x) 
f GUID (i, z, x) 
1 
L( z, x)i 2
2 z
1 
L( z, x)i 2
2 x
(9)
(10)
A simple U-I and U-U type magnetic model is taken for
the calculation of the forces. Magnetic potential losses in
the iron parts (electromagnet and rail) and the leakage
fluxes are neglected, and the magnetic flux flows in the air
gaps in a constant section, for any value of z and x. For a
given z, the more the electromagnet is far from the central
position, the greater is the mean distance of the magnetic
flux lines in the air gap.
Figure.3. Levitation and guidance forces with a flat or I-shaped guide
way
III. FINITE ELEMENT METHOD (FEM) ANALYSES
The finite element method (FEM) (sometimes referred to
as finite element analysis (FEA)) is a numerical technique
for finding approximate solutions of partial differential
equations (PDE) as well as of integral equations. The
solution approach is based either on eliminating the
differential equation completely (steady state problems), or
rendering the PDE into an approximating system of
ordinary differential equations, which are then numerically
integrated using standard techniques such as Euler's
method, Runge-Kutta, etc. Finite Element Analysis (FEA)
is one of these methods. The Finite Element Method is a
good choice for solving partial differential equations over
complicated domains (like cars and oil pipelines), when the
domain changes (as during a solid state reaction with a
moving boundary), when the desired precision varies over
the entire domain, or when the solution lacks smoothness.
The arrangement is working on DC that is why a static
magnetic field problem has been analyzed by the Finite
Element Method (FEM). The static magnetic field problem
can be described by the following Maxwell‘s equations
[9,10]
Figure.4. Levitation and guidance forces with a U-shaped rail
We are interested in a mathematical model that gives us
a relationship between the following
variables:
i: the current flowing in the coils
x: the lateral position of the electromagnet
z: the air gap between the electromagnet and the rail
fLEV : the levitation force
fGUID : the guidance force
Usually for the calculation of the guidance force
complete leakage fluxes and wide fringe fluxes are usually
taken into account. We would like to create a simpler
magnetic model, in order to simplify the calculations of
static forces by using FEM analysis or Ansys software
simulations. Even the inductance, as a combination of the
magnetic energy of the circuit will be a function of both coordinates and of the current flowing in the coils [2]
w(i, z, x) 
1
L( z, x)i 2
2
XH  J
(11)
.B  0
(12)
.J  0
(13)
XE  
(8)
B
t
(14)
Where H, B, J and μ are the magnetic field intensity, the
magnetic flux density, the source current density, and the
permeability, respectively. The permeability is supposed to
be constant, μ = μ0 in air.
So we can calculate the levitation and the guidance force
with the well-known formulas [2]
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 5, May 2012)
The vector fields B and H are related through the
permeability μ (in henries/meter) of the medium as [ 9]
B  H
ANSYS electromagnetic solutions enable engineers and
designers to accurately predict the behavior of electrical
and
electromechanical
devices
[7].The
ANSYS
electromagnetic product suite contains both general
purpose and application specific products to address a
broad array of industry applications, different engineering
disciplines. ANSYS Mechanical and ANSYS Multiphysics
software are non exportable analysis tools incorporating
pre-processing (geometry creation, meshing), solver and
post-processing modules in a graphical user interface [7].
These are general-purpose finite element modeling
packages for numerically solving mechanical problems,
including static/dynamic structural analysis (both linear and
non-linear), heat transfer and fluid problems, as well as
acoustic
and
electro-magnetic
problems.ANSYS
Mechanical technology incorporates both structural and
material non-linearities. ANSYS Multiphysics software
includes solvers for thermal, structural, CFD,
electromagnetic, and acoustics and can sometimes couple
these separate physics together in order to address
multidisciplinary. Figure.5. Flow chart of calculation of
force, flux & field by using ANSYS software for U-I and
U-U structure.
(15)
In terms of the magnetic vector potential A (in Wb/meter)
B  XA
(16)
To Eqns. (3) and (6) leads to Poisson‘s equation for
magneto static fields:
 2 A  J
(17)
When J = 0, Eq. (14) becomes Laplace‘s equation:
2 A  0
(18)
Equations (12), (14), (16) and (17) are useful tools in
calculation of magnetic field in magneto static cases [8].
The magnetic field will be used in the calculation of
magnetic force experienced by the levitated object in
EMLS. The electromagnetic force generated by the
electromagnet is the gradient of the magnetic field energy
and depends on the air gap size [9, 10]
dW
dz
(19)
1
 BHdV
2
(20)
F 
And
W
Where F is the electromagnetic force, W is the magnetic
field energy, and V is the air gap volume. The
electromagnetic force is a nonlinear function of the coil
current and the distance between the shaft and
the electromagnet.
IV. ANSYS SOFTWARE BASED SIMULATION
ANSYS is engineering simulation software which
develops general-purpose finite element analysis and
computational fluid dynamics software. In this paper
ANSYS is used for analysis purpose of U-I and U-U
structure While ANSYS has developed a range of
computer-aided engineering (CAE) products, it is perhaps
best known for its ANSYS Mechanical and ANSYS
Multiphysics products [7]. The ANSYS program has many
finite-element analysis capabilities, ranging from a simple,
linear, static analysis to a complex, nonlinear, transient
dynamic analysis. Electromagnetic simulation from
ANSYS provides industry leading analysis tools that enable
the accurate simulation of electromagnetic fields.
Figure.5. Flow chart of calculation of force, flux & field by using
ANSYS software for U-I and U-U structure.
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 5, May 2012)
V. SIMULATION RESULTS AND DISCUSSIONS
Two-dimensional FEM simulation has been carried out
to determine flux pattern, working flux density, field
intensity, force etc. in the actuator and guide-way.
Commercial FEM software ANSYS has been used for this
purpose.The ANSYS simulation plot of the flux pattern and
flux density for U-I structure during shifting of guide-way
(both direction) has been observed in Figure.6 to Figure.13.
The vector plot of flux density and force has been
presented as shown Figure.14 to Figure.17.It has been
noticed from Figure.18 and Figure.19 that the flux and flux
density is decrease with increase the shifting distance. The
levitation force and guidance forces depend on the position
of the electromagnet, described by shifting distance(x) and
air-gap (z). It has been noticed that the levitation force is
maximum when the electromagnet is centered (x=0),
whereas the guidance force is zero. The rail is shifted both
side from the centre to 20 mm. By increasing the value of
shifting distance, shifting force is increased and levitation
force is decreased as shown Figure.21 and Figure.22. It has
been noticed from figure 20 and figure 21. the guidance
force of U-U structure is more than U-I structure but the
levitation force of U-I structure is more than U-U structure.
For the same dimension of electromagnet and rail, it has
been observed from Figure.23 and Figure.24 that any
operating condition the lift force developed between the UI structure (U-core magnet and flat guide-way) is more than
the U-U structure. But the guidance force developed is
more in U-U structure. It is to be mentioned that the
levitation force is maximum when the electromagnet is
placed centrally with the guide-way, whereas the guidance
force is zero as shown Figure.23. In the EMLS, other than
levitation force, guidance force is also developed between
actuator and rail. In ANSYS simulation both the guidance
and levitation force is observed. In actual Maglev rail
system there will be always a relative change in distance
between guide-way and rail. Here the effect on levitation
and guidance force with the shifting of rail (guide-way) has
been studied through FEM analysis. It has been noticed
(Figure.23 and Figure.24) the levitation force is maximum
when the electromagnet is placed centrally with the guideway, whereas the guidance force is zero. The shifting of
rail has been done both directions with respect to central
position. With the change of rail position in either
direction, the levitation force has been reduced and the
guidance force has been increased.
Figure.6. Flux pattern for U-I structure for N=500,z=1 and x=1(-ve
shifting)
Figure.7. Flux pattern for U-U structure for N=500,z=1 and x=1(-ve
shifting)
Figure.8. Flux pattern for U-I structure for N=500,z=1 and x=1
(+ve shifting)
36
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 5, May 2012)
Figure.12. Flux density for U-I structure for N=500,z=1 and x=1
(+ve shifting)
Figure.9. Flux pattern for U-U structure for N=500,z=1 and x=1
(+ve shifting)
Figure.13. Flux density for U-U structure for N=500, z=1 and x=1
(+ve shifting)
Figure.10. Flux density for U-I structure for N=500,z=1 and x=1
(-ve shifting)
Figure.14. Flux density for U-I structure for N=500, z=1 and x=1
(+ve shifting)
Figure.11. Flux density for U-U structure for N=500, z=1 and x=1
(-ve shifting)
37
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 5, May 2012)
Figure.15. Flux density for U-U structure for N=500, z=1 and x=1
(+ve shifting)
Figure.18. Flux vs shifting distance for U-I and U-U structure for
N=500,z=1 and x=1
Figure.19. Flux density vs shifting distance for U-I and U-U structure
for N=500,z=1 and x=1
Figure.16. Vector plot of force for U-I structure for z=1 and x=1
(+ve shifting)
Figure.20. Levitation force vs shifting distance for U-I and U-U
structure for N=500,z=1 and x=1
Figure.17. Vector plot of force for U-U structure for N=500,z=1 and
x=1(+ve shifting)
38
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 5, May 2012)
VI. CONCLUSIONS
The effect of shifting of guide-way (rail) on levitation
and guidance force has also been studied.
A two
dimensional FEM analysis has been carried out utilizing
ANSYS software. 3-D curve for Guidance and Levitation
Force for U-I and U-U shifting structure has been
presented. ANSYS simulation plots of flux pattern, vector
plot of flux density and force has been presented. The
guidance force of U-U structure is more than U-I structure
but the levitation force of U-I structure is more than U-U
structure. The simulated results of flux, flux density and
force are determined by FEM-based analysis using the
Maxwell's stress tensor and virtual work.
Figure.21.Guidance force vs shifting distance for U-I and U-U
structure for N=500,z=1 and x=1
VII. ACKNOWLEDGEMENTS
The author wishes to acknowledge DST, Govt. of
India for sponsoring the Project entitled ―Development of
DC Electromagnetic Levitation Systems –Suitable for
Specific Industrial Applications‖
REFERENCES
[1] B.V. Jayawant, 'Review lecture on electromagnetic suspension and
levitation techniques', Proc. R. Soc. Lond. A416, 1988, pp.245-320.
[2] D‘Arrigo Aldo, Rufer Alfred, ―Design of an integrated
electromagnetic levitation and guidance system for Swiss Metro‖,
EPE '99 – Lausanne.
[3] P.K. Sinha, Electromagnetic Suspension, Dynamics and Control,
Peter Peregrinus Ltd., London, 1987.
[4] N. A. Shirazee and A. Basak, ―Electro permanent suspension system
Figure.22. 2-D curve for Guidance and Levitation Force vs. Air-gap
for U-I and U-U shifting structure
for acquiring large air-gaps to
[5] Suspend loads', IEEE Trans. on Magnetics, Vol.31, No.6, Nov.1995,
pp.4193-4195.
[6] A. Bittar and R. M. Sales, ―H2 and H. control for maglev vehicles‖,
IEEE Control Systems
pp.18-25.
Magazine, Vol.18, No. 4, Aug.1998,
[7] Reference Guide ANSYS CFX-Solver, Release 11.0
[8] S.Banerjee, P.Biswas, R.Bhaduri, ―A Comparative study between
different structures of Rail and Actuator used in Electromagnetic
levitation systems‖, proc in 5th IET Intentional Conference on Power
Electronics, Machines and drives,PEMD 2010,UK,19-21 April 2010.
[9] Matthew N.O.Sadiku, ―Elements of Electromagnetic‖, OXFORD
University press.
[10] Rothwell E.J., Cloud M.J., ―Electromagnetics‖, CRC Press 2001.
[11] Hammond P., Sykulski J.K., ―Engineering Electromagnetism –
Physical Processes and Computation‖, Oxford University Press,
New York 1994.
[12] Kwang-Ok An, Chang-Hwan Im, Chang-Hwan Lee, Hyun-Kyo
Jung, ―Optimal design of magnetic scale for linearizing magnetic
flux density and force‖, Proc. in International Journal of Applied
Electromagnetics and Mechanics", Volume 18, Number 4/2003,
pp.251-258.
Figure.23. 3-D curve for Guidance and Levitation Force vs. Air-gap
for U-I (left) and U-U (right) shifting structure
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 5, May 2012)
[13] Guirong Wang, Hong Xu, Jian Sun, Wei Wei , ―Electromagnetic
field analysis and dynamic modeling of force for motor in Maglev
train‖, Proc. of 7th World Congress on Intelligent Control and
Automation, WCICA 2008., pp. 8198 – 8202.
[14] J. E. Paddison, R. M. Goodall, ―EMS Maglev Suspension Control
System Comparison and Trends‖, MAGLEV‘98, Mt. Fuji, Japan,
1998.
[15] R. D. Fruechte, R. H. Nelson, T. A. Radomski. ―Power conditioning
system for a magnetically levitated test vehicle‖, IEEE transaction
on vehicular technology, Vol VT-29, No 1, Feb 1980, pp 50-60.
[16] Y. Hikasa, Y. Takeuchi, ―Detail and experimental results of
ferromagnetic levitation system of Japan Air Lines HSST-01/-02
vehicles‖, IEEE transaction on vehicular technology, Vol VT-29, No
1, Feb 1980, pp 35-41.
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