Electrical Dc Machines Dr Af-bati

5/26/2018 Electrical Dc Machines Dr Af-bati

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Electrical Machines Notes Dr. AF BATI Page 1

ELECTRICAL MACHINES

REFERENCES:

1. D.BROWN&E.P.HAMILTONELECTROMECHANICAL ENERGYCONVERSIONMACMILLAN,

NY1984.

2. H.COTTONADVANCEDELECTRICALTECHNOLOGYPITMAN,LONDON1967.

3. A.R.DANIELSINTRODUCTIONTOELECTRICALMACHINESMACMILLAN,LONDON1976.

4. A.DRAPERELECTRICALCIRCUITS INCLUDINGMACHINESLONGMAN,LONDON1972.

5. A.DRAPERELECTRICALMACHINES2NDEDITION,LONGMAN,LONDON.

6. A.E.FITZGERALD,D.E.HIGGINBOTTOM,&A.GABRIELBASICELECTRICALENGINEERING

5THED.MCGRAWHILL,NY1981.

7. A.E.FITZGERALD,C.KINGSLEY,&S.D.UMANSELECTRICALMACHINERY,4TH

ED.

MCGRAWHILL,TOKYO1983.

8. J.HINDMARSHELECTRICALMACHINESANDTHEIRAPPLICATIONS4THED.PERGAMON,

OXFORD1984.

9. E.HUGHESELECTRICALTECHNOLOGYLONGMANS,LONDON.

10.G.MCPHERSONANINTRODUCTIONTOELECTRICALMACHINESANDTRANSFORMERS

WILEY,NY1981.

11.S.A.NASARELECTRICMACHINESANDELECTROMECHANICS MCGRAWHILL(SCHAUM),

NY1981.12.S.A.NASAR&L.E.UNNEWEHRELECTROMECHANICSANDELECTRICMACHINES,2

NDED.

WILEY,NY1983.

13.J.ROSENBLATT&M.H.FRIEDMANDIRECTANDALTERNATINGCURRENTMACHINERY2ND

ED.MERRILL,COLOMBUSOHIO1984.

14.Theraja Bl, Theraja Ak ELECTRICALTECHNOLOGY .

15.A.S.LANGSDORFTHEORYOFALTERNATINGCURRENTMACHINERY2ND

ED.MCGRAW

HILL,NY1955. DCMACHINESONLY:

16.A.E.CLAYTON&N.M.HANCOCKTHEPERFORMANCEANDDESIGNOFDIRECTCURRENT

MACHINES3RDED.PITMAN,LONDON1959.

17.M.G.SAY&E.O.TAYLOR DIRECTCURRENTMACHINESPITMAN,LONDON1980.


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CHAPTER1: PRINCIPLEOFOPERATION

1.1 SOMEBASICRULES

Righthandscrewrule(crossproductoperationinvectoralgebra)

A1XA2=A3

A1,A2,andA3arevectors.RotateRHfingersfromthedirectionofthefirstvector,A1,tothe

directionofthesecondvector,A2, throughthesmallangle(


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1.2Singleconductor

Consider astraightconductormovingatauniformspeed u inauniformmagneticfieldB, and

carryingacurrent I. Let

L= activelength(i.e.lengthofconductorsegmentimmersedinthefield);

Fm=appliedmechanicalforce,[N].

u & B give E=B.L.u and I&B give Fd=B.I.L

E.I=(B.L.u).I=(B.I.L).u= Fd.u E.I=Fd.u=Pc=conversionpower

Note:Becausethespeed u isconstant,FdandFm mustbeequalandopposite(otherwisethere

wouldbeaccelerationordeceleration).

E.I iselectricalpower ,andFd.u(Fm.u) is mechanicalpower.

I indirectionof E; Fdoppositeto u. I oppositeto E;Fdin Directionof u.

Generationaction. Motoraction


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V=E I.R V=E+ I.R

t

SF

t

WP

mm

in

=

= Pin=V.I=(E+I.R).I

=Fd.u=Pc =E.I+I2.R=Pc+Pcu

Pcu=copperlosses

Pout=V.I= (EI.R).I Pout=t

SF

t

Wmm

=

=E.II2.R=Pc Pcu =Fd.u= Pc

=Pin Pcu Pin= Pout + Pcu

Pin Pout= Pcu Pin Pout = Pcu

1.3 Wireloop

Considernowawirelooprotatingatauniformspeedinamagneticfield B. Conductors a

and b aretheactivepartsoftheloop;theremainingpartsareend connectionsandleads.


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Fda=Fdb zeroresultantforce Td=developedtorque

i indirectionofe;Td opposesrotation i opposese;Tdaidsrotation

Generatoraction. Motoraction.

KVL: e=ea + eb=loopemf

1.4Sliprings

Slip ringsandbrushesmaybeusedtomake electricalcontactwitharotatingloop.Sliprings

rotatewithloop,whilebrushesarestationarytogiveslidingcontact.Aslipringandabrushfor

eachterminal.


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Theinducedemfisalternating,andthedevelopedtorqueoscillates(aboutthevertical

position).Clearly,slipringsarenotsuitablefor dc machines(theyareusedin ac machines).

1.5Commutator

Acommutatorisaconductingringsplitintosegments;eachsegmentiselectricallyconnectedtooneterminaloftheloop.Itismountedontheshaft,butiselectricallyinsulatedfromit.The

brushesarestationaryandmakeslidingcontactwiththesegments.

A2isalwayspositive;A1isalwaysnegative: >>>et isalwayspositive,& Td isalways

CW(whendirectcurrentsuppliedtobrushes),butemf&current withinlooposcillate.

Although et and Td arenowunidirectional(i.e.remaininthesamedirectionorsense),theydo

notrepresentsteady dc operationbecausetheyfluctuate:eachismaximumwhentheloopis

inposion 0 ,and zerowhenitisinposion2.

1.6Multipleloops

Moreuniform dc operationisachievedbyusinganumberofloopsdisplacedfromeachother

inspace.Theemfsadd(seriesconnection),andthedevelopedtorquesaideachother.Asthe

numberofloopsisincreased,ideal dc operationisapproached.


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2loops 4loops

1.7 Magneticcircuit

Themagneticfieldmaybeobtainedbymeansofpermanentmagnets(PM),or,more

commonly,bymeansofelectromagnets(fieldcoilswithironcores).

Permanentmagnet electromagnet practicalconstruction

(withsoftironextension)

Thevalueoftheresultingfluxisdeterminedbythemmf(magneticmotiveforce)(ofthePMor

electromagnet)andthemagneticreluctanceinthepathoftheflux.Ironhasveryhighmagnetic

permeability,sothatitistheairgapinthepathofthefluxthatlimitsitsvalue.Theairgapmust

thereforebemadeshorttoincreasetheeffectiveflux.Theairgapcannotbeavoided

completely(why?).


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Aircore cylindricalironcore slottedironcore(armature)

1.8Multiplepoles

A dc machinecanhave2,4,6,8,. Poles(anevennumberwhy?)

2p=numberofpoles;(i.e.p=numberofpole

pairs)

Onerevoluon=360mechanicaldegrees;

Onepolepair=360electricaldegrees;

Electricalangle=p X mechanicalangle;

Polepitch=180o

electrical=360o

mech/2p .

Eacharmatureloopisplacedoveronepole

pitch.Electrically,everythingrepeatsaftertwo

polepitches.

1.9loopemf

D=diameterofthearmature[m];

L=activelengthofarmature[m];

n=rotationalspeed[rps=revolutionpersecond];

u=speed=Dn[m/s];

r=angularspeed=2n [rad/s].

Ap=armaturesurfaceareacorrespondingtoonepolepitch=DL/2p [m2].

=fluxperpole[wb=weber];totalmagneticfluxthroughpoleface:sameforallpoles;

B=airgapfluxdensity[T=tesla=wb/m2];normalfieldatarmaturesurface;


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Bav=ave

=ApB.

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Averagecommutatedemf

Wireloop: Eloop=Ea+Eb=2Bav.L.u=2.D.L.n.Bav=(2.D.L.n)(/Ap)

=4p.n.=(2P.r.)/ (=/t=2/(1/2pn))

Conductor (onesideofloop):

Econ=1/2.Eloop=Bav.L.u=.D.L.n.Bav=2p.n.=(P.r.)/

Coil (N=numberofturns=numberofloopsinseries):

Ecoil=NxEloop=2N.Bav.L.u=2.D.L.N.n.Bav=4p.N.n.=(2P.N.r.)/ (=N/t)

1.10looptorque

Theinstantaneousforceonsideais

fa=B.Ia.L

Thenormalfield B variesoverapolepitch,andhence fa

alsovaries.Theaverageforceonsidea is

Fa= Bav.Ia.L

Bav,andhence Fa,areconstantoverapolepitch

correspondingtoagivenpole.Moreover,becauseof

commutation, Iareversesoverthenextpolepitchsothat

Faremainsinthesamesensearoundtheaxisofthe

armature.Theresultantforceduetoallarmature

conductorsiszero,butthereisdevelopedtorquebecause

allforcesactinthesamesensearoundtheaxis.

Averagedevelopedtorque

Wireloop Tloop=Fa.D/2 +Fb.D/2=D/2(Bav.Ia.L +Bav.Ib.L )=D.L.I.Bav [Nm]

Where Ia=Ib, >>>> Tloop=D.L.I(/Ap)=2p.I./


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Coil (Nturns): Tcoil=NXTloop=D.L.N.I.Bav=2p.N.I./

Forconstantrotationalspeed n,andassumingnofriction,thedevelopedtorqueisequalto

theappliedmechanicaltorque.

1.11Conversionpower

A dcmachinemayrunasageneratororasamotor.Ineachofthetwomodesofoperation,

thereisinducedemfanddevelopedtorque(givenbytheequaonsofsecon1.9and1.10).

Whatdeterminesthemode(generatorormotor)isthedirectionalrelationshipbetween E,and

I,andbetween Td and n:

Generatormode: I with E, Td opposite n;

Motormode : I opposite E, Td with n.

Recallthecoilequaonsofsecon 1.9 and1.10; E=Ecoil and Td=Tcoil, wecanwrite

E.I=(4p.N.n.).I=4p.N.r..I/2=(2p.N.I./).r=Td.r

Thisrepresentselectromechanicalenergyconversion.Theconversionpowerisdefinedas

Pc= E.I = Td.r { E.I ontheelectricalside Td.r onthemechanicalside

Generatoraction

R=resistanceofthecoil

Tm=mechanicaldrive

torque

Mech i/p: Pin=r.Td=Pc

Electo/p: Pout=V.I=(EI.R).I=E.II2.R= Pc Pcu

>>>>Pout= Pin Pcu


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Motoraction

Electi/p: Pin=V.I=(E+I.R).I=E.I+I2.R =Pc+Pcu

Mech o/p: Pout=r.Td= Pc

>>>>>Pout=: Pin Pcu

Moregenerally, Pout=: Pin losses

Wherethelossesinclude(inadditiontocopperlosses)mechanicallosses(frictionandwindage),

andironlosses(hysteresisandeddycurrent).

Example 1:

Giventhattheairgapfieldisdistributedsinusoidallywithamaximumfluxdensityof Bm. Show

that =Bm.D.L/p and Bav=2.Bm/

Solution: Bav=1/ B .sin d=cos

=

=Bav.Ap=

...

..

Tutorial1:

Giventhattheairgapfieldisdistributedasshowninfig.1 overapolepitch yp.Showthat

= Bm.D.L/p and Bav=.Bm where =

Bm

0

ya

yp

Fig.1


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Example2:

Thearmatureofa dc machineis 80cmlongandhasadiameterof50cm.Themaximumair

gapfluxdensityis1.5T.Thepolearccovers70%ofthepolepitch.Thearmaturespeedis500

rpm.

(a) If themachinehas2poles,findthefluxperpoleandtheaverageairgapfluxdensitywhen

thefielddistribuonis(i)sinusoidal ,(ii)asinfig.1ofT.1.

(b)Repeatpart aforasixpolemachine.

Forallcasesofparts aandb,findtheaverageemf,developedtorque,andconversion

powerforafullpitchwirelooponthearmature&carrying9A.current.

Solution:

a(i) Sinusoidalfielddistribution

Bav=

=.

=0.955T

=Bav.Ap=0.955X . .

=0.6 Wb.

Eloop=4p.n.=4X1X =20 Volts

Tloop= .I.= 2x9x0.6/ =3.437 N.m

Pc=r.Tloop=2 XX 3.437 =180Was

a(ii)fielddistribuonasinfig.1

Bav=.Bm=

.Bm=0.7X1.5=1.05T

= .Bm.D.L/p= 0.66 Wb.

Eloop=4.p.n.=22Volts

Tloop= .I.= 3.78 N.m

Pc=r.Tloop=198Was

b(i)when2p=6

=0.2Wb.


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Eloop=20 Volts

Tloop=3.437 N.m

Pc=180 Watts

b(ii)

=0.22 Wb.

Eloop=22 Volts

Tloop=3.78 N.m

Pc=198 Was

Tutorial2:

Thearmatureofa4pole dc machineisrotangat840rpm.Thearmaturelengthand

diameterare40cm and 30cmrespecvely.Thefluxperpoleis65mWb.Fora5turnfull

pitchedarmaturecoil:

a.Findtheaverageemfinducedinthecoil.

b.Whatcurrentmustflowthroughthecoilifitistodevelopatorqueof8.0N.m?whatis

theresultingconversionpower?

Answer(36.4V,7.25A.;264W.)

CHAPTER2: construction

Electrical machinesareessentiallyelectricalandmagneticcircuitscoupledtoeachotherto

develop emfsandtorques.Actualmachinescanvarygreatlyindetails.

2.1Materials

a.Iron:highmagneticpermeability>>minimizereluctanceofmagneticcircuit>>highworking

fields.

Highgradesteel(e.g.siliconsteels)for magneticcores.Lowergradesteels(e.g.castiron,cast

steel,mildsteel)forconstructionalparts.Relativepermeabilityofthelinearpartofthe

magnetization(BH)curveisoftheorderof1000,andishigherforhighergradesteels.


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Saturationlimitsmaximumfluxdensityin

ironto 2Torless;theresulngaverage

gapfluxdensityisthenaround0.8 T for

practicalindustrialmachines.

b.copper: highelectricconductivity>>>

minimizeresistanceofelectriccircuits>>

highworkingcurrents.Aluminumis

seldomusedbecauseofspacelimitations;

(whyissilvernotusedeitheraslongasits

resistivityisthelowest?)

c.Air:airgapinpathoffluxnecessaryto

allowmotion.

d.Insulatingmaterials:theyarenecessarytoinsulateconductorsfromeachotherandfrom

adjacentironparts(whicharealsoconducting).

Theeconomicfactor: machinesaregenerallydesignedtoyieldtherequiredperformanceat

minimumcost.

Cost: costofmaterials+costofmanufacture.

Requiredperformance:describedintermsofoperatingvoltage,current,power,torque,speed,

efficiency,weight,volume,reliability,temperaturerise,function,noise,pollution,etc.

2.2 Losses

Powerlossesin dc machinesinclude: copperlosses(I2.Rlossesinconductors);ironlosses(

hysteresis&eddycurrents);frictionandwindage.Alllossesareundesirablebecausethey

representwastedpower,andcausethetemperaturetorise.

Materialsretaintheirdesiredproperties(electrical,magnetic,andmechanical)withinspecific

temperaturelimits.Temperatureriseismostcriticaltoinsulatingmaterials:theirinsulation

capabilitydeterioratesatsufficientlyhightemperatures(around100o

C,dependingonthe

particularinsulator),andultimatelybreaksdowncausingshortcircuitsandpossiblytotalmachinefailure.Tolimittemperaturerise,themachinedesignmustminimizelosses,and

provideforefficientoperation.


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Cooling.Thearmaturewindingsareplacedinslotsaroundthearmatureperiphery.The

conductorsareheldinplacebywedges,orbybandswrappedaroundthearmature.The

slotsaresometimesskewedtoreducenoise.

2.5Airgap

Theairgapisthespacebetweenstatorandrotorneededtoallowrelativemotionbetween

them(i.eitismechanicallynecessary).Magnetically,it introducesahighreluctanceinthepathoftheworkingflux(mostofthefieldmmfisconsumedintheairgap);itisthereforemadeas

shortaspossible,typically0.55.0mm.Thearmaturesurfaceandthepoleshoesfacing it

requireprecisemachiningtoavoidasymmetryandvibration.

2.6Commutator

Thefunctionofthecommutatoristointerfacebetweenthealternatingcurrentsandemfs in

therotatingarmaturecoilsontheoneside,andthedirectcurrentandvoltageatthemachine

terminals.Itismadeupofcoppersegmentsinsulatedfromeachotherandmountedonthe

shaft(i.eitrotateswiththerotor)inacylindricalform.Vringsholdthebarsinplace.Theleadsofeacharmaturecoilareconnectedtorisers(eachofthetwoleadsofacoilgoestoadifferent

commutatorsegment).

Brushesarecarbonorgraphiteblocksmountedin stationaryholderswithspringpressureto

maintain goodelectricalcontact withtherotatingcommutatorsegments.Thebrusheswear

outwithtimeandmustbereplacedregularly.

Thecommutatorisacriticalpartofthemachine: from brushes, carbonfillingsanddirt

accumulatecausingcurrentleakagebetweensegments.Intermittentcontactbetweenbrushes

andsegmentsoftenleadstosparking,whichmaybecomequiteserious.

2.7Mechanicalitems

Shaft;spider;bearings(withgreasepackorlubricationsystem).

Bolts;clamps,spacers,brackets.


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2.9Machineratings

The nameplateofamachineservestoidentifythemachine.

Itgivesratedvoltage,current,power,speed,andpossiblyother

datausefultotheuser.Themachineratingsarethevaluesof

thevariousparametersforwhichthemachinewillrun

continuouslywithoutoverheatingorotherdamage.Inpractice,theratingscanbeexceededfor

shortperiods.If,however,theratings are exceededforconsiderableperiodsoftime,there

maybepermanentdamage, particularlytoinsulation.

Machinesareusuallymanufacturedinstandardframesizes.They alsocomeindifferent

enclosurestosuitvariousenvironmentalconditionsandduties(e.g.dripproof,splashproof,

andsubmersible).

Allmaterialsaresubjecttophysicallimitations,i.e.limits beyondwhichtheynolongerretain

theirdesiredphysicalcharacteristics.Properdesignanduseofmachines(andindeedall

apparatus)shouldensurethatnoneoftheconstituent materials exceedsitsphysical

limitationsundernormaloperatingconditions.

Toselectanappropriatemachineforhissystem,theusermustknowclearlytherequirements

ofthatapplication(e.g.speed,voltage,power,etc.)andtheconditionsunderwhichthe

machinewillberunning.Hewillthenbeabletoselectthemosteconomicalmachinethat

meetstheserequirementsandconditions.

Chapter3: Armaturewindings

The coils onthearmatureareconnectedtoeachotherandtothe commutatorsegmentsto

formwhatiscalledanarmature winding.

3.1Coildetails

Coilsides:activepartsofcoil;placedinsideslots.

Coilspan:separationbetweenthetwocoilsidesalongthearmaturesurface(i.e.thearc

coveredbythecoil).

Fullpitchedcoil:coilspanexactlyequaltopolepitch.

Chordedorshortpitchedcoil:coilspanslightlyless(orpossiblymore)thananexactpolepitch.


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Allsectionsofthecoilareinsulated:fromeachother,fromadjacentcoils,andfromcoreiron.

Thelevelofinsulationatanypointisdeterminedbythepotentialdifferencebeinginsulated.

Coilsdesignedforlowvoltageandhighcurrenthavefewturnsoflargesections;conversely,

coilsforhighvoltageandlowcurrenthavemanyturnsofsmallsections.Largemachineshave

fewturns/coil,possiblyonlyone,madeofpreformedcopperbars.Smallmachinescoilsare

madeofmanyturnsofflexiblewirewoundandbenttoshape.

3.2Twolayerwindings

Machinewindingaremadeintwolayers:foreachcoil,onecoilsideisplacedinthetophalfof

itsslot(toplayer),andthesecondcoilsideisplaced inthebottomhalfofitsslot(bottom

layer).Thismakesiteasytoarrangeendconnections(front&back)inaregularmanner;all

coilsarethenidenticalsothatthewindingissymmetricalandcompact.Thereareatleasttwo

coilsidesineachslot,oneinthetoplayerandoneinbottomlayer.Inlargemachines,there

maybe2,3,4,etc.coilsidesperslot.

Forexample,ifwehave 3coilsides/slot/layer and2turns/coil then:

Numberofconductors/slot/layer=3X2=6

Conductors/slot=2X6=12 (also,wecansay6 coilsides/slot)

3.3 Somenumbers

C=totalnumberofcoilsonarmature; N=numberofturnsineachcoil;

NC=totalnumberofloops; Z=totalnumberofarmatureconductors=2NC

2C=Z/N=totalnumberofcoilsides; S=totalnumberofslotsinarmature;

Z/S=2NC/S=numberofconductors/slot; 2C/S=numberofcoilsides/slot;

NC/S=numberofconductors/slot/layer; C/S=numberofcoilsides/slot/layer;

S/2P=numberofslots/pole=polepitchmeasuredinslots.


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3.4Interconnectionofcoils

Allthecoilsonthearmatureareconnectedtogethertoformasingleclosedcircuit(calledthe

armaturewinding): startingwithanycoil,itsendisconnectedtothebeginningofasecondcoil;

theendofthesecondcoilisconnectedtothebeginningofathirdcoil,andsoon.Thisis

repeateduntilthelastcoil,Cthcoil,isreached;itsendisconnectedtothebeginningofthefirst

coil,sothatthecircuitisclosed.Theinterconnectionsbetweenthecoilsaremadeonthe

commutator:thesecondleadofthe1st

coilandthefirstleadofthe2nd

coilaresoldered

togetherontheriserofonecommutatorsegment;thesecondleadofthe2nd

coilandthefirst

leadofthe3rd

coilaresolderedtogetherontheriserofanothercommutatorbsegment;finally,

thesecondleadofthelast(Cth)coilandthefirstleadofthe1st

coilaresoldered totheriserof

onecommutatorsegment.

1 2 3 C1 C Coils

Commutatorsegments

Afulllineindicatesacoilsidelyinginthetoplayer,andadashedlineindicatesacoilsidelying

inthebottomlayer.Arrowsoncoilsidesmaybetakentoindicatedirectionofeitherinduced

emforcurrent.

Itshouldberememberedthat

Totalnumberofcommutatorsegments=totalnumberofcoils=C

3.5Windingschemes

Armaturecoilsmaybeinterconnectedaccordingtooneoftwoschemes,givingrisetotwo

typesofarmaturewindings,lapandwave.

yC=commutatorpitch=numberofcommutatorsegmentsadvancedfromthefirstcoilleadto

thesecond(sameforallcoils).


23/102

3.5.1La

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24/102

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25/102

Electrical Mac ines Notes Dr. AF ATI

P a g e

Pa

|25

ge 25


26/102


P a g e

Pa

|26

ge 26


27/102


P a g e

Pa

|27

ge 27


28/102


P a g e

Pa

|28

ge 28


29/102


P a g e

Pa

|29

ge 29


30/102


P a g e

Pa

|30

ge 30


31/102


P a g e

Pa

|31

ge 31


32/102


P a g e

Pa

|32

ge 32


33/102


P a g e

Pa

|33

ge 33


34/102


P a g e

Pa

|34

ge 34


35/102


P a g e

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|35

ge 35


36/102


P a g e

Pa

|36

ge 36


37/102


P a g e

Pa

|37

ge 37


38/102


P a g e

Pa

|38

ge 38


39/102

P a g e |39


3.6Parallelpaths

Fromtheprevioussection,itcanbeseenthatthearmaturecoilsformaclosedwindingthatis

tappedbythebrushesatcertainpoints. Ineffect,thebrushesdividesthewindingintoa

numberofparallelpathseachofwhichiscomposedofanumberofcoilsinseries.Theterminal

currentisdividedamongtheparallelpaths.Atanymomentduringoperation,thereare short

circuitedcoils;thesearenotincludedinthepaths.Thecircuitdiagramsforthelapandwave

windingsareshownbelow.Ineachcase,the terminalvoltageisequaltothevoltageofthe

individualparallelpaths.

Fromthesequencediagraminpage29 forthelapwdg.,itcanbeseen thatallthebrushesare

necessary:ifanybrushisremoved,therewillbeopposingemfsinseries(whichwouldcancel

out).Thusthenumberofbrushesisequaltothenumberofpoles,andhencethenumberof

parallelpathsisalsoequaltothenumberofpoles:

Lapwdg: 2a=2p,>>> a=p ,2a=numberofparallelpaths; a=numberofpairsofparallel paths

Fromthesequencediagraminpage36forthewavewdg,ontheotherhand,itcanbeseenthat

onlytwobrushesarereallynecessary;alternate brushesareconnectedtoeachotherinternally

throughshortcircuitedcoils.Thus2brushesmaybedisconnectedandremovedwithout

affectinginducedemfsandcurrents.Inotherwords,thebrushesdividethewdgintotwo

parallelpathsonly:

Wavewdg: 2a=2, >>>>>a=1.

Theextrabrushesmayberemoved,butinpractice,theyaresometimeskepttoobtainbetter

currentdistributionoverthecommutator.

Generalsymbolicrepresentation


40/102

P a g e |40


3.7Comparisonoflapandwavewindings

Alapwdghas2pparallelpathsandmusthave2pbrushes(orbrushgroups).Awavewdghas

twoparallelpathsandrequiresonlytwobrushes(orbrushgroups),butitcanhave2pbrushes.

Alapwdgcanbemadetofitanynumberofcoilsandpoles.Awavewdgcanbefittedonlyifthenumberofcoilsandpolesyieldanintegercommutatorpitch yC(=(C 1)/p).

Abrushonalapwdggenerallyshortcircuitsonecoilduringcommutation.Inawavewdg

havingonlytwobrushes,eachbrushshortcircuits p coilsinseries;inawavewdghaving 2p

brushes,acoilisshortcircuitedbytwobrushesinseries.

Assumenowthatagivenwdgcanbeconnectedineitherlaporwave.Thecoilemfandcurrent

arethesameinbothcases. Thelapconnectedwdgwillhaveahighterminalcurrentandalow

terminalvoltage,whilethewaveconnectedwdgwillhavealowterminalcurrentandahigh

terminalvoltage(for2p

4).Thetwowdgswillhavethesamepower.

Conversely,assumeamachineistohaveaspecifiedterminalvoltageandaspecifiedterminal

current.Ifitisconnectedinlap,itwillhavealow currentpercoil,andahighvoltagepercoil;

thereforeeachcoilwillhavemanyturnsofsmallcrosssection,andahigherlevelofinsulation

isneeded.Ifitisconnectedinwave,itwillhaveahighcurrentpercoilandalowvoltageper

coil;thereforethecoilswillhaverelativelyfewturnsandlargesections,andarelativelylower

levelofinsulationisneeded.Inthisrespect,wavewdgsarebetterthanlapwdgsbecausethey

allowforbettercoolingofwdgs,andbecausetheyhavehigherspacefactors(spacefactor=

copperarea/totalslotarea).Ingeneral,wavewdgsareusedinalmostallmachinesupto50KW,andinallhighvoltagemachines.Lapwdgsareusedmostlyinlargemachineshavinglow

voltage/highcurrentratings.

3.8Equalizers

Inlapwdgs,eachpathisassociatedwithapairofpoles.Thusifthereisasymmetryinthe

magneticcircuit(duetowearofbearings,oreccentricityofshaft),theemfsinducedinthe

pathswillnotallexactlyequaltoeachother.Unequalemfsconnectedinparallelgiveriseto

circulatingcurrentsthatcanbequitelarge, causingheavyandunnecessaryheating.

Toreducethiseffect ,pointsthatshouldhavethesamevoltageareconnectedtoeachotherby

meansofequalizers(orequalizingconnections, orequalizingrings). Suchpointsarelocated

twopolepitchesapart.Eachequalizingringisconnectedto p points in alternate paths.

Inthewavewdg,thereareonly twopathsthroughthearmature.Thecoilsofeachpathare

distributeduniformlyaroundthearmature,andhencecoverallpolepairs. Anyasymmetryin


41/102

P a g e |41


themagneticcircuitwillhavethesameeffectonbothpaths,sothatthetwoinduced emfs

willbeidentical.Thuswavewdgsdonotrequireequalizers,whichisanotheradvantageofwave

wdgs.

I

R IC R V Atnoload I=0and IC=

E1 E2

3.9Multiplexwindings

Thelapandwavewdgsdescribedsofararecalledsimpleorsimplexwdgs.Duplexwdgsare

composedoftwosimplexwdgsinterleavedaroundthearmature,andconnectedsoastohave

twiceasmanyparallelpaths:

Duplexlap wdg: 2a=4p Duplexwavewdg: 2a=4

a=2p a=2

similarly,theremaybetriplexwdgs,andsoon. Suchmultiplexwdgs are rarelyused.

3.10Armaturecalculations

Considerasymmetricalwdgcomposedof 2a idencalparallelpaths.Ithas

C/2a coils/path, Ip

C/a coilsides/paths, Ip VA

Z/2a=NC/a conductor/path Rp

Let Ep

Ep=inducedemfineachpath;


42/102

P a g e |42


Ip=currentflowingthrougheachpath; brush IA

Rp=resistanceofeachpath. Rpp VA

Alsolet EA

VA=armatureterminalvoltage;

IA=armatureterminalcurrent; Theveninequivalent forarmaturewdg

EA=armatureemf=Theveninequivalent emf forarmaturewinding;

Rpp=Theveninequivalentresistanceforarmaturewinding;

RA=totaleffectivearmatureresistance.

Applying KVL:

Generator: VA=EA IA.RA

Motor : VA=EA + IA.RA

3.10.1Armatureresistance

Singleloop: Rloop=

Where =resistivityofcopperattheworkingtemperature; IA IA

lm=meanlengthofasingleloop; RA RA

A=crosssectionalareaoftheconductor. VA VA

coil Rcoil=NxRloop=

EA EA

Path Rp=XRcoil=

=

Winding:Rpp=Rp=

=

Generator Motor

Commonsymbolicrepresentationofarmaturewinding

Effectivearmatureresistance: RA=Rpp +Rbrushes+Rcontact;

Rbrushes istheresistanceofthecarbonbrushes.Rcontactistheresistanceofthe

brush/commutatorcontactsurface;itisnonlinear,andisusuallytakenasequivalenttoa

constantvoltdrop(forexample 1volt).

G M


43/102

P a g e |43


3.10.2 Armatureemf

Theaveragecoilemfderivedinsecon1.9isthesameforallarmaturecoils.Thus,foreach

path

Ep= XEcoil= n.

Butallpathsareinparallelwitheachother,sothatthearmatureemfisequaltotheindividual

pathemfs:

EA=Ep=XEcoil=

n.=Ke.n. (Ke=

=

)

Analternativeexpressioncanbeobtainedintermsofr (=2.n):

EA=(Ke/2)r.=K.r. (K=Ke/2=

=)

3.10.3Torque

Accordingto KCL,theterminalcurrent IA isthesumofallpathcurrents:

IA=2aXIp >>>>>> Ip=IA/2a

Apathiscomposedofcoilsinseries,sothatthepathcurrent Ipflows throughtheindividual

coils:

Icoil=Ip

Theaveragecoiltorquewasderivedinsecon1.19:

Tcoil= N.Icoil.=

N.Ip.=

.IA.

Thetotalarmaturetorqueisthesumofallcoiltorquesactinginthesamedirectionandaiding

eachother:

T=CXTcoil=

.IA.=K.IA. (K==

asbefore)

3.10.4 Conversionpower

Theconversionpowercorrespondingtoelectromechanicalenergyconversioninthemachineis

givenby:

Ontheelectricalside:PC=EA.IA


44/102

P a g e |44


Onthemechanicalside::PC=r.T

Notethat PC=EA.IA=(k.K.IA. ).r= r.T

Using Pin todenoteinputpowertothearmature,and Pout todenoteoutputpowerfromthe

armature,wehave:

Generator : Pin=r.T=PC , Pout=VA.IA=EA.IA IA2.RA= PC PCu

Motor : Pin=VA.IA=EA.IA + IA2.RA= PC + PCu , Pout=r.T=PC

PCu isthetotalcopperloss(orohmicloss)inthearmature.

Example3:

A6polemachinehas53slotswith 8conductors/slot.Thefluxperpoleis50mWb,andthe

speedis420rpm.Calculate:

1.Thenumberofturnspercoil;

2.Ecoil,EA;

3.Tcoil, T;

4.conversionpower,Ifthewindingis (a)simplelapwinding;

(b)simplewavewinding.

Assumearmaturecurrenttobe IA=50A.

Solution:(a)simplelapwinding

2a=2p=6, C=53, Z=53x8=424 conductors, 2C=Z/N=2 X53=106 >N=424/106=4turns/coil

Ecoil=NxEloop=4X4p.n.=16X3X(420/60)X50X103

=16.8 V.

EA=Ep=(C/2a).Ecoil=53X16.8/6=148.4 V.

Or EA=

n.=148.4 V.

Tcoil=N X Tloop=4 X.IA.=3.183 N.m

T=C.Tcoil=53X3.183=168.7 N.m

Pc=EA.IA=148.4X50=7420 W.


45/102

P a g e |45


.(b)Simplewavewinding

2a=2, Ecoil=16.8 V.

EA=Ep=53X16.8/2=445.2 V.

Tcoil=N.Tloop=.IA.=9.549 N.m

T=C.Tcoil=506.11 N.m

Pc=EA.IA=22260 W.

Tutorial3:

A6pole,1500rpm dc machineislapwoundwith 732 acveconductors,eachcarrying 20A.

Thefluxperpoleis 30 mWb.(a)find IA,EA, T andPc.

.(b)Repeatpart(a)ifthemachineisreconnectedinsimplewave.

Example4:

A10polesimplelapwoundgeneratorisratedat 110V., 600A., and750rpm.Ithasa

windingresistanceof 7.2 m,andiswoundin 163 slots with4 coilsides/slot and 2

turns/coil.Assumeabrush voltagedropof1.5V.(a)findtheratedloadpower, (b)findthe

resistance, emf, andterminalvoltagepercoilandperturn, and(c)findthedevelopedtorque

andfluxperpole.

Solution:

Pout=VA.IA=110x600=66KW

2a=2p=10

RP=RA x10=72m

Coilsides=S X coilsides/slot

2C=163 X 4=652 coilsides

C=326 coils

Coils/path=32.6


46/102

P a g e |46


Rcoil=

/=72/32.6=2.2 m

EA=VA +IA.RA +Vbrushes=110 +600 X0.0072 +2 x1.5=117.32 V.=Ep

Ecoil=

/=117.32/32.6=3.55 V.=4pNn>>>>>=7.1mWb.

Vcoil=Ecoi IP.Rcoil=3.417V.

Vturn=Eturn IP.Rturn=1.78 60X1.1X103

=1.714 V.

T=K.IA.= .IA.=5x326X2X600 X7.1X10

3/5=884 N.m

Tutorial4:

Repeat thesamerequirementinEx.4,ifthefluxandspeedarekeptthesame,forwave

winding.

CHAPTER 4 THEMAINFIELD

The operation of dc machines is based ontheinteractionbetweenthearmatureconductors

andtheairgapfield,whichresultsininducedemfanddevelopedtorque.Themainfieldisthe

fieldproducedbythefieldcoils(orPMs)onthestator.

Tobeabletostudythemainfield byitself,weshallassumethereisnoarmaturecurrent,i.e.

themachineisoperatingatnoload.

4.1Mainfielddistribution

Ifthefieldcoilsactalone(i.e.nocurrentinarmatureconductors),thefluxin the dc machine

willhavethegeneralpattern ,suchthat mostofthefluxinthepolecorescrossestheairgapto

linkthearmaturewindings;thisistheusefulfluxperpole .However,someofthefluxlines

completetheirpathswithoutlinkingthearmaturewdg; thisistheleakageflux.

Theusefulflux isproducedbythemmfofthefieldcoils.The mmfperpole Mf isthesumof

themmfsofallcoilsplacedononepole(whichmaybeone,ortwo,ormore).Thus

Mf= Nf.IF ampereturn/pole


47/102

P a g e |47


Ifyoufollowthelinesoftheusefulflux,youwillfindthatthepathoftheusefulfluxis

composedofthefollowingpartsinseries: statoryoke ,polecore, poleshoes,airgap,

armatureteeth,andarmature core. As aseriescircuit,theoverallreluctanceisdominatedby

thehighestreluctances inthepath,whichare(a)theairgap,and(b)armatureteeth(when

saturated).

ThefigureontheLHSshowsthefluxdistributionalloverthemachine,whilethefigureonthe

RHSshowsthefluxdensitydistributionintheairgap,i.e.theeffectivefieldseenbythearmatureconductors.Thecurveissmoothifthearmaturesurfaceisassumedtobesmooth;in

fact,armatureslotsintroducearipplethatmovesalongthecurveasthearmaturerotates;we

shallneglecttheslottingeffect.Amuchmoreseriousdistortionofthemainfieldiscausedby

armaturereaction.

4.2Fieldexcitation

Themainfieldmaybeproducedbymeansofpermanentmagnets(PMDC),orbymeansofcoils

placed onthepoles(woundpole).PMsare compact(smallsize),requirenosupplyforthe

field,andareeconomicalinoperation(noohmiclosses);however,theyareveryexpensive.Woundpolemachinesaremuchcheaper,andallowcontrolofthefield;theyaremuchmore

commonlyused.

Fieldcoilsinwoundpolemachinesmaybeconnectedinvariousways.Theymaybedividedas

follows:

Separatelyexcited:fieldcoilssuppliedfromseparatesource.


48/102

P a g e |48


Self excited:fieldcoilsareconnectedwiththearmature.Theymaybeinparallel(shuntfield),

orinseries.Compoundmachineshavebothshuntandseriesfields.

Shuntfieldcoilsaremadeofmanyturnsofthinwire;theyaredesignedtocarryacurrentmuch

smaller(lessthan10%)thanthearmaturecurrent IA.Theshuntfieldcurrentmaybecontrolled

byconnectingavariableresistor(rheostat)inserieswiththecoils.

Seriesfieldcoilsaremadeofjustafewturnsofthickwire;theycarrythearmaturecurrent IA

(inshortshuntcompoundmachines,theseriesfieldcurrentdiffersfromthearmaturecurrent

byanamountequaltotheshuntfieldcurrent,whichissmall).Theseriesfieldcurrentmaybe

controlledbyplacingavariableresistorinparallelwiththecoils.

Compoundmachinesmaybeconnectedinlongshuntorinshort shunt.Thereisnomajor

differencebetweenthetwotypesofconnection.Theshuntandseriescoilsmayproducefields

thataideachother,andcompoundingissaidtobecumulative;conversely,theshuntandseries

fieldsmayopposeeachother,andthecompoundingisthensaidtobedifferential.Ingeneral,

theshuntfieldissubstantiallygreaterthantheseriesfield,andhencedominates.

Fromtheabove,itshouldbeclearthattheresistanceofshuntfieldcoilsisquitelarge,while

thatofseriesfieldcoils isquitesmall.Moreover,controlofthefieldcurrentresultsincontrol

oftheinducedemf,andhencecontrolofgeneralmachineoperation.

Some specialpurpose dc machineshavemorethantwosetsoffieldcoils;eachsetofcoilsis

fedfromadifferentcontrollingsignal,sothatmotoroperationisdeterminedbytheoverall

combinationofcontrollingsignals.Suchmotorsarecommonlyusedincontrolapplications.


49/102

P a g e |49


4.3Themagnetization curve

Inwoundpolemachines,thefluxis producedbythefieldexcitation, i.e.bythemmf ofthe

fieldcoils.The magnetizationcurveistherelationshipbetweenthefluxperpole andthe

mmf perpole Mf producingit.

Mf isappliedtoamagnetic circuit composedoftheairgap reluctanceinserieswiththe

reluctance ofironparts(assumingtheleakagefluxisnegligible).Theairgapreluctanceis

constant,butthereluctanceofironpartsincreasesastheyenterintosaturation.

Atlowexcitation(sayMf1),theironisunsaturatedsothatitspermeabilityisveryhigh,andits

reluctance isnegligiblerelativetothatoftheairgap;themmfdropintheironisnegligible,

and practicallyalltheapplied mmf Mf1istakenupindrivingtheflux 1acrosstheairgap.At

higherexcitation(say Mf2),ironpartsbegin tosaturatesothattheirpermeabilitygoesdown

andtheirreluctance goesup;themmfdropintheironisnolongernegligiblerelativetothe

mmfdropintheairgap.Theappliedmmf Mf2 dividesbetweentheairgapandtheiron

accordingtotheratiooftheirreluctances(similartovoltagedivisioninelectriccircuits).Asthe

excitationisincreasedfurther(to,say,Mf3),theironpartsaredrivenfurtherintosaturationso

thattheyconsumealargerproportionoftheapplied mmf Mf3;indeed,themmfdropiniron

maybecome greaterthanthemmfdropintheairgap.Armature

teethsaturatefirst,followedbythepoles,andthenthearmature

coreandyoke.

Therelationshipbetweenthefluxperpole andthemmfdrop

intheairgap(whichislessthanMf)islinear; itisrepresentedbytheairgaplineinfig.4.4. Atlowexcitaon,themagnezaon

curvefollowstheairgapline.Asexcitationincreases,the

machinebeginstosaturate, andthecurvemovesawayfromthe

line(kneeofthecurve).Atheavyexcitation,themachineiswell

intosaturation,andthecurveiswellawayfromtheline.Itis

notedthatatzerofieldexcitation,thereissomeremanent

magnetism( duetohysteresisintheiron)sothattheflux is

notzero.

Now,fromchapter3,wehave

EA=Ke.n.=K.r. and T=K.IA.

WhereKe and K areconstantsdependingonmachineparameters.If isknown,then EA may

becomputedforagivenspeed n, and T maybecomputed foragiven IA. However,ifitisthe


50/102

P a g e |50


fieldexcitation Mf thatisknown,wemustfirstfind fromthemagnetizationcurve; the

procedureisgraphicalbecausethereisnoreadyformula giving interms of Mf.

Atagivenconstantspeed no

EAo=Ke.no.

Sothattheverticalaxisofthemagnetizationcurvemaybescaledintermsof EAo insteadof .

If,moreover,onlyonefieldwinding(i.e.onesetoffieldcoils)isexcited,then

Mf=Nf.If

Where Nf and If correspondtothewdgexcited; since Nf is constant,thehorizontalaxisof

themagnetizationcurvemaybescaledintermsof If insteadof Mf. Theseformsof the

magnezaoncurveareshowninfig.s4.5and4.6respecvely. Thelastformofthe

magnetizationcurve(EA

x If)canbeobtainedexperimentallybythesimpletestshownin

fig.4.8: themachineisdrivenatconstantspeed no; thefieldcurrent If isvaried,andthe

correspondingvaluesof emf EAo arerecorded.Ifthetestisperformedatratedspeed,the

resultingmagnetizationcurveiscalledtheopencircuitcharacteristic(OCC).

To obtainthemagnezaoncurveatdifferentspeedsasinfig.4.7,weneedtoperformthe

(opencircuit)testonlyonceat,say,no;atagivenvalueoffieldcurrent,say Ifo,wehave

EA1=ke.n1. =Ke.no.(n1/no)=EAo(n1/no)

Thustheemf valuesat n1 areobtainedbymultiplyingthecorresponding emf values atnoby

thespeedratio (n1/no).

Ifthe OCC isavailable,themagnetization curve EA vs. Mf maybe obtainedif Nfisknown,

andthemagnetizationcurve vs. Mf maybeobtainedif Ke or K isknown.


51/102

P a g e |51


Testtomeasure OCC;machinedrivenatconstant

speed no

Chapter5 Armature Reaction

Whenamachineisloaded, currentswillflowinthearmaturecoils,andanarmaturefieldisset

up.Thisarmaturereactiondistortsthefielddistributioninthemachine,andresultsinsome

adverseeffectsthatmustbetreatedforsatisfactoryoperation.

5.1Armaturefield

Whenthemachineisloaded,currentflowsinthearmatureconductors,andtendstosetupamagnecfieldasshowninfig.5.1.The armaturemaybeviewedasasinglecoilactinginthe

qaxis ; mostofthefluxfollowsthepathcomposedof :armteeth,airgap,poleshoes,and

armcore. Noteinparticularthatthearmfieldisperpendiculartothemainfield showninfig.

4.1 andrepeatedhereinfig.5.3, whichactsinthedaxis.Thearmature mmf isdistributed

alongtheairgapasshowninfig.5.2(withtheactualslotsapproximatedbyaconnuousbelt

ofcurrent).Thearm mmf Ma peaksattheqaxisandiszeroatthedaxis; itspeakvalueis

Mam= .

.

=

.IA=

.IA

Thearm mmf tendstosetuptheairgapfluxdensitydistribuonshowninfig.5.2 ;although

the mmf ismaximumattheqaxis,thefluxdensityisseentofallbecauseofthelarge

reluctancethereresultingfromthelongairpath.


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P a g e |52


Fig.5.3

Fig.5.4Resultantfluxdistribuon


53/102

P a g e |53


Fig.5.5Airgapfluxdensitydistribution

MF:mainfield;

AF:armaturefield;

RF:resultantfield

5.2Resultantfield

Fig.5.1 showsthearm fieldbyitself,whilefig.5.3showsthemainfieldbyitself. Notethatthe

mainfield actsalongthedaxis,whilethearmfieldactsalongtheqaxis.Inthearmcoreand

poleshoes,thetwofieldsareperpendiculartoeachother.Intheairgap,however,thearm

fieldaidsthemainfieldoverahalfpolepitch,andopposesitoverthenexthalfpolepitch.

Superpositionofthetwofieldsyieldstheresultantfluxdistribuonshowninfig.5.4;thisisthe

actualdistributioninthemachinewhenbotharmatureandmainfieldsarepresent,i.e both

armandfieldwdgsareexcited.Notehowarmaturereactionhasdistortedthefielddistribution;

note,inparticular,howthemagneticneutralaxisisnowshiftedfromtheqaxis(ormechanical

neutralaxis,orbrushaxis).Theairgapfluxdensityisstrengthenedinonepoletipand

weakenedintheotherpolep,asshowninfig.5.5.thezerocrossingofthefluxdensitywave

isnowshiftedfromtheqaxis.

Thedireconsofmainfield andarmcurrentsinfig.5.4 correspondto(a)generatoroperaon

forCWarmrotation,orto(b)motoroperationforCCWarmrotation; thisiseasilyverifiedby


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nongthatthetorqueonthearmconductorsisCCW.Itisthusseen,fromfig.5.4 or 5.5,that

thefluxispulledinthedirectionofrotationforgeneratoroperation,andinthedirection

oppositetorotationformotoroperation; thustheshiftinthemagneticneutralaxisisinthe

directionofrotationforgeneratoroperation,andinthedirectionoppositetorotationfor

motoroperation.

5.3Demagnetizingeffect

Thearmreactionactsontheqaxisandisthereforegenerallyperpendicularto(orin

quadraturewith)themainfieldwhichactsonthedaxis;itisthuscalledcrossmagnetizing

armaturereaction.Foralinearmagneticcircuit,thecrossmagarmreactionhasnoeffecton

,theusefulfluxperpole:thearm mmf inonehalfpolepitchisequalandoppositetothearm

mmfintheotherhalf;thereforeitaddsandsubtractsequalamountstothemainfluxwhich

thusremainsunchanged.Itfollowsthattheaverage emf EA=k.r. andtheaveragetorque

T=K.IA. areunaffectedbycrossmag AR because itselfisunaffected.However,becauseofthe distortionoftheairgapfluxdensity,fig.5.5,theinstantaneous emf andtorqueareno

longerthesameforallconductorsunderthepoleface.

Butthemagneticcircuitisactuallynonlinearbecauseitincludesironpartswhichtendto

saturateathighfields. Inthehalfpolepitchwherethearm mmf aidsthemainfield,theiron

parts(armteethandpoletips)aredrivendeeplyintosaturationsothattheincreaseinflux

densitythereislessthanthedecreaseinfluxdensityintheotherhalfpolepitch(wherearm

mmfopposesmainfieldsothatironpartsaredrivendownthekneeofthemagcurveintothe

linearpart).Thismeansthatthepeaksofthedistortedfluxdensitywavearechippedoffas

shownbydoedcurvesinfig.5.5.Italsomeansthatthereisanetdecreasein ;i.e.cross

magnetizing ARhasademagnetizingeffect.Thedecreasein resultsinreductionofthe

average emf EA andaveragetorque T.

Clearly,then,theeffectivemagnetizationcurveonload(IA>0)liessomewhatbelowtheOCC(IA=0), and

islowerforhigherarmaturecurrents; seefig.5.6.Thecurvesmergewiththe OCCattheairgapline

becausethereisnosaturationatlowexcitation.

Thereductionintheusefulfluxdueto AR isanonlinearfunctionof both fieldandarmature mmfs,

andhenceoffield andarmature currents, If andIA. Thedemagnetizingeffectof AR maybe

represented asareductionininduced emf, E ,or as areductionineffectivefieldcurrent, If;

seefig. 5.7.At afieldcurrent If andzero armcurrent IA=0,wehave

VA=EA and EA=EAoc then VA=EA=EAoc

Atthesamefieldcurrent If,butwithanonload arm current IA 0, wehave

VA=EA IA.RA and EA=EAoc E >>>>>VA=(EAoc E ) IA.RA


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Or VA=EAoc(IA.RA E )

Thuswemayview EAocastheinducedemf,and E asavoltagedropthatsubtractsfromthearm

resistancedrop IA.RAformotoroperation, andaddsto it forgeneratoroperation.Alternatively,we

mightview AR as areductionineffectivefieldmmf: atafieldcurrent If and anarm current IA, the

effectivefieldcurrentis

If=If If

Onthe OCC,If givestheactual induced emf EA, while If givesthe emf EAocwhich wouldbeinduced

whentheloadisremoved.

Fig.5.6Effectofloadonmagnezaoncurve. Fig.5.7Representaonof

Demagnetizingeffectofarmature

Reaction.

Exercise

The OCC ofa dc machinerunningat 800 rpmisgiveninthetablebelow. Plotit,(a)onthesame

graph,plotthecurvesat600rpmandat1000rpm.(b)ifeachfieldcoilhas630turns, plotthe

magnetizationcurves EAvs. Mf .(c)ifthemachineiswavewoundwith6poles,andhas46 armature

coilsof 3turnseach,plotthe magnetizationcurveas vs. Mf.(d)at800 rpm,esmatethe mmf

dropsintheairgap andintheironwhentheemf is 50,100,150,200,250,and00 volts.(e)whatisthe


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residual(orremanent) fluxperpole? (f) whatistheinduced emf whenthefieldcurrentis5.5A. and

thespeedis 1500rpm?.

If

(amps)

0 .3 .5 1 1.5 2 2.5 3 3.5 4 4.5 5 6 7 8 9 10

EA

(volts)

8 28 46 94.5 143 175 195.5 211 224 24.5 248.5 251.5 265 276.5 286 294 302

The dc machine whose OCC isgiven intheabovetable hasawdg resistance of 75m and a

constant brushcontactdropof1.5V. Themag curvesatdifferentarmatureloadings and constant

speed 800 rpm arelistedinthetablegivenbelow.Plotthesecurves, togetherwiththe OCC.Overthefieldcurrentrangeshownhere.(a)determine E , and If whenthearmcurrentis80A andthe

fieldcurrentis 8A.(b)determinetheterminalvoltagewhenthefieldcurrentis7A andthearmcurrent

is 60A, and themachineisoperangasagenerator.(c)repeat partb formotoroperaon.(d)ifthe

machineisoperangasageneratorwithterminalvoltage 260 V andarmaturecurrent 100A, fi

If 3.5 4 4.5 5 6 7 8 9 10

EA IA=

100

217 225.5 232.5 239.5 252 262.5 270.5 277 283

IA=

80

219 228 235.5 243 256 267 275.5 283 290

IA=

60

221 230.5 238.5 246.5 260 271.5 280.5 288.5 296


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5.4Effectsofarmaturereaction

Thedistortionofthefielddueto AR hasanumberofadverse(bad)effects:

(1)Demagnezingeffectasdiscussedinsecon5.3:asarmcurrentincreases,theuseful

fluxperpoledecreases,andhencetheinduced emfanddevelopedtorquedecrease.(2)Shiftofthemagneticneutralaxisfromthebrushaxismeansthatcoilsidesofcoils

undergoingcommutationaresubjectedtononzerofluxdensity,sothatanonzeroemf

isinducedinthem.

(3)AR concentratesthefluxatonepolep,fig.5.5.Althoughtheaverage emf is

approximatelythesame(slightlyreduced fig.5.6),theinstantaneous emf isincreasedfor

coils whosesidesarepassingunderthesetips;theincrease canbequitelarge,especiallyif

themachineisoverloaded(large IA).Thesecoilsareconnectedtocommutatorsegments

thatarenearthebrusheswheretheairishighlyionizedduetonormalsparking.Highinter

segmentvoltageappliedtoionizedaircancausebreakdownoftheair(arcingbetween

segments). Thismaycausefurtherionizationandfurtherarcing; inseverecasesitmay

resultintotalflashoverfrombrushtobrush.Theheatfromthearccandamagethebrushes

andmeltholesinthecommutator.

Clearly,then, AR canhaveseriousconsequencesthatlimittheoperationalconditionsof

themachine.Thedesignandconstructionofthemachinemustthereforeaimatreducing

armaturereaction:

(1)Machinesaredesignedtohaveastrongmainfieldsothatrelativedistortiondueto AR

remainssmall.

(2)Themachineisdesignedtohaveahighreluctanceinthepathofthearmaturecrossflux

(armteeth,airgap,poleshoesseefig.5.1).

Thismaybedonebyconstrucngpoleswithalternatelaminaonsasinfig.5.9:withthe

amountofironinthepoletipsreduced,thefluxdensityisincreased,andthetipsaredriven

quicklyintosaturation,andhencehighreluctance.Alternatively,theairgapunderpoletips

ismadelongerbyusingpoleswitheccentricpolefacesasinfig.5.9(orchamferedfaces).

Theincreasedreluctancealsoreducethemainflux,butthereductionismuchsmallerthan

thereductioninthearmaturecrossflux.

(3)Toavoidflashovertheinstantaneousvoltagebetweencommutatorsegmentsmustnot

exceed3040volts. Machinesarethereforedesignedtohaveanaveragevoltagebetween

segmentsnotexceeding2030volts.


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(4)In somemachines,thepoleshoesaremadewithslotsinwhichanaddionalwindingis

placed,fig.5.10.Thecurrentsinthesepolefacewdgsorcompensatingwdgsare

arrangedtoflowindirectionsoppositetothoseofarmatureconductors,sothattheir

mmfs canceloutunderthepolefaceasshowninfig.5.10.

Compensangwdgsareconnectedinserieswiththearmature,fig.5.11,sothat

cancellationoccursforallloads(asIAincreases, AR willincrease,butsowillthe

compensatingwdg mmf also).

Forfullcompensation,wemust have

(Nc).IA=(

).IA >>>>>> Nc=.Z/4pa=.NC/2pa

Where Nc=compensatingwindingconductorsperpole, and =polearc/polepitch.

Computing Nc inthisway,itisunlikelytocomeoutaninteger;asmallerintegernumberisusedbecause6070%compensangisusuallysufficient.Compensangwdgsarevery

expensivetoinstall; theyareeconomicallyjustifiedonlyinverylargemachines,andin

somespecialpurposemachines.

Fig.5.8 VA=EAIA.RA Alternatepolelaminations Eccentricpoleface

Fig.5.9methodsofincreasingreluctanceatpoleps

Fig.5.10compensangeffectofpolefacewdg Fig.5.11dcM/CwithCW


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5.5Brushshift

Sometimes brushesarenotintheexactneutralposition(qaxis).Suchbrushshiftmaybe(a)

unintentional:incorrectpositioninginmanufacture,orpoorbrushfit,etc., oritmaybe(b)intentional:inveryoldmachinesandinsomeverysmallmachines,brushesareshiftedto

improvecommutation.Withthebrushesthusshifted,thearmfieldisnolongerinstrict

quadraturewiththemainfield(i.e.daxis), fig.5.12. The daxiscomponentofthearmfield

mayoppose(demagnetizing)oraid(magnetizing)themainfield; thisdependsonthedirection

ofbrushshiftrelativetorotation, and onthemodeofoperation,generatingormotoring;see

fig.5.12.

Totestforcorrectpositioningofbrushes,themachineisrotatedinbothdirectionsasaloaded

generator;iftheload,speed,andfieldexcitationarethesameforbothdirectionsof rotation,

theterminalvoltagewillbethesameifthebrushesarecorrectlyplaced.If,however,the

brushesarenotattheexactneutralposition,theterminalvoltagewill differforthetwo

directionsofrotation.

Fig.5.12Effectofbrushshi.MF:mainfield;AF:armaturefield;Ad & Aq=direct&quadrature

componentsofarmaturefield.


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CHAPTER6 Commutation

Thecommutatorisacharacteristicfeatureof dc machines.Itspurposeistomatchthe

alternatingcurrentsandvoltagesofthearmature coilstothedirectcurrentandvoltageofthe

brushesasalready explainedinchapters1and3.However,thecommutaonprocessisquite

complicated, andgivesrisetosecondaryeffectsthatplacelimitsontheoverallperformance

ofthemachine.

6.1Theprocessofcommutation

Fig.6.1showsageneralarmcoil C movingtotherightasitrotateswiththearmature;itis

connectedtocommutatorbars a and b whichmovewithit.(a)whenthecoilsidesareunder

thepoles, thecoilispartofacertainarmaturepathandcarriesapathcurrent Ia

Ia =

(b)Asthecoilsidesapproachtheqaxis(orbrushaxis),therewillbeaninstant t1 atwhich

thebrushcontacts bars a and b simultaneously;thusstartstheshortcircuitofthecoilby

thebrush.(c)Thecoilcontinuestobeshortcircuitedbythebrush; itissaidtobeundergoing

commutation.(d)As coilsidesmoveawayfromtheqaxis,therewillbeaninstant t2 at

which bar b breaks contact withthebrushsothattheshortcircuitends.(e)Coilsidesmove

underpoles,and thecoilisnowpartofadifferentpath; thecoilcurrentis Ia again,butina

directionoppositetotheoriginalone.

Clearly,then, thecoilisshortcircuitedforaninterval Tc

Tc=t2 t1

Duringthisinterval,thecoilcurrentchangesfrom Ia to Ia ; i.e. itreversesor

commutates. Asshowninfig.6.2, thechangeincurrentmustfollowsometimecurvefrom

thepoint(t1,Ia) tothepoint(t2,Ia). Depending onvariousconditionsthatwillbeexplainedin

latersecons,wemayhavelinearcommutaon (curve1), overcommutaon(curve2),or

undercommutation(curve3).

TocalculatetheSCinterval(orcommutationinterval),let uc denotethespeedofthebars;thus

uc=2rcn

where rc istheradiusatthecommutatorsurface.Fromfig.6.3,itisseenthattheleadingedge

ofbar a moves from x1 at t1 to x2 at t2;


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Thus

uc =

Therefore

Tc=

y (

(yo=

Asexpected,thelengthofthe SC interval,Tc, isdeterminedbythespeedofrotationn, the

relativedimensions of barsand

brush,andthenumber ofcommutator

bars.

Fig.6.3aidtocalculate Tc

Fig.6.1Theprocessofcommutaon>>

Fig.6.2 Reversalofcurrentincoil

undergoingcommutation


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6.2Equivalentcircuitofcommutatingcoil

During commutating,thecoil SC current is circulatesinapath composedof: thecoilitself,

risers, bars,contactsurfaces,andbrush(seefig.6.4). Asimplified equivalent circuitisshown

infig.6.5with :

Rc=coilresistance;

Ec=rotaonal emfincoil=2N(B.L.u)

Lc=selfinductanceofcoil;

r1=contactresistancebetweenbrushandtrailingbar;

r2=contactresistancebetweenbrushandleadingbar.

Thecircuitoffig.6.5involvesthefollowingsimplificaons:

1. theresistanceofriser,bar,andbrushisnegligiblew.r.tcontactresistance;

2. mutualinductancewithadjacentcoilsisneglected;

3. brushassumedtoshortcircuitonecoilatatime.

Notethatlowercasesymbolsareusedforquantitiesthataretimevaryingduring Tc;these

are ec,is,i1,i2, r1,and r2;indeed,isandpossibly ecreverseduring Tc. Also notethat

from KCL

i1=Ia is andi2=Ia+ is

sothat

i1 + i2=2Ia

asexpected.

Theterminalvoltageofthecoil vc isgiven by

Vc=ec isRc Lc(dis/dt)

Therotational emf ecissmallbecausefieldissmallaroundtheqaxis(see,forexample,fig.

5.5). Lc(dis/dt)iscalledthereactancevoltage;itisinducedbythechangein is.


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Fig.6.4currentdistribuoninbrushand Fig.6.5Equivalentcircuitforbrush

Commutatingcoil. Andcommutating coil.

Figure6.6, Fig.6.7 , & Fig.6.8


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6.3Linearcommutation(resistancecommutation)

Insmallmachines,thecoilvoltage vcis smallerthan thecontactdrops i1r1andi2r2. If we

assumethat vcisnegligibly small,then theequivalent circuit offig.6.5 reducestothatoffig.

6.6.Inthiscase,r1and r2 areinparallel sothatbycurrentdivision

1

2

2

1

r

r

i

i=

Ifwefurtherassumethat r1 and r2 arelinearresistances(whichinfacttheyarenot),then

1

2

2

1

A

A

r

r=

Wherethecontactareas A1 and A2 aredefinedinfig. 6.7. Thus

2

1

2

1

A

A

i

i=

i.e.thecurrentdivisionbetweenbarsisindirectproportion totheirrespective contactareas.

Ifintheaboveexpressionwesubstitutefori1 and i2intermsof Ia and is(seesecon6.2),

andrearrange, weget

is= ab

IA

AA.

12

(derivethisequation?)

asthecommutatorslidesagainstthebrushatconstantspeed, A1 increaseslinearlywithtime,

while A2decreases linearlywithtime. Thus is varies linearly from Ia at t1 to Ia at t2 ,

and we havelinear commutaon asincurve 1of fig.6.2 .Linear commutaonis also

called resistance commutation because thecurrentvariation iscontrolled bythecontact

resistances r1 and r2(seefirstequationinthissection).

Notethatwe derivedlinearcommutationasanapproximation based ontwoassumptions:

negligible vc andlinearcontactresistances.Theseassumptionsdonotgenerallyholdin

practicesothatweseldom havelinear commutation. Commutationapproacheslinearityin

smallmachineswheretheseassumptionsareapproximatelytrue.


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6.4 Reactancevoltage

Reactancevoltageisthevoltageinducedinthecoilduetothetimevariationof is;itappears

across Lc intheequivalentcircuitoffig.6.5 ,andisequal to Lc(dis/dt). Reactance voltage

hasagreateffectoncommutationprocess, sothatlinearcommutation(whichisbasedon

neglectingreactancevoltage)isusuallytobeachievedinpractice.Theroleofreactancevoltage

inthecommutationprocessmaybedescribedqualitatively as follows:

Thereactancevoltageisinducedbythechangeofcoilcurrentfrom Ia to Ia. According to

Lenzslaw,thereactancevoltagewillbeinducedinsuchawayastoopposewhatiscausing it,

i.e. itopposesthechangeincurrent. Therefore thereactancevoltageretardsordelaysthe

changeincurrent.

DuetoRV,then,thecurrenttendstofollowacurveabovethatoflinearcommutation,for

examplecurve3infig.6.2; thegreaterthecoilinductance Lc,thehigherthecurve.

Ifcurrentreversalisnotcomplete(i.e.currenthasnotreached Ia)whenbar b breaks

contactwiththebrush at t2, thecurvewillbeasshowninfig.6.8. This resultsinsparking

whichisexplainedasfollows:

At t2 thecoil current attempts tojump to Ia almostinstantaneously.Thisresultsinvery

high RV(why?),whichcausesbreakdownintheair.Thearcprovides apathbetween brush

andbar b throughwhichcurrentflowstocompleteitsreversal to Ia.

Sparkingisharmfulbecauseitcausesheatingandhencewearofbothbrushandcommutator

bars. It becomesmoresevereasloadincreases(asthearmaturecurrent IAincreases, sodoes

thepathcurrent Ia).

Treatmentofsparking

Insomesmallmachines,theresistivecontactdropismuchgreater thanthe RV sothat

sparkingislimitedbytheeffectofresistancecommutation, i.e.commutationapproachesthe

linearcase.

Inlargermachines,someadditionalmeansmustbefoundtolimitsparking,i.e.tocounterthe

effectof RV whichistheprimecauseofsparkingasexplainedabove.Modernmachinesuseinterpoles,whileoldermachines(andsomesmallmachines)usebrushshift; thesetwo

methods areexplainedinthefollowingsections:

6.5Interpoles (commutatingpoles,compoles)

Nearlyallintegralhorsepowermachineshaveinterpoles(IP). IParenarrowpoleswithlargeair

gapplacedbetweenmainpolesasinfig.6.9.Theircoilsareconnectedinserieswiththe


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armaturesothatthe IP fieldisproportionaltoarm current IA(thelargeairgapprevents

saturationintheiron).The IP field actsoncommutatingcoilsattheqaxis.

The IP mmf Miisgivenby

Mi=NiIA

Where Ni isthenumberofturnsineach IP coil.Thenumberofturns Ni ischosentomake

the IP mmf some 25% graterthan Mam ,thecrossmagnetizingarmaturemmf attheq

axis(seesecon 5.1);thus

Mi=1.25Mam so that Ni=1.25(NC/4pa)

Inthisway, Mi is madetoservetwopurposes:(1)theaddional 25%neutralizesthe

commutangcoilflux(whichinducestheRV).Thisisclearinfig6.10 a,b,and c:theIP fieldnot

onlyreducestheqaxisfieldtozero, butdrivesadditionalfluxinthenegativedirectionto

neutralize RV.Figs.6.10 d and e show theresultantfieldininterpolemachines,without

andwithcompensangwindings;comparethemwithfigs5.5and5.10(NB IPstreatarm

reactionintheqaxis,whilecompensatingwdgstreatarmreactionunderthepoles).

Asthemachineisloaded,thearmaturecurrent IAincreasessothatarmaturereaction and RV

increase; butthe IP field is also to IA, andwillincrease automaticallytoneutralize

armaturereaction(intheqaxis)and RV. IPswillcontinuetodotheirjobproperlyforeither

modeofoperation,motororgenerator,and for eitherdirectionofrotation,forwardor

reverse.

Fig.6.11 showsthegeneralconneconof a dc machine.Notall windingsshownarepresent

inallmachines. IP orcommutating wdgsarefoundonintegralhorsepowermachines(rated

power > one hp); compensating wdgs arefoundonlargemachinesand onsomespecial

machines; manymachineshaveonlyonemainfieldwdg, shuntorseries; compoundmachines

haveboth.The terminalsofmainfieldwdgs(shuntandseries)areusuallybroughtouttothe

terminalboxtoallowusermanipulation; theterminalsofcompensatingandcommutating

wdgsarenotbroughtouttotheterminalboxbecausetheyarepermanentlyconnectedin

serieswiththearmature.


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6.6Brushshift

Asecondmethodforimprovingcommutationtolimitsparkingistoshiftthebrushesfromthe

qaxis . The principle isasfollows:

Recallfigs.5.4and5.5whichshowhowthemagnecneutralaxis(mna)movesawayfromthe

qaxisduetoarmreaction.ifnowthebrushesareshiftedinthesamedirection, theywillbein

aregionwherethearmfieldopposesthemainfield.Atcertain locationthe twofieldscancel

out; placingthebrushesatthislocationeliminatestherotational emf ec(seefig.6.5). Thisis

notenough becausetherestillisthe RV.Toneutralize RV,thebrushesareshiftedalittle

furtherinthesamedirection; thesidesofcommutatingcoilwillthenbesubjectedto asmall

(butnonzero)fieldthatopposesthecoilflux whichinducesthe RV.Iftheopposingfluxescan

bemadeequal,the RV iseliminated.

Asamethodforimprovingcommutation,brushshiftisnotasgoodas IPsbecauseithasthe

followingdisadvantages:

1.As theload onthemachinechanges,thearmcurrentIAchangessothat AR andthe mna

shiftalsochange.Forcorrectoperation,thebrushshiftmustbechangedaccordingly,whichis

impractical.Inpractice,thebrushesareplacedinapositionthatgivesminimumsparkingatratedload,sothattheremaybeconsiderablesparkingatotherloads.

2.Fromfig.5.4,itisseenthatthemnashisinthedireconofrotaonforgenerator

operation,andinthedirectionoppositetorotationformotoroperation.Thusbrushshift

(whichisinthesamedirectionasthemnashift)cannotbeusedwithmotorsintendedtorunin

bothdirections,orwithmachinesintendedforvariablemodeofoperation:ifbrushshiftis

correctforonecase,itisincorrectfortheother!

3.Brushshi causesdemagnezingarmaturereacon(seefig.5.12).

Becauseofthesedisadvantages,brushshiftisusedonlyinsmallfractionalhorsepower

machines(ratedpowerlessthanonehp)whereitisnoteconomicaltouse IPs.Brushshiftwas

alsousedinoldmachinesbeforetheinventionofIPs.


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CHAPTER7 POWERCONVERSIONANDLOSSES

Theinputpowertothe dc machine undergoeselectromechanicalconversiontoproducethe

outputpower;theprocessyieldsanumberoflossesthatappearasheatwhichhasharmful

effectsontheperformanceofthemachine.

7.1Powerbalance

Mostoftheinputpowersuppliedtoa dcmachineisconvertedintousefuloutputpower;the

reminderoftheinputpowerislossandheat.Theprincipleofconversionofenergyrequires

totalpowerbalance

Pin=Pout + LOSSES

Itissometimesusefultothinkofpowerasflowingthroughthemachine.Powerflowisdivided

intotwostages,theborderlinebeingtheactualelectromechanicalenergyconversionprocess.

Pc=EAIA=rTd

Itisalsocalledtheinternalpowerbecauseitisdefinedwithinthemachine; incontrast,Pinand

Pout areexternalpowersthatcanbemeasured. EA and Td areinternalquantitiesthatcannotbemeasureddirectly.

Pin=Pc + LOSS1 and Pc=Pout +LOSS2

Thetotallossismadeupof 2parts:LOSS1 occursbeforeconversion,andLOSS2 occursaer

conversion.Clearly

Pin>Pc>Pout

Motoroperation

The inputpoweriselectrical,andtheoutputpowerismechanical.Partoftheinputpoweris

lostaselectrical(copper)lossesinthewindings,andtheremainder isavailablefor

electromechanicalenergyconversion; partoftheconvertedpowerislostsupplyingthelosses

duetorotation, andtheremainderisavailableasamechanicaloutputpowertodrivetheload.

Notethat


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Pmech>>>> rTL>>>> TLPc >>>>rTpm>rTd >>>>Tpm>Td

Thatis, theshafttorqueproducedbytheprimemover, Tpm,isgreaterthanthedeveloped

torqueTd;thedifferenceisthetorqueneededtoovercomefrictionandotheropposing

torques.

7.2Losses

Thelossesofa dc machineareofvarioustypesandoccurindifferentpartsofthemachine.

Althoughdifferentlossesareproduceddifferently, theyallappearasheat,i.e.theyrepresent

conversiontounlessthermalenergy.Theheatgeneratedbythelosseshastwomajoreffects:

(i) Lossesraisethetemperatureinsidethemachine,andthusaffecttheperformanceandlifeofthematerialsofthemachine, particularlyinsulation.Thereforelosses

determinetheupperlimitsonmachinerating.

(ii) Losses areawasteofenergy,andenergycostsmoney;thereforelossesresultina

wasteofmoney(intheoperatingcostofthemachine).

Lossescannotbeeliminated,buttheycanbereducedbyproperdesign; thedesignmust

alsoprovideforventilationtodispersetheheatgenerated.Thuslosseshaveasignificant

effectontheinitialcostofthemachine.

Thecostofwastedenergyinitem(ii)aboveisimportantwithindustrialmotorswherethe

powersinvolvedarequitehigh;itisnotimportantwithsmallcontrolmotorswherethe

powersinvolvedareverysmall.However,thetemperatureriseinitem(i)isimportantfor

allmotors.


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Electricallosses

Electricallossesarealsocalledcopperlosses,windinglosses,I2Rlosses,andohmiclosses.

copper lossesoccurinallwindingsduetoflowofcurrentthroughthem;theyare

LOSSarm=IA2

RA=armaturecircuitcopperloss

LOSSser=IS2RS=seriesfieldwindingcopperloss

LOSSsh=If2Rf=shuntfieldwindingcopperloss

IncomputingLOSSarm,RAincludestheresistancesofcommutatingandcompensating

windings(ifpresent).Theseriesfieldcurrent ISmayormaynotbeequaltothearmature

currentIA.

Thecopperlossinagivenwdgisproportionaltothesquareofthecurrentinthatwdg; if

thecurrentisdoubled,thecopperlossincreasesfourtimes. LOSSarm andLOSSserdepend

onarmaturecurrent, andhencetheydependontheloadonthemachine(IA increases

withload). LOSSshdependsontheterminalvoltage,andvarieswithitssquare.

Theaboveexpressionscanbeusedtocalculate copperlossesusingmeasuredvaluesof

windingresistances.Thewdgresistancemustbeatthecorrectwdgtemperature;ifthe

temperatureatwhichthelossisrequiredisnotknown, itisassumedtobe 75oC.ifthe

wdgresistanceisknown(saybymeasurement)atatemperature T1,itcanbefoundata

differenttemperatureT2 from

RR

T 234.5T 234.5

Thebrushcontactlossisalsoanelectrical loss.Sincethebrushcontactdrop Vb is

approximately constantoverawiderangeofarmaturecurrents, thelossisproportionalto

thearmaturecurrentitself(andnotitssquareasinwdglosses):

Losscontact=IAVb

Magneticlosses

Magneticlossesarealsocalledironlossesorcorelosses.Theyresultfromhysteresisand

eddycurrentsincoressubjectedtovaryingmagnetization,i.e.mainlyinthearmatureteeth

andcore,butalsointhepoleshoes(duetoarmatureslotting).

Ironlossesaredistributedinthecoresincomplicatedpatterns, sothattherearenosimple

formulaethatgivetheirvaluesaccurately.Itisknown,however,thatironlossesdependon


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themagnetizationlevel(fluxdensity)inthecores,andonthefrequencywithwhichit

alternates, f=pn.

Forthehysteresisloss,wehave

LOSShyst fBx

max

Wheretheconstantofproportionalityisdeterminedbythevolumeofthecoreandits

magneticcharacteristic(hysteresisloop).Thesteinmetzexponent x dependsonthetypeof

ironused,andrangesfrom1.5 to 2.5(usuallyaround 2);itisanempiricalconstant

(obtainedfromexperienceanttesting,notfromelectromagnetictheory).Fortheeddy

currentloss,wehave

LOSSeddy f2B

2max(laminationthickness)

2

Wheretheconstantofproportionalityisdeterminedbythevolumeofthecoreandits

electricalcharacteristics(resistivity).Clearly,thinlaminationsreduceeddycurrentlosses.

The armatureisalwayslaminated,andthepoleshoesareusuallylaminated.Ifamotoris

tobedrivenfromamodernsolidstatecontrolledrectifier,allcoresmustbe

laminated(includingpolesandyoke).

Mechanicallosses

Mechanicallossesarisefromfrictionandwindage(frictionwithair)duringrotation.They

dependonthespeedofrotation,eachtypeofmechanical lossbeingproportionaltosome

power of n. Bearingfrictionlossdependsonthetypeofbearingusedandontheviscosityofthelubricant; improperlubrication(toolittleortoomuch)increasetheloss.

Brushfrictionlossisproportionaltotheareaofcontactandtothebrushpressure; italso

dependsonthebrushandcommutatormaterials,theirstateofpolish,andthetemperature

atthecontactsurface;itisoftenthelargestfrictionloss.Windagelossesarisefrommoving

theairaroundthearmature(airfriction);theydependontheshapeoftherotatingsurface

(smoothorrough).Ventilationlossisanadditionalwindagelossduetofansandvent ducts

usedtocoolthemachine.

Strayload

loss

Strayloadlossesareadditionallossesthatoccurinthemachinewhenloaded,andcannot

beincludedwiththeconventionallosseslistedabove.Theyinclude:

additionalcorelossresultingfromarmaturereactiondistortion;


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copperlossduetoshortcircuitcurrentduringcommutation(incommutatingcoils,

commutatorsegments,andbrushes);

nonuniformcurrentdistributioninlargearmatureconductors.

Strayloadlossesaresmallanddifficulttocalculate.Theymaybeneglectedforsmallmachines,andareusuallyassumed1%ofoutputforlargemachines.

7.3Classificationoflosses

Table7.1Classificaonoflossesin dc machines.

Loss type rotational With

load

dependence

Armaturecircuitcopperloss elect No variable IA2

Seriesfieldcopperloss elect No variable IA2

Shuntfieldcopperloss elect No constant Vt2

Brushcontactloss elect No variable Ia

Hysteresisloss mag Yes constant fBx

max

Eddycurrentloss mag Yes constant f2B

2max

Frictionloss mech Yes constant powerofn

Windageloss mech Yes constant powerofn

Strayloadloss Elect&mech Yes variable indeterminate


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Table7.2Typical valuesof dc machinelossesforindustrialmotorsintherange1100KW;

lowerpercentagelossesareforthehigherratedmotors.

losses Percentofrated

power

Armaturecctelectricalloss

Shuntfieldelectricalloss

Rotationallosses

36%

15%

315%

Table7.3Typicalefficienciesofindustrialmotors.

Ratedpower KW efficiency

1

50

500

5000

75%

90%

94%

97%

Constantandvariablelosses

Constantlossesarelossesthatdonotchangeastheloadonthemachinechanges;theyare

independentofarmaturecurrent,andincludemechanicallosses,corelosses,andshuntfield

windingloss.Variablelossesare lossesthatincreaseastheloadonthemachineincreases;they

areelectricallossesincludingarmaturecircuitcopperloss,seriesfieldloss,andbrushcontact

loss.Copperlossesincreasewith I2

A,whilebrushcontactlossincreasewith IA itself.Wemay

thereforewrite

LOSSEStotal=Ko+K1IA+K2I2

A


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ThefirsttermontheRHSrepresentsconstantlosses,whilethesecondandthirdterms

representvariablelosses.Atfullload,constantlossesare420%,andvariablelossesare36%;

seetable7.2.

Remark

Strayloadlossesareindeterminatefunctionsofarmaturecurrentandspeed.Theycomplicate

classification,butaresmallenoughtobeneglectedinmostcases.

7.4Measurementoflosses

Thereareanumberofpracticalteststomeasure thevariousmachinelosses.Inmostcases,a

giventestyieldsthesumoftwoormorelossestogether;sometimesthecomponentlossescan

beseparatedbyfurthertesting.

Intesting,itisquiteeasytomeasureelectricalquantities(resistance,voltage,andcurrent)and

speed,somewhatdifficulttomeasuretorque,andquitedifficulttomeasuremagnetic

quantities(fluxandfluxdensity).Powersaredetermined,ontheelectricalside,bytheproduct

ofvoltageandcurrent,andonthemechanicalsidebytheproductoftorqueandangularspeed.

Inaloadtest,themachineisloadedatagivenspeedandfieldexcitation(i.e.fieldcurrent);the

inputandoutputpowersaremeasured.Thetotallossatthatspeed,excitation,andloadcan

beobtainedfrom

LOSSEStotal=Pin Pout

Thetotallosscanbeseparatedintoelectricalandrotationallossesbycalculating I2R products

inthevariouswindingsusingwdgcurrentsmeasuredduringtheloadtestand(hot)wdg

resistancesmeasuredpreviously.Withtheelectricallossesthuscalculated,therotationallosses

areobtainedfrom

LOSSrotational=LOSSEStotal LOSSelec

Loadtestsforlarge machinesareimpracticalintestlabs:theyrequireverylargeloads,and

wastelargeamountsofenergy.Thereareotherteststhatyieldthelossesindividually.

Inanoloadtest,themachineisdrivenbyasuitableprimemover(possiblyanothermachine)

withitsterminalsopencircuited(i.e.itoperatesasunloadedgenerator).Theinputpowerto

thetestmachineismeasuredmechanically(torqueandspeed),orelectricallybymeasuringthe

inputpowertothedrivemotorandsubtractingitslosses(whichmustthereforebeknown).If

thetestmachineisunexcitedthen Pin=LOSSmech.Ifthetestmachineisthenexcitedbutleft

unloadedweget Pin=LOSSrot;thecorelossisobtainedfrom


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LOSScore=LOSSrot LOSSmech

(Exercise:suggestatestforseparatingthebrushfrictionloss).

Ifnosuitabledrive(primemover)isavailable,rotationallossesmaybeobtainedbyrunningthe

machineasamotorwithnoexternalload;thisistherunninglighttest,orSwinburnetest.

The inputpowerwillmainlygotorotationallosses,buttherewillalsobe alittlecopperloss

(why?).Thecopperlossmaybecomputedandsubtractedfromtheinputpowertoyield

rotationallosses.Intherunninglighttest,rotationallossescannotbeseparatedinto

mechanicalandcorelosses(why?).

Asseenfromtheabovetests,itisalwayspossibletodeterminecopperlossesfromthe

measured valuesofwdgcurrentsduringthetests,andpreviouslymeasuredwdgresistances.

Windingresistancesaremeasuredbystandardmethods(voltmeterammeter,Wheatstone

bridge,etc.);thewdgtemperaturesmustbemonitoredatthetimeofresistancemeasurement(why?),orthemeasurementismadewiththemachinehot(forexampledirectlyafteraload

test).

Thenoloadandrunninglighttestsdeterminemachinelosseswithoutloadingit.Othertests

havebeendevisedtooperatethemachineatfullloadconditionswithoutrequiringanexternal

load.

Anexampleofsuchtestsistheoppositiontest(KappHopkinsontest)whichrequirestwo

identicalmachines.Themachinesarecoupledmechanically,andconnectedinparallelwith

eachothertothemains.Byincreasing theexcitationforonemachineanddecreasingitforthe

other,thefirstwilloperateasagenerator,andthesecondasamotor:thegeneratorsupplies

themotorelectrically,whilethemotordrivesthegeneratormechanically;thepowerinput

fromthemainssuppliesthelossestokeepthesystemrunning.Bysuita

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