Table Of ContentComputer-Aided Design in Magnetics
D. A. Lowther P. P. Silvester
Computer-Aided Design
in Magnetics
With 84 illustrations
Springer-Verlag
Berlin Heidelberg New York Tokyo
D. A. Lowther P. P. Silvester
Associate Professor Professor of Electrical
of Electrical Engineering Engineering
McGill University McGill University
Montreal H3A 2A7 Montreal H3A 2A 7
Canada Canada
Library of Congress Cataloging in Publication Data
Lowther, D. A.
Computer-aided design in magnetics.
Bibliography: p.
Includes index.
1. Magnetic devices-Design and construction-Data
processing. 2. Computer-aided design. I. Silvester,
P. P. II. Title.
TK454.4.M3S55 1985 621.34 85-17227
© 1986 by Springer-Verlag New York Inc.
Softcover reprint of the hardcover 1s t edition 1986
All rights reserved. No part of this book may be translated or reproduced in any
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York, New York 10010, U.S.A. The use of general descriptive names, trade
names, trademarks, etc., in this publication, even if the former are not especially
identified, is not to be taken as a sign that such names, as understood by the Trade
Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
Media Conversion and Typesetting by House of Equations, Newton, New Jersey.
lSBN-13: 978-3-642-70673-8 e-lSBN-13: 978-3-642-70671-4
DOl: 10.1007/978-3-642-70671-4
Preface
Computer-aided design has come of age in the magnetic devices industry.
From its early beginnings in the 1960s, when the precision needs of the
experimental physics community first created a need for computational
aids to magnet design, CAD software has grown to occupy an important
spot in the industrial designer's tool kit.
Numerous commercial CAD systems are now available for magnetics
work, and many more software packages are used in-house by large
industrial firms. While their capabilities vary, all these software systems
share a very substantial common core of both methodology and objec
tives. The present need, particularly in medium-sized and nonspecialist
firms, is for an understanding of how to make effective use of these new
and immensely powerful tools: what approximations are inherent in the
methods, what quantities can be calculated, and how to relate the com
puted results to the needs of the designer. These new analysis techniques
profoundly affect the designer's approach to problems, since the analytic
tools available exert a strong influence on the conceptual models people
build, and these in turn dictate the manner in which they formulate prob
lems. The impact of CAD is just beginning to be felt industrially, and the
authors believe this is an early, but not too early, time to collect together
some of the experience which has now accumulated among industrial and
research users of magnetics analysis systems.
In its early versions, this book has been used by students in the authors'
one-semester course at McGill University. It has also served as the corner
stone for numerous short courses given to industrial audiences. The
authors wish to acknowledge their indebtedness to Dr. G. K. Cambrell,
for his meticulous reading of the manuscript, and to Dr. E. M. Freeman,
for our many discussions and his contributions to an early draft of several
chapters. Particular thanks are due, however, to the many colleagues and
students whose suggestions, help, and numerous examples have shaped
this book.
D. A. Lowther
P. P. Silvester
Contents
Preface v
Introduction 1
Analysis Methods in Electromagnetics 1
The System Life-Cycle 3
Computing Equipment for CAD 7
Finite Element Analysis Systems 10
Magnetic Material Representation 13
Modelling of B-H Curves 13
Management of Material Property Files 16
Data Entry and Editing 21
Complex Magnetic Materials 28
Curve Modelling Theory 32
The Potential Equations of Magnetics 37
Electromagnetic Fields and Potentials 37
Potential Problems of Electromagnetics 44
Magnetic Scalar Potentials 50
Time-Varying Potential Problems 55
Rotational and Translational Symmetries 60
Problem Modelling and Mesh Construction 68
Geometric Modelling and Discretization 68
Mesh Generation and Editing 76
Multi-Model Operations and Model Libraries 84
Batch and Interactive CAD Systems 89
Practical Mesh Construction 94
Automating the Mesh-Building Task 105
Assembly of Problems III
Contents
Vlll
Field Problems in Magnetic Devices 119
Analysis in Design 119
Analysis by Successive Refinement 122
Subproblem Analysis 131
Boundary Conditions 134
Geometric Shape Alteration 145
Reducing Three Dimensions to Two 149
Planning the Solution 157
Postprocessing Operations in CAD 160
Inductance Calculations 160
A Transformer Design Problem 176
Mutual Inductances 188
Force Calculations 191
Local Field Values 202
Linear Time-Varying Problems 211
Electrosta tic Calculations 218
Effects of Numerical Approximations 223
Postprocessing Systems for Magnetics 228
Postprocessor Structure and Use 228
Manipulation of Local Data 230
Mathematical Postprocessor Operations 237
Graphic Displays of Results 246
Graphic Input 252
The Custom Postprocessor 254
CAD Systems Present and Future 258
System Structure 258
Processes in CAD 265
Interactive Command Languages 269
Programmability of CAD Systems 274
Workstation Layout 278
Interactive CAD Systems for Magnetics 282
Batch-Run CAD Systems 290
The Literature of CAD in Magnetics 293
Publications on Magnetics CAD 293
An Annotated Bibliography 295
Index 321
Introduction
Magnetic devices have traditionally been designed by combining empiri
cal rules based on experimental evidence with simplified magnetic circuit
models. This technique may be labelled design by rule. But as devices
become increasingly varied and complex, conventional design rules are no
longer adequate and design by analysis, based on reasonably detailed solu
tion of the underlying electromagnetic field problems, becomes the nor
mal practice. Design by analysis really means design by numerical
analysis since no other tools are capable of dealing with both the
geometric complexity and nonlinearity found in such disparate devices as
vertical recording heads and direct current machines. Design by analysis
therefore inevitably means at least computer-aided analysis, and increas
ingly has come to mean full-fledged computer-aided design.
This book outlines what can and what cannot be done with the
computer-aided analysis systems now available commercially. Its main
purpose is to show how the new techniques can be brought to bear on
design problems; how design rules or novel approximations can be
developed for new situations; and how CAD system capabilities can be
stretched to cover problems that the software designers may not have had
in mind. It assumes that analysis methods for electromagnetics problems
are now sufficiently well known and addresses itself largely to the
engineering task of formulating electromagnetics problems in a comput
able fashion. It is principally, indeed almost exclusively, concerned with
two-dimensional analysis, for two good reasons. First, nearly all commer
cially available CAD software deals with two-dimensional problems.
Secondly, and more importantly, learning to use three-dimensional
analysis tools is a very great deal more difficult that working in two
dimensions; it pays, as the saying goes, to learn to walk before you run.
Analysis Methods in Electromagnetics
The techniques used for electromagnetic device analysis in practical
design may be divided into two classes: the traditional techniques, which
2 In trod uction
rely on notions of magnetic circuit analysis, and the newer numerically
implemented approaches. Both have been used in computer-aided design
systems, but there is little doubt that the modem field theoretic techniques
are gaining the upper hand. This book is concerned primarily with such
new techniques, and with ways of marrying the old with the new.
Traditional Design Methods
Traditional development, analysis, and design of electromagnetic devices
have tended to use extremely simple analytic models, supplemented by
experimental evidence. Most of these consist of electric or magnetic
equivalent circuits postulated on the basis of experience and intuition.
Frequently, such simple approaches lead to qualitatively correct but quan
titatively inaccurate results, which are supplemented with correction
parameters, thus leading to design rules. The simplified models and rules
so developed have long provided, and continue to provide, designers with
data concerning specific device features such as the input impedance,
transient and subtransient reactances, power output and efficiency. How
ever, they are usually restricted to very narrow classes of devices, because
the various numerical correction factors are empirically introduced, and
can be relied on only for designs substantially similar to those which fur
nished the experimental evidence. Occasionally, more sophisticated ana
lytic techniques derived from basic electromagnetic principles have been
used when a more detailed insight has been required. But these are labor
intensive and require high levels of expertise in electromagnetics and
mathematics. The traditional methods have the advantage, from the
design engineer's viewpoint, of being relatively easy, and fast to apply. In
quite a few cases, they can be expressed in the convenient form of design
tables or curves.
The principal shortcoming of traditional design methods lies in their
inability to accommodate new situations. New magnetic materials, both
hard and soft, can place additional restrictions and at the same time open
new possibilities. Legal requirements relating to electromagnetic interfer
ence, safety, noise, and pollution levels lead to new forms of design. Other
considerations, such as weight and size, may need detailed knowledge of
the field distribution within the device. And last but not least, there are
many devices which have never been built before: perpendicular record
ing heads and magnetic print heads are just two particular examples!
Numerical Methods
The advent of the digital computer, and its subsequent development, pro
vided engineers with a tool capable of manipulating large volumes of data
at very high speeds. In the three decades since computers became com
mon, methods have been developed for solving the electromagnetic field
equations for a great range of geometries and materials. The finite ele-
The System Life-Cycle 3
ment technique in particular has proved particularly flexible, reliable, and
effective in the hands of nonspecialist users.
For the design engineer these new computational tools could provide
solutions to problems with a greater degree of accuracy than was previ
ously possible. During the decade of the 1970s, conventional wisdom held
that the availability of good computational methods had turned the clock
back a hundred years, to that golden era in which magnetic devices were
designed almost exclusively by solving the underlying magnetic field
equations-until the range of analytically solvable problems was exhausted
early in the twentieth century. In fact, history may well be repeating itself
a century later. Two-dimensional (and some three-dimensional) problems
are now relatively easy to solve yet still difficult enough to preclude the
exclusive use of finite element programs in preference to classical rule
based design. Indeed, a major use of the new CAD tools will very likely
be in deriving new, more sophisticated design rules. The new element for
the designer may well become the disposable design rule, created for a
relatively narrow class of designs as the result of extensive computer simu
lation. The narrow range of applicability of a highly specialized design
rule is not a problem in an era of cheap computing, in which new rules
can be created by additional quick simulations as needed.
The System Life-Cycle
All engineering software is necessarily highly specialized. Its content is
shaped by the needs of potential users as the system designer perceives
them, by the analytic techniques available when the system is designed,
and by the computer hardware in reasonably common use at the time. All
three factors change with time at a greater or lesser speed, so that the
life-span of any software package is limited.
Good engineering analysis software takes time to design and perfect. A
typical large-scale finite element package involves tens of thousands of
lines of code, taking man-years to design and test. Such an analysis pack
age normally requires 2-3 years to create and must remain on the market
for 7-10 years if its high initial cost is to be justified. Its total life-cycle is
therefore about 10-12 years, a long time in a high-technology world.
Hardware Development
Currently, major changes in computer hardware occur about every 3-4
years. This rate of change applies equally to processor hardware and to
input-output devices. Changes in processor hardware are often unspectac
ular from an analyst's point of view, since they usually result in esta
blished operations being carried out more conveniently, quickly, or chea
ply. Changes in input-output devices, on the other hand, tend to have a
more revolutionary aspect, since they frequently alter the external appear-
4 Introduction
ance of systems fundamentally. For example, the introduction of graphics
terminals in the 1970s amounted to more than just an increase in plotting
speed: it altered the way work was done.
Since the economic life of software systems is substantially longer than
the hardware life-cycle, every analysis system must reside on obsolete
hardware at least half its lifetime. Conversion to different hardware sys
tems is commonly done, but it is at best a half-measure, for the software
structure is influenced very strongly by what the hardware is capable of
doing. For example, a light pen and a graphics tablet have a great deal of
superficial similarity in use, but the tablet can be used to digitize drawings
and curves directly, while the light pen cannot. Software transported
from light pen environments to graphics tablets therefore ends up merely
using the tablet to mimic a light pen, without taking advantage of its
additional abilities. As another very familiar example, keyboard terminals
fully capable of writing both upper and lower case characters were for
years (and in many systems still are!) used to display capital letters only,
because the software systems driving them were originally written for ter
minals incapable of printing lower case characters.
Transportation of software systems to new hardware usually means
making the new hardware act like the old. Such mimicry is often easy, in
the sense that the newer devices normally provide all the capabilities of
the old and furnish new functions besides. But alteration of software to
make good use of new hardware capabilities may imply not just a few
alterations but basic redesign. Ignoring the capabilities of new hardware is
thus possible for a few years, but only for a few, because the unused
hardware facilities eventually come to predominate over those actually
exploited by the programs. A new start is then indicated.
A very rapidly evolving area, in which most current packages leave
much to be desired, is that of man-machine communication. To be fair
and charitable to package designers, this area is very strongly dependent
on terminal hardware, a particularly fast-changing part of an exception
ally fast-moving industry.
The Software Environment
A problem at least as vexing as rapid hardware evolution is the continual
and rapid change of system software in which any CAD system must live.
Operating systems are subject to even more updates, alterations, and
corrections than hardware.
Because elementary operations in arithmetic processing, all input
output operations, and many other processes are hardware-dependent,
they normally call on machine-language routines resident in the operating
system software. Indeed, the whole point of operating systems is to isolate
the user from too intimate an involvement with the hardware details of
the machine. Computer users-even experienced programmers-often do
not appreciate quite how major a part of machine action is really not car-
