analysis and evaluation of the transverse flux circumferential current machine

7/29/2019 Analysis and Evaluation of the Transverse Flux Circumferential Current Machine

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I EEE Industry Application SocietyAnnual MeetingNew Orleans, Louisiana, October 5-9,1997

Analysis and Evaluationof the Transverse FluxCircumferential Current Machine

Surong Huang* Jian Luo ThomasA. Lip0Department of Electrical&Computer Eng.

1415 Engineering Drive

Student Member, IEEE Fellow, IEEE"College of AutomationShanghai University University of Wisconsin-Madison147 Yan-Chang RoadShanghai, 200072,P. R. China Madison,WI 53706-1691, U.S.A.

Abstract- With the evolution of novel high powerdensity machines, it becomes important to compare thepower potential of such machines with vastly differenttopologies having a varietyof different waveforms of backemf and current. The approach of this paper is based ongeneral-purpose sizing and power density equations,which will permit a comparison of the main dimensionsand power of such machines. In this paper, thecomparison method of machine power densities isextended to include the Transverse Flux circumferentialCurrent type permanent magnet (TFCCPM) machine,and furthermore to compare the power productioncapability between the TFCCPM machine and the well-known squirrel cage induction machine.

1. INTRODUCTIONTraditional design of AC electrical machines is based on thepremise that the machine has a cylindrical shapewith radiallydirected air-gap flux and a single stator and rotor supplied bya sinusoidal source which assumes a sinusoidal emf at the air-gap of the machine. It was recognized in [11 and [2],howeverthat the emergence of power electronic has removed the needfor suchaconcept asthe basis for machine design. Beginningwith the switched reluctance machine, a new perspective ofelectrical machine design is evolving based on the principlethat the best machine design is the one that simply producesthe optimum match between the machine and the powerelectronic converter, the converter fed machine (CFM) [ I ] .The logical structureof a CFM system is idealizedin Fig.1.In order to study or compare among such systems, threetypes of analysis tools need be implemented; (1) a sizinganalysis and optimization method for such electricalmachines; (2) a convenient interface definition between thetwo objects of Fig. 1; (3) sizing and cost analysis of theassociated converter. Although a practical optimized0-7803-4067-1 97/$1OB0 0 1997 IEEE.

synthesis of a CFM can be developed only after these threetools are available, the sizing analysis, an optimization andcomparison, as well as the definition of the interface are thefirst main steps in such an approach and is the topic of thispaper. As long as the models of electrical machines and theinterface are clearly defined and studied, a design of a CFMcan then be easily predicted based on a balanced selectionbetween the converter rating (cost) and machine performance.SOwCe I nt~ace Loadh a d /source

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Fig. 1A CFh4systemIn general, comparison of different machine types is avery formidable task. Only recently, in 1996,S. Huang et. al.[4] developed general-purpose sizing and power densityequations and established a systematic method to compare thecapabilities of machines with greatly different topologies. Theprocedure includes (1) a concept for comparing the powerdensity on the basis of total occupied volume instead of air-

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gap volume; (2) special factors which were introduced toaccount for the effects of current and back emf waveforms.These factors also serve as a convenient interface definitionfor quantities related to both the converter and electricalmachine; (3) comparison methods which were focused onradial flux and axial flux type machines respectively in [4]and [SI.

As developments have occurred in the field of transverseflux PM machines, issues have been raised concerning thepower density of unconventional machines when comparedwith more conventional topologies 131. In this paper, as afurther contribution to this study, a detailed approach will bepresented in this paper for the application of the general-purpose sizing and power density equations to the TFCCPMmachine, followed by a comparison of the TFCCPM machinewith traditional induction machines.11 SIZING EQUATIONS AND POWER DENSITIES

Derived in Ref. [4], the general purpose sizing equations takethe form,

Or

where,PR rated output power of the machine.K+ ratio of electrical loading on rotor and stator.(In a machine without a rotor winding, K+=O.)m number of phases of the machine.ml number of phases of each stator (if there ismorethan one stator, each stator has the sameml).K , emf factor which incorporates the windingdistribution factor K,and the per unitportion ofthe total air gap area spanned by the salientpoles of the machine (if any).K i current waveform factor.Kp electrical power waveform factor.q machine efficiency.B,A

flux density in the air-gap.total electrical loading includes both the statorelectrical loadingA,vand rotor electrical loadingA,.f converter frequency.p machine pole pairs.

Do diameter of the outer surface of the machine.Le effective stack length of the machine.KL aspect ratio coefficient of the effective stack

length vs. the diameterof the air-gap surfaceinradial air gap flux machines.ratio of the diameter of the air-gap surface vs.the diameter of the outer surface of the machine.l o

In order to study the suitability of using the above generalparameters for transverse flux machines, it is useful toconsider the power production of this machine in detail. Ingeneral, if stator leakage inductance and resistance areneglected, the output power for any electrical machine can beexpressed as [4],

wherevn is the phase number, and the emf e(t)andEpkare thephase air-gap emf and its peak value. The currents i(t) and zpkare the phase current and the peak phase current, and T is theperiod of one cycle of the emf. The factorKpis defined as

(4)

where fe(t)=e(t)/Epkand fi (t)=i(t)/I pk are the expressions forthe normalized emf and current waveforms.The emf in Eq. (3) for the transverse flux machines isgiven by

dI l 0) fdt Pe(t)= =K, N,B, -. D, L , ,(t)

where A, is the air-gap flux linkage per phase, Nt is thenumber of turns per phasle, D, is the equivalent diameter ofair-gap surface. From Eq. i(5) it is apparent thatE,,k=K,N,B, f Q, L , (6)PThe current waveform factorK j s definedin Ref. [4]as

where fm,s s the rms phase current which is related to thestator electrical loadingA,s.Due to the structureof transverseflux machines, there are double sided stator and air-gap

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For convenience in design and for purpose of comparison thecorrespondingD a sizing equation can be found to bepR=---- 1 K,Ki K,, K L 2qBR A f h;D;2 1+K + PThe transverse flux machine power density for the totalvolume can now finally be defined as

By examining the back emf and current waveform for aparticular machine type, the factors, Ki and Kp in the sizingequation can be determined. Several typical waveforms andtheir corresponding Ki and K,,, repeated from Ref. [4], areshown in TableI.111. APPL ICAT ION OF GENERAL PURPOSESIZING EQUATION TO TFCCPMMACHINESThe concept of the transverse flux circumferential currenttYPe permanent magnet (TFCCPM) machine has been 1.Statorsoftiron 2. Ring winding 3.Rotor fiber rinpresented in Ref. [3]. A simplified representation of theTFCCPM topology isshown onFig. 2.The outer diameter of 4. Rotor soft iron 5. Permanent magnetFig. 2Transverse Flux Circumferential Current PM(TFCCPM)Machine(18)The diameter of the outer air-gap surfaceis obtained through a finite element study or through dexperience. The most notable feature of this machine ithe factorKfKU,an be readily adjusted by changing the rRuORi-~ M2g height of the rotor to obtain the desired flux density in th

structure that is very suitable for ferrite magnets.where g s the length Of the air-gap Ref [61 Offers the gap. The topology results in a concept for flux-focfollowing equation for estimating the air-gap=4.7x p - ~ . ~~ The depthof the outer stator slotd,,, can be calculate(20)

(22he radial height of the permanent magnet in the rotorHPMdepends on the flux focusing factor Kf,,, and pole pairsby

4 h 4 =

As2 ,K , Ks4. w=

whereK, is the ratio of the axial length of stator slotL,, veffective length of the machine L e. The depth of the stator cored,, isexpressedasnD#K,,8PKd (21)whereKdis the flux leakage factorof the PM machine (1 - K,W,B,2Bc.rdcso= (23

Referring toEq. (14) the ratioh, can be derived as


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surfaces in the radial direction. Hence, the stator electricalloadingA, includes both the electrical loading of outer statorwindingA,mand the electrical loading of inner stator windingA.i, as shown in Eq. (8)A, =A,Ti+A,= 2 N, I,L ,

In the general case, the total electrical loadingA shouldinclude both the stator electrical loading A, and rotorelectrical loadingA, sothat, again from Ref. [4],A

1+ K )A,= A-A,=- (9)From Eqs. (7), (8), and (9) an expression for the peak

current can be foundLe

1+ K, =N*KiA -IpL=-CombiningEiqs. (3), (6), (lo), the L;Dg sizing equation forthe transverseflux machines takes the form,pR=-- 1 K, K~~~qB,A - L , ~,2 1+K , P

The aspect ratio coefficient is typically defined as[4 ]

This ratio should be selected based upon the practicalrequirements of the application. nserting Eq. (12) into (1 I ), itis possible to obtain the followingD: sizing equationpR=-- 1 K, K~K , K~qB~A -~ g 32 1+K , P

Torealize theD,L, relationship necessary for sizing, it isuseful to define the ratio [4 ]

whered,,,, is the depthof the outer stator slot,d,, is the depthof the outer stator core and Hpmis the radial height of thepermanent magnet in the rotor. In general, a procedure needs

to be developed to deterimne h, when studying a specificmachine or structure, which incorporates the effects oftemperature rise, losses, and efficiency requirements on thedesign. In practice, the depths&,,,and d depend upon thestator electrical loadingA,T,the current density.lY,heslot fillfactor K , , and the flux density in the iron core. The radialheightHpmdepends on the flux focusing factor KrocUsnd polepairs. The equivalent diameter of air-gap surface DR isdetermined by Eq. (13).

TIModelSinusoidalwaveform

SinusoidalwaveformRectangularwaveformTrapezoidalwaveformTriangularwaveformRectangular

&TrapezoidalwaveformRectangular

&TrapezoidalWaveformTrapezoidalwaveformRectangular

&TrapezoidalwaveformRectangularwaveform

TABLE IWAL PROTOTYPEWAVEF RMS

K, K,45 +&

A 0.5

1 1

1.134 0.777

8 0.333

1.134 0.8

1.3890.556

1.3890.519

1.50.333

1.2250.667

The final general purpose sizing equation ultimately takeson the form(15)R=-- 1 K, K~K~~ , ~ q, A - h,2~,2,2 1+K b P

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From Eq. (24), it can be noted that the ratio h, not onlydepends upon the electrical loadingA,vand the current densityJ ,T,but also upon the distribution of flux density over thedifferent portions of the machine. Due to the doubly salientstructure, theflux densitiesin the stator core the air gap(B&,and the rotor core (Bcr)have essentially the same value.The choice of the flux density in the stator core can beestimated by [4]0.35;

-0.40"0. 3

5.47 f >4oHZ1.7 to 1.8 f 54OHzcr :

fe-16fe-12

-The air-gapflux densityBEcan also be expressed asBg= K&ur Bu (26)The flux focusing factor Kfncuss related to the details of thestructure of the permanent magnet machine. Generally 141

where A,, is the surface area of permanent magnets, A, issurface areaof working pole per phase.For the TFCCPM topology (Fig. 2), it can be determinedthat the emf factor for this machine is K, =pn(1-K,s)/2, henumber of phases of the machinem=2. Because there is norotor winding K+=0. Considering the trapezoidal waveformsin Table I (row 4), it can be determined that KiK, =0.881.From Eq. (15), the following TFCCPM machine sizingequation is then obtainedinwhich all units areSI,

The power density of the TFCCPM machine is consequently,

In Eqs. (28) and (29), the only independent terms existingareKL and K, while the other terms either depend onKL or K, ,or have certain physical limitations.

The optimal values of the ratio KL and K, were givenconsidering power density and efficiency. A moredetailed

0. 6-0.55 -

o?3 0.5--$0.45 -r

10 500 1000 1500 2000 2500 3000.25' Rated MechanicalSpeed(rpm)Fig. 3 Optimal value of KL of the TFCCPM machine vs. ratedmechanical speedn,vwith different pole pairsp for maximumpower density.

A=60U lm, s=6.2x10 Alm2,P R=75kw ,p=6 (fe-12) and p=8 (fe-16) using ferrite PM,g=6 (re-12) andp=8(re-16) using rare earthPM .investigation using numerous candidate machine designsindicates that an optimal value of K, i s about 1/6 for apractical design, while the optimal value of KL has a closeconnection with the rated mechanical speed I I , ~.Under a givenelectrical loading A , current density J ,v,nd the rated outputpower PR,a groupof curves can be generated which indicatethe relationships between the optimal value of KL and therated mechanical speedn, for different pole pairs p (Fig. 3).From this data, through power regression, it is possible toobtain the following expression,

p=60.3087n,,0~02y5p=8p=61. 1545ns4' . ' 1' h = 8

Ferrite Magnets.1 77Chy0.n8380.92762s4.n7'2 Rare- earth Magnets

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IV. COMPARISON BETWEEN INDUCTIONAND TFCCPM M ACHINES

,-2.5E3z 2 -g81.5-n 1 -

0.5

It is now possible to compare the power densities oftransverse flux (TFCCPM) machines through the use of thesizing and power density equations that have been derived.Because the squirrel cage induction machine is regarded asthe workhorse of the ac machine family it can be consideredas a point of reference for the other machines.

-

-

3. 5

IO 500 1000 1500 2000 2500 3000Rated MechanicalSpeed (rpm)

Fig. 4 Power densities of four pole induction machine andTFCCPM machines (A =60kAlm, J ,=6.2x lo6A h 2 PR=75kw).

Fig. 4 shows a comparison of power densities among the4-pole induction machines (IM-4) (Ref.[4]), the 16-poleTFCCPM machines with ferrite magnet (fe-16) and the 16-pole TFCCPM machines with rare earth magnet (re-16). Notethat with the transverse principle a power density improve-ment of nearly a factor of two can be achieved for low speedmachines if rare earth magnets are used. Although machineswith rare earth magnets can achieve higher power density,further study has verified that the application of ferrite mag-nets to this structure is much more economical as might beexpected. Thus, the proper material should again be chosenaccording to the purpose intended.

V. THE M AJ OR DIFFERENCE BETW EENTRANSVERSE FLUX TFCCPM MACHINESAND TRA DITIONAL M ACHINES

In the traditional electrbcal machines, one coil of the windingnormally links the flux of one pole. If the pole number of themachine doubled, the flux linked by each coil decreases tohalf, also, the turns of each coil has to decreased to half dueto the limit of the slot area. Although the total number of coilsdoubles, the total peak .flux linkage of the winding decreasesto one-half. Hence, if the machine operates at the same speed,the back-emf remains unchanged.To make this point clear, the following approach can beoutlined. For machine 1, the pole number isp1, the total turnsof one phase isN, the peak flux linked by one coil isQ , therated speed iso, he current rating is I . The average poweroutput of one phase then is

-PIFor machine2, if the current rating and machine size remainunchanged, and the pole number is doubled(p2=2pl), the fluxlinked by one coil must decrease to one-half ( Q2=Ql/2),theturns per coil has to decreased to one-half due to the limit ofthe slot size. Even though the number of coils has doubled,the total turns per phase still remains the same(N).Hence,

P2

It is thus clear that the power rating of the machine remainsthe same even when the pole number has doubled.Unlike the traditional electrical machines, the TFCCPMmachine appears to belong to another family of machines--circumferential current machines in which the coil of thewinding links all the flux of the machine rather than the fluxof one pole. Hence, when the pole number of the machinechanges, the peak flux linkage of the winding does not changeif leakage flux is neglected. A similar comparison betweentwomachines of different pole number can be made:Machine 1:-PIMachine2

-P2

Hence, the power of circumferential machine increases as itspole number increase even when the rated speed remains thesame.

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The same principle can also be found in the sizingequations. For traditional machine, the power density isproportional tof l p as shown in Eq. (l),while for TFCCPMmachine, as shown in Eq. (28), the power density isproportional tof. Hence, the power density ratio STFCCPM6 1 ~then is proportional to the pole number p. If a TFCCPMmachine and an induction machine are compared at the samerated speed, the transverse flux machine will have higherpower density when its pole number becomes greater than acertain threshold value. In this paper, it is found that thisvalueis roughly 16 for machines with a medium power rating(75 KW). For different power ratings, this number may varyand can also be found with the same sizing equation approachoutlined in this paper.

VI. CONCLUSIONIn this paper, the following results have been obtained:1. A detailed approach has been outlined to realize specificsizing and power density equations for the transverse fluxmachine by application of the general-purpose sizing andpower density equations previously developed [4,5]. Bydefining suitable ratios and by considering the dualitybetween transverse and radial flux machines, the sizingequations for the transverse flux machine takes a similar formto the general purpose sizing equations of radial fluxmachines. These equations permit adirect comparison of thecapability of two basically different machine topologies basedupon their overall occupied volume.2. It has been shown that optimization of the aspect ratio KLwill achieve a maximum power density design and producealso machine with nearly the highest efficiency. Incomparison with traditional optimization methods,optimization based on the sizing equation using the outerdiameter is shown to haveagreater benefit, especially for thecomparison of transverse flux machines with machines oftraditional design.3. The optimal value of KL depends upon electrical loading,flux density, frequency, permanent magnet materials, andmachine topology etc. However, further study shows it ismore dependent on machine permanent magnet materialsmore than other factors. Hence, for a given machine andchoice of PM, the optimal value of KL varies over a relativelysmall range. For example, in fe-16 machine, the optimal KL isbetween 0.365 to 0.40. On the other hand, differentpermanent magnet materials will result in a largely differentrange of the optimal KL For example, for the re-16 machine,the range is 0.435 to 0.61.

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4. I t is shown in the paper that the transverse fluxcircumferential machines have higher power density than thetraditional induction machine over a wide range of ratedspeeds. In particular, when the rare earth magnet is appliedthe improvement can reach by over two times. Even when theferrite magnet is used for low cost, the power density can stillbe improved at low speed.

REFERENCES[l ] T. A. Lip0 and Yue Li, CFMs- A New Famly of ElectricalMachines, JESC95, Japan, 1995, pp. 1-6.[2] T. A. Lip0 and F. X . Wang, Design and Performance ofConverter Optimzed AC Machines, IEEE Trans. on IndustryApplications,vol. IA-20, No.4 July/August1984,pp. 834-844.[3] H. Weh, On the Deveopment of Inverter Fed ReuctanceMachines for High Power Densities and High Outputs, etz Archiv,Bd. 6, 1984, pp. 135-144(In German).[4] S. Huang, J. Luo, F. Leonardi, and T. A. Lipo, A GeneralApproach to Sizing andPower Density Equations for Comparisonof Electrical Machines,IEEE -1AS Annua Meeting, Oct. 1996, pp836-842[5] S. Huang, . Luo, F. Leonardi, andT.A. Lipo, A Comparisonof Power Density for Axia Flux Machines Based on GeneralPurpose Sizing Equations, IEEE Power Engineering Transaction.(accepted)[6] E. Levi, Polyphase Motors -- A Direct Approach to TheirDesign, John Wiley and Sons, Inc., New York, 1984.

analysis and evaluation of the transverse flux circumferential current machine

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