Electrical and Electronic Engineering 2012, 2(2): 64-67
DOI: 10.5923/j.eee.20120202.12
Modelling Electromagnetic Suspension Force Using
Measured Inductance-Airgap Data
Musaab Hassan
Department of Mechanical Engineering, Faculty of Engineering, Sudan University of Science and Technology, Southern Campus,
Khartoum, Sudan
Abstract Electromagnetic suspension system is commonly used in the field of high-speed vehicle, conveyor system, tool
machines and frictionless bearing. Modelling a magnetic system requires modelling the magnetic force characteristics to-
gether with the current and the position. In this work; a 1D look-up table, of measured data, was used to represent the in-
ductance as a function of the airgap. A 2D look-up table was generated to represent the electromagnetic force as a function of
the current and the airgap. The proposed model account for both inductance variation and current variation as the airgap is
changing.
Keywords Electromagnetic, Suspension, Inductance, Levitation Systems
1. Introduction
One of the main problems in modelling a magnetic sus-
pension system is the nonlinearity inherent in the electro-
magnetic circuit. To model the magnetic levitation force, the
force-position-current equation is often used[1,2,3, and 4].
Simulation data together with lookup tables was also im-
plemented to model the system[5]. Experimental data which
relate the force to the airgap is considered to be more realis-
tic[6]. When applying a DC voltage into an electromagnet
that is suspending an iron object (the object is freely sus-
pended in the air), the voltage applied and the current in-
duced in the circuit are related through the flux linkage as
follows:
(, ) iz
V Ri
t
φ ∂
= +
∂
(1)
where; R is coil resistance, φ is the flux-linkage, i is the
current flowing in windings, t is the time, and z is the
airgap.
To model the full nonlinearity of the system, eqn.1 has to
be used. There were various approaches to this problem
discussed in[7] where different forms of equation.1 were
applied. Methods carried out to handle the nonlinear data
through mathematical approaches using curve fitting to
represent the nonlinear data introduce some errors, and these
errors will increase by the process of differentiation.
* Corresponding author:
musaabh@hotmail.com (Musaab Hassan)
Published online at http://journal.sapub.org/eee
Copyright © 2012 Scientific & Academic Publishing. All Rights Reserved
2. Modelling of a Magnetic Suspension
System
The electromagnetic force is the rate of change of the
co-energy
(, )
(, ) constant
Wiz
Fiz i
z
∂
= =
∂
(2)
In the absence of leakage flux the same flux links the
N-turn winding N times and also that the flux density is
constant over the cross section, the magnetic co-energy can
be written in the following form[8];
2
1
2
W Li = (3)
Assuming linear flux-current characteristics, the induc-
tance can be written as[9],
2
0
NA
L
z
µ
= (4)
0
µ is permeability of free space, N is the number of turns,
and A is the cross sectional area .
By substituting the inductance into energy equations,
equation.2 can be written as follows;
2 2
0
(, )
6
NA i
Fiz
z
µ
=
(5)
Nichols[10] used equation.5 to characterise an electro-
magnetic suspension system. In modelling electromagnetic
system, equation.1 can be simplified as follow;
(, ) iz
V Ri
t
φ ∂
= +
∂
(6)
( ) Li
V Ri
t
∂
= +
∂
(7)