A Review of the Design Issues and Techniques for Radial-flux Brush Surface and Internal Rare Earth...

8/17/2019 A Review of the Design Issues and Techniques for Radial-flux Brush Surface and Internal Rare Earth PM Motors

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 9, SEPTEMBER 2011 3741

A Review of the Design Issues and Techniques forRadial-Flux Brushless Surface and Internal

Rare-Earth Permanent-Magnet MotorsDavid G. Dorrell, Senior Member, IEEE , Min-Fu Hsieh, Member, IEEE , Mircea Popescu, Senior Member, IEEE ,

Lyndon Evans, David A. Staton, Member, IEEE , and Vic Grout, Senior Member, IEEE

Abstract—This paper reviews many design issues and analysistechniques for the brushless permanent-magnet machine. It re-views the basic requirements for the use of both ac and dc ma-chines and issues concerning the selection of pole number, windinglayout, rotor topology, drive strategy, field weakening, and cooling.These are key issues in the design of a motor. Leading-edge designtechniques are illustrated. This paper is aimed as a tutor for motordesigners who may be unfamiliar with this particular type of machine.

Index Terms—Analysis, brushless permanent-magnet (PM)motors, design, internal PM (IPM), torque.

I. INTRODUCTION

THERE ARE MANY excellent books on the design of

brushless permanent-magnet (PM) motors. Examples of

well-known and established texts are given in [1]–[5], while

more recently, there have been tutorials at leading international

conferences with accompanying Course Notes Texts [6]. These

cover dc and ac motors and mostly cover the design of ferrite-

magnet machines although rare-earth machines are also cov-ered. Materials are discussed in a variety of specialized texts;

these include magnets [7], [8], steels [9], [10], and insulation

systems [11]. Noise is also covered by several texts [12], [13].

This list is far from comprehensive, and there are many other

monographs that cover specialist aspects of electric motor

operation that are relevant to brushless PM motors. There is

still relatively little on the thermal design of electrical machines

in terms of texts although the number of technical papers

is increasing; illustrations of this are [14] and [15], while

Manuscript received April 14, 2010; revised July 23, 2010; acceptedOctober 1, 2010. Date of publication October 28, 2010; date of current versionAugust 12, 2011.

D. G. Dorrell is with the School of Mechanical, Electrical and MechatronicSystems, University of Technology Sydney, Sydney, N.S.W. 2007, Australia(e-mail: [email protected]).

M.-F. Hsieh is with the Department of Systems and Naval MechatronicEngineering, National Cheng Kung University (NCKU), Tainan 701, Taiwan(e-mail: [email protected]).

M. Popescu, L. Evans, and D. A. Staton are with Motor Design Ltd.,SY12 9DA Shropshire, U.K. (e-mail: [email protected];[email protected]; [email protected]).

V. Grout is with the Centre for Applied Internet Research, Glyndwr Univer-sity, LL11 2AW Wrexham, U.K. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2010.2089940

[16]–[18] show coupled electromagnetic and thermal consid-

erations in PM machines. In recent years, there have been many

papers that cover various aspects of the electromagnetic design

on rare-earth PM motors; for instance, [19]–[25] show recent

papers on PM-motor design in a variety of situations.

The aim of this paper is not to highlight particular design

aspects of one form of brushless PM motor but rather to givean overview of many of the factors dictating option selection

and design solutions. Therefore, in this paper, the key design

points related to the design of brushless rare-earth PM ma-

chines are outlined and solutions are discussed. Techniques for

analysis are outlined, and these should be useful to a machine

designer who is unfamiliar with this particular type of machine.

Section II will consider electromagnetic and structural is-

sues, while Section III will discuss thermal considerations.

Section IV will put forward analysis techniques. Design exam-

ples are included in the discussions.

II. INITIAL E LECTROMAGNETIC D ESIGN C HOICES

In this section, some basic design choices are discussed.

These are necessary at the outset of the design procedure.

A. Radial or Axial Flux?

Generally, most PM motors are of the radial-flux type. The

reason for this is that fabrication is straightforward and estab-

lished, using slotted stators with standard round radial lami-

nations, and the electrical loading can be maximized because

of the use of the slots. However, there are good examples of

using axial-flux machines, and the design of these machines

is discussed in [26]. In these machines, the windings tend tobe air-gap windings (although they can have teeth [27]) which

can limit the amount of copper that can be used and, hence,

can limit the amount of loading possible. The windings tend

to be specially formed and shaped, and often, Torus windings

are used; Mendrela et al. [27] review different options for

this type of machine. Axial-flux machines are often used as

motors although they have many advantages (usually related

to their low armature reactance) in the area of generation

[28], particularly in wind generation [29]. However, axial-flux

applications can still be considered as niche, and the focus of

this paper will be on radial-flux laminated motors since these

constitute the majority of brushless PM motors.

0278-0046/$26.00 © 2010 IEEE


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3742 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 9, SEPTEMBER 2011

TABLE ITYPICAL TRVs [1]

B. Ratings, Motor Classes, and TRV

The rating of a machine is important and will dictate the size

and design demands for a machine. The torque-per-unit-rotor

volume (TRV) is a useful guide to how “good” a machine is.

The TRV is related to the tangential stress by

TRV = 2σmean (1)

where σmean is the sheer stress on the rotor (in newtons persquare meter). The sheer stress will be discussed later. Common

limits for the TRV in various machines are quoted in [1], and

these are listed in Table I. However, it can be seen that, gen-

erally, the larger and better cooled the machine, the higher the

TRV. In totally enclosed fan-cooled machines, typical winding-

current-density levels are in the region of 5–6 A/mm2. This

limits the electric loading and, hence, stress, which results in

a low-range TRV. Larger water- or oil-cooled machines can

push this much higher. In electric vehicle (EV) and hybrid EV

drive motors [30], the peak power rating is a transient rating

at lower speeds, and the current density during a transient (or

acceleration) period can be in excess of 20 A/mm2 for a period

of several seconds or tens of seconds. Some basic motor types

are listed in Table I although, at this stage, no distinction ismade between ac- and dc-controlled brushless PM machines.

These volumes can be used to calculate an approximate rotor

size. However, initially, a diameter has to be selected based on

the choice of pole number, magnet size, and rotor topology.

The geometry may also be dictated by the space in which the

motor has to fit. Starting with a two-pole motor geometry, the

diameter-to-axial-length ratio will be close to unity and will

increase with pole number (moving from a long cylindrical

shape to a disk shape). This is a crude sizing approximation

for radial-flux machines over a wide power range. The first key

point to remember is that the stator yoke thickness is governed

by the flux per pole (since it has to carry this); therefore,it decreases as the pole number increases. High-pole-number

machines tend to have a much higher diameter compared with

the axial length. In totally enclosed machines, the TRV tends

to be in the range of 7–14 kN · m/m3 for small ferrite-magnetmotors, 20 kN · m/m3 for bonded Nd–Fe–B magnets, and14–42 kN · m/m3 for rare-earth magnets, and it is hard toincrease beyond this without using a very specialized topology.

If high-energy magnets are used, then high-efficiency machines

can be designed, and also, it allows the motor to be more

compact. When Nd–Fe–B magnets are utilized, it is reasonable

to expect a peak electromagnetic efficiency of over 90% even

on smaller machines.

In terms of the sheer or tangential air-gap stress, (1) shows adirect relationship to the TRV, as proved in [1]. The TRV gives

an engineering approach to sizing the rotor. The sheer stress

allows a more fundamental stress-limiting calculation, as shown

in the Appendix, based on the electric loading and the air-gap

flux-density limits. As can be seen in Table I, there is a wide

variation in TRV—a median for first-pass design of a larger,

efficient, and well-designed rare-earth magnet machine would

be about 40 kN · m/m3

, which is a sheer stress of 2 N/cm2

.

C. AC or DC Control?

Brushless PM motors generally fall into two classes: ac and

dc. There are different requirements when designing them, and

this is related to the back-EMF waveform and the rotor-position

sensing. Consider a three-phase operation. For ac operation, the

phase current will be sinusoidal, and there is a 180◦ conductionfor each inverter leg using a pulsewidth-modulation strategy

with a position encoder. For dc control, the current waveform is

trapezoidal with 120◦ conduction with three Hall effect probesusually used to detect the switching positions. Hence, an ac

machine requires sinusoidal back EMF generated by the PM

rotor, while the dc machine requires a more trapezoidal back-

EMF waveform. Some machines have back-EMF waveforms

that are intermediate and can be used with either ac or dc con-

trol. Generally, dc motors are suitable for power drives which

can tolerate some torque ripple and do not require substantial

field weakening at higher speeds, while ac motors are more

suitable for servo drives where smooth operation and extended

field weakening are required. DC control can offer a higher

power density, and this is illustrated in the Appendix. The

characteristics for DC and AC operations can be summarized.

The following are the characteristics of dc operation:

1) full-pitched and concentrated windings for trapezoidalback EMF;

2) higher power density;

3) Hall effect probes to detect the correct current switching

positions (low cost);

4) suitable for power drives.

The following are the characteristics of ac operation:

1) distributed and fractional-slot windings for sinusoidal

back EMF and smooth operation;

2) better control and extended field weakening;

3) shaft encoder to control current (high cost);

4) suitable for servo drives and drives requiring excellent

field-weakening capabilities.

There are several strategies to make the machines sensorless

(no Hall probes or shaft encoder) although the norm in indus-

trial applications is still to use position feedback.

Generally, the current phasor from the three-phase-winding

current set should be located on the rotor q -axis unless fieldweakening is used. This is used above the base speed when,

essentially, the inverter voltage has reached its maximum where

the current cannot be controlled and the maximum current

cannot be achieved. The inverter switching is advanced, and this

can be effective up to maybe 15–20 electrical degrees depend-

ing on the machine. This is shown in Fig. 1 for a small four-pole

dc-controlled machine [shown later in Fig. 6(b)]. It can be seenthat the torque range is extended from about 2500–3000 r/min.


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DORRELL et al.: REVIEW OF DESIGN ISSUES AND TECHNIQUES FOR PERMANENT-MAGNET MOTORS 3743

Fig. 1. Field weakening (phase advance) for a small surface-magnet dcmachine.

Fig. 2. Surface- and interior-PM four-pole rotors with red and blue magnetsoppositely polarized. Gray areas denote the laminated core. Red and blueareas are oppositely magnetized magnets. (a) Nonsalient surface-magnet rotor.(b) Salient interior-magnet rotor.

Phase advance has the effect of weakening the main field by

rotating the current phasor so that there is a component on

the −d-axis. AC-controlled machines with internal-PM (IPM)rotors can have much higher field-weakening capability, and the

machine used in [30] has 60◦ phase advance—this is studiedlater. IPM motors can have considerable reluctance torque as

well as excitation torque. The machine in [30] is required to

have a wide field-weakening capability because the base speed

is 1500 r/min, whereas the maximum speed is 6000 r/min.

D. Choice of Rotors

There are many possible topologies for the rotor—too many

to comprehensively list here. They lie in two basic topologies.

One has surface magnets with little saliency, which are commonin dc motors as already mentioned (although they are also often

used in ac motors), while the second has embedded magnets

and considerable saliency. Fig. 2 shows some examples of

these. Many of these topologies can be simulated in the SPEED

simulation package from the University of Glasgow, U.K., and

Miller [31] lists many brushless PM-motor rotor arrangements.

For a surface-magnet nonsalient rotor, X d = X q, as shownin Fig. 2(a). Embedded magnets are possible in the rotor, as

shown in Fig. 2(b). These are used in ac machines, although

they can be used in dc machines. They have q -axis saliency(i.e., X q > X d). The advantage of this is that the peak torque ismoved from the q -axis to an angle of about 100–120 electrical

degrees away from the d-axis. This means that if there is atransient overload when the current is on the q -axis, there

Fig. 3. Phasor diagram and equivalent circuits for brushless permanent acmachines. (a) Phasor diagram for salient-pole PM motor—the q -axis is oftentaken as the vertical-axis reference (in surface-magnet rotors, X e = X q).(b) Per-phase equivalent circuit for nonsalient PM motor. (c) d–q-axis equiv-alent circuits for salient-pole PM motor.

will be extra torque available to bring the motor back to the

correct firing angle, preventing pole slipping. The saliency also

offers additional reluctance torque, and this is illustrated by theexample in Section IV-B.

The phasor diagram for the two types of rotor is shown

in Fig. 3(a) (assuming ac control). This is a general case in

steady state; the difference in operation is that if there is no

saliency, then X d = X q and the steady-state circuit in Fig. 3(b)can be utilized. If there is q -axis saliency, then the steady-statecircuits have to be resolved into two (onto the d- and q -axes), asshown in Fig. 3(c); this represents an IPM machine. Under low-

saturation conditions, then X d and X q are independent and arefunctions of the d- and q -axis reluctances. However, when thereis high saturation, there is cross-coupling between the d- and

q -axis components so that X d = f

(I d, I q) and X q = f

(I d, I q).If an extended field-weakening range (from the base speedupward) is required, then the IPM rotor should be used. A

surface-magnet motor simply cannot cope with this range be-

cause the field-weakening capability is limited. This occurs

when the current phasor is advanced away from the q -axis sothat there is a component on the −d-axis, as shown in Fig. 3(a).This has three effects: It can be seen that there is a negative

X dI d phasor on the q -axis. This weakens the motor flux whichreduces the iron loss at high speed. Additionally, it reduces the

voltage requirement from the inverter supply. The third effect

is the introduction of reluctance torque in the machine. This is

shown in Fig. 3(c), which breaks down the voltages onto the

d- and q -axes. The power due to the excitation torque is 3EI q(where E is the back EMF induced into the rotor by the IPM


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Fig. 4. Pole-face slots for control of X q in IPM rotor.

rotor), whereas the total output power, including the reluctance,

is 3E I q [where E is the total rotor EMF due to the magnetsand q -axis saliency, as defined in Fig. 3(c)]. In Fig. 2(b), itcan be seen that it is possible for q -axis flux to flow acrossthe surface of a pole face which may lead to excessive X q,in which case, holes or slots can be used in the pole face to

control X q (Fig. 4). The use of the pole-face slots will also

control the cross-saturation, making the machine performancemore predictable and stable.

E. Pole-Number Selection

It is important to select the correct pole number for the

machine. DC machines tend to have lower pole numbers

(2, 4, 6, etc.), while ac motors often have higher pole numbers

(8, 12, 16, etc.), although this is not a firm guideline. Higher

pole numbers enable fractional-slot windings. The pole number

should be a function of the speed of the machine, and the

following points should be addressed.

1) The flux in the machine should not alternate at a high

frequency; otherwise, the iron losses will be excessive,although field weakening can be used at higher speed to

limit the iron losses (see example later).

2) Flux frequency = Rotor rotational frequency × pole-pairnumber.

3) For normal laminated steels, do not go beyond 150–

200 Hz, although at lower fluxes, it is possible to operate

successfully at maybe 400 Hz even for normal steels.

4) A two-pole PM motor can be difficult to fabricate, and

also, the end windings are long (leading to increased

losses) and the stator yoke is wide (leading to increased

machine diameter).

Popular pole numbers tend to be higher in fractional-slot acmachines to enable distributed windings. In smaller machines,

a nine-slot eight-pole number is popular [32] although 9/6

arrangements are used and a 12/10 machine was reported in

[33]. In [34], the base slot number of 18 was used with different

rotors with 12 and 16 poles. In [35], an unusual rotor design

using consequent IPM poles (alternate magnet and iron poles)

with dovetail-shaped magnetic poles is discussed with pole

numbers varying between 6 and 14. All the machines in [32]–

[35] are ac drives.

F. Noise, Vibration, Cogging Torque, and Torque Ripple

This should not be ignored. Larger drives should be smootherin operation; otherwise, they will cause excessive noise. The

9/8 machine reported in [32] is popular for small machines but

it creates high unbalanced magnetic pull (UMP—a net radial

force on the rotor). This makes it more unsuitable for larger

machines. The UMP is much less in a 9/6 machine. In [34],

the effects of winding harmonics on the UMP were studied;

Zhu et al. [36] followed a very similar method with more

slot/pole combinations but without the detailed method.However, UMP is not the focus of this paper. More relevant

is the production of cogging torque due to the rotor-magnet

and stator-slot combination (which is an alignment torque)

and torque ripple due to the interaction of the magnet air-gap

flux waves with stator MMF spatial harmonics (which is an

excitation torque).

Cogging torque is an alignment torque between the stator

teeth and rotor magnets and is most prominent in surface-

magnet motors with integral slots per pole or pole pair. It is a

reluctance type of torque, and there are a variety of methods for

calculating it using analytical methods [37] and finite-element

analysis (FEA) (there are many studies of cogging using this

method, e.g., [38]). There are also several ways to improve the

cogging torque, such as skew (gradual in either stator or rotor

or using skewed axial rotor segments [38]), bifilar teeth [38],

pitching and staggered magnet spacing in a surface-magnet

rotor [39], and slot opening adjustment, and in ac machines,

fractional slotting is a standard way to reduce cogging. This

means that there is a fractional number of slots per pole, e.g.,

the 9/8 configuration aforementioned is an example of this.

Cogging torque in brushless dc machines was reviewed in [40].

Load torque ripple is a function of the interaction of the PM

air-gap flux waves with the winding MMF. This is reviewed in

[41] (which also discussed nodal vibration and noise). Torque

ripple under load is often neglected in studies, with a preferencefor static or mean torque. This is because accurate calculation

of torque, even by using FEA, can be difficult [42], [43]. Mean

torque can be calculated using current–flux-linkage loops [44]

(indeed, so can cogging torque [45]) although many still only

do a load calculation at one position. Torque ripple tends to

be implicit in a dc machine due to the fully pitched windings

and the need to get a trapezoidal winding. For an ac machine,

there is a greater emphasis in smooth operation so the winding

layout is more sinusoidal and torque ripple is minimized. Skew

will also help reduce the load torque ripple. Considering the

equation for stress in (1), the torque (for an unskewed machine)

will be

T (t) = LD

2

πD 0

σ(y, t) dy

= LD

2

πD 0

br(y, t)J st(y, t) dy (2)

where y is the circumferential distance around the air gap (sothat ky = θ and k = 2/D where D is the mean air-gap diame-ter) and L is the axial length. We can define the stator electricloading as a stator surface current density J s (in amperes per

meter), while we can define the rotor radial flux density in theair gap as br. The product of these at any particular point will


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give the sheer stress. The air-gap flux density due to the PM

rotors is

br(y, t) =m

Bmr cos(mp(ωrt − ky + φm)) (3)

where m = 1, 3, 5, etc. A general phase angle is set by φm. The

synchronous rotational velocity of the rotor is ωr, and this ismatched to the supply frequency ωs (in radian per second) bythe equation ωs = pωr where p is the pole-pair number of themachine.

In many machines, it can be assumed that the winding

is a balanced three-phase winding. However, in a fractional-

slot machine, it should not be assumed so that the winding

MMF is made with a fundamental one-pole-pair harmonic with

second, third, fourth, fifth, sixth, seventh, etc., windings. The

fundamental harmonic has to be taken as two for the general

case, and harmonics are eliminated if they are zero. Hence,

assuming the current phasors are in phase with the rotor flux

J s(y, t) =nw

J nws cos(ωst − nwky + φnw)

=nw

J nws cos( pωrt − nwky + φnw) (4)

where nw = ±1,±2,±3, etc., for the general case in a three-phase winding. Using (2), the product of (3) and (4) shows that

torque is a function of the product of the cosine terms when

the phase angles are equal. For the main torque, nw = mp,where m = 1 and time variation is zero, i.e., a steady torque.Working through the mathematics, the general case for the

torque vibration is

f m±1torque = (m ± 1)f supply|nw=±mp (5)

where m = 1, 3, 5, etc. This does not necessarily mean thatthese torque vibrations exist. If there is no matching spatial

winding harmonic and magnet flux wave, then there is no

torque. There can be winding harmonics below the pole num-

ber, and these have no effect since there is no corresponding

magnet flux wave. This tends to mean that dc machines have

some torque vibration while ac machines tend to have winding

harmonics and flux waves that, spatially, do not match so that

there is less torque ripple. This is investigated in the next

section.

G. Winding Arrangement

There are a variety of methods for winding a brushless PM

motor depending on whether it is an ac or dc motor. The aim of

an ac winding is to obtain a sinusoidal open-circuit back-EMF

waveform. For a dc winding, it is to obtain a trapezoidal wave-

form. Therefore, is it appropriate to consider them separately.

Slot fill is considered in Section II-J.

1) AC Windings: Distributed windings are often utilized

in ac machines with coil pitches of one slot. An excellent

examination of this arrangement was put forward in [46]. The

correct winding for a machine is very much a function of thepole number and slot number and whether there are one or

Fig. 5. Example of 18-slot 8-pole ac machine with one slot skew. (a) Dis-tribution of one phase for three-phase sine winding. (b) Half cross-section forIPM machine. (c) Three-phase controlled sinusoidal current on rotor q-axis.(d) Three-phase back EMF. (e) Electromagnetic torque.

TABLE II18-SLOT 8-POLE IPM AC MOTOR EXAMPLE—OPERATING

AN D GEOMETRIC PROPERTIES

two coil sides per slot (concentric, lap, or concentrated round

one tooth), as discussed in [31]. Here, a simple example of an

18-slot 8-pole IPM machine is shown in Fig. 5. This is a

fractional-slot machine. The winding is illustrated for one phase

in Fig. 5(a), showing the distributed nature of the winding.

The rotor arrangement is shown in Fig. 5(b). The machine

was modeled using the SPEED software package PC-BDC [47]

from the University of Glasgow, U.K., and the machine data are

given in Table II; this gives the operating point data together

with various geometrical and winding data. There is one stator-

slot skew in this machine which helps form the back EMF intoa very sinusoidal wave, as shown in Fig. 5(d), so that the torque


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Fig. 6. Comparison of idealized short-pitched and fully pitched windingsin a 12-slot 4-pole dc machine. The windings are one phase of a balancedthree-phase set in each case. (a) Short-pitched coils (two-third pitching).(b) Fully pitched concentrated coils. (c) Trapezoidal 120-electrical-degreethree-phase current set. (d) Three-phase back EMF with short-pitched wind-ings. (e) Electromagnetic torque with short-pitched winding. (f) Three-phaseback EMF with fully pitched windings. (g) Electromagnetic torque with fullypitched winding.

is smooth, as shown in Fig. 5(e). The efficiency is only 85%,

but at 6000 r/min with eight poles, the frequency in the iron is

400 Hz. This may require high-grade aerospace steel, although

this was not used in this instance (Losil 800 was used), andtherefore, the iron loss dominated the loss components.

2) DC Winding: DC machines require a different winding

strategy with the aim of obtaining a trapezoidal back-EMF

waveform. This will interact with the trapezoidal current (with

120◦ conduction period) to produce a smooth torque. Thisrequires fully pitched concentrated windings. Fig. 6 shows the

winding layout for one phase of a three-phase set for a 12-slot

4-pole machine. The first simulation uses a short-pitched dis-

tributed winding, while the second uses a fully pitched concen-

trated winding. The waveforms illustrate the torque production

and the fact that there is inherent torque ripple with the short-

pitched winding. This is very much an idealized waveform. The

back EMF usually has some distortion to produce ripple, andthis arrangement would have substantial cogging torque since

Fig. 7. Interaction of back EMF and current in dc machine, illustrating torque-producing region in waveforms.

there are three slots per pole which is not accounted for in the

waveforms.

It is also necessary to consider the torque-producing region of

the waveforms. This is shown in Fig. 7. If the back-EMF wave

is too narrow, then there is torque ripple when the back EMF

is multiplied by the current. In addition, the dc machine used

Hall probes, and if they are only slightly out of position, then

there will be considerable torque ripple. This was investigated

in [39].

3) Delta Connection: Delta connection is not recommended

in a brushless PM machine. If there is any third time harmonic

in the phase back EMF, then this will induce a circulating zero-

order current in the mesh, as shown in Fig. 8. This will cause

excessive current and copper losses and potential burnout of thewinding.

H. Magnet Selection and PC

The type of magnet used will have a great effect on the

motor performance and cost. The increased cost of high-energy

magnets may be offset by the fact that less magnet material

is required and the motor will be more compact. Typical

remanent magnetism and recoil permeability values at 25 ◦Cfor various magnets are listed Table III. Further details are

put forward in [7] and [8]. The nonlinear characteristics of the

specific magnets should be inspected. The magnets should notbe used in the nonlinear area, as shown in Fig. 9, and sufficient

design tolerance should be built in so that the magnets are not

demagnetized even under overload. The operating point can be

found by calculating the permeance coefficient (PC) and also

the electric loading effects. For ferrite-magnet motors, a PC of

at least eight is usually required, but for rare-earth magnets, this

can be lower since the magnets are much stronger and linear.

The PC can be improved by the use of a narrow air gap and

shorter flux path lengths and wide teeth and stator yoke. Lower

flux-density levels also improve the PC.

The thermal performance of the magnet material also has

to be considered, as shown in Fig. 10. While this paper is

mostly concerned with rare-earth magnet machines, it is worthconsidering ferrite-magnet material for completeness. The


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Fig. 8. Zero-order 3rd time harmonics in delta-connected brushless PM motor. (a) 3-phase current and 3rd time harmonics. (b) Circulating zero-order set.

TABLE IIITYPICAL MAGNET DATA

Fig. 9. Second quadrant operation for ferrite (grades 1 and 5) and Nd–Fe–B(Crumax 2830) magnets.

ability to withstand demagnetization for a magnet is dependent

upon the magnet temperature and the magnet type. The typical

values of temperature coefficient for the magnet intrinsic coer-

civity H cj are as follows:

1) ferrite: +0.4%/◦C;2) Sm–Co:−0.2%/◦C to −0.3%/◦C;3) Nd–Fe–B: −0.6%/◦C to −0.11%/◦C.Ferrite is worse at lower temperatures due to the negative

temperature coefficient, whereas rare-earth magnets are worse

at higher temperature. Ferrite magnets have a nonlinear

region which can be easily moved into with overload and

overtemperature operation. The following points summarize

the discussion for ferrite magnets.

1) Ferrite magnets need a good magnetic circuit and a low

reluctance; otherwise, their load line will not be steep

enough and the operating point will be close to the

nonlinear region.

2) The slope of the load line is equal to negative PC when

the x-axis is scaled by µ0.3) PC = (magnet thickness×air-gap area)/(air-gap length×

magnet area). The PC can be used to set the magnet

thickness.4) Air-gap area ≈ magnet area for surface magnet.

Fig. 10. Ferrite and rare-earth magnet thermal considerations. (a) Ferrite-magnet example. (b) Rare-earth magnet example.

5) Therefore, the magnet thickness has to be considerably

greater that the air-gap length.

6) Hence, a lot of magnet material is required.

To summarize the discussion for rare-earth magnets:

1) The PC does not need to be as high when using rare-

earth magnets so that less material is required (which is

necessary since it is more expensive), and again, the PC

can be used to set the magnet thickness.

2) They have high energy, and handling can be difficult

when magnetized.3) Premagnetizing may be required.


8/17


Fig. 11. Illustration of demagnetization of rare-earth magnet with thermaloverload. Red dots illustrate points after permanent demagnetization.

4) It is possible to demagnetize the magnets under thermal

stressing, as shown in Fig. 11.

I. Steel Selection and Iron Loss

The two basic properties of interest are the B/H curve and the

iron loss in the steel. The B/H curve sets the flux levels possible

in the machine and the degree of saturation, while the iron

loss is important to the machine efficiency. The loss calculation

is often done by using a modified version of the Steinmetz

equation to obtain hysteresis and eddy-current loss [48].

This loss-calculation method is used in the SPEED mod-eling software used in this paper, and the equation utilized

for the watts-per-cubic-meter iron loss in [31] and [47] is ob-

tained from

P = C hf Ba+bBpkpk + C e1

dB

dt

2(6)

where there are various coefficients necessary for accurate

calculation. The loss calculation is really an estimate and only

good if the material loss data are accurate (often, they are

not). Lookup iron-loss tables are often utilized rather than the

implementation of a complicated equation set, and these aregiven in [9]. As an example of the effect of steel, consider

the ac motor design in Section II-G1. The material used in this

example was Losil 800/65, and the iron loss was calculated to

be 623 W. The material can be replaced with Transil 35, which

has a lower flux density for a given MMF, as shown in Fig. 12.

However, it is a low-loss steel, as shown in the comparison in

Fig. 12, so that the iron loss is now 122 W. Loss is often a

function of the amount of silicon in the steel. Increasing the

amount of silicon (up to a maximum of 3% [9]) can reduce the

loss in the steel. Reference should be made to manufacturer’s

data. The thickness of the lamination also makes a significant

difference to the eddy-current loss. For instance, for Transil

330, at 1.5 T and 50 Hz, 0.35-mm laminations have a loss of 2.9 W/kg, while 0.5-mm laminations have 3.15 W/kg [1].

Most magnet steels will saturate between 1.5 and 1.7 T

(where the knee points of the B/H curves are in Fig. 12). Thesheer stress can be maximized in high-performance machines

by increasing the flux using cobalt–iron alloys. These alloys

can have a knee point above 2 T [64]; however, they tend to bevery expensive and applicable to premium-cost applications.

Manufacturing affects the iron loss. The properties of thesteel are affected by punching and cutting. If a complicated

lamination shape is used, the properties will be affected. Worn

lamination punches will tend to lead to increased iron losseswith lamination edges having burr, which causes shorting be-

tween laminations and increased eddy-current loss. For an IPM

rotor, a very fine cut across the surface can remove a lot of theburr and improve iron loss.

J. Insulation Systems, Slot Fill, and Mechanical Aspects of

Rotor Structure

Insulation systems have been standardized and graded by

their resistance to thermal aging and failure. Four insulationclasses are in common use, as set by the National ElectricalManufacturers Association (NEMA), U.S., and these have been

designated by the letters A, B, F, and H, as shown in Table IV.

The temperature capabilities of these classes are separated fromeach other by 25 ◦C increments. The temperature capability of each insulation class is defined as the maximum temperature at

which the insulation can be operated to yield an average lifeof 20 000 h. A maximum temperature rise is also set. There

have been new classifications introduced in 2009 (although notyet extensively adopted) which correspond to the traditional

classifications; the new equivalent International Electrotechni-

cal Commission classes are also quoted.

In terms of low-voltage machines with random-wound coils,the system will consist of a slot liner into which the coil is

inserted. The coil will be formed from enameled copper wire,and the coil will be automatically wound in situ, or automati-

cally or manually inserted as a complete coil. There may be top

wedges to lock the coil into the slot, and if there are two coilsides in the slot, then there may be a phase separator. The stator

may be dipped in an epoxy-resin-type varnish with the aim of impregnating deep into the slot. This varnish has two functions.

It will fill and set so that the winding is not loose in the slot,

which will prevent vibration damage. It will also provide goodthermal conduction from the coil to the core, which is necessary

for effective cooling. Loose windings in slots are not a goodmanufacturing solution. If the stator is not dipped in resin, thenit is often trickled as a hot solution down into the slots in order

to secure the coils. Different insulation systems are described

in [11].If the wire is too thick for winding the coil, then wind

with multiple strands and connect in parallel. These are oftendescribed as “strands in hand” and should not be confused

with parallel windings, where complete coils are connected in

parallel.The fill factor is the ratio of the copper in a slot to the

slot area. A common mistake made is to assume a fill factor

that cannot be realized. There is a slot liner, and there may be

wedges which will occupy slot space. Also, the conductors areround and have an enamel insulation coating so that there will


9/17


Fig. 12. Comparison of B/H and frequency/iron-loss curves for Losil 800/65 and Transil 35 steels (B = 1.7 T for loss data).

TABLE IVINSULATION CLASSIFICATIONS [NEMA MG 1-2006]

(AMBIENT BELOW 40 ◦C)

be space even when tightly packed. Therefore, high fill factors

should be approached with caution. For instance, automotive

alternators are low voltage (12 V) and often have very few turnsof very thick wire. Manufacturers often work with a maximum

slot fill of 30% or less.

Many machines have environmental considerations that re-

quire the stator and/or rotor to have a protective can which

can be conducting (for instance, from stainless steel [49])

or nonconducting. These cans can add eddy-current loss to

the machine and lengthen the air-gap length so that the canscan be accommodated. However, they can add considerable

mechanical stability to the rotor and help retain the magnets

on the surface of the rotor. Both surface magnets and IPM

motors have structural issues with retaining the magnets and

pole faces (in IPM rotors). The mechanical stresses in an IPM

rotor were described and discussed in [50], while the use of

retaining sleeves in a high-speed surface-magnet rotors was

highlighted in [51] and mechanical retention of magnets was

further discussed in [52]. The mechanical integrity of a rotor

may restrict the maximum speed of a machine and also the

possible maximum rotor diameter.

The losses in the machine can be split up into copper, iron,

and mechanical losses. Some of these losses can be difficult to

assess. For instance, there will be eddy-current losses in surface

magnets due to slotting [53] and possibly proximity losses in

conductors if they are air-gap windings or even thick conductors

[54]. However, these are normally low; Yamazaki [55] gives a

good account of the loss distribution in an IPM motor.

K. Sizing-Issues Summary

The sizing of a machine can be a complex matter. To sum-

marize the issues, the following points should be considered.

1) Is there a restriction on length or diameter?

2) Is it in an environment that is sensitive or hazardous?3) What are the application torque requirements?

4) What is the duty cycle?

5) How effectively can we cool the machine?

The latter two points will affect the thermal rating of the

machine, and this is addressed in the next section.

III. COOLING AND T HERMAL I SSUES

There is a strong requirement for more energy-efficient mo-

tors. Improved thermal design can lead to a cooler machine with

reduced losses. Copper loss is a function of winding resistance

and, therefore, is a function of temperature. Rare-earth PM

flux reduces with increased temperature. The size of a motor

is ultimately dependent upon the thermal rating. The motor

components that are limited by the temperature are wire or

slot liner/impregnation, bearings (life), magnet (loss of flux

and demagnetization limit), plastic cover (low melting point),

encoder, and housing (safety limit).

The temperature of the winding insulation has a large impacton the life of the machine. Many companies use curves such as

that shown in [56] to estimate motor life, and these are related

to the insulation classifications in Table IV.

Magnets are usually isolated from the main heat sources

so that they are protected from severe transient overloads.

The windings are most susceptible to transient overloading.

However, rare-earth magnets (Sm–Co and Nd–Fe–B) exhibit

local eddy-current losses as heat sources, which are difficult

to estimate or measure. Hence, there is a much longer time

constant for magnets compared with windings although it is

essential to know the magnet temperature for transient and

demagnetization calculation.In this section, traditional thermal designs will be outlined,

and then, modern techniques will be reviewed.

A. Traditional Thermal-Sizing Methods

Traditional thermal sizing uses a single parameter, which is a

thermal resistance, as shown in Fig. 13(a), for the housing heat-

transfer coefficient. In addition, the winding current density

and specific electric loading are considered. Traditional thermal

modeling tends to be empirical with data obtained from the

following:

1) simple rules of thumb, e.g., for a totally enclosed ma-

chine, a conductor current density of 5 A/mm2 and a heat-transfer coefficient [Fig. 13(b)] of 12 W/m2/◦C;


10/17


Fig. 13. Traditional thermal modeling using single thermal resistance and sin-gle heat-transfer coefficient. (a) Thermal resistance from winding to ambient.(b) Heat-transfer coefficient.

TABLE VTYPICAL CURRENT DENSITY AND HEAT-TRANSFER COEFFICIENTS

2) tests on existing motors;

3) competitor catalogue data for similar products.

These methods can be inaccurate. A single parameter fails

to describe the complex nature of motor cooling, and there is

poor insight into which aspects of the thermal performance of a

motor need to be focused upon. Table V lists typical values for

the current density and heat-transfer coefficient.

B. Modern Thermal Design Techniques

There are two options for modern thermal design. These

are lumped-circuit analysis (network analysis) [14], [15], [18],

[57]–[59] and numerical analysis using FEA and computational

fluid dynamics [16]. While computational fluid dynamics gives

more accurate solutions for particular examples, it can be time

consuming to set up the model. In the design office, the lumped-

circuit analysis is more useful for faster and more interactive

design procedures. It can be linked into electromagnetic design,

as illustrated in [18] where the thermal package Motor-CAD

from Motor Design Ltd., U.K., [60] is linked with the SPEED

software [47]. In the examples put forward in this paper, these

environments are used. A typical lumped circuit from Motor-CAD is shown in Fig. 14; the literature has several examples

of this type of circuit as developed by many researchers (e.g.,

[14]–[18], which are, by no means, comprehensive). When

there is a high temperature gradient, more nodes are required

so the slot is modeled as a multishell structure, as shown in

Fig. 14(b). The accuracy of the circuit model in Fig. 14(a) very

much depends on the accuracy of the lumped parameters; if one

is substantially inaccurate, then it can affect the temperatures

of the surrounding nodes. Therefore, the components have to

account for the heat flow in terms of the conduction, convection,

and radiation. Several aspects of the model are manufacturing

dependent as well as material dependent. For instance, the ther-

mal conductivity of the coil is a function of the impregnation of the resin.

C. Cooling Types and Methods

Motor-CAD covers several thermal networks including a

range of cooling types that represent the standard methods of

motor cooling.

1) Natural convection (TENV): This is very common with

many housing design types.

2) Forced convection (TEFC): There are many fin channel

design types, and fans are commonly fitted to industrial

drives.

3) Through ventilation: This utilizes rotor and stator cooling

ducts.

4) Open end-shield cooling.

5) Water jackets: There are many design types (axial and

circumferential ducts), and they can be for either stator

or rotor.

6) Submersible cooling.

7) Wet rotor and wet stator cooling: This is common for

pumping.

8) Spray cooling.9) Direct conductor cooling using slot water jacket.

10) Conduction: Internal conduction and the effects of

mounting.

11) Radiation: Both internal and external.

Hence, there are many ways to implement effective motor

cooling.

IV. MOTOR D ESIGN T ECHNIQUES AND E XAMPLES

Modern design techniques usually use detailed analytical

algorithms and electromagnetic FEA methods to analyze a

design. While the SPEED package already mentioned used

analytical calculations, sometimes, detailed calculations require

FEA, such as to obtain accurate cogging torque and load torque

in IPM motors with phase advance. A finite-element bolt-on

package can be used for this [61]. This arrangement is not

unique; many finite-element packages now feature spreadsheet

and initial calculation tools to enter data for an initial motor de-

sign. In this section, some additional motor-analysis techniques

will be highlighted and design and analysis examples put will

be forward.

A. Current–Flux-Linkage Loops (I–Psi Diagrams)

The mean torque can be obtained in a brushless PM ma-chine in a similar way to the switched reluctance by forming

a current-against-flux-linkage loop (I–Psi). This method was

detailed in [44] and [45]. The area enclosed (W ) is equal tothe work done during the rotation so that the torque is then the

work done divided by the distance moved. For a machine with

m pole pairs and n phases, the electromagnetic torque is

T e = n × m2π × W. (7)

For a balanced machine, each phase will trace out the same

loop with area W . By using the example with the short-pitchedmachine in Section II-G2, with both sine- and square-wave

excitation, the loops are shown in Fig. 15. The mean torque forthe dc control is 1.0 N · m, while for ac control, it is 0.87 N · m.


11/17


Fig. 14. Thermal circuits and winding model of machine. (a) Lumped thermal model (part model) with heat sources, thermal resistances, and thermalcapacitances—surface-magnet rotor. (b) Multilayer winding representation when there is a high temperature gradient. Traditional winding for random-woundcoils and 54% slot fill.

Fig. 15. Comparison of I–Psi loops for dc and ac controls.

The peak current for both simulations was 15 A, and the same

short-pitched winding in Fig. 6(a) was utilized. Interestingly,in the Appendix, the theoretical ac/dc control rating ratio was

calculated to be 1.5. Here, by simply changing from sine-

to square-wave control, the torque increases by 1.15. If the

winding is fully pitched for the dc control, then the torque is

1.07 so that the ratio is 1.23. However, the rms current with

the dc control is higher. Using the same rms currents and fully

pitched winding in the dc simulation gives a torque ratio of

1.07. These results were obtained in the SPEED PC-BDC and

PC-FEA environments.

B. Frozen Permeability Method

This method is a very powerful tool for separating out thedifferent torque components due to excitation and reluctance

Fig. 16. Prius PM-motor cross section in SPEED PC-BDC—this shows twomagnets per pole and high saliency.

torques [62]. This technique is used in an FEA, and many

packages allow this function. To summarize, using a magne-tostatic model, a full nonlinear solution is carried out, and the

total torque can be obtained from this solution. The saturated

magnetic permeances are then locked. If the magnets are then

“switched off” (by setting the remanent magnetism Br to zero)and the solution restarted with the locked permeances from the

full solution, then the reluctance torque can be calculated. This

reluctance torque includes the saturation effects from the full

solution. An example is shown in Fig. 16, which is a SPEED

simulation of the Toyota Prius machine in [30]. This machine

operates at a high phase advance to allow for a very wide

field-weakening range (from 1500 to 6000 r/min) and relies on

substantial reluctance torque. This is an eight-pole machine.

The peak current occurs at the base speed of 1500 r/min.This is a transient point, and the current density (over


12/17


Fig. 17. One-pole machine from static FEA solution. Peak flux density inteeth is about 2.10 T. Load current is 190.9 A on the q-axis (1500 r/min).

20 A/mm2 at 190.9 A) and flux densities are high if the current

is maintained on the q -axis, as shown in Fig. 17. The frozenpermeability method was implemented at 1500 and 6000 r/min,

and the results are shown in Figs. 18 and 19. It can be seen

that the torque peaks between 30◦ and 50◦ phase advance. With60◦ phase advance, it was found that the base speed currentcould be reduced to 141.1 A at 1500 r/min for a required

maximum torque of about 300 N · m. Comparison of Fig. 18,where the current level is much higher, with Fig. 19 shows

different curve shapes for both the excitation and reluctance

torques. This illustrates the effect cross-saturation can have on

the performance, as discussed earlier.

C. Efficiency Plots

Efficiency is becoming a more important factor in machine

design and is indeed crucial in many designs. Computational

design solutions are becoming increasingly rapid, and it is now

possible to scan a range of operating points and produce a

plot of the efficiencies over a 2-D array of torques and speeds.

In [30], measured efficiency plots were used to illustrate the

motor operation, and these can be obtained from simulationstoo. Fig. 20 shows the efficiency plot for the machine in the

previous section using SPEED PC-BDC. For a brushless PM

motor, there are several parameters that can be set. In this

case, at each load point, the phase angle advance was set at

0◦, 30◦, and 60◦, and the current varied until the correct torquewas obtained. The highest efficiency was then selected as the

operating point. The selected phase angle is shown in the top

chart, while the efficiencies are shown as colored regions and

contour lines in the bottom plot.

D. Fractional-Slot Design-Size Rationalization

Here, an example is put forward for the rationalization of a motor design by consideration of the thermal design [63].

The existing motor has 50 mm of active length (core length), a

130-mm-long housing with a traditional lamination, and over-

lapping windings. The new motor still has 50 mm of active

length; however, the housing is now only 100 mm long. It

produces 34% more torque for the same temperature rise. The

machine uses segmented-lamination nonoverlapping windings

(one-slot pitch concentrated coils). In order to optimize the newdesign, an iterative mix of electromagnetic and thermal analysis

was performed. Extensive thermal modeling was carried out.

The new design is shown in Fig. 21. Both arrangements had an

80-mm diameter; however, the traditional design had 18 slots

and 6 poles [Fig. 21(b)] and overlapping windings, while the

new design has concentrated windings and a 12-slot 8-pole

layout [Fig. 21(c)]. This illustrates that the slot/pole combi-

nation is flexible for a particular application. The traditional

winding only had a 54% slot fill but the new arrangement and

the techniques that can be applied to manufacture it (precision

bobbin wound) means that this was increased to 82% in the new

design.

Potting/impregnation material improvement was also possi-

ble. The new design has a k factor of 1 W/m/◦C, whereasprevious materials have a k factor of 0.2 W/m/◦C. This gavea 6%–8% reduction in winding temperature (with respect to

Celsius scale). A potted (encapsulated in resin) end-winding

design showed a 15% reduced temperature compared with that

of the previous nonpotted design. Vacuum impregnation can

eliminate air pockets. The new design here shows 9% decrease

in temperature in a perfectly impregnated motor compared with

the one with 50% impregnation.

All these design and manufacturing improvements lead to a

much improved thermal performance for the new motor design.

This means it can be more highly rated, and so, the size can bereduced by a reduction in the active axial length.

V. CONCLUSION

This paper has described the design philosophy for dc and ac

PM machines. It goes on to discuss many of the modern-day

analysis techniques that can be used to assess the performance

of a machine. Many of the techniques are illustrated with

examples, and the need to consider the electromagnetic design,

thermal analysis, and manufacturing techniques in conjunction

is stressed. This paper will be very useful to an electrical ma-

chine designer who requires more detailed information about

the steps necessary to analyze and improve a motor design of this ilk.

A. Further Literature

There are many sources of design method information from

many researchers. In terms of further texts, [65] gives a treatise

specific to PM motor design, while general ac machine design

and operation are considered in [66] and [67], which can

be very helpful in terms of winding theory and practice and

other aspects of machine operation. The technology is rapidly

developing due to new material design refinement. There are

continuing developments of algorithms that are aimed at the

automated and precise design of an electrical machine; [68]and [69] are illustrations of these, and a literature review would


13/17


Fig. 18. Separation of torque at 1500 r/min with 190.9-A loading—variation of current phase with respect to q-axis.

Fig. 19. Separation of torque at 6000 r/min with 35.4-A loading—variation of current phase with respect to q-axis.

Fig. 20. Efficiency plot for PC-BDC simulations using phase angles of 0◦,30◦, and 60◦.

highlight further examples. This paper has not considered noise

and vibrations; however, these are important. There are severalpapers on this subject as applied to brushless PM motors, and

Fig. 21. Design renationalization using concentrated one-tooth windings and

T-piece stator sections. (a) New design manufactured and T-piece stator.(b) Previous design. (c) New design.

[70] is a further example in addition to the text in [13] and

technical publications [17] and [36].

B. Commercial Design Tools

The work in this paper often uses various commercial soft-

ware products as the working environments while discussing

the fundamental design concepts. The products are not neces-

sarily unique, and a designer should consider trying different

products in order to assess their suitability and even developing

their own design software using the large body of scientific

algorithms and design and analysis techniques already pub-lished. In terms of alternatives, there are other notable examples


14/17


Fig. 22. Air-gap flux density and stator surface current density for ac and dcmotors. (a) B and J for ac machine. (b) B and J for dc machine.

such as RMxprt from Ansoft (Ansys), U.S. This uses first-pass

analytical calculations to feed into Maxwell FEA. Infolytica

Corporation, Canada, has developed MotorSolve BLDC (and

other packages) for template-based design which feeds intothe MagNet FEA package. Cedrat Group, France, uses Flux

and Motor Overlays to specify template geometries for motor

simulation in Flux2D and 3-D, and indeed, SPEED can feed

into this package. JSOL Corporation, Japan, has developed the

JMAG FEA package, and this also has Motor Template (similar

to Motor Overlays) and JMAG-Studio and JMAG designer

can be accessed through CAD Link. This package also has a

SPEED link. The FEA package Opera from Cobham, U.K.,

(formerly Vector Fields) has application-specific tools for front-

end design of rotating machines. These examples illustrate

a commonality between many packages; these tend to allow

easy geometry, material, and control setup for faster motordesign. Many packages now link to standard mechanical CAD

packages so that geometries can be imported and initial design

calculation can be done before resorting to more complex and

slower FEA solutions.

The aforementioned list is far from comprehensive but rep-

resents a global cross section of examples; many companies

and specialists have developed their own in-house design tools,

as already suggested as an option. The market is continually

changing, hence the recommendation for trial of products.

APPENDIX

The maximum mean sheer stresses can be estimated for

brushless dc and ac machines in order to compare their torque

densities. Consider Fig. 22. The dc machine has a trapezoidal

waveform for the current density if the winding is fully pitched

and 120◦ conduction exists, while the ac has low harmoniccontent and the current is sinusoidal. The idealized stress

waveforms are shown for both control strategies, and approx-

imate stress calculations can be derived to illustrate that the dc

machine has a higher theoretical mean stress.

AC Control—Flux Density Limited by Peak of Fundamental

Sinusoidal Flux Wave: In an IPM motor, the flux density in

the air gap can be shaped for smoother operation. This is

particularly important in a servo system. Ideally, the air-gapflux wave would be sinusoidal for low torque ripple, and the

peak of the flux density wave is limited by the steel satura-

tion characteristics. The analysis here makes that assumption.

Hence, under ac control, only the fundamental of the air-gap

flux density wave should be considered, together with the main

current density wave. This is for a distributed winding, and a

three-phase winding is assumed. The mean stress is then

σmean = Bpk(fund)J pk

2 =

Bpk(fund)J rms√ 2

(A1)

where the stator current density can be estimated from a sinu-

soidal spatial variation on the stator surface [Fig. 22(a)] so that

J rms = 3K ACW

2 × N phI rms

D . (A2)

The mean air-gap diameter is D, the number of series phasewinding turns is N ph, the fundamental winding factor is K

ACW ,

and the winding current (assuming no parallel winding) is I rms.The 3/2 factor is valid for a three-phase sinusoidal current set.

Assuming the winding factor is unity, then from (A1) and (A2)

σmean = 3Bpk(fund)N phI rms

2√

2D= 0.55

6Bpk(fund)N phI rms

πD .

(A3)

AC Control—Fully Pitched Surface-Magnet Rotor: If we

assume that the air-gap wave is trapezoidal (and a full square

wave with 180-electrical-degree pitch), then the air-gap flux

will be limited by the peak of the trapiziodal wave, as in

Fig. 1(b); a Fourier analysis of a fully pitched trapezoidal wave

gives a peak fundamental ratio where

Bpk(fund) = 4

π

Bpk(trap). (A4)

Hence

σmean = 4

π

3Bpk(trap)N phI rms

2√

2D= 0.7

6Bpk(trap)N phI rms

πD .

(A5)

DC Control: Assuming trapezoidal flux density and current

density with a 120-electrical-degree pulsewidth

σmean = 2

3 × Bpk(trap)J pk. (A6)

Again, assuming trapezoidal current density, this can be related

to the phase current by

J pk = K DCW ×

2N phI pk2/3 × πD/2 = K

DCW ×

6N phI pkπD

. (A7)

For a trapezoidal current waveform with a width of 120 electri-

cal degrees [Fig. 22(b)], the rms current is

I rms =

2

3I pk. (A8)

Putting (A5) into (A7) gives

σmean = 2

3

3

2 × 6Bpk(trap)N phI rms

πD

= 0.82 6Bpk(trap)N phI rmsπD

. (A9)


15/17


Comparison of Stresses: Comparing (A3)–(A9) shows that,

for a given phase current (whether sinusoidal or trapezoidal),

dc control gives higher stress density than ac control for a given

peak flux density in the ratio 0.82/0.55 = 1.5. However, dccontrol tends to give more torque ripple and is more suitable

for power drives. If a surface-magnet rotor is used, then (A4)

can be compared with (A9), and this time, the theoretical stresslimits are in the ratio 0.82/0.7 = 1.17, which is much closer.

Relationship Between DC Link Voltage and Power Con-

version: Assume that the machines operate with unity power

factor. In a three-phase ac machine where the phase voltages

and currents are sinusoidal and where there is 180◦ conductionin the inverter, the voltages and currents can be related to each

other where I dc = I pk and V dc = 3V pk/2. Therefore

V dcI dc = 3V pkI pk

2 = 3V rmsI rms. (A10)

For a dc machine, where the waveforms are trapezoidal and

where there is 120◦ conduction in the inverter, I dc = I pk andV dc = 2V pk. The rms-to-peak values are

V rms =

2

3V pk and I rms =

2

3I pk (A11)

so that the relationship between the dc link and ac rms values is

V dcI dc = 2V pkI pk = 3V rmsI rms. (A12)

Comparing (A10) and (A12) shows that the same relationship

holds whether it is ac or dc.

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David G. Dorrell (M’95–SM’08) is a native of St. Helens, U.K. He received the B.Eng. (Hons.)

degree in Electrical and Electronic Engineering fromThe University of Leeds, Leeds U.K., in 1988,the M.Sc. degree in Power Electronics Engineeringfrom The University of Bradford, Bradford, U.K., in1989, and the Ph.D. degree from The University of Cambridge, Cambridge, U.K., in 1993.

He has held lecturing positions with RobertGordon University, Aberdeen, U.K., and the Univer-sity of Reading, Berkshire, U.K. He was a Senior

Lecturer with the University of Glasgow, Glasgow, U.K., for several years. In2008, he took up a post with the University of Technology Sydney, Sydney,Australia, where he was promoted to Associate Professor in 2009. He isalso an Adjunct Associate Professor with National Cheng Kung University,Tainan, Taiwan. His research interests cover the design and analysis of variouselectrical machines and also renewable-energy systems with over 150 technicalpublications to his name.

Dr. Dorrell is a Chartered Engineer in the U.K. and a Fellow of the Institution

of Engineering and Technology.

Min-Fu Hsieh (M’02) was born in Tainan, Taiwan,in 1968. He received the B.Eng. degree in mechani-cal engineering from National Cheng Kung Univer-sity (NCKU), Tainan, in 1991 and the M.Sc. andPh.D. degrees in mechanical engineering from theUniversity of Liverpool, Liverpool, U.K., in 1996and 2000, respectively.

From 2000 to 2003, he served as a Researcherwith the Electric Motor Technology Research Center,NCKU. In 2003, he joined the Department of Sys-tems and Naval Mechatronic Engineering, NCKU, as

an Assistant Professor. In 2007, he was promoted to Associate Professor. Hisarea of interests includes renewable-energy generation (wave, tidal current, andwind), electric propulsors, servo control, and electric machine design.

Dr. Hsieh is a member of the IEEE Magnetics, Industrial Electronics,Oceanic Engineering, and Industrial Applications Societies.

Mircea Popescu (M’98–SM’04) received the D.Sc.in electrical engineering from Helsinki University of Technology, Helsinki, Finland, in 2004.

He has more than 25 years of experience in electri-cal motor design and analysis. He worked for the Re-search Institute for Electrical Machines, Bucharest,Romania; Helsinki University of Technology; andSPEED Laboratory, University of Glasgow,Glasgow, U.K. In 2008, he joined Motor DesignLtd., Shropshire, U.K., as an Engineering Manager.He published over 100 papers in conferences and

peer-reviewed journals.

Dr. Popescu was the recipient of the first prize best paper awards from IEEEIndustry Applications Society Electric Machines Committee in 2002, 2006,and 2008.


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Lyndon Evans received the B.Sc. (Hons.) degree incomputer networks from Glyndwr University, Wales,U.K., in 2008.

He qualified as a Television and Video ServiceEngineer in 1988 and worked in this field for over15 years before returning to study and receiving hisB.Sc.(Hons.) degree. He is a Software Developerwith Motor Design Ltd., Shropshire, U.K., in part-

nership with Glyndwr University, and is studying fora research degree.Mr. Evans is a member of The Institution of En-

gineering and Technology and an associate member of the British ComputerSociety.

DavidA. Staton (M’90)received thePh.D.degree incomputer-aided design of electrical machines fromThe University of Sheffield, Sheffield, U.K., in 1988.

Since then, he has worked on motor design andparticularly the development of motor design soft-ware at Thorn EMI; the SPEED Laboratory, Uni-versity of Glasgow, Glasgow, U.K.; and ControlTechniques, U.K. In 1999, he set up a new company,Motor Design Ltd., Shropshire, U.K., to develop athermal analysis software for electrical machines. Hepublished over 50 papers in conferences and peer-

reviewed journals.

Vic Grout (M’01–SM’05) received the B.Sc.(Hons.) in Mathematics and Computing from TheUniversity of Exeter, Penryn, U.K., in 1984,and a Ph.D. in Communication Engineering fromPlymouth Polytechnic, Devon, U.K., in 1988

He is a Professor of Network Algorithms and theDirector of the Centre for Applied Internet Research,Glyndwr University, Wales, U.K. He has worked in

senior positions in both academia and industry forover 20 years and has published and presented over200 research papers and 4 books. He is an Electrical

Engineer, Scientist, Mathematician, and IT Professional.Mr. Grout is a Chartered Engineer and a Fellow of the Institute of Mathe-

matics and its Applications and British Computer Society and The Institutionof Engineering and Technology.

A Review of the Design Issues and Techniques for Radial-flux Brush Surface and Internal Rare Earth...

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Transcript of A Review of the Design Issues and Techniques for Radial-flux Brush Surface and Internal Rare Earth...