416 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006

Design of High-Power Density and RelativelyHigh-Efficiency Flux-Switching Motor

John F. Bangura, Member, IEEE

AbstractA new class of electronically commutated brushlessmotor, namely, the flux-switching (FS) motor is gradually emerg-ing in power tools and household appliances. This motor offersadvantages of both high-power density and relatively high effi-ciency. There are a number of papers introducing this new class ofmotor. However, almost all of these papers focused on the analy-sis, and not the design, of the FS motor. Thus, this paper presentsthe design and analysis of the FS motor. Design equations are an-alytically derived for initial calculations of the main dimensions,number of turns, and inductances of the FS motor. Furthermore,a comprehensive time-stepping finite element (TSFE)-behavioralmodel is developed and utilized for detailed analysis and designrefinements of a prototype 8/4-pole FS motor. Finally, test resultsof the prototype motor are provided to verify the design equationsand efficacy of the design methodology.

Index TermsAnalogue behavioral model, brushless ac,CSPICE, electronically commutated motors, finite element, flux-switching (FS) motor, high-power density, power electronic con-verter, spice, time-stepping.

I. INTRODUCTION

MOST power tools and household appliances use univer-sal motors (UMs) that can deliver high torque and/orvariable speed. However, these motors have poor efficiency andrelatively short lifetimes. On the other hand, induction motors(IMs) are often used in power tool machinery applications andhousehold appliances requiring silent operation, long life, andhigh safety levels. However, these motors have relatively lowpower density. Thus, electronically commutated brushless mo-tors are becoming increasingly more attractive and viable dueto the rapidly falling cost of electronic control solutions.

Recently, a new class of motor termed the flux-switching(FS) motor has been introduced [1][3]. The FS motor can of-fer the advantages of both high-power density and relative highefficiency in a smaller and lighter package. The FS motor incor-porates the features of a conventional switched reluctance (SR)machine [4][6] and a conventional dc machine. Thus, the FSmotor has a simple double salient construction and retains theapparent features of mechanical robustness, high speed, hightorque, high power density, and relatively high efficiency. How-ever, almost all of these papers [1][3] on the FS motor focusedon the analysis, and not on the design and related aspects thatare crucial to designing this type of motor. The analysis re-ported in these papers cannot help design engineers initiate thedesign process. In addition, these papers analyzed specific de-

Manuscript received September 30, 2005; revised September 30, 2005. Paperno. TEC-00198-2005.

The author is with Pacific Scientific-Electro Kinetics Aerospace Division,Danaher Corporation, Santa Barbara, CA 93013 USA.

Digital Object Identifier 10.1109/TEC.2006.874243

signs and the machine dimensions, mainly the diameters andstack lengths, of the designs were known parameters. As a mat-ter of fact, the initial calculation of the motor dimensions andparameters, such as the core diameter, stack length, number ofturns, and inductance values is considered crucial to the designprocess. Furthermore, a model that incorporated a time-steppingfinite element (TSFE) approach was applied in demonstratingthe viability of the FS motor for automotive applications [3].However, the effects of armature reaction and mutual couplingwere not taken into account in the model. The FS motor hasa highly nonlinear magnetic circuit and the mutual coupling isrequired to develop useful electromagnetic power; thus, the as-sumptions adopted in [3] are considered gross and leaves muchto be desired.

Therefore, the main objective of this paper is to first presentthe design details of the FS motor, thus providing the designengineer a practical way to make initial calculations of the maindimensions and parameters. Second, to present a robust andeasy to implement in commonly available circuit simulators,such as PSPICE, CSPICE, Saber, SIMPORER, etc., behavioralmodeling approach that can be readily integrated with a finiteelement algorithm, thus providing the design engineer a meansto readily perform detailed design analysis and refinements.This in turn promises a more comprehensive exploration of de-sign alternatives and a better performing final design. The finiteelement behavioral model developed in this paper sufficientlyaccounts for magnetic saturation, significant space harmonicsdue to the physical design and nature of the motor, as well astime harmonics due to the converter switching. The model isextensively utilized to: 1) refine the prototype motor designand calculate its performance characteristics; 2) size the powerelectronics components of the controller; and 3) account forthe interactions between the effects of magnetic saturation andpower electronic switching. Finally, the validity and efficacy ofthe design equations are confirmed by comparing parameterscalculated using these equations with those obtained from thefinite element behavioral model, which in turn is adequatelyvalidated by comparing its results with those obtained from tests.

II. THEORY

A. FS Motor TopologyFig. 1 is shows the prototype FS motor topology with eight

stator poles (teeth) and four rotor poles. It has a double salientstructure similar to SR machine. It comprises a fully pitched fieldwinding, labeled F, that carries unipolar (dc) current, and a fullypitched armature winding, labeled A, that carries ac. The fieldwinding can be connected in series or shunt for dc excitationwith the armature winding that is electronically controlled for ac

0885-8969/$20.00 2006 IEEE

BANGURA: DESIGN OF HIGH-POWER DENSITY AND RELATIVELY HIGH-EFFICIENCY FS MOTOR 417

Fig. 1. An 8/4 FS motor topology.

Fig. 2. FS motor and power electronic controller schematic.

excitation. Thus, the FS motor operates on the interaction of dcand ac magnetic fields. Unlike the series connection, the shuntconnection facilitates independent control of the field-windingcurrent. However, in this paper, the focus is on the design of aseries-connected FS motor. Meanwhile, Fig. 2 shows the motorand its power electronics controller for a series-connected FSmotor drive system [6]. The field and armature windings areconnected to the power electronics controller such that dc and acexcitations are provided to the field and armature, respectively.

B. Principle of OperationThe FS motor operates on the resultant flux vectors due to the

interaction between the ac and dc magnetic fields produced bythe currents in the armature and field windings. The resultantflux vectors are directed along the axes centered through thestator poles. Fig. 3(a) shows the rotor at a location r = 22.5,with respect to the reference rotor position, r = 0, as indicatedin Fig. 1. The field winding is excited with a unipolar currentthat creates flux vectors that are directed along the centers of thearmature slots. Meanwhile, the armature winding is excited witha positive current that creates flux vectors that are directed alongthe centers of the field slots. Therefore, the resultant flux vectorsare directed along the centers of the stator poles, and this willsubsequently cause the rotor poles to align with the stator polesas shown in Fig. 3(b). This is because, like all motors with double

Fig. 3. Flux patterns for armature- and field-winding excitations.

salient construction, the torque is developed by the tendency ofthe rotor poles to align with the stator poles at positions ofminimum reluctance when the magnetic circuit is energized. Asthe rotor continues to rotate, the field and armature windings areexcited in the same direction as shown in Fig. 3(c) and (d). Thus,the resultant flux vectors are directed along the same stator poles.However, as the rotor approaches the next alignment positionshown in Fig. 3(e), the armature-winding excitation is reversedwhile the field-winding excitation is maintained in the samedirection. As a result, the directions of the field flux vectorsare unchanged and those of the armature flux vectors are nowshifted by 180 electrical degrees. The resultant flux vectors havenow switched between the sets of adjacent stator poles linked

418 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006

Fig. 4. Idealized winding inductance (self and mutual) and current waveforms.

by the field winding. Consequently, the rotor poles will alignwith these stator poles to maximize the flux. This process ofsequential commutation of the armature current repeats once therotor rotates past the position shown in Fig. 3(f). Therefore, thereversal of current direction in the armature winding causesthe resultant stator flux vectors to switch between the adjacentstator poles linked by the field winding; hence, the name FSmachine. These resultant stator flux vectors do not rotate butrather oscillate between the adjacent stator poles linked by thefield winding. However, with the proper sequential commutationof the armature current with respect to the rotor angular position,the rotation of the rotor can be maintained.

C. Idealized Winding Self- and Mutual InductancesIn the following discussion, it is assumed that the ideal in-

ductances shown in Fig. 4 vary linearly with rotor position. Asthe rotor rotates from the aligned position to the position shownin Fig. 3(c), the self-inductances of the armature and field wind-ings decrease linearly to a minimum value due to the increase inthe reluctance. This value corresponds to the point at which theleading edges of the rotor poles just begin to overlap with thestator poles. However, as the rotor continues to rotate, the self-inductances remain fairly constant until the trailing edges of therotor poles just begin to leave the stator poles. This is becausethe total overlapped area between the stator and rotor poles is un-changed. With further rotation of the rotor, the self-inductancesincrease linearly since the rotor poles are approaching alignmentwith the stator poles.

Meanwhile, the mutual inductance between the armature andfield windings decreases linearly from its maximum positivevalue as the rotor rotates from the aligned position in Fig. 3(b)to the position where the rotor poles are between adjacent statorpoles as shown in Fig. 3(d). The value of the mutual inductanceat this location is zero. This is because the total flux linkingthe armature winding when the field winding is excited or thetotal flux linking the field winding when armature winding isexcited is zero, see Fig. 3(g) and (h). As the rotor continues to

Fig. 5. Simplified geometry of the prototype 8/4-pole FS motor.

rotate toward the next alignment position, Fig. 3(e), the resultantflux will switch between the poles linked by the field winding,and thus the mutual inductance becomes negative. The mutualinductance value will decrease to its minimum negative at theend of the half cycle. Similarly, for the remaining half cycle, themutual inductance increases linearly to its maximum positivevalue at the end of the cycle.

From the idealized inductance waveforms, the average valueis the predominant component of the self-inductances while thefundamental is the predominant component of the mutual in-ductance. Hence, the mutual inductance is the major contributorto the developed power and torque production. This means thattorque production is obtained where the polarities of the windingcurrents are arranged for mutual inductance to provide positivecontribution to the torque production. For positive torque pro-duction, the corresponding idealized winding currents are to becontrolled as shown in Fig. 4. Note that the zero-current inter-val, 20, between the positive and negative armature currents ispurposely provided to ensure successful current reversal. Mean-while, during the zero-current interval of the armature current,the idealized field-winding current will consequently decay tozero. The torque developed is given as

Tdev =12i2A

dLAdr

+12i2F

dLFdr

+ iA iF dLAFdr

(1)

where, iA and iF are the armature- and field-winding currents;LA, LF, and LAF are the self- and mutual inductances of andbetween armature and field windings, respectively. Clearly, forpositive developed torque, it implies that the following must besatisfied:

iA iF > 0dLAFdr

> 0(2a)

iA iF < 0dLAFdr

< 0. (2b)

III. DESIGN EQUATIONSIn this section the design equations for initial calculations

of the machine inductances, dimensions, and the number ofturns are derived. In the following development, the simplifiedgeometry of the magnetic circuit of the prototype 8/4-pole FS

BANGURA: DESIGN OF HIGH-POWER DENSITY AND RELATIVELY HIGH-EFFICIENCY FS MOTOR 419

Fig. 6. MMF waveforms of the developed half-geometry configuration for:A(+) and F(0), A(0) and F(+), and A(+) and F(+) excitations, respectively.

motor with identical armature and field slots, as shown in Fig. 5,is used. The iron core is assumed to be of infinite permeabilityand flux leakage effects are neglected.

A. Magnetomotive Force (MMF) and Magnetic LoadingConsider Fig. 6 that shows the idealized air-gap MMF dis-

tributions of the developed layout of the simplified geometrygiven in Fig. 5. These distributions correspond to the casesfor: 1) only positive armature excitation; 2) only positive fieldexcitation; and 3) both positive armature and field excitations,respectively. Each of these MMF distributions can be expressedusing Fourier series in terms of the stator reference position an-gle (see Fig. 5), , and the rotor angular position r with respectto a fixed point on the stator as

Fs(, r) =

h=1,3,5

fsh cos(

h( 0)2ps

h)

(3)

where h is the harmonic order, ps is the stator pole pitch,h is the phase shift of the h th harmonic, 0 is the phase shiftwith respect to the reference rotor position, r = 0, and fsh isthe magnitude of the h th harmonic.

The air-gap flux density, which is an important parameter re-lated to the magnetic loading, flux linkage, and electromagneticpower of the machine, can be calculated by multiplying theresulting MMF distribution function by the inverse of the effec-tive air-gap function. The effective air-gap function essentiallyrepresents the air-gap length at a given point, and is a func-tion of both stator and rotor geometries as well as rotor angularposition. That is, the effective air-gap function can be viewedas comprising two rotor-position-dependent components 1) anair-gap function due to a slotted rotor and a smooth stator and2) an air-gap function due to a slotted stator and a smooth rotor.These rotor and stator air-gap functions corresponding to Fig. 5are depicted in Fig. 7. In general, each of these air-gap functionscan be expressed using Fourier series as

gsr(, r) = gsr0 +

h=1

(g1h cos

(2h( r)

p

)

+ g2h sin(

2h( r)p

))(4)

Fig. 7. Rotor and stator air-gap functions at r = /4.

where gsr0 is the average value of the air-gap function and p isthe pole pitch. The parameters, gsr0, g1h , and g2h are functionsof the geometric parameters indicated in Fig. 5, and are givenas

gsr0=2gmin1 + gmax2

p(5)

g1h=2(

gmax gminh

)cos(

h(21 + 2)p

)sin(

h2p

)

(6)

g2h=2(

gmax gminh

)sin(

h(21 + 2)p

)sin(

h2p

).

(7)The air-gap function due to a slotted rotor and a smooth sta-tor, denoted as gr (, r), can be deduced by substituting in (4)through (7) as follows:

1 = 3 = 0.5pr 2 = pr prgmax = gl + gmin p = pr. (8)

Similarly, for the air-gap function due to a slotted stator and asmooth rotor, denoted as gs(), can be deduced by substitutingas follows

1 = 3 = 0.5ps 2 = ps ps r = 0gmax = gs + gmin p = ps. (9)

Here, gmin is related to the minimum air-gap height g0 at thealigned rotor position as gmin = 0.5g0. Once the air-gap func-tions due to a slotted rotor and a smooth stator as well as aslotted stator and a smooth rotor are derived, the effective air-gap function ge(, r) due to a slotted rotor and a slotted statorcan be easily deduced. Therefore, the air-gap flux density cannow be expressed in terms of the inverse of the effective air-gapfunction as

Bs(, r) = 0

h=1,3,5

Fsh cos(

h( 0)2ps

h)

g1e (, r).

(10)

420 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006

Fig. 8. Idealized back EMF in the armature and field windings.

Upon obtaining the flux density in the air-gap, the flux link-ages of the armature and field windings are deduced by integrat-ing the air-gap flux density in the region covered by the coils ofthese windings. That is

w(r) = 0LRs 20

N(, r)Fs(, r)g1e (, r) d (11)

where N(, r) is equal to the coil turns in the region coveredby these coils and zero otherwise, 0 is the permeability of freespace, andRs is the inner stator radius. Also, the self- and mutualinductances of and between the armature and field windings cannow be calculated, and are reported in Section IV.

B. Rotational Voltage and Output EquationThe rotational voltage induced in the armature and field wind-

ings expressed in terms of the winding inductances are

EA =d

dt(LAiA + LAFiF) = r d

dr(LAFiF) (12)

EF =d

dt(LFiF + LAFiA) = r d

dr(LAFiA). (13)

The rotational voltage expressions have been simplified furtherin terms of the mutual inductance whose predominant funda-mental component contributes significantly to the torque pro-duction. The predominant dc (average) components of the self-inductances do not contribute to the torque production. Thisphenomenon, which is clearly observable in the ideal induc-tance profiles given in Fig. 4, is at variance with a conventionalshort-pitched SR machine in which the torque production is de-rived mainly from the variations of the self-inductances. Basedon Fig. 4, (12), and (13), the resulting idealized rotational volt-age waveforms of the armature and field windings are shown inFig. 8. Note that the frequency of the rotational voltage inducedin the field winding is twice that of the armature winding.

The rotational voltage induced in the armature winding dueto the flux produced by a constant field-winding excitation canbe expressed as

EA = NAd(r)

dt= NAr

d(r)dr

= NAr 2max( 4 20

) .(14)

Meanwhile, the maximum value of the mutual flux max isgiven by

max = kmklkskpLpsBg. (15)

Here:NA Number of armature series turns.r Motor speed in mechanical radians/s.(/4 20) Stroke angle in radians.km Factor for MMF consumed in the iron.kl Factor for incomplete mutual coupling.ks Stacking factor of the lamination.kp Stator pole arc factor.L Stack length.Bg Air-gap flux density.ps = Ds/Ps Stator pole pitch.Ds Inner diameter of stator.Ps Stator number of poles.Pr Rotor number of poles.

Substituting (15) and the stator pole pitch, ps, into (14) yields

EAmax = 2NAkmklkskpLDsBg

Ps(

4 20

) r. (16)From the idealized waveforms in Figs. 4 and 8, the input powerinto the motor can be expressed as

Pm =1T

T0

E(r)I(r)dr

= 2(EAmaxIAmax + EFmaxIFmax)(

/4 20pr

).

(17)Under balanced MMF conditions for optimum performance andusing (12) and (13), it can be deduced that the average powersupplied to the armature and field windings are equal, and canbe expressed as

Pm = 8(

1Ps

)(NAIAmax)kmklkskpLDsBgr. (18)

The electric loading expressed in terms of the rms values of thewinding currents is

Al =

IrmsDs

=2(NAIArms + NFIFrms)

Ds=

4NAIArmsDs

.

(19)From Fig. 4, the magnitude of the armature current is related toits root mean square (rms) value as

i =IAmaxIArms

=IAmax

1T

T0 i

2a(r) dr

=1

2(

/420pr

) (20)

where i is the current factor. By substituting (19), (20), pr =2/Pr, and r = 2nr/60 into (18), where nr is the operatingspeed of the machine, the power supplied to the machine isdeduced as

Pm =2

30

(PrPs

)ikmklkskpAlLD

2sBgnr. (21)

Upon accounting for the motors resistive and core losses, fric-tion and windage, and neglecting converter-switching losses,the output power of the drive system can be expressed in terms

BANGURA: DESIGN OF HIGH-POWER DENSITY AND RELATIVELY HIGH-EFFICIENCY FS MOTOR 421

of the overall efficiency, denoted as , as

Pout =2

30

(PrPs

)ikmklkskpAlLD

2sBgnr. (22)

Meanwhile, the output power expressed in terms of the inputpower into the drive is given as

Pout = VINIIN cos(PF) (23)where VIN, IIN, and cos(PF) are the input rms voltage, inputrms current, and load-dependent input power factor of the drivesystem. For a series-connected FS motor drive system, Fig. 2,the field- and armature-winding currents are related to the inputcurrent by the relationships

IF = iIIN (24)IA = itIIN (25)

where i is the ratio of field-winding current to input current,and is strongly dependent on the load, and t is the ratio of thefield and armature number of turns.

Thus, the output power equation derived in (22) describesthe relationship between the output power and the principaldimensions of the machine and the quantities that define thespecific utilization of the materials of its magnetic and electriccircuits. Moreover, this equation shows that the output poweris directly proportional to the ratio of rotor to stator numberof poles and the stroke angle. Therefore, for given electric andmagnetic loading conditions, a larger rotor to stator pole ratiocould result in higher power density. Similarly, a larger strokeangle could result in higher power density. Meanwhile, (23)provides a relationship between the output power, input voltage,input current, input power factor, and overall efficiency of themotor drive system.

IV. DESIGN PROCEDURE

A. Initial Motor Sizing and Calculations of Winding TurnsThe sizing equation can be derived from (22) as

D2sL =Pout

0.82

30

(PrPs

)ikmklkskpAlBgnr

. (26)

It is worth pointing out that (22) was derived based on ideal-ized rectangular current and back EMF waveforms, while theactual current and back EMFs are rather more trapezoidal. Inaddition, the design experience of this author in designing otherprototypes indicates that 80% of the value given by (22) is closeto the actual value of the output power. Therefore, a correctionfactor of 0.8 has been taken into account, as applied in (26). Theranges and values of the parameters, km, kl, ks, kp, t, i, andAl have all been determined through extensive use of the finiteelement-behavioral model discussed in Section V.

The first step in the design process is to determine the cor-responding magnitude of the armature-winding MMF, MMFA,that is required to produce a specified flux density, Bg, in theair gap. Once the magnitude of the armature MMF, and hencethe ampere loading, Al, is determined the corresponding innerdiameter Ds of the stator is readily computed. From (26) and

TABLE IDESIGN DATA FOR THE PROPOSED 8/4-POLE FS MOTOR

using the calculated value for the inner diameter of the stator,the corresponding stack length of the motor laminations is ob-tained. Furthermore, knowing the main dimensions of the motor,the other structural dimensions such as the stator outer diameter,pole heights, air-gap height, and pole arcs can be specified.

From (23)(25), the number of turns of the armature and fieldwindings can then be readily computed in terms of the supplyvoltage, magnitude of the armature-winding MMF, input powerfactor, ratio of field current to input current, and turns ratio as

NA =MMFAVIN cos(PF)

itPout(27)

NF = tNA. (28)Based on the above design equations and procedure, the cor-responding initial dimensions, parameters (inductances, poleswidths, etc.), number of turns, and turns ratio of the prototype8/4-pole FS motor were calculated. The initial and final designdata in per unit for the prototype 8/4-pole FS motor are given inTable I.

V. MODEL DEVELOPMENT AND ANALYSIS

Upon completing the preliminary motor design, as de-tailed above, a robust and integrated-system-level computationalmodel was developed for evaluation and refinements of the pre-liminary design. This is deemed necessary because the magneticcircuit of the FS motor is highly nonlinear and the winding de-sign can have substantial effects on the behavior of the associatedpower electronic converter, output power, and efficiency of theoverall drive. The model comprises a TSFE algorithm [7], [8],and an analog behavioral modeling (ABM) algorithm. The ABMalgorithm was implemented in CSPICE.

A. TSFE Model and AnalysisThe FS machine can be treated as a quasi-static magnetic sys-

tem that is modeled using two-dimensional (2-D) finite elementmethod. Based on Maxwells equations, the partial differentialequation governing the physical behavior of the magnetic fielddistribution in the x y plane cross section of the machine

422 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006

Fig. 9. Computed flux density distributions at r = 0.

solution domain can be expressed as [7][9], [10]

x

(AZx

)+

y

(AZy

)= JZ (29)

where is the magnetic reluctivity of the medium; JZ and AZare the axial (z) components of the total current density andmagnetic vector potential. Meanwhile, the current density, JZ ,in (29) is uniformly distributed in the stator armature and fieldwindings. The finite element computations were performed onone-half of the machine geometry with the appropriate boundaryconditions applied along the boundaries M1M2 and N1N2, seeFig. 5. The TSFE model was used to compute the set of all pa-rameters of interest from nonlinear magnetic field solutions. Inthis work, the parameters of interest include the air-gap flux den-sity waveforms, periodic and nonsinusoidal winding inductanceprofiles, and elemental flux density waveforms for core-losscomputations [7], [8].

The effectiveness of the design equations derived in this paperare validated by comparison of the air-gap flux density wave-forms and winding inductance profiles computed using (10) and(11) and the TSFE model. The air-gap flux density waveformscomputed analytically using (10) for MMFA = 1480 AT andMMFF = 1480 AT are compared with those computed fromTSFE nonlinear magnetic field solutions as shown in Figs. 9through 11, respectively. Meanwhile, the corresponding TSFE-model-computed flux plots of the magnetic field distributionsat the aligned and nonaligned rotor positions are shown inFig. 12. The analytically computed and TSFE-computed un-saturated self- and mutual inductances of and between the ar-mature and field windings are depicted in Figs. 13 and 14,respectively. Meanwhile, the saturated self- and mutual induc-tances corresponding to the armature and field MMFs givenabove are given in Fig. 15. Examining these figures, it is clearthat there is appreciable agreement between the analytically andTSFE-computed parameters, thus validating the efficacy of thedesign equations used for computing the machine parameters.The effects of magnetic saturation on the machine inductancesare clearly discernable from comparison of Figs. 14 and 15.

B. The ABMThe ABM is a multiport network formulation of the FS motor

drive system. The ABM technique essentially describes the setof equations that represent the circuit relationships between the

Fig. 10. Computed flux density distributions at r = 30.

Fig. 11. Computed flux density distributions at r = 60.

Fig. 12. TSFE-computed magnetic field distributions.

Fig. 13. Analytically computed unsaturated inductances.

BANGURA: DESIGN OF HIGH-POWER DENSITY AND RELATIVELY HIGH-EFFICIENCY FS MOTOR 423

Fig. 14. TSFE-computed unsaturated inductances.

Fig. 15. TSFE-computed saturated inductances.

physical machine windings flux linkages and terminal voltagesas well as the effects of electromechanical torque on motor per-formance. The nature of the formulation assures the inclusionof all the significant space harmonics due to the physical de-sign and nature of the motor as well as time harmonics dueto the converter switching. The ABM technique utilizes devicessuch as resistors, inductors, capacitors, linear and nonlinear con-trolled voltages, and current sources to describe the FS motordrive system equations. This makes it easy to implement usingcommonly available circuit simulators, for example, CSPICE,PSPICE, SIMPLORER, Saber, Simulink, etc.

In general, the terminal voltages in terms of the induced Fara-day voltages and currents of the armature and field windings canbe expressed as

VA = RAiA +dAdt

(30)

VF = RFiF +dFdt

. (31)Here VA, VF, iA, iF, A, and A denote the terminal voltages,currents and flux linkages of the armature and field windings,respectively. The flux linkages can be expressed in terms of theinductances and currents as

A = LAiA + LAFiF (32)F = LFiF + LFAiA. (33)

Based on the ABM technique, the derivatives of the fluxlinkages in (30) and (31) are represented using 1.0 H inductorsconnected across nonlinear current sources whose values aregiven by the expressions in (32) and (33), respectively. TheABM representations of (30) through (33) are given in the fluxlinkage model and flux linkage derivative model in Fig. 16,respectively. The motor flux linkages are the parameters throughwhich the TSFE model of the machine is coupled to its externallyassociated power electronic converter.

Fig. 16. The TSFE-ABM representation of the FS motor drive system.

Similarly, the effect of electromechanical torque on the dy-namic behavior of the motor drive system can be incorporatedby using the relationship

Jdmdt

= Tdev TL. (34)

Here, J is the inertia of the rotor, m is the rotor speed, Tdev isthe instantaneous developed torque profile, and TL is the loadtorque profile. The expression for the developed torque term,Tdev, of (34) is given in (1). Similarly, the ABM representationof the inductance derivatives of (1) is given in the inductancederivative model of Fig. 16. Finally, the ABM representation of(34) is given in the torque model of Fig. 16. The complete ABMrepresentation of the FS motor drive system shown in Fig. 16was implemented using CSPICE [9].

VI. MODEL VERIFICATION

To compute the performance parameters and characteristics,such as inductances, input current, input power, output power,efficiency, and power factor, etc., at any given load-operatingpoint, involves an iterative process that is continued until con-vergence is achieved. The iterative process requires the TSFEand ABM algorithms to constantly and automatically exchangedata, which are primarily the winding inductance profiles andcurrents. The winding inductance profiles are computed by theTSFE algorithm and the currents are computed by a SPICE cir-cuit simulator [9]. The nature of the iterative process is similarto that detailed in [7], [8]. It should be emphasized here thatthe developed system model has been extensively utilized torefine the prototype design. That is, a parametric study in whichthe parameters, which include power circuit component valuesof the controller, device current and voltage ratings, maximumpulse width, advanced angle, pole widths, slot geometry, air-gapheight, winding turns and turns ratio, were varied one at a time toquantify their effects on the FS drive with regards to maximumoutput power and maximum efficiency.

The power electronic converter shown in Fig. 2, includingits microprocessor-based controller, were designed and built to

424 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006

Fig. 17. Computed and measured armature open-circuit voltage.

Fig. 18. Output power versus torque.

Fig. 19. Efficiency versus torque.

drive the prototype 8/4-pole FS motor. Performance tests wereperformed on the bare motor in which the armature open-circuitvoltage, output power, and efficiency were measured. The com-puted and measured open-circuit armature voltages at variouslevels of field currents versus motor speed are shown in Fig. 17.The computed and measured output power and efficiency atvarious load torque levels are displayed in Figs. 18 and 19,respectively. The computed data compares very well with themeasured data. Clearly, the FS prototype motor offers relativelyhigh efficiencies over a wide range of output power or torquelevels. This is a highly desirable feature for the power tool ma-chinery applications being considered. The maximum efficiencyobtained for the FS motor drive is about 75%.

Performance curves that include output power and efficiencyfor the prototype 8/4-pole FS motor are compared with those ofequivalent IM and UM as shown in Figs. 20 and 21. It should be

Fig. 20. FS and IM performance comparison.

Fig. 21. FS and UM performance comparison.

mentioned that these motors are considered equivalent becausethey have similar volumetric dimensions (inner diameter, outerdiameter, and stack length), and were designed and used for thesame applications as the FS motor. In these figures, the outputpower is denoted as watts out (WO) and efficiency is denotedas EFF. The maximum efficiency obtained for the IM is about77% and that obtained for the UM is about 65%. Meanwhile,the maximum output power obtained for the IM is about 0.58per unit and that for the UM is about 0.70 per unit. Note that theFS motor has a lot more reserved before reaching its maximumoutput power capability. Clearly, the FS motor offers higheroutput power than equivalent UM and IM, and high efficiencycomparable to that of the IM. Therefore, the FS motor is capableof offering both advantages of high-power density of UMs andrelatively high efficiency of IMs.

VII. CONCLUSIONIn this paper, the design and analysis of a new class of elec-

tronically commutated brushless FS motor has been presented.The design equations that essentially describe the relationshipsbetween the output power and the principal dimensions of themachine, as well as the quantities (magnetic and electric load-ings) that define the specific utilization of the materials of itsmagnetic and electric circuits have been derived. These equa-tions provide a practical way for the design engineer to makeinitial calculations of the motor frame size, number of turnsand inductances. An initial design of a prototype 8/4-pole FSmotor based on these design equations was obtained, and sub-sequently refined using a more accurate model based on a 2-DTSFE-behavioral modeling approach.

BANGURA: DESIGN OF HIGH-POWER DENSITY AND RELATIVELY HIGH-EFFICIENCY FS MOTOR 425

The final design of the prototype 8/4-pole FS motor was builtand tested. Comparison between the simulated and test resultsdemonstrated good agreement and correlation that clearly con-firm the effectiveness of the design equations and approach.Furthermore, the merits of the FS motor were demonstrated bycomparing its output power and efficiency curves with those ofequivalent IM and UM. The comparison demonstrates that FSmotors are capable of offering both advantages of high-powerdensity of UMs and relatively high efficiency of IMs.

Finally, the FS motor has tremendous potential for other ap-plications where size and weight, power density, relatively highefficiency, motor speed control, and other smart features, suchas overload protection, etc., are of interest.

ACKNOWLEDGMENT

The author wishes to acknowledge the technical expertise andsupport of the other members of the BLACBIRD Project teamat BLACK & DECKER, Inc.

REFERENCES

[1] C. Pollock and M. Wallace, The flux switching motor, a dc motor withoutmagnets or brushes, in Proc. Conf. Rec., IEEE-IAS Annu. Meeting, vol. 3,Oct. 37, 1999, pp. 19801987.

[2] H. Pollock, C. Pollock, R. T. Walter, and B. V. Gorti, Low cost, highpower density, flux switching machines and drives for power tools, inProc. Conf. Rec., IEEE-IAS Annu. Meeting, vol. 3, Oct. 1216, 2003,pp. 14511457.

[3] C. Pollock, H. Pollock, R. Barron, R. Sutton, J. Coles, D. Moule, andA. Court, Flux switching motors for automotive applications, in Proc.Conf. Rec., IEEE-IAS Annu. Meeting, vol. 1, Oct. 1216, 2003, pp. 242249.

[4] Y. Li, J. D. Lloyd, and G. E. Horst, Switched reluctance motor with dcassisted excitation, IEEE Trans. Ind. Appl., vol. 32, no. 2, pp. 801807,Oct. 1996.

[5] B. C. Mecrow, New winding configurations for doubly salient reluctancemachines, IEEE Trans. Ind. Appl., vol. 32, no. 6, pp. 13481356, Nov.Dec. 1996.

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John F. Bangura (S96M99) received the B.S.E.E.degree from Clarkson University, Potsdam, NY, andthe M.S.E.E. and Ph.D. degrees from Marquette Uni-versity, Milwaukee, WI, in 1996 and 1999, respec-tively.

From 1999 to 2004, he was a Senior Engineer atBlack & Decker, Inc., Towson, MD, where he workedon brushless ac/dc motor drives for power tool ap-plications. From 2002 to 2004, he was an AdjunctProfessor with the Department of Mechanical En-gineering, University of Maryland, Baltimore. From

2004 to 2005, he was with Alltrade Tools, Long Beach, CA, where he steeredthe development of compressors, power equipment, and other related products.In 2005, he joined the advanced development group at Pacific Scientific-ElectroKinetics Aerospace Division, Danaher Corporation, Santa Barbara, CA, whereis currently working on permanent magnet and hybrid homopolar generators forcommercial and military aerospace applications. His current research interestsinclude modeling and designing of permanent-magnet and hybrid homopolarmachines as well as associated field control techniques.

Dr. Bangura is a member of the American Society of Engineering Educationand a member of Sigma Xi.