Brushless_Permanent_Magnet_Motor_Design(1).pdf

1、Brushless Permanent Magnet Motor Design Second Edition Dr.Duane Hanselman Electrical and Computer Engineering University of Maine Orono,ME 04469 USA MAGNA PHYSICS PUBLISHING Preface to the Second Edition Preface to the First Edition Chapter 1 Basic Concepts 1.1 Scope 1.2 Shape 1.3 Torque 1.4 Motor A

2、ction 1.5 Magnet Poles and Motor Phases 1.6 Poles,Slots,Teeth,and Yokes 1.7 Mechanical and Electrical Measures 1.8 Motor Size 1.9 Units 1.10 Summary Chapter 2 Magnetic Modeling 2.1 Magnetic Circuit Concepts Basic Relationships Magnetic Field Sources Air Gap Modeling Slot Modeling Example 2.2 Magneti

3、c Materials Permeability Ferromagnetic Materials Core Loss Permanent Magnets Permanent Magnet Magnetic Circuit Model 2.3 Example 2.4 Summary Chapter 3 Electrical and Mechanical Relationships 3.1 Flux Linkage and Inductance Self inductance 45 Mutual Inductance 46 Mutual Flux Due to a Permanent Magnet

4、 49 3.2 Induced voltage 50 Faradays Law 50 Example 51 3.3 Energy and Coenergy 53 Energy and Coenergy in Singly-Excited Systems 53 Energy and Coenergy in Doubly-Excited Systems 55 Coenergy in the Presence of a Permanent Magnet 56 3.4 Force,Torque and Power 56 Basic Relationships 56 Fundamental Implic

5、ations 57 Torque From a Macroscopic Viewpoint 58 Force From a Microscopic Viewpoint 61 Reluctance and Mutual Torque 62 Example 63 3.5 Summary 64 Chapter 4 Brushless Motor Fundamentals 67 4.1 Assumptions 67 Rotational Motion 67 Surface-Mounted Magnets 67 4.2 Fundamental Concepts 68 Magnetic Circuit M

6、odel 68 Magnetic Circuit Solution 71 Flux Linkage 74 Back EMF and Torque 76 Multiple Coils 78 4.3 Multiple Phases 80 4.4 Design Variations 82 Fractional Pitch Coils 82 Fractional Pitch Magnets 84 Fractional Slot Motor 86 4.5 Coil Resistance 90 4.6 Coil Inductance 94 Air Gap Inductance 95 Slot Leakag

7、e Inductance 96 End Turn Inductance 98 4.7 Series and Parallel Connections 100 4.8 Armature Reaction 103 4.9 Slot Constraints 104 Slot Fill Factors 104 Slot Resistance 105 Wire Gage Relationships 106 Constancy of Ni 107 4.10 Torque Constant,Back EMF Constant,and Motor Constant 108 4.11 Torque per Un

8、it Rotor Volume 110 4.12 Cogging Torque 111 4.13 Summary 115 Chapter 5 Motor Design Possibilities 117 5.1 Radial Flux Motors 117 Inner Rotor 117 Outer Rotor 120 5.2 Axial Flux Motors 121 5.3 Li near Mo tor s 123 5.4 Summary 124 Chapter 6 Windings 125 6.1 Assumptions 125 6.2 Coil Span 126 6.3 Valid P

9、ole and Slot Combinations 127 6.4 Winding Layout 129 Example 131 Example 134 Winding Layout Procedure 137 6.5 Coil Connections 139 6.6 Winding Factor 140 6.7 Inductance Revisited 143 Single Tooth Coil Equivalence 144 Air Gap Inductance 144 Slot Leakage Inductance 148 6.8 Summary 150 Chapter 7 Magnet

10、ic Design 7.1 Air Gap Magnetic Field Distribution 151 152 Air Gap Region Solution 153 Magnet Region Solution 153 Symmetry 154 7.2 Influence of Stator Slots 154 7.3 Tooth Flux 158 7.4 Stator Yoke Flux 162 7.5 Influence of Skew 165 7.6 Influence of Ferromagnetic Material 169 7.7 Back EMF 173 7.8 Slotl

11、ess Motor Construction 176 Concentrated Winding 176 Sinusoidally-Distributed Winding 180 7.9 Summary 181 Chapter 8 Electrical Control 183 8.1 Fundamentals of Torque Production 183 8.2 Brushless DC Motor Drive 185 Ideal Torque Production 185 Motor Constant 187 Torque Ripple 187 8.3 AC Synchronous Mot

12、or Drive 188 Ideal Torque Production 188 Motor Constant 189 Torque Ripple 189 8.4 General Drive 193 Ideal Torque Production 193 Torque Ripple 195 Motor Constant 195 8.5 Motor Drive Topologies 196 Half Bridge 196 Full H-Bridge 196 Y-Connection 198 zl-Connection 200 8.6 Summary 201 Chapter 9 Performan

13、ce 203 9.1 Motor Constant 203 General Sizing 203 Motor Constant Maximization 206 9.2 Cogging Torque Relationships 209 9.3 Radial Force Relationships 214 9.4 Core Losses 217 Basic Concepts 217 Core Loss Modeling 219 Application to Motor Design 222 Conclusion 223 9.5 AC Winding Resistance 223 9.6 Summ

14、ary 226 Chapter 10 Examples 229 Common Characteristics 229 Presented Results 230 Notes 231 Two Pole Motors 232 Four Pole Motors 234 Six Pole Motors 250 Eight Pole Motors 258 Ten Pole Motors 278 Twelve Pole Motors 294 Fourteen Pole Motors 300 Sixteen Pole Motors 312 Twenty Pole Motors 320 Twenty-Four

15、 Pole Motors 326 Thirty-Two Pole Motors 330 Appendix A Fourier Series 335 A.l Definition 335 A.2 Coefficients 336 A.3 Symmetry Properties 337 A.4 Mathematical Operations 337 Addition 338 Scalar Multiplication 338 Function Product 338 Phase Shift 338 Differentiation 339 Mean Square Value and RMS 339

16、A.5 Computing Coefficients 339 Procedure 340 A.6 Summary 341 Appendix B Magnetic Field Distributions in Polar Coordinates 343 B.l Problem Formulation 343 B.2 Polar Coordinate Application 345 B.3 Air Gap Region Solution 348 B.4 Magnet Region Solution 350 B.5 Summary 352 B.6 Magnetization Profiles 353

17、 Radial Magnetization 354 Parallel Magnetization 355 Radial Sinusoidal Amplitude Magnetization 356 Sinusoidal Angle Magnetization 356 B.7 Examples 357 B.8 Summary 360 Appendix C Magnetic Field Distributions in Rectangular Coordinates 361 C.l Rectangular Coordinate Application 362 Single Magnet and S

18、ingle Air Gap Case 363 Two Magnet,Single Air Gap Case 364 One Magnet,Two Air Gap Case 365 C.2 Magnetization Profile 366 C.3 Summary 366 Appendix D Symbols,Units,and Abbreviations 367 Appendix E Glossary 373 Bibliography 381 Books 381 Articles 384 Index 387 This chapter develops a number of basic mot

19、or concepts in a way that appeals to your intuition.In doing so,the concepts are more likely to make sense,especially when these concepts are used for motor design in later chapters.Many of the con-cepts presented here apply to most motor types since all motors are constructed of similar materials a

20、nd all produce the same output,namely torque.1.1 Scope This text covers the analysis and design of rotational brushless permanent 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 differen

21、t application niches,but their operating principles are essentially identical.Thus,the material presented in this text is applicable to all three of these motor types,with particular emphasis given to brushless DC and PM synchronous motors.To put these motor types into perspective,it is useful to sh

22、ow 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.Brushless DC motors are typically characterized as having a trapezoidal back

23、elec-tromotive force(EMF)and are typically driven by rectangular pulse currents.This mimics the operation of brush DC motors.From this perspective,the name brush-less DC fits even though it is an AC motor.PM synchronous motors differ from brushless DC motors in that they typically have a sinusoidal

24、back EMF and are driven by sinusoidal currents.Step motors in general have high pole counts and therefore require many periods of excitation for each shaft revolution.Even though they can be driven like other synchronous motors,they are typically driven with cur-rent pulses.Step motors are typically

25、 used in low cost,high volume,position,-cqntrol applications where the cost of position feedback cannot be justified.Figure 1.1 A classification of motors.The most common motor shape is cylindrical as shown in Fig.1-2a.This motor shape and all others contain two primary parts.The nonmoving or statio

26、nary part is called the stator.The moving or rotating part is called the rotor.In most cylindrical motors,the rotor appears inside the stator as shown in Fig.1-2a.This construction is popular because placing the nonmoving stator on the outside makes it easy to attach the motor to its surroundings.Mo

27、reover,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.Figs.1-2a and 1-2b show the two cylindrical shapes

28、.When the rotor appears on the outside of the stator as shown in Fig.1-2b,the motor is often said to be an inside-out motor.For these motors,a mag-netic 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 h

29、aving a pancake shape are shown in Figs.l-2c and 1-2d.In these axial flux motors,the magnetic field between the rotor and stator travels in the axial direction.Figure 1-2.Motor Construction Possibilities.Brushless PM motors can be built in all the shapes shown in Fig.1-2 as well as in a number of ot

30、her more creative shapes.All brushless PM motors are constructed with electrical windings on the stator and permanent magnets on the rotor.This construc-tion is one of the primary reasons for the increasing popularity of brushless PM motors.Because the windings remain stationary,no potentially troub

31、lesome moving electrical contacts,i.e.,brushes are required.In addition,stationary windings are eas-ier to keep cool.The common cylindrical shape shown in Fig.1-2,leads to the use of the cylindrical coordinate system as shown in Fig.1-3.Here the r-direction is called radial,the z-direction is called

32、 axial,and the-direction is called tangential or circumferential.1.3 Torque All motors produce torque.Torque is given by the product of a tangential force and the radius at which it acts,and thus torque has units of force times length,e.g.,ozf in,lbf-ft,or N-m.To understand this concept,consider the

33、 wrench on the nut shown in Fig.1-4.If a force F is applied to the wrench in the tangential direction,i.e.,perpen-dicular to the handle,at a distance r from the center of the nut,the twisting force or torque experienced by the bolt is This relationship implies that if the length of the wrench is dou

34、bled and the same force is applied at a distance 2r,the torque experienced by the nut is doubled.Like-wise,shortening the wrench by a factor of two 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.Furt

35、hermore,it is only force acting in the tangential direc-T=Fr(1.1)Figure 1-3.The cylindrical coordinate system.Figure 1-4.A wrench on a nut.tion 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 t

36、he direction of applied force into account,torque can be expressed as T=Frsin0,where 0 is the angle at which the force is applied with respect to the radial direction.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 lo

37、osen the nut.And the force applied to the wrench is most efficient when it is in the circumferential direction,i.e.,in the direction tangential to a circle centered over the nut as shown in Fig.1-4.Clearly if the force is applied in an outward radial direction,the nut experiences no torque,and the w

38、rench comes off the nut.1.4 Motor Action With an understanding of torque production,it is now possible to illustrate how a brushless permanent magnet motor works.All thats required is the rudimentary knowledge that magnets are attracted to iron,that opposite magnet poles attract,that like magnet pol

39、es 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 to spin about its center,but is oth-erwise fixed.The magnet is the rotor and the i

40、ron ring is the stator,and they are separated by an air gap.As shown in the figure,the magnet does not have any pre-ferred resting position.Each end experiences an equal but oppositely-directed,radial force of attraction to the ring that is not a function of the particular direction of the magnet.Th

41、e magnet experiences no net force,and thus no torque is produced.Next consider changing the iron ring so that it has two protrusions or poles on it as shown in Fig.1-6.As before,each end of the magnet experiences an equal but oppo-Figure 1-5.A magnet free to spin inside a steel ring.sitely directed

42、radial force.Now however,if the magnet is spun slowly it will have the tendency to come to rest in the aligned position at 0=0 or 0=180.That is,as the magnet spins it will experience a force that will try to align the magnet with the sta-tor poles.This occurs because the force of attraction between

43、a magnet and iron increases dramatically as the physical distance between the two decreases.Because the magnet is free to spin,this force is partly in the tangential direction and torque is produced.Fig.1-7 depicts this torque graphically as a function of motor position.The posi-tions where the torq

44、ue is zero are called detent positions.When the magnet is aligned with the poles,any small disturbance causes the magnet to restore itself to the aligned position.Thus these detent positions are said to be stable.On the other hand,when the magnet is halfway between the poles,any small disturbance ca

45、uses the magnet to move away from the unaligned position and seek alignment.Thus,una-ligned detent positions are said to be unstable.While the shape of the detent torque is approximately sinusoidal in Fig.1-7,in a real motor its shape is a complex function of motor geometry and material properties.T

46、-7T-7if 2 0 I/2 T t Figure 1-7.Torque experienced by the magnet in Fig.1-6.The torque described here is formally called reluctance torque,and more commonly cogging torque.In most applications,cogging torque is undesirable.Now consider the addition of current carrying coils to the poles as shown in F

47、ig.1-8.If current is applied to the coils,the poles become electromagnets.In particular,if the current is applied in the proper direction,the poles become magnetized as shown in Fig.1-8.In this situation,the force of attraction between the bar magnet and the opposite electromagnet poles creates anot

48、her type of torque,formally called mutual or alignment torque.It is this torque that is used in brushless PM motors to do work.The term mutual is used because it is the mutual attraction between the magnet poles Figure 1-8.Current-carrying windings added to Fig.1.6.that produces torque.The term alig

49、nment is used because the force of attraction seeks to align the bar magnet and coil-created magnet poles.This torque could also be called repulsion torque,since if the current is applied in the opposite direction,the poles become magnetized in the opposite direction as shown in Fig.1-9.In this situ

50、ation the like poles repel,sending the bar magnet in the opposite direction.Since both of these scenarios involve the mutual interaction of the magnet poles,the torque mechanism is identical,and the term repulsion torque is not used.To get the bar magnet to turn continuously,it is common to employ m