A Review of the Design Issues and Techniques for Radial ... · DORRELLet al.: REVIEW OF DESIGN ISSUES AND TECHNIQUES FOR PERMANENT-MAGNET MOTORS 3743 Fig. 1. Field weakening (phase

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 ofmachine.

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

I. INTRODUCTION

THERE ARE MANY excellent books on the design ofbrushless permanent-magnet (PM) motors. Examples of

well-known and established texts are given in [1]–[5], whilemore recently, there have been tutorials at leading internationalconferences with accompanying Course Notes Texts [6]. Thesecover 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 insulationsystems [11]. Noise is also covered by several texts [12], [13].This list is far from comprehensive, and there are many othermonographs that cover specialist aspects of electric motoroperation that are relevant to brushless PM motors. There isstill relatively little on the thermal design of electrical machinesin terms of texts although the number of technical papersis 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 manypapers that cover various aspects of the electromagnetic designon rare-earth PM motors; for instance, [19]–[25] show recentpapers on PM-motor design in a variety of situations.

The aim of this paper is not to highlight particular designaspects of one form of brushless PM motor but rather to givean overview of many of the factors dictating option selectionand design solutions. Therefore, in this paper, the key designpoints related to the design of brushless rare-earth PM ma-chines are outlined and solutions are discussed. Techniques foranalysis are outlined, and these should be useful to a machinedesigner 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 ELECTROMAGNETIC DESIGN CHOICES

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. Thereason 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 becauseof the use of the slots. However, there are good examples ofusing axial-flux machines, and the design of these machinesis discussed in [26]. In these machines, the windings tend tobe air-gap windings (although they can have teeth [27]) whichcan limit the amount of copper that can be used and, hence,can limit the amount of loading possible. The windings tendto be specially formed and shaped, and often, Torus windingsare used; Mendrela et al. [27] review different options forthis type of machine. Axial-flux machines are often used asmotors although they have many advantages (usually relatedto their low armature reactance) in the area of generation[28], particularly in wind generation [29]. However, axial-fluxapplications can still be considered as niche, and the focus ofthis paper will be on radial-flux laminated motors since theseconstitute the majority of brushless PM motors.

0278-0046/$26.00 © 2010 IEEE

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 sizeand design demands for a machine. The torque-per-unit-rotorvolume (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. Commonlimits for the TRV in various machines are quoted in [1], andthese are listed in Table I. However, it can be seen that, gen-erally, the larger and better cooled the machine, the higher theTRV. In totally enclosed fan-cooled machines, typical winding-current-density levels are in the region of 5–6 A/mm2. Thislimits the electric loading and, hence, stress, which results ina low-range TRV. Larger water- or oil-cooled machines canpush this much higher. In electric vehicle (EV) and hybrid EVdrive motors [30], the peak power rating is a transient ratingat lower speeds, and the current density during a transient (oracceleration) period can be in excess of 20 A/mm2 for a periodof several seconds or tens of seconds. Some basic motor typesare 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 rotorsize. However, initially, a diameter has to be selected based onthe choice of pole number, magnet size, and rotor topology.The geometry may also be dictated by the space in which themotor has to fit. Starting with a two-pole motor geometry, thediameter-to-axial-length ratio will be close to unity and willincrease with pole number (moving from a long cylindricalshape to a disk shape). This is a crude sizing approximationfor radial-flux machines over a wide power range. The first keypoint to remember is that the stator yoke thickness is governedby the flux per pole (since it has to carry this); therefore,it decreases as the pole number increases. High-pole-numbermachines tend to have a much higher diameter compared withthe axial length. In totally enclosed machines, the TRV tendsto 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 machinescan be designed, and also, it allows the motor to be morecompact. When Nd–Fe–B magnets are utilized, it is reasonableto expect a peak electromagnetic efficiency of over 90% evenon 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 stressallows a more fundamental stress-limiting calculation, as shownin the Appendix, based on the electric loading and the air-gapflux-density limits. As can be seen in Table I, there is a widevariation in TRV—a median for first-pass design of a larger,efficient, and well-designed rare-earth magnet machine wouldbe 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 anddc. There are different requirements when designing them, andthis is related to the back-EMF waveform and the rotor-positionsensing. Consider a three-phase operation. For ac operation, thephase current will be sinusoidal, and there is a 180◦ conductionfor each inverter leg using a pulsewidth-modulation strategywith a position encoder. For dc control, the current waveform istrapezoidal with 120◦ conduction with three Hall effect probesusually used to detect the switching positions. Hence, an acmachine requires sinusoidal back EMF generated by the PMrotor, while the dc machine requires a more trapezoidal back-EMF waveform. Some machines have back-EMF waveformsthat are intermediate and can be used with either ac or dc con-trol. Generally, dc motors are suitable for power drives whichcan tolerate some torque ripple and do not require substantialfield weakening at higher speeds, while ac motors are moresuitable for servo drives where smooth operation and extendedfield weakening are required. DC control can offer a higherpower density, and this is illustrated in the Appendix. Thecharacteristics 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 sinusoidalback 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-windingcurrent 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 wherethe current cannot be controlled and the maximum currentcannot be achieved. The inverter switching is advanced, and thiscan be effective up to maybe 15–20 electrical degrees depend-ing on the machine. This is shown in Fig. 1 for a small four-poledc-controlled machine [shown later in Fig. 6(b)]. It can be seenthat the torque range is extended from about 2500–3000 r/min.

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 byrotating the current phasor so that there is a component onthe −d-axis. AC-controlled machines with internal-PM (IPM)rotors can have much higher field-weakening capability, and themachine used in [30] has 60◦ phase advance—this is studiedlater. IPM motors can have considerable reluctance torque aswell as excitation torque. The machine in [30] is required tohave a wide field-weakening capability because the base speedis 1500 r/min, whereas the maximum speed is 6000 r/min.

D. Choice of Rotors

There are many possible topologies for the rotor—too manyto 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 oftenused in ac motors), while the second has embedded magnetsand considerable saliency. Fig. 2 shows some examples ofthese. Many of these topologies can be simulated in the SPEEDsimulation package from the University of Glasgow, U.K., andMiller [31] lists many brushless PM-motor rotor arrangements.

For a surface-magnet nonsalient rotor, Xd = Xq, as shownin Fig. 2(a). Embedded magnets are possible in the rotor, asshown in Fig. 2(b). These are used in ac machines, althoughthey can be used in dc machines. They have q-axis saliency(i.e., Xq > Xd). The advantage of this is that the peak torque ismoved from the q-axis to an angle of about 100–120 electricaldegrees 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, Xe = Xq).(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 thecorrect firing angle, preventing pole slipping. The saliency alsooffers additional reluctance torque, and this is illustrated by theexample in Section IV-B.

The phasor diagram for the two types of rotor is shownin Fig. 3(a) (assuming ac control). This is a general case insteady state; the difference in operation is that if there is nosaliency, then Xd = Xq 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 Xd and Xq are independent and arefunctions of the d- and q-axis reluctances. However, when thereis high saturation, there is cross-coupling between the d- andq-axis components so that Xd = f(Id, Iq) and Xq = f(Id, Iq).

If an extended field-weakening range (from the base speedupward) is required, then the IPM rotor should be used. Asurface-magnet motor simply cannot cope with this range be-cause the field-weakening capability is limited. This occurswhen 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 negativeXdId phasor on the q-axis. This weakens the motor flux whichreduces the iron loss at high speed. Additionally, it reduces thevoltage requirement from the inverter supply. The third effectis the introduction of reluctance torque in the machine. This isshown in Fig. 3(c), which breaks down the voltages onto thed- and q-axes. The power due to the excitation torque is 3EIq

(where E is the back EMF induced into the rotor by the IPM


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

rotor), whereas the total output power, including the reluctance,is 3E ′Iq [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 Xq,in which case, holes or slots can be used in the pole face tocontrol Xq (Fig. 4). The use of the pole-face slots will alsocontrol the cross-saturation, making the machine performancemore predictable and stable.

E. Pole-Number Selection

It is important to select the correct pole number for themachine. 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. Higherpole numbers enable fractional-slot windings. The pole numbershould be a function of the speed of the machine, and thefollowing points should be addressed.

1) The flux in the machine should not alternate at a highfrequency; otherwise, the iron losses will be excessive,although field weakening can be used at higher speed tolimit 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 operatesuccessfully at maybe 400 Hz even for normal steels.

4) A two-pole PM motor can be difficult to fabricate, andalso, the end windings are long (leading to increasedlosses) and the stator yoke is wide (leading to increasedmachine 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 9/6arrangements are used and a 12/10 machine was reported in[33]. In [34], the base slot number of 18 was used with differentrotors with 12 and 16 poles. In [35], an unusual rotor designusing consequent IPM poles (alternate magnet and iron poles)with dovetail-shaped magnetic poles is discussed with polenumbers 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 butit creates high unbalanced magnetic pull (UMP—a net radialforce on the rotor). This makes it more unsuitable for largermachines. 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 moreslot/pole combinations but without the detailed method.

However, UMP is not the focus of this paper. More relevantis the production of cogging torque due to the rotor-magnetand stator-slot combination (which is an alignment torque)and torque ripple due to the interaction of the magnet air-gapflux waves with stator MMF spatial harmonics (which is anexcitation torque).

Cogging torque is an alignment torque between the statorteeth and rotor magnets and is most prominent in surface-magnet motors with integral slots per pole or pole pair. It is areluctance type of torque, and there are a variety of methods forcalculating it using analytical methods [37] and finite-elementanalysis (FEA) (there are many studies of cogging using thismethod, e.g., [38]). There are also several ways to improve thecogging torque, such as skew (gradual in either stator or rotoror using skewed axial rotor segments [38]), bifilar teeth [38],pitching and staggered magnet spacing in a surface-magnetrotor [39], and slot opening adjustment, and in ac machines,fractional slotting is a standard way to reduce cogging. Thismeans 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 PMair-gap flux waves with the winding MMF. This is reviewed in[41] (which also discussed nodal vibration and noise). Torqueripple under load is often neglected in studies, with a preferencefor static or mean torque. This is because accurate calculationof torque, even by using FEA, can be difficult [42], [43]. Meantorque can be calculated using current–flux-linkage loops [44](indeed, so can cogging torque [45]) although many still onlydo a load calculation at one position. Torque ripple tends tobe implicit in a dc machine due to the fully pitched windingsand the need to get a trapezoidal winding. For an ac machine,there is a greater emphasis in smooth operation so the windinglayout is more sinusoidal and torque ripple is minimized. Skewwill also help reduce the load torque ripple. Considering theequation 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)Jst(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 Js (in amperes permeter), while we can define the rotor radial flux density in theair gap as br. The product of these at any particular point will


give the sheer stress. The air-gap flux density due to the PMrotors 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. Thesynchronous 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 windingis a balanced three-phase winding. However, in a fractional-slot machine, it should not be assumed so that the windingMMF is made with a fundamental one-pole-pair harmonic withsecond, third, fourth, fifth, sixth, seventh, etc., windings. Thefundamental harmonic has to be taken as two for the generalcase, and harmonics are eliminated if they are zero. Hence,assuming the current phasors are in phase with the rotor flux

Js(y, t) =∑nw

Jnws cos(ωst − nwky + φnw

)

=∑nw

Jnws 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 thattorque is a function of the product of the cosine terms whenthe 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 thetorque vibration is

fm±1torque = (m ± 1)fsupply|nw=±mp (5)

where m = 1, 3, 5, etc. This does not necessarily mean thatthese torque vibrations exist. If there is no matching spatialwinding harmonic and magnet flux wave, then there is notorque. There can be winding harmonics below the pole num-ber, and these have no effect since there is no correspondingmagnet flux wave. This tends to mean that dc machines havesome torque vibration while ac machines tend to have windingharmonics and flux waves that, spatially, do not match so thatthere is less torque ripple. This is investigated in the nextsection.

G. Winding Arrangement

There are a variety of methods for winding a brushless PMmotor depending on whether it is an ac or dc motor. The aim ofan ac winding is to obtain a sinusoidal open-circuit back-EMFwaveform. 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 utilizedin ac machines with coil pitches of one slot. An excellentexamination of this arrangement was put forward in [46]. Thecorrect 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

AND GEOMETRIC PROPERTIES

two coil sides per slot (concentric, lap, or concentrated roundone tooth), as discussed in [31]. Here, a simple example of an18-slot 8-pole IPM machine is shown in Fig. 5. This is afractional-slot machine. The winding is illustrated for one phasein Fig. 5(a), showing the distributed nature of the winding.The rotor arrangement is shown in Fig. 5(b). The machinewas modeled using the SPEED software package PC-BDC [47]from the University of Glasgow, U.K., and the machine data aregiven in Table II; this gives the operating point data togetherwith 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


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 is400 Hz. This may require high-grade aerospace steel, althoughthis 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 windingstrategy with the aim of obtaining a trapezoidal back-EMFwaveform. This will interact with the trapezoidal current (with120◦ conduction period) to produce a smooth torque. Thisrequires fully pitched concentrated windings. Fig. 6 shows thewinding layout for one phase of a three-phase set for a 12-slot4-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 productionand the fact that there is inherent torque ripple with the short-pitched winding. This is very much an idealized waveform. Theback 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 thewaveforms.

It is also necessary to consider the torque-producing region ofthe waveforms. This is shown in Fig. 7. If the back-EMF waveis too narrow, then there is torque ripple when the back EMFis multiplied by the current. In addition, the dc machine usedHall probes, and if they are only slightly out of position, thenthere will be considerable torque ripple. This was investigatedin [39].

3) Delta Connection: Delta connection is not recommendedin a brushless PM machine. If there is any third time harmonicin the phase back EMF, then this will induce a circulating zero-order current in the mesh, as shown in Fig. 8. This will causeexcessive 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 themotor performance and cost. The increased cost of high-energymagnets may be offset by the fact that less magnet materialis required and the motor will be more compact. Typicalremanent magnetism and recoil permeability values at 25 ◦Cfor various magnets are listed Table III. Further details areput forward in [7] and [8]. The nonlinear characteristics of thespecific magnets should be inspected. The magnets should notbe used in the nonlinear area, as shown in Fig. 9, and sufficientdesign tolerance should be built in so that the magnets are notdemagnetized even under overload. The operating point can befound by calculating the permeance coefficient (PC) and alsothe electric loading effects. For ferrite-magnet motors, a PC ofat least eight is usually required, but for rare-earth magnets, thiscan be lower since the magnets are much stronger and linear.The PC can be improved by the use of a narrow air gap andshorter flux path lengths and wide teeth and stator yoke. Lowerflux-density levels also improve the PC.

The thermal performance of the magnet material also hasto be considered, as shown in Fig. 10. While this paper ismostly concerned with rare-earth magnet machines, it is worthconsidering ferrite-magnet material for completeness. The


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 dependentupon the magnet temperature and the magnet type. The typicalvalues of temperature coefficient for the magnet intrinsic coer-civity Hcj 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 worseat higher temperature. Ferrite magnets have a nonlinearregion which can be easily moved into with overload andovertemperature operation. The following points summarizethe discussion for ferrite magnets.

1) Ferrite magnets need a good magnetic circuit and a lowreluctance; otherwise, their load line will not be steepenough and the operating point will be close to thenonlinear region.

2) The slope of the load line is equal to negative PC whenthe 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 magnetthickness.

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 considerablygreater 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 isnecessary since it is more expensive), and again, the PCcan be used to set the magnet thickness.

2) They have high energy, and handling can be difficultwhen magnetized.

3) Premagnetizing may be required.


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 thermalstressing, as shown in Fig. 11.

I. Steel Selection and Iron Loss

The two basic properties of interest are the B/H curve and theiron loss in the steel. The B/H curve sets the flux levels possiblein the machine and the degree of saturation, while the ironloss is important to the machine efficiency. The loss calculationis often done by using a modified version of the Steinmetzequation 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 utilizedfor the watts-per-cubic-meter iron loss in [31] and [47] is ob-tained from

P = Chf Ba+bBpkpk + Ce1

(dB

dt

)2

(6)

where there are various coefficients necessary for accuratecalculation. The loss calculation is really an estimate and onlygood if the material loss data are accurate (often, they arenot). Lookup iron-loss tables are often utilized rather than theimplementation of a complicated equation set, and these aregiven in [9]. As an example of the effect of steel, considerthe ac motor design in Section II-G1. The material used in thisexample was Losil 800/65, and the iron loss was calculated tobe 623 W. The material can be replaced with Transil 35, whichhas 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 inFig. 12, so that the iron loss is now 122 W. Loss is often afunction of the amount of silicon in the steel. Increasing theamount of silicon (up to a maximum of 3% [9]) can reduce theloss in the steel. Reference should be made to manufacturer’sdata. The thickness of the lamination also makes a significantdifference to the eddy-current loss. For instance, for Transil330, at 1.5 T and 50 Hz, 0.35-mm laminations have a loss of2.9 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 machinesby increasing the flux using cobalt–iron alloys. These alloyscan 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 complicatedlamination shape is used, the properties will be affected. Wornlamination 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 IPMrotor, 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 ofRotor Structure

Insulation systems have been standardized and graded bytheir 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 beendesignated 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 ofeach insulation class is defined as the maximum temperature atwhich the insulation can be operated to yield an average lifeof 20 000 h. A maximum temperature rise is also set. Therehave been new classifications introduced in 2009 (although notyet extensively adopted) which correspond to the traditionalclassifications; 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 isinserted. 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 topwedges to lock the coil into the slot, and if there are two coilsides in the slot, then there may be a phase separator. The statormay be dipped in an epoxy-resin-type varnish with the aim ofimpregnating 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 necessaryfor 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 orderto secure the coils. Different insulation systems are describedin [11].

If the wire is too thick for winding the coil, then windwith multiple strands and connect in parallel. These are oftendescribed as “strands in hand” and should not be confusedwith parallel windings, where complete coils are connected inparallel.

The fill factor is the ratio of the copper in a slot to theslot area. A common mistake made is to assume a fill factorthat cannot be realized. There is a slot liner, and there may bewedges which will occupy slot space. Also, the conductors areround and have an enamel insulation coating so that there will


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 factorsshould be approached with caution. For instance, automotivealternators are low voltage (12 V) and often have very few turnsof very thick wire. Manufacturers often work with a maximumslot fill of 30% or less.

Many machines have environmental considerations that re-quire the stator and/or rotor to have a protective can whichcan be conducting (for instance, from stainless steel [49])or nonconducting. These cans can add eddy-current loss tothe machine and lengthen the air-gap length so that the canscan be accommodated. However, they can add considerablemechanical stability to the rotor and help retain the magnetson the surface of the rotor. Both surface magnets and IPMmotors have structural issues with retaining the magnets andpole faces (in IPM rotors). The mechanical stresses in an IPMrotor were described and discussed in [50], while the use ofretaining sleeves in a high-speed surface-magnet rotors washighlighted in [51] and mechanical retention of magnets wasfurther discussed in [52]. The mechanical integrity of a rotormay restrict the maximum speed of a machine and also thepossible 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 toassess. For instance, there will be eddy-current losses in surfacemagnets due to slotting [53] and possibly proximity losses inconductors if they are air-gap windings or even thick conductors[54]. However, these are normally low; Yamazaki [55] gives agood 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 themachine, and this is addressed in the next section.

III. COOLING AND THERMAL ISSUES

There is a strong requirement for more energy-efficient mo-tors. Improved thermal design can lead to a cooler machine withreduced losses. Copper loss is a function of winding resistanceand, therefore, is a function of temperature. Rare-earth PMflux reduces with increased temperature. The size of a motoris ultimately dependent upon the thermal rating. The motorcomponents that are limited by the temperature are wire orslot liner/impregnation, bearings (life), magnet (loss of fluxand 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 asthat shown in [56] to estimate motor life, and these are relatedto the insulation classifications in Table IV.

Magnets are usually isolated from the main heat sourcesso 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) exhibitlocal eddy-current losses as heat sources, which are difficultto estimate or measure. Hence, there is a much longer timeconstant for magnets compared with windings although it isessential to know the magnet temperature for transient anddemagnetization 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 athermal resistance, as shown in Fig. 13(a), for the housing heat-transfer coefficient. In addition, the winding current densityand specific electric loading are considered. Traditional thermalmodeling tends to be empirical with data obtained from thefollowing:

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;


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 failsto describe the complex nature of motor cooling, and there ispoor insight into which aspects of the thermal performance of amotor need to be focused upon. Table V lists typical values forthe current density and heat-transfer coefficient.

B. Modern Thermal Design Techniques

There are two options for modern thermal design. Theseare lumped-circuit analysis (network analysis) [14], [15], [18],[57]–[59] and numerical analysis using FEA and computationalfluid dynamics [16]. While computational fluid dynamics givesmore accurate solutions for particular examples, it can be timeconsuming to set up the model. In the design office, the lumped-circuit analysis is more useful for faster and more interactivedesign procedures. It can be linked into electromagnetic design,as illustrated in [18] where the thermal package Motor-CADfrom Motor Design Ltd., U.K., [60] is linked with the SPEEDsoftware [47]. In the examples put forward in this paper, theseenvironments are used. A typical lumped circuit from Motor-CAD is shown in Fig. 14; the literature has several examplesof this type of circuit as developed by many researchers (e.g.,[14]–[18], which are, by no means, comprehensive). Whenthere is a high temperature gradient, more nodes are requiredso the slot is modeled as a multishell structure, as shown inFig. 14(b). The accuracy of the circuit model in Fig. 14(a) verymuch depends on the accuracy of the lumped parameters; if oneis substantially inaccurate, then it can affect the temperaturesof the surrounding nodes. Therefore, the components have toaccount for the heat flow in terms of the conduction, convection,and radiation. Several aspects of the model are manufacturingdependent as well as material dependent. For instance, the ther-mal conductivity of the coil is a function of the impregnation ofthe resin.

C. Cooling Types and Methods

Motor-CAD covers several thermal networks including arange of cooling types that represent the standard methods ofmotor cooling.

1) Natural convection (TENV): This is very common withmany housing design types.

2) Forced convection (TEFC): There are many fin channeldesign types, and fans are commonly fitted to industrialdrives.

3) Through ventilation: This utilizes rotor and stator coolingducts.

4) Open end-shield cooling.5) Water jackets: There are many design types (axial and

circumferential ducts), and they can be for either statoror 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 ofmounting.

11) Radiation: Both internal and external.Hence, there are many ways to implement effective motor

cooling.

IV. MOTOR DESIGN TECHNIQUES AND EXAMPLES

Modern design techniques usually use detailed analyticalalgorithms and electromagnetic FEA methods to analyze adesign. While the SPEED package already mentioned usedanalytical calculations, sometimes, detailed calculations requireFEA, such as to obtain accurate cogging torque and load torquein IPM motors with phase advance. A finite-element bolt-onpackage can be used for this [61]. This arrangement is notunique; many finite-element packages now feature spreadsheetand initial calculation tools to enter data for an initial motor de-sign. In this section, some additional motor-analysis techniqueswill be highlighted and design and analysis examples put willbe 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 forminga current-against-flux-linkage loop (I–Psi). This method wasdetailed in [44] and [45]. The area enclosed (W ) is equal tothe work done during the rotation so that the torque is then thework done divided by the distance moved. For a machine withm pole pairs and n phases, the electromagnetic torque is

Te = n × m

2π× W. (7)

For a balanced machine, each phase will trace out the sameloop with area W . By using the example with the short-pitchedmachine in Section II-G2, with both sine- and square-waveexcitation, 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.


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 sameshort-pitched winding in Fig. 6(a) was utilized. Interestingly,in the Appendix, the theoretical ac/dc control rating ratio wascalculated to be 1.5. Here, by simply changing from sine-to square-wave control, the torque increases by 1.15. If thewinding is fully pitched for the dc control, then the torque is1.07 so that the ratio is 1.23. However, the rms current withthe dc control is higher. Using the same rms currents and fullypitched winding in the dc simulation gives a torque ratio of1.07. These results were obtained in the SPEED PC-BDC andPC-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 manypackages allow this function. To summarize, using a magne-tostatic model, a full nonlinear solution is carried out, and thetotal torque can be obtained from this solution. The saturatedmagnetic 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 thefull solution, then the reluctance torque can be calculated. Thisreluctance torque includes the saturation effects from the fullsolution. An example is shown in Fig. 16, which is a SPEEDsimulation of the Toyota Prius machine in [30]. This machineoperates at a high phase advance to allow for a very widefield-weakening range (from 1500 to 6000 r/min) and relies onsubstantial 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


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 currentis 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 seenthat 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 requiredmaximum torque of about 300 N · m. Comparison of Fig. 18,where the current level is much higher, with Fig. 19 showsdifferent curve shapes for both the excitation and reluctancetorques. This illustrates the effect cross-saturation can have onthe performance, as discussed earlier.

C. Efficiency Plots

Efficiency is becoming a more important factor in machinedesign and is indeed crucial in many designs. Computationaldesign solutions are becoming increasingly rapid, and it is nowpossible to scan a range of operating points and produce aplot of the efficiencies over a 2-D array of torques and speeds.In [30], measured efficiency plots were used to illustrate themotor operation, and these can be obtained from simulationstoo. Fig. 20 shows the efficiency plot for the machine in theprevious section using SPEED PC-BDC. For a brushless PMmotor, there are several parameters that can be set. In thiscase, at each load point, the phase angle advance was set at0◦, 30◦, and 60◦, and the current varied until the correct torquewas obtained. The highest efficiency was then selected as theoperating point. The selected phase angle is shown in the topchart, while the efficiencies are shown as colored regions andcontour lines in the bottom plot.

D. Fractional-Slot Design-Size Rationalization

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

The existing motor has 50 mm of active length (core length), a130-mm-long housing with a traditional lamination, and over-lapping windings. The new motor still has 50 mm of activelength; however, the housing is now only 100 mm long. Itproduces 34% more torque for the same temperature rise. Themachine uses segmented-lamination nonoverlapping windings(one-slot pitch concentrated coils). In order to optimize the newdesign, an iterative mix of electromagnetic and thermal analysiswas performed. Extensive thermal modeling was carried out.The new design is shown in Fig. 21. Both arrangements had an80-mm diameter; however, the traditional design had 18 slotsand 6 poles [Fig. 21(b)] and overlapping windings, while thenew design has concentrated windings and a 12-slot 8-polelayout [Fig. 21(c)]. This illustrates that the slot/pole combi-nation is flexible for a particular application. The traditionalwinding only had a 54% slot fill but the new arrangement andthe techniques that can be applied to manufacture it (precisionbobbin wound) means that this was increased to 82% in the newdesign.

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 toCelsius scale). A potted (encapsulated in resin) end-windingdesign showed a 15% reduced temperature compared with thatof the previous nonpotted design. Vacuum impregnation caneliminate air pockets. The new design here shows 9% decreasein temperature in a perfectly impregnated motor compared withthe one with 50% impregnation.

All these design and manufacturing improvements lead to amuch 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 acPM machines. It goes on to discuss many of the modern-dayanalysis techniques that can be used to assess the performanceof a machine. Many of the techniques are illustrated withexamples, and the need to consider the electromagnetic design,thermal analysis, and manufacturing techniques in conjunctionis stressed. This paper will be very useful to an electrical ma-chine designer who requires more detailed information aboutthe steps necessary to analyze and improve a motor design ofthis ilk.

A. Further Literature

There are many sources of design method information frommany researchers. In terms of further texts, [65] gives a treatisespecific to PM motor design, while general ac machine designand operation are considered in [66] and [67], which canbe very helpful in terms of winding theory and practice andother aspects of machine operation. The technology is rapidlydeveloping due to new material design refinement. There arecontinuing developments of algorithms that are aimed at theautomated and precise design of an electrical machine; [68]and [69] are illustrations of these, and a literature review would


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 noiseand 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 andT-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] andtechnical 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 discussingthe fundamental design concepts. The products are not neces-sarily unique, and a designer should consider trying differentproducts in order to assess their suitability and even developingtheir own design software using the large body of scientificalgorithms and design and analysis techniques already pub-lished. In terms of alternatives, there are other notable examples


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-passanalytical calculations to feed into Maxwell FEA. InfolyticaCorporation, Canada, has developed MotorSolve BLDC (andother packages) for template-based design which feeds intothe MagNet FEA package. Cedrat Group, France, uses Fluxand Motor Overlays to specify template geometries for motorsimulation in Flux2D and 3-D, and indeed, SPEED can feedinto this package. JSOL Corporation, Japan, has developed theJMAG FEA package, and this also has Motor Template (similarto Motor Overlays) and JMAG-Studio and JMAG designercan be accessed through CAD Link. This package also has aSPEED 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 illustratea commonality between many packages; these tend to alloweasy geometry, material, and control setup for faster motordesign. Many packages now link to standard mechanical CADpackages so that geometries can be imported and initial designcalculation can be done before resorting to more complex andslower FEA solutions.

The aforementioned list is far from comprehensive but rep-resents a global cross section of examples; many companiesand specialists have developed their own in-house design tools,as already suggested as an option. The market is continuallychanging, hence the recommendation for trial of products.

APPENDIX

The maximum mean sheer stresses can be estimated forbrushless dc and ac machines in order to compare their torquedensities. Consider Fig. 22. The dc machine has a trapezoidalwaveform for the current density if the winding is fully pitchedand 120◦ conduction exists, while the ac has low harmoniccontent and the current is sinusoidal. The idealized stresswaveforms are shown for both control strategies, and approx-imate stress calculations can be derived to illustrate that the dcmachine has a higher theoretical mean stress.

AC Control—Flux Density Limited by Peak of FundamentalSinusoidal Flux Wave: In an IPM motor, the flux density inthe air gap can be shaped for smoother operation. This isparticularly 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-gapflux density wave should be considered, together with the maincurrent density wave. This is for a distributed winding, and athree-phase winding is assumed. The mean stress is then

σmean =Bpk(fund)Jpk

2=

Bpk(fund)Jrms√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

Jrms =3KAC

W

2× NphIrms

D. (A2)

The mean air-gap diameter is D, the number of series phasewinding turns is Nph, the fundamental winding factor is KAC

W ,and the winding current (assuming no parallel winding) is Irms.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)NphIrms

2√

2D= 0.55

6Bpk(fund)NphIrms

πD.

(A3)

AC Control—Fully Pitched Surface-Magnet Rotor: If weassume that the air-gap wave is trapezoidal (and a full squarewave with 180-electrical-degree pitch), then the air-gap fluxwill be limited by the peak of the trapiziodal wave, as inFig. 1(b); a Fourier analysis of a fully pitched trapezoidal wavegives a peak fundamental ratio where

Bpk(fund) =4π

Bpk(trap). (A4)

Hence

σmean =4π

3Bpk(trap)NphIrms

2√

2D= 0.7

6Bpk(trap)NphIrms

πD.

(A5)

DC Control: Assuming trapezoidal flux density and currentdensity with a 120-electrical-degree pulsewidth

σmean =23× Bpk(trap)Jpk. (A6)

Again, assuming trapezoidal current density, this can be relatedto the phase current by

Jpk = KDCW × 2NphIpk

2/3 × πD/2= KDC

W × 6NphIpk

πD. (A7)

For a trapezoidal current waveform with a width of 120 electri-cal degrees [Fig. 22(b)], the rms current is

Irms =

√23Ipk. (A8)

Putting (A5) into (A7) gives

σmean =23

√32×

6Bpk(trap)NphIrms

πD

= 0.826Bpk(trap)NphIrms

πD. (A9)


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 givenpeak flux density in the ratio 0.82/0.55 = 1.5. However, dccontrol tends to give more torque ripple and is more suitablefor 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 powerfactor. In a three-phase ac machine where the phase voltagesand currents are sinusoidal and where there is 180◦ conductionin the inverter, the voltages and currents can be related to eachother where Idc = Ipk and Vdc = 3Vpk/2. Therefore

VdcIdc = 3VpkIpk

2= 3VrmsIrms. (A10)

For a dc machine, where the waveforms are trapezoidal andwhere there is 120◦ conduction in the inverter, Idc = Ipk andVdc = 2Vpk. The rms-to-peak values are

Vrms =

√23Vpk and Irms =

√23Ipk (A11)

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

VdcIdc = 2VpkIpk = 3VrmsIrms. (A12)

Comparing (A10) and (A12) shows that the same relationshipholds whether it is ac or dc.

REFERENCES

[1] J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent-Magnet Motors. Oxford, U.K.: Clarendon, 1994.

[2] J. R. Ireland, Ceramic Permanent-Magnet Motors. New York: McGraw-Hill, 1968.

[3] T. Kenjo and S. Nagamori, Permanent-Magnet and Brushless DC Motors.Oxford, U.K.: Clarendon, 1994.

[4] J. F. Gieras and M. Wing, Permanent Magnet Motor Technology.New York: Marcel Dekker, 2002.

[5] D. C. Hanselman, Brushless Permanent Magnet Motor Design.Lebanon, OH: Magna Physics, 2006.

[6] N. Bianchi, M. D. Prè, L. Alberti, and E. Fornasiero, “Theory de-sign of fractional-slot PM machines,” Tutorial Course Notes, IEEEIAS’2007 Annu., Meeting, Sep. 23, 2007, CLEUP editor (Padova, Italy);New Orleans: USA.

[7] P. Campbell, Permanent Magnet Materials and Their Applications.Cambridge, U.K.: Cambridge Univ. Press, 1994.

[8] L. R. Moskowitz, Permanent Magnet Design and Application Handbook.Melbourne, FL: Krieger, 1995.

[9] P. Beckley, Electrical Steels for Rotating Machines. London, U.K.: IEE,2002.

[10] P. Beckley, Electrical Steels. Newport, U.K.: Eur. Elect. Steels, 2000.[11] G. C. Stone, E. A. Boulter, I. Culbert, and H. Dhirani, Electrical Insulation

for Rotating Machines. Piscataway, NJ: IEEE Press, 2004.[12] S. J. Yang and A. J. Ellison, Machinery Noise Measurement. Oxford,

U.K.: Clarendon, 1985.[13] P. L. Timár, Noise and Vibration of Electrical Machines. Amsterdam,

The Netherlands: Elsevier, 1989.[14] M. A. Valenzuela and J. A. Tapia, “Heat transfer and thermal design

of finned frames for TEFC variable-speed motors,” IEEE Trans. Ind.Electron., vol. 55, no. 10, pp. 3500–3508, Oct. 2008.

[15] J. Nerg, M. Rilla, and J. Pyrhonen, “Thermal analysis of radial-flux elec-trical machines with a high power density,” IEEE Trans. Ind. Electron.,vol. 55, no. 10, pp. 3543–3554, Oct. 2008.

[16] F. Marignetti, V. Delli Colli, and Y. Coia, “Design of axial flux PMsynchronous machines through 3-D coupled electromagnetic thermal

and fluid-dynamical finite-element analysis,” IEEE Trans. Ind. Electron.,vol. 55, no. 10, pp. 3591–3601, Oct. 2008.

[17] A. Di Gerlando, G. Foglia, and R. Perini, “Permanent magnet machinesfor modulated damping of seismic vibrations: Electrical and thermalmodeling,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3602–3610,Oct. 2008.

[18] D. G. Dorrell, “Combined thermal and electromagnetic analysis ofpermanent-magnet and induction machines to aid calculation,” IEEETrans. Ind. Electron., vol. 55, no. 10, pp. 3566–3574, Oct. 2008.

[19] L. Parsa and L. Hao, “Interior permanent magnet motors with reducedtorque pulsation,” IEEE Trans. Ind. Electron., vol. 55, no. 2, pp. 602–609,Feb. 2008.

[20] K. I. Laskaris and A. G. Kladas, “Internal permanent magnet motor designfor electric vehicle drive,” IEEE Trans. Ind. Electron., vol. 57, no. 1,pp. 138–145, Jan. 2010.

[21] N. P. Shah, A. D. Hirzel, and B. Cho, “Transmissionless selectivelyaligned surface-permanent-magnet BLDC motor in hybrid electric ve-hicles,” IEEE Trans. Ind. Electron., vol. 57, no. 2, pp. 669–677,Feb. 2010.

[22] K. Yamazaki and H. Ishigami, “Rotor-shape optimization of interior-permanent-magnet motors to reduce harmonic iron losses,” IEEE Trans.Ind. Electron., vol. 57, no. 1, pp. 61–69, Jan. 2010.

[23] J. Hur, “Characteristic analysis of interior permanent-magnet synchronousmotor in electrohydraulic power steering systems,” IEEE Trans. Ind. Elec-tron., vol. 55, no. 6, pp. 2316–2323, Jun. 2008.

[24] P.-D. Fister and Y. Perriard, “Very-high-speed slotless permanent-magnetmotors: Analytical modeling, optimization, design, and torque measure-ment methods,” IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 296–303,Jan. 2010.

[25] M. Andriollo, M. De Bortoli, G. Martinelli, A. Morini, and A. Tortella,“Design improvement of a single-phase brushless permanent magnet mo-tor for small fan appliances,” IEEE Trans. Ind. Electron., vol. 57, no. 1,pp. 88–95, Jan. 2010.

[26] J. F. Gieras, R.-J. Wang, and M. J. Kamper, Axial Flux Permanent MagnetBrushless Machines. New York: Springer-Verlag, 2008.

[27] E. A. Mendrela, R. Beniak, and R. Wrobel, “Influence of stator struc-ture on electromechanical parameters of Torus-type brushless dc mo-tor,” IEEE Trans. Energy Convers., vol. 18, no. 2, pp. 231–237,Jun. 2003.

[28] B. J. Chalmers, A. M. Green, A. B. J. Reece, and A. H. Al-Badi,“Modelling and simulation of the Torus generator,” Proc. Inst. Elect.Eng.—Electr. Power Appl., vol. 144, no. 6, pp. 446–452, Nov. 1997.

[29] E. Muljadi, C. P. Butterfield, and Y.-H. Wan, “Axial-flux modularpermanent-magnet generator with a toroidal winding for wind-turbineapplications,” IEEE Trans. Ind. Appl., vol. 35, no. 4, pp. 831–836,Jul./Aug. 1999.

[30] M. Olszewski, “Evaluation of the 2007 Toyota Camry hybrid synergydrive system,” Oak Ridge Nat. Lab., U.S. Dept. Energy, Oak Ridge, TN,2009.

[31] T. J. E. Miller, SPEED’s Electrical Motors. Glasgow, U.K.: SPEEDLab., Univ. Glasgow, 2006.

[32] Z. Q. Zhu, D. Ishak, D. Howe, and J. Chen, “Unbalanced magnetic forcesin permanent-magnet brushless machines with diametrically asymmetricphase windings,” IEEE Trans. Ind. Appl., vol. 43, no. 6, pp. 1544–1553,Nov./Dec. 2007.

[33] M. S. Ahmad, N. A. A. Manap, and D. Ishak, “Permanent magnet brush-less machines with minimum difference in slot number and pole number,”in Proc. IEEE Int. PECon, Johor Baharu, Malaysia, Dec. 1–3, 2008,pp. 1064–1069.

[34] D. G. Dorrell, M. Popescu, and D. Ionel, “Unbalanced magneticpull due to asymmetry and low-level static rotor eccentricity infractional-slot brushless permanent-magnet motors with surface-magnetand consequent-pole rotors,” IEEE Trans. Magn., vol. 46, no. 7, pp. 2675–2685, Jul. 2010.

[35] J. Kolehmainen, “Optimal dovetail permanent magnet rotor solutions forvarious pole numbers,” IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 70–77, Jan. 2010.

[36] Z. Q. Zhu, Z. P. Xia, L. J. Wu, and G. W. Jewell, “Influence of slot andpole number combination on radial force and vibration modes in fractionalslot PM brushless machines having single- and double layer windings,” inProc. IEEE ECCE, Sep. 20–24, 2009, pp. 3443–3450.

[37] J. F. Gieras, “Analytical approach to cogging torque calculation of PMbrushless motors,” IEEE Trans. Ind. Appl., vol. 40, no. 5, pp. 1310–1316,Sep./Oct. 2004.

[38] N. Bianchi and S. Bolognani, “Design techniques for reducing the coggingtorque in surface-mounted PM motors,” IEEE Trans. Ind. Appl., vol. 38,no. 5, pp. 1259–1265, Sep./Oct. 2002.


[39] D. G. Dorrell, “Tolerance variations and magnetization modelling inbrushless permanent magnet machines,” in Proc. IEE Int. Conf. PowerElectron., Mach. Drives, Bath, U.K., Jun. 4–7, 2002, pp. 398–403.

[40] M. S. Islam, S. Mir, and T. Sebastian, “Issues in reducing the coggingtorque of mass-produced permanent-magnet brushless dc motor,” IEEETrans. Ind. Appl., vol. 40, no. 3, pp. 813–820, May/Jun. 2004.

[41] F. Magnussen and H. Lendenmann, “Parasitic effects in PM machineswith concentrated windings,” IEEE Trans. Ind. Appl., vol. 43, no. 5,pp. 1223–1232, Sep./Oct. 2007.

[42] D. M. Ionel, M. Popescu, M. I. McGilp, T. J. E. Miller, and S. J. Dellinger,“Assessment of torque components in brushless permanent-magnet ma-chines through numerical analysis of the electromagnetic field,” IEEETrans. Ind. Appl., vol. 41, no. 5, pp. 1149–1158, Sep./Oct. 2005.

[43] D. G. Dorrell, M. Popescu, and M. I. McGilp, “Torque calculation infinite element solutions of electrical machines by consideration of storedenergy,” IEEE Trans. Magn., vol. 42, no. 10, pp. 3431–3433, Oct. 2006.

[44] D. A. Staton, R. P. Deodhar, W. L. Soong, and T. J. E. Miller, “Torqueprediction using the flux-MMF diagram in ac, dc, and reluctance motors,”IEEE Trans. Ind. Appl., vol. 32, no. 1, pp. 180–188, Jan./Feb. 1996.

[45] R. P. Deodhar, D. A. Staton, T. M. Jahns, and T. J. E. Miller, “Predictionof cogging torque using the flux-MMF diagram technique,” IEEE Trans.Ind. Appl., vol. 32, no. 3, pp. 569–576, May/Jun. 1996.

[46] A. M. EL-Refaie, “Fractional-slot concentrated-windings synchronouspermanent magnet machines: Opportunities and challenges,” IEEE Trans.Ind. Electron., vol. 57, no. 1, pp. 107–121, Jan. 2010.

[47] T. J. E. Miller and M. I. McGilp, PC-BDC 8.0 for Windows—Software,SPEED Lab., Univ. Glasgow, Glasgow, U.K., 2008.

[48] J. Reinert, A. Brockmeyer, and R. W. A. A. De Doncker, “Calculationof losses in ferro- and ferrimagnetic materials based on the modifiedSteinmetz equation,” IEEE Trans. Ind. Appl., vol. 37, no. 4, pp. 1055–1061, Jul./Aug. 2001.

[49] E. Peralta-Sánchez and A. C. Smith, “Line-start permanent-magnet ma-chines using a canned rotor,” IEEE Trans. Ind. Appl., vol. 45, no. 3,pp. 903–910, May/Jun. 2009.

[50] E. C. Lovelace, T. M. Jahns, T. A. Keim, and J. H. Lang, “Mechanicaldesign considerations for conventionally laminated, high-speed, interiorPM synchronous machine rotors,” IEEE Trans. Ind. Appl., vol. 40, no. 3,pp. 806–812, May/Jun. 2004.

[51] C. Bailey, D. M. Saban, and P. Guedes-Pinto, “Design of high-speeddirect-connected permanent-magnet motors and generators for the petro-chemical industry,” IEEE Trans. Ind. Appl., vol. 45, no. 3, pp. 1155–1165,May/Jun. 2009.

[52] D. M. Saban, C. Bailey, K. Brun, and D. Gonzalez-Lopez, “Beyond IEEESTC 115 & API 546: Test procedures for high-speed multi-megawattpermanent-magnet synchronous machines,” in Proc. IEEE IAS PCIC,Sep. 14–16, 2009, pp. 1–9.

[53] K. Yoshida, Y. Hita, and K. Kesamaru, “Eddy-current loss analysis in PMof surface-mounted-PM SM for electric vehicles,” IEEE Trans. Magn.,vol. 36, no. 4, pp. 1941–1944, Jul. 2000.

[54] P. H. Mellor, R. Wrobel, and N. McNeill, “Investigation of proximitylosses in a high speed brushless permanent magnet motor,” in Conf. Rec.41st IEEE IAS Annu. Meeting, Oct. 8–12, 2006, vol. 3, pp. 1514–1518.

[55] K. Yamazaki, “Torque and efficiency calculation of an interior permanentmagnet motor considering harmonic iron losses of both the stator androtor,” IEEE Trans. Magn., vol. 39, no. 3, pp. 1460–1463, Jul. 2003.

[56] Test Procedure for Evaluation of Systems of Insulating Materials forRandom-Wound AC Electric Machinery, (revised, 1984), Std. 117-1974,1974.

[57] A. Boglietti, A. Cavagnini, and D. A. Staton, “TEFC induction motorsthermal models: A parameter sensitivity analysis,” IEEE Trans. Ind. Appl.,vol. 41, no. 3, pp. 756–763, May/Jun. 2005.

[58] D. A. Staton, A. Boglietti, and A. Cavagnini, “Solving the more difficultaspects of electric motor thermal analysis in small and medium sizeindustrial induction motors,” IEEE Trans. Energy Convers., vol. 20, no. 3,pp. 620–628, Sep. 2005.

[59] P. H. Mellor, D. Roberts, and D. R. Turner, “Lumped parameter thermalmodel for electrical machines of TEFC design,” Proc. Inst. Elect. Eng.B—Electr. Power Appl., vol. 138, no. 5, pp. 205–218, Sep. 1991.

[60] D. A. Staton, Motor-CAD V2. Shropshire, U.K.: Motor Design Ltd.,Oct. 2005.

[61] M. Olaru, T. J. E. Miller, and M. I. McGilp, PC-FEA 5.5 forWindows—Software, SPEED Lab., Univ. Glasgow, Glasgow, U.K., 2007.

[62] J. A. Walker, D. G. Dorrell, and C. Cossar, “Flux-linkage calculationin permanent-magnet motors using frozen permeabilities method,” IEEETrans. Magn., vol. 41, no. 10, pp. 3946–3948, Oct. 2005.

[63] D. A. Staton, “Servo motor size reduction—Need for thermal CAD,” inProc. Drives Controls Conf., Mar. 13–15, 2001, pp. 1–10.

[64] R. V. Major, “Development of high strength soft magnetic alloys for highspeed electrical machines,” in Proc. IEE Colloq. New Magn. Mater.—Bonded Iron, Lamination Steels, Sintered Iron and Permanent Magnets(Digest No. 1998/259), London, U.K., May 28, 1998, pp. 8/1–8/4.

[65] R. Krishnan, Permanent Magnet Synchronous and Brushless DC MotorDrives. Boca Raton, FL: CRC, 2010.

[66] J. Pyrhonen, T. Jokinen, and V. Hrabovcova, Design of Rotating ElectricalMachines. Chichester, U.K.: Wiley, 2007.

[67] T. A. Lipo, Introduction to AC Machine Design. Madison, WI: Univ.Wisconsin Press, 2004.

[68] W. Ouyang, D. Zarko, and T. A. Lipo, “Permanent magnet machine designpractice and optimization,” in Conf. Rec. 41st IEEE IAS Annu. Meeting,Tampa, FL, Oct. 8–12, 2006, pp. 1905–1911.

[69] S. Huang, M. Aydin, and T. A. Lipo, “Torque quality assessment andsizing optimization for surface mounted permanent magnet machines,”in Conf. Rec. 36th IEEE IAS Annu. Meeting, Chicago, IL, Sep. 30–Oct. 4,2001, pp. 1603–1610.

[70] S. Huang, M. Aydin, and T. A. Lipo, “Electromagnetic vibration and noiseassessment for surface mounted PM machines,” in Proc. IEEE PowerEng. Soc. Summer Meeting, Vancouver, BC, Canada, Jul. 15–19, 2001,pp. 1417–1426.

David G. Dorrell (M’95–SM’08) is a native ofSt. 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 ofCambridge, 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 Institutionof 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 ofTechnology, 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 IEEE

Industry Applications Society Electric Machines Committee in 2002, 2006,and 2008.


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.

David A. Staton (M’90) received the Ph.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 insenior 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.

Documents

A Review of the Design Issues and Techniques for Radial ... · DORRELLet al.: REVIEW OF DESIGN ISSUES AND TECHNIQUES FOR PERMANENT-MAGNET MOTORS 3743 Fig. 1. Field weakening (phase