Journal of Magnetism and Magnetic Materials 254–255 (2003) 228–233

Designing and prototyping for production. Practicalapplications of electromagnetic modelling

A.J. Moses*, F. Al-Naemi, J. Hall

Cardiff University, Wolfson Centre for Magnetics Technology, School of Engineering, Newport Road, P.O. Box 925,

Cardiff CF24 0YF, UK

Abstract

Electromagnetic modelling using numerical methods such as finite element analysis (FEA) is well established for

solving problems beyond the scope of analytical methods. This paper focuses on two case studies showing the

advantages of FEA in speeding up the design process and improving the final design of electromagnetic devices.

r 2002 Elsevier Science B.V. All rights reserved.

Keywords: Computer simulation; FEA; Devices; Electromagnetic field computations

1. Introduction

Many spheres of engineering have seen enormous

advances in design processes made possible by the

development of computer-aided simulations. This is no

different for electromagnetic engineering. The aim of

this paper is to set out, using two case studies, how

numerical modelling tools such as finite element analysis

(FEA) can improve the design process and the

performance of the final product. The first case study

compares the FEA technique with the traditional design

method to demonstrate the improvement in the design

procedure of a conventional electromagnetic actuator.

The second case study shows how FEA can be used in

research to improve the final design of a non-conven-

tional electromagnetic device.

2. Analytical approach

The traditional analytical method makes use of circuit

theory, phasor diagrams, and equivalent circuit techni-

ques to represent the operation of an electromagnetic

device under specific conditions. Although these techni-

ques have been refined over time, they are still only

suited to relatively simple electromagnetic circuits.

Considerable experience is required because of the need

to include correction factors, which must be introduced

to minimise the difference between measured and

predicted performance. For example, in the analytical

approach of the modelling of some rotary machines,

generalised machine theory is used where the actual

three-phase armature windings are transformed to

equivalent d, q windings by Park’s transformations [1].

This produces an equivalent circuit and a phasor

diagram representing the machine by a set of electrical

parameters related to its magnetic components. How-

ever, the basic assumptions of the generalised theory

neglect saturation, harmonics and employ coarse mag-

netic lumping. The relative simplicity of the resulting

equivalent circuit is an advantage and can produce a

model which is adequate but with the limitation that the

rotor and stator iron cannot be adequately represented

in most models. Likewise in the prediction of transfor-

mer no-load losses, the FEA method can only give a

certain degree of information since the effect of practical

building parameters and material anisotropy cannot be

adequately represented [2,3].

3. Finite element method

FEA was adapted for the simulation of electromag-

netic devices more than 20 years ago [4]. The method

*Corresponding author. Tel.: +44-29-2087-6854; fax: +44-

29-2087-6729.

E-mail address: mosesaj@cf.ac.uk (A.J. Moses).

0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 9 6 3 - 0

involves the subdivision of the region of interest into

smaller areas (or volumes in the case of 3D) called finite

elements. The spatial variation of magnetic potential

(vector or scalar) throughout the region is described by

non-linear partial differential equations derived from

Maxwell’s equations. These equations are usually

written in terms of vector potential ‘‘A’’ which facilitates

the determination of field quantities such as flux density.

Accordingly, the equations are solved after discretisa-

tion in terms of A and the other quantities such as flux

density are calculated from the nodal values of A in the

post-processing phase.

FEA solutions can be obtained for a wide range of

problems beyond the scope of the analytical methods.

The limitations imposed by the analytical methods, such

as their restriction to homogeneous, linear and steady-

state conditions, can be overcome. The tremendous

increase in computational power and the development of

commercial simulation software have enabled the FEA

technique to be implemented into industrial design.

Using such software, it is now feasible to model

complicated geometries incorporating non-linear mag-

netic properties of the materials and arbitrary-shaped

excitation waveforms.

4. Case study to demonstrate an improved design process

The FEA technique can be used in the design process

of linear electromagnetic actuators to minimise proto-

typing time and cost and to optimise design configura-

tions. Actuators consist of an electromagnet with a fixed

magnetic yoke and a moving part (plunger) made of a

magnetic material, which undergoes linear motion along

a prescribed stroke length. The operation is based on the

reluctance principal in which, when excited, electro-

magnetic force moves the plunger from a higher to a

lower reluctance position. Actuators are usually char-

acterised by the force versus stroke length, which is a

function of the magnetic circuit. In this example, an

actuator was required to drive a valve gate over a

specified distance. A constant force greater than 20N

over the full stroke length was to be achieved within

certain electrical, geometrical and cost specifications.

The analytical and FEA design processes are described

below.

4.1. Analytical design

There are general rules in governing the design of

linear actuators based on Rotor’s method [4] in which an

index number defined byffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiforce=stroke length

pis related

to the characteristics of many actuator designs and four

formulae calculating the force, voltage, numbers of turns

and coil temperature. Using these rules and experience, a

series of prototypes can be developed which incorpo-

rates refinements, which result in a suitable design.

Following the conventional design rules, a flat-faced

plunger actuator, as shown in Fig. 1, was selected. The

outer diameter of the magnetic can (casing) is approxi-

mately 46mm and it length was around 57mm. The coil

magnetomotive force (mmf) (NI), voltage and heating

equations were solved and a preliminary design was

obtained. The equations below were used to calculate

the electromagnetic force F ; which is a function of theair-gap flux density Bg:

F ¼B2g

2m0a; ð1Þ

NI ¼Bg

m0lg þ

XHclc: ð2Þ

The term Bglg=m0 represents the mmf needed to establishthe flux across the air gap of length lg: The term

PHclc

represents the mmf necessary to establish the flux in the

Fig. 1. 3D representation of a quarter section of the actuator and the 2D flux distributions of the various designs.

A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 254–255 (2003) 228–233 229

iron path of the circuit of length lc: m0 is the magneticconstant and a is the surface area of the plunger.

To achieve sufficient force from restricted dimensions,

a high air-gap flux density was required. However, this

leads to the yoke magnetic material operating close to

saturation. To achieve the constant force characteristic,

the fixed yoke has to be shaped in such a way that it

becomes more highly saturated as the gap length

decreases. Saturation and flux leakage make it difficult

to accurately predict the performance of the actuator

over its full stroke length using analytical methods. This

is partly because the mmf of the iron path usually

accounts for 10–30% of the NI depending on the

magnetic properties of the iron used. The analytical

design calculation shows the preliminary design will

provide a force of 20N with a flat shape characteristic. It

is usual for the first prototype to be built and tested at

this stage. The speed of convergence towards final

design, perhaps going through several prototyping

stages, will depend on the experience of the designer.

4.2. FEA design

FEA allows a faster route towards final design

optimisation by removing the need for the intermediate

prototyping stages. The actuator geometry with given

magnetic material characteristics and coil excitation,

was modelled using a 2D non-linear magnetostatic, axi-

symmetric technique [5]. From the non-linear field

solutions, the electromagnetic force acting on the

plunger was calculated numerically for various plunger

positions along the stroke length. The force character-

istic is shown in Fig. 2. These results show that the

preliminary design failed to meet the required character-

istic in terms of force pattern and magnitude.

The graphical representation of the flux distribution

and flux density of the preliminary design was a helpful

feature in design refinement procedures. The level of

saturation in the device shows room for a tight-tolerance

design, which maximises the air-gap flux density and

hence increases the force.

The potential performance was improved by a series

of modifications to the magnetic circuit of the pre-

liminary design, as shown in Fig. 2. Keeping the

actuator excitation constant, a modification to the shape

of the fixed and moving parts alters the characteristic of

the actuator. In designs I and IV, the flat plunger was

changed to a tapered shape. It was possible to evaluate

the effect of taper angle in relation to the saturation of

the plunger. In design II, the fixed part of the yoke was

adjusted with respect to the plunger shape allowing the

latter to gradually approach saturation in proportion to

its displacement along the stroke path. In design III a

301 conical shape plunger was used.

The performances of all modified designs meet the

required specification. It was also possible to carry out a

design sensitivity analysis, which highlighted for exam-

ple, the effect of manufacturing tolerance on the

performance. The results show that the performance of

design II was more consistent than the others since not

such close dimensional tolerances were required. A

prototype was built based on design II and its

performance was measured. A comparison between

computed and measured force–stroke characteristic

shows an average discrepancy of 8–10%.

4.3. Practical implementation of FEA into design cycle

In this case study and indeed in many other

conventional devices such as electrical machines and

transformers, the FEA could be used in conjunction

with the analytical design procedures. Electric circuit

and design equations could be used to produce the initial

design and predicted performance and further design

development would be achieved using FEA. There are

many commercial packages available in the market, and

practically they mainly differ in the ease in which a

model can be constructed and the speed at which results

can be obtained.

One of the major concerns in using FEA as a design

and simulation tool is the solution speed and a level of

expertise, which is not widespread amongst design

engineers. These are important considerations for the

integration of FEA into the design office. In this case

study, the 2D-magnetostatic solver is sufficient to

achieve the purpose. The PC-based package complies

with the Microsoft OLE automation interface allowing

communication with other mathematical software used

in analytical design.

The interface between the designer and the FEA is

also important. This was tackled by ensuring flexibility

of the software in the automation of pre-processing,

solving, and post-processing stages. The communication

flexibility allows FEA to be initiated from a familiar

design screen enabling the designer to export the design

0

5

10

15

20

25

30

35

40

45

0 1 2 3 4 5

Stroke or gap length (mm)

Fo

rce

(N

)

Preliminary Design Design I Design II

Design III Design IV

Fig. 2. Performance characteristics of the preliminary and

modified actuator designs.

A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 254–255 (2003) 228–233230

geometry from the engineering drawing package to the

FEA package and the solution can be automatically

started after selecting the magnetic material and excita-

tion characteristics. Behind the design screen, the FEA

program has to create a mesh composed of triangular

elements covering the defined geometry, which is

subsequently optimised by the user. For example, the

meshing needs to be particularly fine around the air gap

to provide an accurate representation of the magnetic

field in that region. It requires some experience to

correctly refine the mesh in this way but automatic

meshing checking of solution accuracy by monitoring

errors in magnetic field continuity across element edges

[6] can reduce the need for manual mesh control. Fig. 3

shows an actuator model with a simple mesh and an

automatically refined mesh. After the solving process, a

wide selection of field quantities, such as flux linkage

and force, which relate to the performance of the

actuator are readily computed using a set of commands

and macros [7].

4.4. Parameterisation

It is often necessary to examine the performance of

several similar devices. This can be simplified by using a

parameterised FEA model where the effects of changes

in parameters such as geometry, position, magnetic

material or excitation can be readily examined. For

example, in the actuator design referred to earlier, the

force was calculated automatically at each position

along the stroke by applying position and geometrical

parameters to the position and tapered angle of the

plunger.

5. Case study to demonstrate the use of FEA to improve

final design performance

This case study describes the use of FEA in the design

of the axial magnetisation of a ferrite-loaded coaxial

line. Hollow cylinders of soft ferrite enwrapping the

transmission line are used in pulse compression applica-

tions. The applications of an axial magnetic field to the

ferrite-loaded line is found to reduce the leading edge

shock front rise time to 100–200 ps [8]. The axial

magnetisation properties of the ferrite were required to

establish how much axial field is required to obtain a

given level of saturation in the ferrite.

The axial field is usually provided by a solenoid.

However, in this case, high field permanent magnet

arrangements were required to replace the solenoid

excitation. This excitation arrangement was to provide

an axial field large enough to homogeneously saturate

the ferrite. The axial length of the ferrite bead was larger

than the cross-sectional dimension. This made estima-

tion of the optimum axial magnetising field difficult due

to uncertainty of the internal demagnetising field

distribution.

The configuration shown in Fig. 4 was one of the

several designs studied in which the ferrite cylinder was

positioned between the poles of permanent magnets

forcing the flux to flow axially through the ferrite. An

accurate representation of the flux distribution in the

ferrite line with this excitation arrangement cannot be

accurately achieved using the magnetic circuit approach

due to the difficulties in exact reluctance calculations of

each part of the circuit. A 3D non-linear magnetostatic

solver [7] was used to model the arrangement of the

permanent magnets and the ferrite. The flux distribution

and flux density are shown in Fig. 5. At the post-

processing stage, the graphical interface allowed the

model to be studied and to evaluate the results along the

axial length of the ferrite.

Optimisation required refinement of the geometry of

both the ferrite and the magnetisation arrangement. For

example, magnetisation of the ferrite is dependent on the

axial length due to leakage flux. Therefore, the axial

length, inside and outside diameters of the ferrite, the

permanent magnet size and shape, and the clearances

between magnet and ferrite all needed to be optimised.

Manual optimisation of a 3D model is usually a lengthy

procedure, which requires the building of a new model

for each change in geometry. However, parameterisation

Fig. 3. A—Initial mesh, B—Automatic modified mesh in a

typical actuator design.

A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 254–255 (2003) 228–233 231

of the FE model allows rapid study of each iteration,

leading to the optimum design. To optimise the

clearance between permanent magnet poles and the

ferrite, a spatial parameter was assigned to the position

of the ferrite, which is changed in a series of steps. The

initial 3D model was constructed first and subsequent

models were automatically generated and solved. Fig. 6

shows typical results for ferrite interpolar gaps. The

parameterisation feature, which is now available in

many FEA packages, allows an optimised design to be

obtained in a reasonable time.

6. Conclusions

The FEA technique for the design of electromagnetic

devices has important advantages over traditional

analytical techniques of equivalent circuit analysis. It

enables the rapid development of fully optimised

designs, avoiding the need for several intermediate

prototyping stages. The FEA design tool allows accurate

prediction of a range of field-dependent characteristics

and, with the incorporation of the parameterisation

technique, it allows efficient assessment of a large

number of small design steps. FEA can be used

often to improve the development process, as well as

help optimise the performance of an electromagnetic

design.

Fig. 4. 3D mesh of ferrite line with a permanent magnet excitation system.

Fig. 5. Flux density distribution in the ferrite line and the

excitation system.

0.0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12

Length along ferrite cylinder (mm)

Axi

al fl

ux d

ensi

ty B

z (T

)

Clearance=2.5mm Clearance=5mm Clearance =10mm

Fig. 6. Axial flux density in the ferrite line along its length.

A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 254–255 (2003) 228–233232

References

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Chapman & Hall, London, 1964.

[2] A.J. Moses, SMM Conference, Bilbao, 2001.

[3] A.J. Moses, IEEE Trans. Magn. 34 (4) (1998) 186.

[4] H.C. Rotor, Electromagnetic Devices, Wiley, New York,

1941.

[5] D.A. Lowther, P. Silvester, Computer Aided Design in

Magnetics, Springer, New York, 1986.

[6] S. McFee, J.P. Webb, D.A. Lowther, IEEE Trans. Magn.

24 (1988) 439.

[7] MagNet Version 6.7 Getting Started Guide, Infolytica

Corporation, 2001.

[8] J.E. Dolan, H.R. Bolton, IEE Proc.—Sci. Meas. Technol.

147 (5) (2000) 237.

A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 254–255 (2003) 228–233 233