Brushless Permanent Magnet Motor Design- P1 pptx

Brushless Motor Operation 61 Assumptions 61 Rotational motion 61 Motor load 61 Motor drive 62 Slotting 62 Surface-mounted magnets 62 Steel 63 Basic Motor Operation 63 Magnetic Circui

static operating point

Brushless Permanent-Magnet

Motor Design

Duane C Hanselman

University of Maine Orono, Maine

McGraw-Hill, Inc New York San Francisco Washington, D.C Auckland Bogotá Caracas Lisbon London Madrid Mexico City Milan

Montreal New Delhi San Juan Singapore

Sydney Tokyo Toronto

Library of Congress Cataloging-in-Publication Data

Hanselman, Duane C

Brushless permanent-magnet motor design / Duane C Hanselman

p cm

Includes bibliographical references and index

ISBN 0-07-026025-7 (alk paper)

1 Electric motors, Permanent magnet—Design and construction

2 Electric motors, Brushless—Design and construction I Title

TK2537.H36 1994

621.46— dc20 93-43581

CIP

Copyright © 1994 by McGraw-Hill, Inc All rights reserved Printed in

the United States of America Except as permitted under the United

States Copyright Act of 1976, no part of this publication may be

repro-duced or distributed in any form or by any means, or stored in a data

base or retrieval system, without the prior written permission of the

publisher

2 3 4 5 6 7 8 9 0 DOC/DOC 9 9 8 7 6 5 4

ISBN 0-07-026025-7

The sponsoring editor for this book was Harold B Crawford, the

editing supervisor was Paul R Sobel, and the production supervisor

was Pamela A Pelton It was set in Century Schoolbook by

Techna Type, Inc

Printed and bound by R R Donnelley & Sons Company

Information contained in this book has been obtained by

McGraw-Hill, Inc from sources believed to be reliable

How-ever, neither McGraw-Hill nor its authors guarantee the

ac-curacy or completeness of any information published herein,

and neither McGraw-Hill nor its authors shall be responsible

for any errors, omissions, or damages arising out of use of this

information This work is published with the understanding

that McGraw-Hill and its authors are supplying information

but are not attempting to render engineering or other

profes-sional services If such services are required, the assistance of

an appropriate professional should be sought

This book is printed on recycled, acid-free paper containing

a minimum of 50% recycled de-inked fiber

Contents

Preface ix

Chapter 1 Basic Concepts 1

Scope 1 Shape 1 Torque 4 Motor Action 5 Magnet Poles and Motor Phases 8

Poles, Slots, and Teeth 9

Mechanical and Electrical Measures 10

Motor Size 11 Conclusion 12 Chapter 2 Magnetic Modeling 13

Magnetic Circuit Concepts 14

Basic relationships 14

Magnetic field sources 17

Air gap modeling 19

Slot modeling 21

Example 24 Magnetic Materials 26

Permeability 26

Ferromagnetic materials 26

Core loss 28 Permanent magnets 30

PM magnetic circuit model 34

Example 36 Conclusion 38 Chapter 3 Electrical and Mechanical Relationships 41

Flux Linkage and Inductance 41

Self inductance 41

Mutual inductance 42

Mutual flux due to a permanent magnet 44

Contents

Induced Voltage 46

Faraday's law 46

Example 47 Energy and Coenergy 48

Energy and coenergy in singly excited systems 48

Energy and coenergy in doubly excited systems 50

Coenergy in the presence of a permanent magnet 51

Force, Torque, and Power 52

Basic relationships 52

Fundamental implications 53

Torque from a macroscopic viewpoint 54

Force from a microscopic viewpoint 56

Reluctance and mutual torque 57

Example 58

Chapter 4 Brushless Motor Operation 61

Assumptions 61 Rotational motion 61

Motor load 61 Motor drive 62 Slotting 62 Surface-mounted magnets 62

Steel 63 Basic Motor Operation 63

Magnetic Circuit Model 64

Flux Linkage 69 Back EMF 70 Force 73 Multiple phases 74

Winding Approaches 75

Single-layer lap winding 76

Double-layer lap winding 77

Single-layer wave winding 77

Self Inductance 78

Air gap inductance 80

Slot leakage inductance 81

End turn leakage inductance 82

Summary 84 Mutual Inductance 85

Current induced winding force 92

Permanent-magnet induced winding force 93

Summary 93 Cogging Force 93

Rotor-Stator Attraction 95

Core Loss 95

Contents vii

Summary 96 Fundamental Design Issues 96

Air gap flux density 97

Active motor length 97

Number of magnet poles 97

Slot current 98 Electric versus magnetic loading 99

Dual Air Gap Motor Construction 99

Summary 101

Chapter 5 Design Variations 103

Rotor Variations 103 Stator Variations 106 Shoes and Teeth 107 Slotted Stator Design 110

Fractional pitch cogging torque reduction 112

Back emf smoothing 113

Distribution factor 113

Pitch factor 115 Cogging Torque Reduction 117

Shoes 118 Fractional pitch winding 118

Air gap lengthening 118

Skewing 118 Magnet shaping 120

Summary 121 Sinusoidal versus trapezoidal motors 121

Topologies 121 Radial flux 122 Axial flux 122 Conclusion 123

Chapter 6 Design Equations 125

Summary 137 Dual Axial Flux Motor Design 137

Magnetic circuit analysis 137

Summary 150 Conclusion 150

Appendix A List of Symbols 183

Appendix B Common Units and Equivalents 185

Bibliography 187 Index 189

Preface

You've just picked up another book on motors You've seen many others, but they all assume that you know more about motors than you do Phrases such as armature reaction, slot leakage, fractional pitch, and skew factor are used with little or no introduction You keep looking for a book that is written from a more basic, yet rigorous, perspective and you're hoping this is it

If the above describes at least part of your reason for picking up this book, then this book is for you This book starts with basic concepts, provides intuitive reasoning for them, and gradually builds a set of understandable concepts for the design of brushless permanent-magnet motors It is meant to be the book to read before all other motor books Every possible design variation is not considered Only basic design concepts are covered in depth However, the concepts illustrated are described in such a way that common design variations follow natu-rally

If the first paragraph above does not describe your reason for picking

up this book, then this book may still be for you It is for you if you are looking for a fresh approach to this material It is also for you if you are looking for a modern text that brings together material nor-mally scattered in numerous texts and articles many of which were written decades ago

Is this book for you if you are never going to design a motor? By all means, yes Although the number of people who actually design motors

is very small, many more people specify and use motors in an infinite variety of applications The material presented in this text will provide the designers of systems containing motors a wealth of information about how brushless permanent-magnet motors work and what the basic performance tradeoffs are Used wisely, this information will lead

to better engineered motor systems

Why a book on brushless permanent-magnet motor design? This book

is motivated by the ever increasing use of brushless permanent-magnet motors in applications ranging from hard disk drives to a variety of

x Preface

industrial and military uses Brushless permanent-magnet motors have become attractive because of the significant improvements in permanent magnets over the past decade, similar improvements in power electronic devices, and the ever increasing need to develop smaller, cheaper, and more energy-efficient motors At the present time, brushless permanent-magnet motors are not the most prevalent motor type in use However, as their cost continues to decrease, they will slowly become a dominant motor type because of their superior drive characteristics and efficiency

Finally, what's missing from this book? What's missing is the "nuts and bolts" required to actually build a motor There are no commercial material specifications and their suppliers given, such as those for electrical steels, permanent magnets, adhesives, wire tables, bearings, etc In addition, this book does not discuss the variety of manufacturing processes used in motor fabrication While this information is needed

to build a motor, much of it becomes outdated as new materials and processes evolve Moreover, the inclusion of this material would dilute the primary focus of this book, which is to understand the intricacies and tradeoffs in the magnetic design of brushless permanent-magnet motors

I hope that you find this book useful and perhaps enlightening If you have corrections, please share them with me, as it is impossible

to eliminate all errors, especially as a sole author I also welcome your comments and constructive criticisms about the material

Acknowledgments

This text would not have been possible without the generous tunities provided by Mike and his staff Moreover, it would not have been possible without the commitment and dedication of my wife Pamela and our children Ruth, Sarah, and Kevin

oppor-Duane C Hanselman

Brushless Permanent-Magnet

Motor Design

Scope

This text covers the analysis and design of rotational brushless manent-magnet (PM) motors Brushless dc, PM synchronous, and PM step motors are all brushless permanent-magnet motors These specific motor types evolved over time to satisfy different application niches, but their operating principles are essentially identical Thus the ma-terial presented in this text is applicable to all three of these motor types

per-To put these motor types into perspective, it is useful to show where they fit in the overall classification of electric motors as shown in Fig 1.1 The other motors shown in the figure are not considered in this text Their operating principles can be found in a number of other texts

Shape

The most common motor shape is cylindrical, as shown in Fig 1.2a This motor shape and all others contain two primary parts The non-moving, or stationary, part is called the stator The moving, or rotating, part is called the rotor In most cylindrical-shaped motors, the rotor appears inside the stator as shown in Fig 1.2a This construction is

1

2

Basic Concepts 3

popular because placing the nonmoving stator on the outside makes

it easy to attach the motor to its surroundings Moreover, confining

the rotor inside the stator provides a natural shield to protect the

moving rotor from its surroundings

In addition to the cylindrical shape, motors can be constructed in

numerous other ways Several possibilities are shown in Fig 1.2

Fig-ure 1.2a and b shows the two cylindrical shapes When the rotor appears

on the outside of the stator as shown in Fig 1.26, the motor is often

said to be an "inside-out" motor For these motors a magnetic field

travels in a radial direction across the air gap between the rotor and

stator As a result, these motors are called radial flux motors Motors

having a pancake shape are shown in Fig 1.2c and d In these motors

the magnetic field between the rotor and stator travels in the axial

direction Thus these motors are called axial flux motors

Brushless PM motors can be built in all the shapes shown in Fig

1.2 as well as in a number of other more creative shapes All brushless

(c) (d)

Figure 1.2 Motor construction possibilities

the cylindrical coordinate system as shown in Fig 1.3 Here the r

direction is called radial, the z direction is called axial, and the 6

direction is called tangential or circumferential

All motors produce torque Torque is given by the product of a gential force acting at a radius, and thus has units of force times length, e.g., oz-in, lb-ft, N-m To understand this concept, consider the wrench

tan-and nut shown in Fig 1.4 If a force F is applied to the wrench in the

tangential direction at a distance r from the center of the nut, the twisting force, or torque, experienced by the bolt is

Basic Concepts 5

This relationship implies that if the length of the wrench is doubled and the same force is applied at a distance 2r, the torque experienced

by the nut is doubled Likewise, shortening the wrench by a factor of

2 and applying the same force cuts the torque in half Thus a fixed force produces the most torque when the radius at which it is applied

is maximized Furthermore, it is only force acting in the tangential direction that creates torque If the force is applied in an outwardly radial direction, the wrench simply comes off the nut and no torque is experienced by the nut Taking the direction of applied force into ac-

count, torque can be expressed as T = Fr sin 6, where 6 is the angle

at which the force is applied with respect to the radial direction Certainly this concept of torque makes sense to anyone who has tried

to loosen a rusted nut The longer the wrench, the less force required

to loosen the nut And the force applied to the wrench is most efficient when it is in the circumferential direction, i.e., in the direction tan-gential to a circle centered over the nut as shown in the figure

Motor Action

With an understanding of torque production, it is now possible to lustrate how a brushless PM motor works All that's required is the rudimentary knowledge that magnets are attracted to iron, that op-posite magnet poles attract, that like magnet poles repel each other, and that current flowing in a coil of wire makes an electromagnet Consider the bar permanent magnet centered in a stationary iron ring as shown in Fig 1.5, where the bar magnet in the figure is free

il-to spin about its center but is otherwise fixed Here the magnet is the rotor and the iron ring is the stator As shown in the figure, the magnet does not have any preferred resting position Each end experiences an equal but oppositely directed radial force of attraction to the ring that

Figure 1.5 A magnet free to spin inside a steel ring

6 Chapter e

Figure 1.6 A magnet free to spin inside a steel ring having two poles

is not a function of the particular direction of the magnet The magnet experiences no net force and thus no torque is produced

Next consider changing the iron ring so that is has two protrusions

or poles on it as shown in Fig 1.6 As before, each end of the magnet experiences an equal but oppositely directed radial force Now, how-ever, if the magnet is spun slowly it will have the tendency to come

to rest in the 0 = 0 position shown in the figure That is, as the magnet spins it will experience a force that will try to align the magnet with the stator poles This occurs because the force of attraction between a magnet and iron increases dramatically as the physical distance be-tween the two decreases Because the magnet is free to spin, this force

is partly in the tangential direction, and torque is produced

Figure 1.7 depicts this torque graphically as a function of motor position The positions where the force or torque is zero are called detent

Figure 1.7 Torque experienced by the magnet in Fig 1.6