vincent del toro - chap 06

7/28/2019 Vincent Del Toro - Chap 06

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Chopter

The d-cmachines a highlyversatilemachine. It can providehighstartingtorquesas well as high acceler ating nd deceleratingorques. It iscapable fquickreversals,ndspeed ontrolovera'rangeof4 : I isachievedwith relativeease n comparisonvith allotherelectromechanicalnergy-conyersionevices.

Theseare eatnres hat are responsibleor its us e n the reallytoughobs

nindustry, such asare found, nsteelmills. Unfortunately,the need or amechanicalectifierin the formof a commutator)o converthe a-cemf hatis nducedn each rniaturecoil o a unidirectiona loltagemakes t oueoftheleast uggecif electricmachines s wellas moreexpensive.

The principlesnderlyiugbasic orqueproductionanclnduced oltagesnthe d-c machine reoutlinedn detail nChapter3. Hererve nvesti gate heoperationalcharacteristicsftheyariousypesofd-c machines, eginningwitha descriptionfhow he direct voltage sobtained.The nfluence fthe arma-ture winding nmf.onmachine ehaviorsexploredwithparticularemphasis nits effectoncnmmutation nd ts external haracteristics.he subjectofcom-mutationoccupies positionof preeminencen thestudy ofd-c rnachinese-

Dlrect-CurrentMschines

cause without good commutationthe machineis renderedalmost useless. hemotor speed-torquecllrves are analyzedanrirlsohe various methodsof speedcoltrol. Ilirrally,the procedureor finding machineperformancethror-rghheuse of the governingequations, he eqliivalentcircuit,tlie power-flowdiagram,arrd the magnetizationcurve isoutlineclarrd illmtratecl.

6 . 1 G S N E R AT ' O NO FUNIDTRECT'ONAI.OI.IAGES

It is helpfult thestartofour studyof d-cmachineso understand orvadirect voltage can beproducedat the armrtnreoutput terrninals. Appearingin Irig.6-1(a) is a plot of the fluxdensity producedby thc fieldwincliug as afunctionof clispiacementalong the periphery of the rotor. Thc flat-topped

' i #


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252 DTRECT-CURRENTAcl,uNEs chop.

portionof the plotis attributable o theconstntair gap beb.weenhe rotorsurface nd lie'ccsfthc polepieces.A sharp lloffoccursn the ntcrpolarspace ecause f theeffectof the argeair gaps here. Figure6-1(b)depicts

Commutoioregmenl

sec . - l GENERATIONOF UNIDIRECTIONAI.OLTAGES 283

effective nvoltageproductionwith this arrangement, unlike theGramme-ringwinding. The copper segmentsare part of the rotorstructure, thereby rotat-ing with it. Any emf that is induced n the coila*a' appearsat these coppersegments. Placedin contact'withthe copper segmentsand fixedin space are-twocarbon brushesBr and 82. These are used to collect thevoitage induceclin the armaturewindingand to make it availableto the external circuit. Thecoilin lig.6-1(b) isshown infour different positionsrelative to the fluxfield.The rotor is assurned evolving at speedn in thp counterclockwisedirection.At time instant1, he emf inclucedn the coilis zerobccause ach coil

side filclsitselfat a point of.zero flur density. At instant 2,there is an emf induceclneach coilside and its rnagnitudes proportionalto the value of fluxdensity, asobtained fromlig. 6-1(a), as wellas o the veiocity and lengthof the coilsides.'rhe directiouof the induced voltagein coilside o is such that it makes thepolarity of brush81 positiue.As the rotor revolvesan additional 90 degrees,the situation illustratedin 3 of ltis.6-1(b) is found to prevail. Again note thezero voltage value.At instant 4, coilside o is underthe influenceof south-poleflux andso has an emf of reversedpoiarity induced. FIowever,note that itsattached commutator segment s norv in contactrvith brush82, u'hichkeepsthis brushat a negative polarity. A completepiot of thc voltage appearing atthe armture tenninals is depicted n ttig.6-1(c) with the fourtime instants ofltis.6-i(b) specificallyndicated. It is importantto note that, althoughth evoltage in each coilside alternatesfor each revolution,the voltage appearingat the brushes s urridirectionalbecauseof the effectof the seementedcom-mutator.t

Althoughthe use of a sirrgiecoil inconjunctionwith the commutator fur-nishes a unidirectionaivoltage, the resulting r,vavehape of rrig.6-1(c)is un-satisfactorybecause he magriitude isnot constant over the full period. Aconsiderable mprovementcan be achievcdby increasingand distributingthenumber of armaturecoils. riigure6-2(a)depictsin developed orm a trvo-polemachirrehavingeight slots on the rotor equipped withtrvo coil sides per slot,yielding a total of eight coils. Thisrepresentationis typical of the situationfound in practicalmachines. Thelower part of the figureillustratesthe man-ner in rvhichthe variouscoil sidesare joined to give. summed quantity. The

r,vindingayout shown is referredto as a waue windingfor obvions reasons.fAs a general ule the sidesof a givencoilare made to span one pole pitch (i.e.,180 electricaldegrees). Nloreover,in the doubie layerrvinding, such as theone illustratedhere, each coilis so placedthat rneside occu.pies lolverposi-tion and the other side an upper position. l'or exauiple, coilsides 1 and l0 are

tForbetterunderstandinghe distinctionilh the a-cgeneratols worthmaking.Thearuangement f FiS. 6-1(b)becomes n a-c generatorwheneachcoil side s connected o aclosedcopper ingand echbrush s made o rideon one ing. Then the positiveand nega-tivevaritionsof inducedemfsre nade o appearat the brushes nd thereforehe armatureterminls.

{Anotherfrequentlyused arrangements the lap winding.

(o)

r l l

I o l ' l @I 1,,----\l

*" r'-6Q\ \H \ o

s:-0" "'R---\s:--o'1 . \, \ ,,----l--E

r-Foh

N-{J:/

/Al\-----l It s ll l(D'

O *

: oY t s s l

u -

d=@1, gop displocemenf

(c)

Fig. 6-1. Generationof unidirectionaivoltage: (a) shape ofair-gap lux density producedby field winding;(b ) emf generatedis a single-coilarmature for fouristants of time; (c)plolof .Boas a function of time, withspecific timeinstants of (b) shown.

cross-sectional view of a two-pole machine having an armature wirrding con-sisting of a simple coil, a*a'. Coil side o is joinecl to coil side o' by a back con-nection hat isnot shown. The frontendsof eachcoilsideare joinedper-marrently o coppersegments s indicted. Notethat both coilsidesare

u

oa, isplocemenlolong ir 9o p


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N S

(c )

Fig.6-2. Generationof a d-c voltage:(a) winding layout for asimple machine; (b) schematic representation of two armaturepaths existing between he brushesat the time 6 llustrated in(a); (c) total induced armature voltageas a function of time;complete cycle is shownfor each of four coils.

sec.. 1 GENERATIONF UNIDIRECTION,ATOTTAGES 285

joincd by the bacli-enrlconnectiono constitlteonc coil. Note that the spanis 180 degrees ncl hat coil side 10occupies he lorverposition in slot 5, rvhileeoil side I occupieshe uppct'positionn slot 1.

A study of liig. 6-2(a) discloseshat the armature rvindingcomplctelycloscs l 'ttselfan d that in particulalth e l'ave n-irrdingas rvo alrnaturepathslvith respecto the brushes. 'Ihc arrcwhcaclsttachcdto ech coil side indicatethe directionin rvhichthe induceclemf causescurrent to florv.lvhena load isplaced cross he brushes. In the plan viervof Fig. c-2(a) the directionof theemf for the directionof rotationshoivn s dorvnrvrcl encath

a northpole

anduprvald berreatha south pole. lior clarity's sake the south pole is rcpeatedonce.; n theleftside he upper coilsidesre specificallyilustratecl,rvhileou theright side he coilsides ocated n the lorverportionsof the slots areshorvn. Alsobrush Bz s assumed o be restingon commutatorsegment4, and simultancous-ly brush ,B1s assuured o be in contact rvith commutator segment8. I,lxam-irrationof the crircuitryt B2discloseshat current couvergest this brush ro mtrvo directious-- from coil si de 2ancl coilside 7. lir.rrthernvestigationrevealsthat coilside2 is associated vitha path that consists f for.rr oils:8-1s,6-l3,4-11, and 2-9. 'Ihese coils aredrau'n rvithsolid linesin f,'ig.6-2(a) and aredenoted by small series-connected-c sources n l 'ig. 6-2(b). simiiarlycoilside 7 is associatedviththe remainingfourcoils:7-10,5-I4,8-12, and 1-10.These coilsare represented n liig.6-2(a)rvithbrolienlinesand in |ig. 6-2(b)by series-connected-c sources.

If attentionis .directedsolely at thefundamentalcomponentof the flux-density curveof lfig.6-1(a),it should be clear that for thctime instantbeingconsidered hc valuesof the coil voltagesare not the sime. Iiolexample, theinstantarreousalues of coils3-12,4*1I,5-14, and G-13ar e displaced ro mtheir position..of maximumvalueby 22i degrees vhile he remainingcoilsareaway by 67f degr:ees.A partial time histor.yof these coil voltagesfor variouspositionsof the armaturerelativeto the fielddistributionis clepictedn fig.6-2(c). The instant represented n tiig. 6-2(a) is identifiedas lo. Note thateach coil voltageover any full cycle appearsas a rectified rvavebecauseof theaction of the commutator. 1,'urthermore,nly the four coilson one sideof thearrnaturewindingare depicted. The total induced voltageappearing betrveen

the brushes Br and 82 at time o s the snrn of the instantaneouscoilvoltages(,8.),i.e., l,)"0 2g^ cos 22|-+ 2E^ cos 67], rvhere L'- isthe peah voltageinduced in thecoil. Ifthe conditionseading to lrig.o-2(b) are analyzedfor atime instanth - 22+ degrees ater then coils5*14and 6-13 rvillexperiencetheir peak values, vhile he emf inclucedn coils 2*gand l-iO rvillbe zero. Theinstantaneottsvalttesof the inducedemfs in thelenu'iningcoils rvillbe E* cos45 degrees. The total contributionat time lr is therefore Eo1 E^+ZE^cos 45" f 0. This total is identifiedin Fig. 6-2(c)and is less than the valueoccurring attime 16.

A glanceat lrig.6-2(c)malies t obvious thit an almostconstaut voltagenow appears between the brushes n contrast to the situationof Fig. 6-1(c).

Tololnduced oltogebetween rushes

Coil5Coi l - 16

Coil1- OCoil -12

totr tx -- art

F'' \ : i i )

r- _--tot*

tno

I I i i R o , o rr ' ; l r o n

(r,,'-i,6


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286 DTREcT-cURRENTAcHtNES

The small ripple sattributableto the smallpracticalnrachineshis nurnber svery algesoableevcnwithsensitive nstruments.

.c!on.

numberof slotsper pole. Inthat the ippleshardlydetect-

sec..2 DIRECT.CURRENTENERATORYPES 287

gap fluxverslrs ieklwindingmmf. Horvever,in the d-c gcnerator rvhcrethervindingconstantK is knorvnand the speedn is fixed,he magnctizationcurvehas come to representa plot of the open-circuitinduced armature voltageasa functionof 'r,hefielcl vindingcurrent. With K andn fixed,trq. (8-62)shorvsthat @dnd E" differonly by a constantfactor. Figure6-5 depictsa typical

O b d Fieldwinding urrent

Fig. 6-5. Illustratingthe build-upprocedureof a seif-excitedshunt generator.

magnetizationcllrve,vaiid for aconstantspeedof rotationof the armature.Itis especially mportantto note in this plot that even rvithzero fielclcurrerrtanemf is inducedin the armatrireof vlueoa. .This voltageis due entirely toresidualmagnetism,which is presentbeeurse of thepreviousexcitationhisioryof the rnagnetic-circuitiron. The linearcurve appearingon the same set ofaxes s t'he.field-resi.stanceine. It is a plot of the currentcar.rsecly the voltageapplied to theserieseombinationof the fieldl'inding and the active portionofthe field rheostat. clearly, then, the slopeof the linear curve is equal to thesum of the field-lvindingresistance l and the activerheostat resistance ?,r..The voltageOo due to residualmagnetisrnappcarsacross he fielclcircit andcausesa fieldcurrent Ob to floiv. But in accordance vitlithe magnetization

curve this fieldcurrent aids the residualflux and thereby produccsa lalgeriuducedemf of valrtec. In turn this increasedemf causesan everr ergcr fieldculrent, which createsmore fluxfor a iarger emf,etc. This processof voltagebuild-up continuesuntil the induceclemf proclucesust enough fielclcurr.ent osustain t. Thiscorrespondso poinl/in Fig.6-5. l(ote tirat inorderfor th ebuild-up plocess o talie place thrce conditionsmust be satisfieci:(1) Theremust be a residuallux. (2) The field rvindingmmf mustact to aid thisresidualflux' (3) The total fi,eld-circuitesistancemust beless han the criticalvalue.The criticqlJeldresistance s that value rvhich makes the resistnce line coin-cide with the linear portionof thesaturation curve.

rn addition to the shunt generatorthere are the other generator trpes*

6 . 2 D I R E C T. C U R R E N IG E N E R ATO RYPES

The d-c machine functionsas a generatorwhen mechanicalenergy is suppliedto the rotor and anelectrical load is connected&crosshe rmature terminals.fn order to supply elect,ricalenergy o the load, horvever,a magnetic fieldmustfirst beestablished n the airgap. The fieldis necessary ecause t servesas hecouplingdevicepelmitting the tlansfer of energyfrom the mechanicalto theelectrical system.There are trvo rvays n rvhichthe fieldrvinclingmay be ener-gizedto produce he magnetic field. Onemethod is to excite thefieldseparate-ly froman auxiliarysortrce as depicted in the schematic diagramof lig.6-3.

SeporoteD-Csotrcey'

T^-]I Hilme I

LT:IJI ertmeII moverI

Fig. 6-3, Schematic diagram ofaseparately xcitedd-c generator.

But clearly this schemes disadvantageousbecauseof the neeclof anotherd-csource. Afterall, the purposeof the d-cgenerator s to make availablesuch asource. Therefore,nvariablyd-c generatorsare excited bythe secondmethodlvhich involvesa processof self-excitation.The rviringdiagram appears nli'ig.6-4, and the arrangeuientis called lhe self-erc'itedh,untgenerator. Thewordshunt is used because he f ieldrvinding appeel's nplrallel u'ith thearma-ture winding. Thatis, the ttvo windings form shunt connection.

To understand horvthe self-excitationprocess alies place rvemust startwith thearagnetiza"tionurueof. he rchine. Sometimeshis is calledLhe aturq,-tion cur'e.Strictlyspeaking, he magnetizationcurverepresentsa plot of air-

Fig. 6-4. Schematic diagram of aself-excited shunt generator.

Mognetizolionurve

Field


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288 DtREcT-cURRENTAcHtNES chop.

the compoundgenerator and the series generator. A compound,generator s ashunt generatorequipped with a serieswindin'g.The serieswinding is a coilofcomparativelyferv urns lvoundon the same magneticaxis as the field windingand connect ed n serieswith thearmaturervinciing. ConsultFig. 6-6. Because

SCC. .3 DEMAGNETIZINGFFECTT THE ARMATUREWINDTNGMMF 289

increasedarmature currentflows,n order to neutralizethe armature windingresistancedrop as rvellas the voltage drops occurringin the feeder rviresleading to the load. In such cases he gerrerator s usually referreclto as acumulatiuelycompounded generator because the series held aids the shuntfieldflux. If the series ield connectionrverereversecl,ts flux rvouldopposethe shunt fieldflux in whichcase he configurationis referreclo as a d,!fer-entiallycompounded generator.

By imposingthe appropriateconstrainton the counectiondiagramdepict-

ed in Fig. 6-6(a),we can ideniifyany one of the three modes of operationofthe d-c generator. Thus in addition to the armature winding we have thefollowing:

' compound generator:shunt and series ieldwindinEsshunt generator: shunt field rvindingseriesgenerator: series ield windinf

since the seriesgenerator is rarely used except for speciar applications,allfurther treatmentof generators s confinedo the shunCarrdcompound modes.

6 - 3 D f A , I A G N E T I Z I N GF F E C T F T H EAR MATUREW'ND'NG MMF

The armaturewindingmmfproduceswo adverseffects:t cuses net ed.uc-tionin the fieldlux,and it"makest more difficultor the armaturecurrentnthe coilso commutate.we turnour attentionto the firsttfthesehere; heproblemof commutations treated n the next section.

A glanceat Fig. 6-6(b)sliows hatthe flowof current in the armaturewindingproducesn ampere-conductoristributionhat makes he armaturebehave ike a solenoid.The associated mf isdirecteddownrvard.long hebrushaxisand n a positionof quadratureo thefielclaxis. If therewerenosaturationof the iron present,he effectof thiscross-arrnature

mf rvouldbemerely o cause distortionof the flux.Horvever,n nrostpracticalmachinesoperationoccurs roundhe knee rf hemagnetizationurveand asa resultanet demagnetizationakes place. To understandwliy thishappens, onsiderthe situationllustratedn Fig.o-7whichs that o f a shuntgenerator eliveringcurrent o a oad the atternotshorvn).fhe armaturemrnfrvaves assumedobe triangular.This is a validassumptionvheneverhe numberof surfacearmaturec


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. 292 DTRECT-cURRENTACHINES chop.

mutation, deterioration ofthe carbou brushes and the copper commutatorsegmettts an rapidlyset in. This c&uses e\cresparkingand thereby rendersthe machine useless. Even such an important characteristic as themaximumtorque islimitedby commutation ratherthan by heatiug.

J

Fig. 6-9. Illustratingthe commutat ion problem: (a)coil 1-10must undergoa completecurrent eversalas t advances ounte-ciockwiseo the left sjde oflhe brush axis; (b) for thepositir-rnshown,coil 1-10 s short-circuitedhrough segments and I by81, and coil 2-9 is shcrt-circuitedhrough segments4 and 5by /lz.

sec.-4 coMMUTATToN293

commntation isconcernedwith providinga suitable ransitionof thearmaturecurrent n acoil roma value I"f a to a valueof -1"/a as t passcsbeneatha brush romone pole o an adjacentpole. A glanceat Fig.6-g(a)makes t evidenthat whencoil 1-10passes eneath hebrushes ndoccupiesthe positionnowbeingoccupied ycoil 15-8,he currentn the coil rvillhavereversed omplctelys nclicatedy thecross-clot otation.Commutationofthe current romcoil 1-tr0beginso takeplace vhenbrush1lrmakescontactwith commutatorsegment1 as sholvn n Itig.6-g(b). Notethat when thishappenscoil 1-10 sactuall;'short-circuitedy brush Brthroughsegmenis8 and 1. Allcommutatorsegments re nsulat edrom one anotherby a suit-ablematerial. Asimilar situationoccursat brush82 rvhereoil 2-g isbeingshtrt-circuited.Because f thisand n the interestof preventingargecircu-latingcurrents nthesecoils, vhich nturn cancause evere parkinggs thecirculatingcurrentsare interruptedupon eavinghe brush, he coilsunder-goingcomrnutationhould befreeof voltagesources.The time instantde+picted n lrig.6-9(b) s 22fdegreesater han that shorvnn lfig.6-2(a). I,Iencecoils1-10and2-9 findthemselvesn the nterp olarpace here he flux densifuod*+'.producedby the fieldmmf iszero. Accordingly,no Bluvoltages inducd&.inthese coils romthis source. However,he presence f the armature"Ud .causcs he resultantluxdensityo havea finitevaluen the intcrpolarspae'tuas s evidentron fig.6-7. sincehe polarityof this flr.rxs the s&mes hat of

the main fieldpolervhich heshort-circuitedoilsare eaving,an emf is in-duced hat actso maintaincurrent lown the same iirectionas existed eforecommutationbegan. Thereforehis inducedemf clueo the armaturemmfacts to hinde rcommutation;t becornes ore difficultor the coilcurrenttoreverseby the time it leaveshe brush.

fypes of commutstion

There are tr,vo ypes of commutationpossible:resistancecornmutationandvoltage commui'ation.Nloreover, the latter may be divided irrtothe twoclassesof undercommutationand overcommutation.The distinctionbetween

these types is depicted by the variouscommutationcurvesof Fig. 6-10.Curve a representsinear commutation,and it occurs only rvhenthe brushcontact resistance s the exclusiveactor irrfluencingcommutation. All in-duced emf's fromwhatever sourcesmust add to zeroand the coil resistancemust be negligiblecomparedrvith the brushcontact resistr,nce.lnder theseconditionsthe current in the coilchangesuniformlyduring the commutationperiod ?". The mechanismof commutationby tliismethod is illustratedinIrig.6-11.rfigure6-11(a)depicts he situationjust beforecommutationof thecurrent in coil 2-9is about to occur. Brush 1]2 sresting on commntatorseg-mert 4, and of the total armaturecurrent1" florving hroughthis brush cemeshalf from one armaturepath involvingcoil 16-7 and theremaining half comes

t a l ,l "4

J

r ^ - 9r 6 t

7{.) /BA r/

N S


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294 DTREcT-cURRENTAcHtNEs chop.

Leodingbrush ip

Fig. 6-10. Commutationcurveof coil 2-9 inFig.6-l). )uringthe commutationperiod the cur.ve s a plot of the cirr:ulating

:' current in the sholt-circuitedcoil undergoing cornniutation.

tflom the secondpath involvingcoil 2*9.The direction of rotationof thearnaturevith especto the brushs owards he eft.Depictedn rig.6-1 (b)i&fhesituationvhere 5 per centof the brush s n contact vith commutator

Fig.6-ll. Illustratinglinear commuttion in coii 2-):(a) conditionsust beforecommutationbegirrs;(b) conditionsat a point one-quarterthroughthe comnruttion perioti; (c)conditionsat e point halfwaytlirough thecommutationpeliocl.

sec , -4 coMMUTATToN295

scgment . The contactesislancef thatpartof thc brushsurfacc nconttct'withsegment isthree imesas argeas he resistancef the brushn corrtactrvithsegment . Ilencedivisionof the currentcoming romthe trvoarmtrrcpaths akcsplacen accordu,ncevithhis ratio. Thushe current1o/2conringfrom the righlsidedividesat junctiono inthe ratio of3 : 1 so hat thecurrcntpassingo .82romsegment rom his sour.t' 1 1" I"ti s42 or5.

'fhcportiorr assing

to 82throughsegment *X*or! r". Similarly,he crirrent-foriginating

from the armaturepath on the eft sidesplits,so that ?^';*! 1" flowso B,throghsegment ana |* "r 1"florvsrom to to segment and thence

to Bz.Thenet current hat florvsromsegmen 4 to Bzisherefore! l, + ! eR / t f

or i 1",rvhereashe net currerrt o Bzrom segmeut is1j * 1j or'-u. The+ - 8 8 - - 4 - " -

rcsultarrturrent n coil2-9 flou'sro mo to b antls equal 2 l" - L- Ior r - v i l u \ r b r r u r r O L ( , t , g - - g f o O f 7 .

consequently, ne-quarter hroughhe periodof commutationhe current ncsii2-9 haschangedrom T to . Iieen n mind thatthe commutationurve

is a plotofthe current nthe short-circuitedoilasa unctionof time.Appear-ingin lrig.cli(c) is the dislributionof currentshat prevailat a tirnemidrvaythrouglithe commutationperiod.Note that nowthe currentin the short-circuited oil szero.

curve b in lig.6-10 representsesistance ommutatio'. It is the curvethat results vhenhe resistance f the short-circuitedcils uot negligiblecompared vithhe brush contactesistance.Notetht at the leadingbrushtip the slope f curve s steeperharr hat of curveo, u,hichndicateshat thecoil resistancenhanceshe current eversal.This isapparent rom anexam-inatiouof lrig.6-11(b) vheret isseen hat at junctiona the presence f coilresistance eans hat morecurrent lorvso segment . I-Iorvever,t the trail-ing bruship (or duringthe second alfof the commutationperiod) hc coil

resistanceerveso retardthe currenteversal. Thecurrentdensity, vhichsrepresented -vhe slopeof the commutationurve,s therefore igherat boththe leadingand railingbrushedgesor resistanceommutation.

The commutationcurvedenotedas c in I'ig.6-10 s described s und,er-commulat'iont is a formof voltagecommutationn rvhichcurrent reversalhas beendelayed y the actionof the errfof self-inductionn the short-cir-cuited coii oraf lhe Bluvollage nducedn the short-circuitedoilby the fluxproducedby thearmaturemmfor ofa combinationof both. A deceleratedcommrttationf this kind ischaracterizedy highctirrentdensityat the trail-ing bmsir tip, r vhichcan prornote detelioration


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296 DTREcT-cURRENTAcHtNEs chop.

A scheme hat is frequentlyused to neutralizethis emf of self-inductionand the effectof the armature mmf is the inclusionof smallpoles ocatedonthe brushaxisanclenergizedby a coilcarryingthe armatnre current. Becauseof tlreir locationancl unction,these poles are called nterpolesor unnmutatingpoles. The useof armature-currentexcittion isdictatedby the factthat boththe emf of self-incluction nthe short-circuitedcoil and the flux inthe bmshaxisproducedby the armaturemmf areproportionalto armaturecurrent. Forgeneratorctionthe polality of the interpolemust be the sarne as that of thefield polento rvhichthe coil ismoving. liigure6-12depictsthe situationfor a

Fig. 6-12. The influenceof interpoles on the resultant flux-density vaveof a d-c machine.

two-polemachine. It is helpfulto compare the resultant flux-densitycurvehere with that appearing inliig.6-7. Note that the value of the fluxdensityon tlre interpolaraxis in Fig.6-12 s opposite to that occurring in lrig.6-T rfthe rnagnitudeof the flux density producedby the interpoleis adjusteclpropcr-ly, it can be made to neutralizethe emf of self-inductioncompletely.of coursethe effect of the armaturemmfhas already been neutralizedin the representa-tion of ltig.6-12because he resultnt flux density is shorvnto be of oppositepolarity. with such an adjustmentthe type of commutationthat prevailsislinear commutation,provided that the coil resistancecomparedto the brushcontact resistance is incousequential. Othelwise resistance commutationtakes place.

A considerable mprovementin the commutationprocesscan be achievedby increasinghe interpolefluxto the poiut at u'hich, inaddition to cancelingthe effectsof the emf of self-incluctionand the rrmaturemmf, there is incluceda voltageequal o trvice thebmsh voltage drop, 2I"Ra. Under theseconditiorrsthat specialconditionof ouercetmmutati,onesultsthat leads to a r'llueof zero

sec. -4 coMMUrATroN 297

currentdensityat the trailingedge f the brush.Thissituations denoted ycurved in lfig.6-10. (ote that thecurrentn the eoilundergoingommutationhas already eachedts valueof -1"/2 before he coil eal'eshe brush. Thisresultsn nosparhing t t he trailingedge f the brushand representshe mostfavorableconditionor goodcommutation.

Fig. 6-13, Illustratinghe arc-type


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.5 COMPUTAT'ONOFGENERAIORPERFOR/r4ANCE

Appearingn Fig.6-14s theequivalent ircuitof the compoundenerator.The armature'windingis replacedby a source voltage havingthe inducedemfz" and a resistance ?", vhichrepresents he armaNure ircuit rcsistance.tThe

Fig, 6-14. Equivalentcircuit ofthe compoundd-c aenerator.

series ields replaced y its resistanceR.", ndthe same or the shunt ield.Thegoverningquationsor determininghe performancere he olorvinq:

m ZD o : # n : K r Q n

OUm Z

f : #" - f o: KI QI "2r aVt : Il " - I"UI"+ R, )I ' : I t * I

sec.-5 COMPUTATIONT GENERATORERFORMANCE99

The porver-flowiagram or the d-cgenerators depictedn Fig. 6-15.Notethe similarity tbears o that of the synchronousenerator.The fieldwinding losss includedn the powerlowdirectlybecauset isassumedhat

Bor P.= EoIo1- -1ff60

,----^-----t l' ISino*Pt Pe=Vllt(electricol' ^ vrlr

Fig. -15. Power-flowiagramof lhe d-cgenerator.

the generator s self-excited.of course, fthe field rvindings separatelyexcited,the fieldlo-qsesre not suppliedfrom theprime mover andso must be hanciledseparately. h{oreover,note that thefield lossesare representecln terms of theproduct of the fieldterminalvoltageand the fieldcurrent. 'fhis ensures hatthe fieldwinding rheostatlossesare includedas well.

EXAMPTE. I'rhe magnetizationcurve of a 10-krv2b0-volt d-c self-excitedshunt generatordriven at 1000'rpmis shorvnin Fig. G-16. Each verticaldivision represents20 voltsancleach horizontalunit represents0.2 ampere. The arnatre circnitresistances 0.15ohm and the fieldcurrent is1.64amperes vhen the terminalvoltage is 250volts. dlso, the rotationallossesare knorvnto be equal to b40rvatts. Irindat rated loarl (a) ihe armature inducedemf, (b) the developedtorque, (c) the efficiency.Assumeconstant-speedoperation.

(6-3)(o-4.,

\o-D/(6-6)

These includethe two basic elationshipsfor inducedvoltage and ele'ctromag-netic torque as developed n Sec.3-4. Equations (G-S)and (6-6)are merelystatements of I(irchiroff'svoltage and current lal's as they apply to theequivalent circuitof lig. 6-14. ror the compc.rundenerator the exprcssionfor the air-gaplttxmust includehe effectof theseries ielclis vellas he shuntfield. Thus

: t F " * Q " (6-z;1where ,denotes he fluxproducedby the shunt fieldrvindingand e" denotesthe fluxcaused y the series ieldwinding. l'ortheshunt genelator, of coursc,, is zero n Eq . (6-7)and so too is 11" n Eq. (6-5).

tThe armature-circuitesistancencludeshe armature indingesistance,nterpolewindingesistance,ompensating'inding esistance,lus the effect f thevoltage ropin the carbon rushes.

fAlgebraicummations permittednlyrvhen aturations negtigible.

298

(a) With thegeneratoreliveringatedoadcurrent t follows

, 10,000t " : f f i w a t t s : 4 o a m P e r e s

Ilencefrom Eq.(6-6)he armaturecurrent st , "t' : 40 + 1'64 41'64amperes

The inducedarmaturevoltagehen ollowsrom Eq.(6-5):Eu : Vt + I"R": 250+ 41.64(0.15)256.26oits (6-8)

(b) To determinehe developedorque t is firstnecessaryo computeheelectromagneticower E,1 l'hus

Eofo= 256.25(41.64) 10,700watts

Solution:that

P mechonicol)

ri!

i t '


11/24

30 0 DTREcT-cURRENTMAcHtNES chop"

o'-1-? 5 6 7 8Fig. 6-16

The power-florviagram revealshat this powermay alsobe foundfromEoIo Po IZR"* V,I : 10kw + (41.64)10.15250(1.G4)

: 10kw + 261+ 410 10,671vatts (6-O;

whichchecks loselywith the precedingcalculation.Hence he developedtorque s

ryt E"Io 10,7'ml' :ffi: ffi : 101.5ewton-meters (o-to

(c ) The efficiencyis found from Eq. (4-27),r'hich for the d-c generatortakes the form

sec. -

fn this case

EXTERNATENERATORHARACTERISTIC.OI..ITINEARNALYSIS 30I

f losses:Prot I\R"*VrI: 540+ 261+ 410 1211warm

"Hence

n : t -l 2 l l - 1 ? l l

id;mo 540 I - ffi: 1- o'108 o'8e2

The efficiencys therefore g.2per cent.

6 .6 S X T E R N A G E N E R ATO RC H A R A C T E R '5 T I C .

N O N 'N FA RA N A Y 5 I 5

Fieldurrenf

The externalcharacteristicofa generatoris a descriptionof the manner in

which the terminal voltage varies with armature current. A plot of theexternalcharacteristicof self-excitedshunt generatoris shorvnin tlie righthalf of !'ig. 6-17. The drop in the curve is attributable to.three factors:the

n: -#+H; ArmotureurrenlFig. 6-1?. Derivationof the extelnal eharacteristicof a self-excitedshunt generator.

Field esistonce

(6-11)

,


12/24

302 DTREcT-cURRENTMACHTNES chop.

effect ofthe arrnature circuit resistancedlop, the demagnetizing actionof thearmature winding mmf, and the decrease nfieldcurrentcausedby the result-ing drop in terminalvoltage associatedwith the first two factors. It isas-sumed that the generatoris drivenat constant speed.

The preciseway in rvhicli theseactors combineto yield a stabie operatingpoint can be understoodin the graphicalreprescntation appearingon the leftside of ltig.6-17. Assume that the followinginformation is available: armatttrecircuit resistance,field cicuit resistance, magnetization curve, and theequivalent fieldcurrent that represents he demagnetizationcaused by thearmaturemmf (i.e.,1). 'Ihe last item is available eitherfrom the designdataor an appropriate test. The intersectionof the field resistanceine with thenonlinear magnetizationcurve shor'vs hat at no-load the equilibrium fieldcurrent is 1o corresponding to the no-load terminalvoltage

-[zo.When the

load condition is such tha,t the armaturccurrent is 1or, he externrlcharacter-isticshows hat the terminal voltagehas the value l'r. Extensionof a horizon-tal line at the 7rlevel resultsn a point of intersection with thefield resistanceline identified asO'. The projectionof O'onto the fieldaxis discloseshat thecurrent florving n the field circuitis now I. A comparisonwith thevalueatno-load makes it ciear that a reductionoccursequal to

AI: Iro r. ' (6-12)

sec. - EXTERNAI.ENERATORHARACTERISTIC.ONTINEARNATYSIS 303

point b parallelto the fieldresistanceine anci ntersectingthe magnetizationcurve in two places. Triangle oab lnay then be translateclto position o,abtaking care o lieepo' o' the fieldresistancerineanclb on the magnetizationcurve' The terminal voltageis the ordinate val'e corresponclingo point a.

-By repeatingthis procedurefor various values of armature current the com-plete characteristics obtr,ined.

A similarproceduremay be used to describe he external characteristicofthe self-excitedumulativelycompoundedgenerq,tor.very often the contribu-tion of the series ield is respornibleor a risingexternalcharacteristiclsuchasthe one depictedon the rightsideof Iig.6-lg. Thischaracteristiccan also be

ArrnolurecurrentFig. -fB. Derivationof the external chartcteristic of abumul_tively comporrndedgeneru or . (

explained n termsof thesame nformationthat is usecl or the shunr generator,but in rdditionnformationabout the series fielcicontribtitiorris requileci,usuallyexpressedn terms of anequivalent lieklcu*e't. TheIast quantity isreadilywrittenas

To find the net ield current, vhichn turn is responsibieor producinghe air-gapfluxthat provideshe inducedarmaturg-rq.ltageo, t isnecessaryo sub-tract from/r the demagneiization ffecttlg)of.the armature rnmf.Thus

I rct : I 1- I a (6-13)Or expressinghis moregenerallyn termsof the field current existingat no-Ioad.we canwrite

f y net : I o- AI - L a (6-14)

The induced armature voltagefor the specifiedoad conclitionEol is thenfound on the nonlinear open-circuit characteristiccorrespondingto 1out.This is representedn Fig. 6-17 by point b. Upon subtractingfrom Ea thearmature circuitresistance drop Inr&",the terminal voltage yl results. The

/orRodrop isdenotedby line ab n Fig. 6-17. It shouldbe noted that thereis

only onepositionin the vicinity of theupper portion of the magnetizationcurve where triangleOtabvtlllproperly fit,between the field resistanceline andthe magnetizationcurve. In fact it is thisposition that defines the equilibriumpoint that is being described. - ... ,.'.

On the basis of the foregoing discussiont can be seen that the externalcharacteristiccan be derived from the magnetizationcurve, thefield resistanceline,and knowledgeof. a and 1?.. To frnd the terminalvoltagecorrespondingto any specified,alue of 1o, irst constructthe triangle Oab at the originasshownin Fig. 6-17. Side ab s equal o I"Roand side Oo s equal to the amountof demagnetizationassociated rvith the specified1,. Then draw a line through

tr, ftt" (6-15)where n sthe fieldcurrentequivalentf theseriesieldmrnf,-ly'*lenotesenumberof turnsof theseriesieldper pole,N denoteshe numberof shuntfieldurns perpole,and 1" s thecurrent lorvinghrough he series ielcrwind-ing. Often1" s equal o the arrnrtlrrecu'rcnt,brrtsolretimesportionof the

foften referredto as ouercompounng.

Field esistonce


13/24

304 DtREcr.cuRRENTA,rAcHtNEs chop.

armature current s divertedthrougha lowresistance hunt(calledadiuerter)placedacross he series ield windingn orderto limit itscontribution.

At no-load heoperatingpointison the magnetizationcurye. Theno-loadterminalvoltages identifiedas 7oand its correspondingield current as Ie.It is helpfulto thinkof this pointas identical with theno-loadpointof theself-excitedhuntgenerator.Nextconsiderhat loadcurrents allowed o flowso that thearmaturecurrentbecomes o1, orrespondingo whichthe ter-minalvoltagebecomes!Zras shown n lig.6-18. Wiih theassumption hat(Vu I") is the newequilibriumpoint,it follows that thefield current isgreaterby the amount A1 whichyieldsa total current in thefield windingof valueIr : Is * AI. The plussign or A1 always appearswhenever he externalcharacteristics a risingone. The current1r s associated ithpointO'onthefield resistanceine.

To the shuntfield currentmustnow be addedheeffectofthe seriesield asexpressed yEq. (6-15).Thisyieldsa total main axisexcitationexpressedy

6.7 D'RECI-CURRENTA,IOTORANA[Y5I5

'a d-cmotor sa d-cgeneratorith hepowerlow eversd.n thed-cmotorelectricalenergy s convertedto mechanicalform. Also,as is the case of thegenerator, there are three types of d-cmotors: the shuntmotor, the cumulatiue-ly compoundedmotor, and the seres motot Thcompound motor isprefixedwith the word cumulativein order to stress

hat the connectionsto the seriesfield windingare such as to ensure that the series ield fluxa,id,she shunt fieldflux' Theseries motor, unlike the series generator, finds wide application,especially ortraction-typeloads. Flencedue attention isgiven to this machinein the treatment that follor,vs.

The performanceof the d-cmotor operating in any one of its three modescan convenientlybe describedn terms of an equivalent circuit, a set of per-formanceequations,a power-flowdiagram, and the magnetizationcurve. Theequivalent circuitis depictedin Fig.6-19. rt is worthwhileto note that now

Fig. 6-19. Equivalentcircuit ofthe d_c motor.

the armature induced voltage is treated as a reaction or counter emf. observethat the defined direction of .I" is reversed.ron the case for a d-c generator.The generated voltage is caused by the relative motion of the rotor withrespect to the magneticfield,and its polarity is independent of the directionof armature current. By imposingconstraintssimilarto those applied to the

d-c generator,we obtain the correctequivarent circuit for the esired modeof operation. For example, for a series motor the appropriate equivaientcircuitresultsupon removing .R rom the circuitryof iS.

-6_fS.

The set of equations needed o cornputethe performanceis listedbelow.

Eo : KnQnT : KrQI"Vt: Eo+ I"(n"+ n, )j " : r l i

(6-16)

The net field current, rvhich sresponsible or the armatureinducedemf,isfound bysubtractinghe demagnetizing ffect ofthe armature mmf. Thus

I oet : f t - fn (6-17)

Correspondingo 1 o"t s the induced armatre volt ageZ'r. The terminalvoltageis thenfound by removing hearmature circuitresistancedrop from,81o, hichyields7r. The I.r(R,* ft,) dropis represented y line obn Fig.6-18.

The externalcharacteristic anbe derived by followinga procedure imilarto that describedor the shuntgenerator.Construct triangle Oabat theorigin.Line obs equal o the armaturecircuit resistancerop for thespecifiedrma-ture current.LineOa s equal o theresultantof the magnetizingeffectoftheseries ield and the demagnetizingffect ofthe armaturemmf,i.e.,

, O o : I " - f a (6-18)

Then through drawa lineparallelo the field resistanceine interscctinghemagnetizationcurve at pointb. Dropping dowrtfromb by the 1,1(,R'+ R-)-dropgives he desired erminalvoltage 7t. A comparisonwith theprocedureemployedor the shuntgeneratordiscloseshat the triangle Ools placedonthe left side of the originrather than theright side. Thisis dictated bythefact that the baseof the triangleforthe cumulativelycompoundedeneratorrepresents net magnetizationather than a net demagnetization.

r t : I t* F; r " : r, * I ,

(6-1e)(6-20)(6-21)(6-22)

305

sec 6-7 DIREcr cURRENToroRANAr sts302


14/24

306 DREcI-cURRENT,AcHlNEs chop.6

The firsttrvo equationsare identical with those usedn generatoranalysis.Note, however,hat the next twoequationsare modifiedto accountfor thefact thatfor themotor7 s the appliedor source oltageand as suchmust beequal o thesumofthe voltagedrops. Similarly heine current,s equal o thesu'mra,lher han thedifrerence f thearmature currentand field currents.

The power-florviagram,depicting he reversedlow from that which oc-cul's n the generator,s illustratedin Fig.6-20. The electricalpowernput

sec.6-7 DIREcr-cURRENToroRANArysts302

Solution: (a) The torquecan be cornputedrom Eq. (6-10),but wefirstneed &'".Hence

Eo : Vr - fo&o:230- 73(0.188)23 0 - lB.7 216.8 oltsAlso

2trn ZrrfilO]l'- : td : t : rza adlsecTherefore

- _ Eoro_ 216.3(73)o)tu 120

,: 132 newton-meters

Io2t o+Rr V I r

P.: EoIo: T.or: T( *I)

(b) , KpQn#ol*":fr orrrsoi.' .@: ?l9fs0)882(1150)

(c) From the power-flowdiagramP"ot: P* - Po : Eofo - 20(746)

(d) First find the sum of tlie losses.

: 0.0128 eber

: 15,800 74,920: 880watts'fhus

Po: To


15/24

Hence

ConsequentlyEL: V,- ILn": 230 91.3(0.188)212.8olts

Returningo Eq.(6-19)we cannowormulate heratioKt@'n'Knn

fromwhich the expressionor thenewoperatingspeedbecomes

"': u$,,,ffifrnso: I4t5pm

,6 -8 A,IOTORPEED.IORQUE

CHARACfER'5IICS.. SPEEDC O N T R O I

Howdoeshed-cmotoreact o theapplicationfa shaftoad?whatis hemechanismy whichhe d-c motoradapts tself to supplyo the load hepowert demands?The answerso thesequestions an be'obtainedby reason-ingin termsofthe performancequationshat appear np. 305. Initially ourremarksare confinedo the shuntmotor,but a similarineofreasoning ppliesfor the othe:'s.For our purposeshe two pertinentequationsare those ortorque andcurrent. Thus

308 DrREcr-cURRENTACHTNES chop.

To obtaininformation about.&'o,we mustdetermine hechange n /", if any.By theconstant-torque onditionwehave

sec.-8 MOTORPEED.TORQUEHARACTERISTICS.PEEDONTROT309

(6-24)

The only variables nvolved are trrespeed n and the rmature cn'r.ent1" andits effect /a. At ratetl output torque the armature cnrrent is et its rated

the manner in which the armature current is made to assume just the rightvalue. In this expression Vr, Ro, Kn, and.iDare fixed.n value. Therefore ihespeed s the critical variable. If, for the moment, it is assumed that the speedhas too l'w a value, then the numerator of Eq. (6-28)takes on an excessive

"value and in turn makes 1. larger than required. At this point trre motorreacts to coruect the situation. The excessive armature currer,t produces adeveloped orque whichexceedshe opposingtorquesof frictionan windage.rn fact this excessserves as an accererating orque, which the r proceeds oincrease he speed o that levelwhichcorrespondso the equilibrium

value ofarmature current. rn other words,the accelerationorque t".or,'". zeroonlywhen the speed s at that value which by lrq. (6-28)yields jus| the right i,needed to overcomethe rotationallosses.

' consider next that a load demanding rated torque is suddenly applied tothe motorshaft. clearly, becanse he deveroped orque at this instant is onlysufficientto overcome friction and windage and not ihe load torque, the firstreaction is for the motor to losespeed. In this way, as Eq. (6-28)reveals, hearmaturecurre't can be increased o that in turn the electromagnetictorquecan increase. As a matter of fact the appliedload torque "u,,."."th. motor toassume hat value of speedwhichyields a current sufficientto produce a de_velopedtorqueto overcomethe appliedshaft torqueand the frictionaltorque.Power balance is thereby achieved, because an eq*ilibrium condition isreached whre the electrmagneticpower E,Io is equat to the mechanicalpower developed, ?c.,-.

A comparisonof the d-c motor with the three-phaserrductionmotor indi_cates that both are speed-sentiue evices n response o applied shaft loacls.An essentialdifference,holvever, s that for the three-phase 'd.uction motordeveloped torque is adverselyinfluencedby the porver-factorangle of thearmature current. of courseno analogoussit'ation prevails in,the caseof thed- cmotor.

on the basis of the foregoingcliscussio'it should be apparent that thespeed-torquecurveof d-cmotorsis an important characte.isiic. eppearing inFig. 6-21 are the general shapes of the speecl-torquecharacteristicsas theyapply for the shnt, cumulativelycompounded, and series motors. l.or thesake of comparisonthe curvesare drarvn through a common pointof ratedtorqug and speed. An understandingof wliythe curvestahe t-heshapes andrelative positionsdepictedin trig.6-21 readilvfollowsfrom an exl,minationfEq. (6-19), vhich nvolvesthe speecr. ,'ortlie shunt motor the speecl quation

can be writtenas

n : = ! " - V ' - I " R rKeQ-n KnQ"n

Kl": KrQ'IL

t b lI'": ,1": Olr73 91.3 mPeres

, T : K y f o

, V, - KEant o : -R ,

ELEo

and

Notethat the ast expressionesults rom replacingE, with Eq.(6-19)n Eq.(6-21).Withno shaftoadapplied,he onlytorqueneededs that whichover-comeshe rotationalosses.Sincehe shuntmotor operatest essentiallyon-stant flux,Eq. (6-20)ndicates hat onlya smallarmaturecurrentis requiredcomparedwithits ratedvalue o furnish theseosses.Equation(6-23)eveals

(6-20)

(6-23)

sec -8 MoroR$pEED ToReuEHARAcrERtsTtcspEED NTR 3ll


16/24

310 DIREcT-cunRENTAcHTNES chop.

valueand so, oo, sthe speed.As the oad torques renoved, he armaturecurrentbecomes orrespondinglymaller,making thenumerator termof Eq.(6-24)arger. This resultsin higherspeeds. The extentto which the speed

\seres\\Cumuloiively

sec. -8 MoroR$pEED-ToReuEHARAcrERtsTtcs.pEEDoNTRor 3ll

zeto. Both effectsact to bringabout an increasen speed. Thereforethespeed egulationof the cumulativelycompounded.motor isgreaterthan forthe shuntmotor. Figure6-21presents his information graphically.

The situation regardinghe speed-torqueharacteristicof theseriesmotor-is significantlyifferentbecause f theabsence f a shunt-fieldwining.Keepin mindthat the establishmentfa flux fieldn the seriesmotorcomes boutsolelyas a resultof the flowofarmaturecurrent,hroughthe series ieldwind-ing. rnthis connection,hen, hespeed quatiolfor the seriesmotorbecomes

n . : E o - Vr - r " ( R ' * R " )- KnQ, K,EI" (6-27)

whereK denotes newproportionalityfactorwhichpermitsiD"o be replacedby thearmaturecurrent1". When ratedtorqueisbeingdevelopedhe currentis at its rated value. The fluxfieldis thereforeabundant. Hwever,as loadtorque isremovedess armaturecurrentflows.Nowsince1oappears n thedenominatorfthe speed quation,t is easy o see hat thespeedwill increasegreatly. In fact, ifthe loadwere o be disconnectedrom the motorshaft,dangerouslyhighspeedswouldresultbecause f thesmallarmature currentthat flows.The centrigufaloicesat, hesehighspeeds an easilydamage hearmaturewinding.For this reason seriesmotor shouldneverhave ts loaduncoupled.

Becausehe armaturecurrentis directlvrelated o the air-gapfluxin theseriesnrotor,Eq. (6-lg)for the developedo.qrr"may be modifiedo readasT : KrQI": K|IZ (6-28)

Thus he developedorque or theseriesmotor sa unctionof thesquare f thearmaturecurrent. Thisstands n contrastto the linearrelatior,rshipf torqueto armaturecurrentn the shuntmotor. of coursen the compoundmotoranintermediateelationsbips achieved. t is nterestingo note, oo, hat as heseriesmotorreacts o developgreater orques, he speeddropscorrespond-ingly. It is this capabilitywhichmakes he seriesmotor so lvell-suitedotraction-typeloads.

Speed onfrol

one of theattractivefeatures he d-cmotoroffersover allother typesis therelativeeasewithwhichspeed ontrolcan be achieved..hevarlousschemesavailableor speed ontrolcanbe deducedrom Eq.(6-2+),whichis repeatedherewithonemodifiiation:

V ' - 1 " ( R " * R " )Ka Q

/ u u i l r u r u r v g r y \compounded\\ -\

- \. - t.

Torque o/oofed)

Fig. G2I. Typical speed-torquecurves of d*cmotors.

increases epends ponhow large hearmature circuitresistanee ropis incomparisonwith theterminal voltageand the value of Ia. It is usuallyaround 5to 10per cent. Accordingly,we can expecthe per cent changenspeedof theshunt motorto beabout'the samemagnitude'This changenspeed s identifiedby a figure ofmeritcalled he speedegulaon.It is definedas ollows:per centof speedegulation noload s-p-99:l--fgt-lgadpeedtoo (o-25)

The speed quationas t a pplies o thecumulativelycompoundedmotortakesthe form

(6-26)

.whereQu enoteshe increase,inluxproducedby the series ieldmmf' (Notethat thisis not alinear additionexceptwhensaturations negligible.)

A comparisonith the analogousxpressionor the shuntmotor bears uttrvodifferences.One, he numerator ermincludeshe voltagedropin the- "seriesieldwindingbesideshat inthe armaturewinding.Two, the denomina-tor termis ncreasedo account or the effectof the seriesieldflux rD".Startingat ratedtorqueand speed,Eq. (6-26)makes t clear hat as load torquesdecreaseda zera here is an increase n the numeratorterm whichis neces-sarilygreater han it is for the shuntmotor. At the sameime, moreover,hedenominatorerm decreasesecauseF" edues


17/24

312 DIREcr-cURRENTMAcHtNEs chop.

The modification involvesthe inclusionof an external armaturecircuitresistanceR". nspectionfEq. (6-29)evealshat thespeed anbe controlledby acijustingany one of the three factorsappearingon the rightside of theequation:Vr,R", orQ. Thesimplest o adjust is a.A field rheostat susedsuchas that shown n lrig.6-19.If the field rheostat esist ances increased 1.the air-gap fluxis diminished,yieldinghigher operatingspeeds. General-purposeshuntmotorsare designed oprovidea 200per cent ncreasen ratedspeedby thismethodof speed ontrol. However, becausef the weakenedfluxfieldthe permissibleorquethat canbe deliveredat the higherspeed scorrespondinglyeduced n order topreventexcessivermaturecurrent.

A secondmethodof speed djustment nvolves heuse of an externale-sistor .Ru onnected n the armaturecircuitas illustratedin Fig. 6-22. The

Fig. 6-22. Speed adjustmint ofa shunt motor by an externalarmature-circu tresistnce.

sizeand cost ofthis resistor areconsiderablygreater han thoseof the fieldrheostat because , must be capableof handlingthe full armaiurecurrent.Equation(6-29)ndicates hat the largerE" is made, the greaterwill be thespeedchange.Frequentlythe externalesistor sselectedo furnish as muchas a 50percent dropn speed rom the ratedvalue. The chief disadvantage fthis methodof control is thepoorefficiencyof operation.tr'orexample,a 50

percent drop nspeeds achieved yhaving approximatelyhalfofthe terminalvoltage.[/appearacross ,. 'Accordingly,almost50per centof the line inputpower s dissipatedn the formofheat in the resistor ,. I{onetheless, rma-ture circuitresistance ontrolis oftenused especiallyor seriesmotors.

A third and finalmethod ofspeed ontrol involvesadjustmentof the ap--" 1"'pliedterminal voltage.This.schemes the mostdesirable rom theviewpointof flexibility and highoperatingefficiency.But it is also the most expensivebecauset requirests ownd-c supply.It meanspurchasinga motor-generatorset with acapacityat least equal o that of the motorto be controlled. Suchexpense s not generallyjustifiedexcept in situationswhere the superior

performanceachievablewith this scheme s indispensable,s is the case nsteelmill applications.Armatureterminalvoltagecontrolis referredo as heWard-Leonardystem. SeeChapter12 forfurtherdetails.

.9 APPLICAT'ONSOFt D_C^4OIORs

Thed-cmotors oftencalled pon o dothe reallyoughobs n industrybe-causeof itshighdegreeof flexibilityand easeof control.These eaturescan-not easilybe matchedby otherelectromechanicalnergy-conversionevices.The d-cmotoroffersa widerangeof controlof speed nd torqueas wellasexcellentaccelerationand deceleration.For example,by the irisertionof anappropriatearrnature circuit resistance, ated torque can be obtained atstartingwithno morethan rated currentflowing.Also,by specialdesignofthe shunt-fieldwindingspeed djustmentsovera rangeof 4 :'1 above atedspeedare readilyobtainable.{f this isthen combinedwitharmature-voltagecontrol,the rangeof speedadjustmentspreads o g : 1. rn some electroniccontroldeviceshat are used o providethe d-cenergy o the fieldand arma-ture circuits,a speed angeof 40 : 1 ispossible.Thsizeof themotorbeingcontrolled,however,s limited.

Table6-1 istssomeof thesalientcharacteristicsand typicalapplicationsof thethreetypesof d-cmotors. rt is interestingo noteihat the maximumtorque n the caseof thed-cmctor is limitedby commutationand not,as withall othermotortypes,by heating. commutationrefers o the passage f cur-rent fromthe brusheso the commutatorand thence o the araturewindingitself. The passagerom the brushes o the commutators an arc discharge.Moreover,as a coilleavesa brushthe currentis interrupted,whichcausessparking.If the armaturecurrents allowedo become *""..i.r",the sparkingcan becomeosevere s to cause lashoverbetweenbrushes. Thisrend.ershemotoruseless.

Another pointof interestin the table is the considerablyhigherstartingtorqueof thecompoundmotorin compariso^viththe shunt motor. Thisfeature is attributableto the contributionof the series ield winding. The

same comments valid as regards he maximumrunningtorque. rn eachcase,of course,he limitfor the armaturecurrentis the same.

sec.-9 APPTICATIONSF D.CMOTORS31 3

Shuntf el dwinding

Toble-l CHARACIER,S7.CSND ,APP'CAT'ONSF D-C/OTORSf


18/24

Toble l CHARACIER,S7.CSND

UsuaIIylimited to about 200by commutation'

Higher thanshunt-up to 350

,APP CAT ONSF D-C/OTORSf

Type

Shunt, constantspeed

Sarting torquet o / \\ /ot

Medium- usually limitedtoless han 250 by a startingresistor but may be in-creased

High - up to 450,dependingupon degreeof compound-ittg

Max. runningtorque,momentary (/) Typical application andgeneralremarks

Essentiallyfor constant-speedapplicationsrequiringmedium starting torque. Maybe used or adjustable speednot greaterhan 2:1 range. For centrifugalpumps,fansr.blowers,conveyors, woodworkingmaclfines,machine ools,priningpressei

Shunt, adjustable speed Same as above

Compound

Same as above, for applicationsrequiringadjustablespeedconrol,eitherconstanitorqueor constantoutout

For drives requiring high starting torqueand onlyfairlyconstanl speed;pulsatingloads with flywheelaction. For plungerpum-ps, shears, conveyors, crushers,bending rolls, punch presses, hoist

Very high- up to 500 For drives requiring very high startingtorque and where adjustable, varyingspeed is satisfactory. This motor issometimes called the traction motor.Loadsmust be positively

connected,notbelted. For hoists, cranes, bridges, cardumpers.To preventoverspeed,ightesloadshouldnot be much less han 15 o20 per cent of full-loacltoroue

tBy permission rom M. Liwschitz-Garikand c. c. whippte, ErectricMachinery, vor. fPrinceton,N. J.: D. Van NostrandCo., nc., 1g46,.

By series heostat

6.IO STARTERS ND CONTROT.I .ERSFOR D-C 'UOTORS

The limitationsimposedby commutationas wellas voltage-diprestrictions, ^+

q4on the source sset orth bythe eieclricutility companymake t necessaryo tt*Jtause a starter or controller onall d-cmachinesvhose atingsexceed2 hp.A | |glanceat Eq. (6-23)discloseshat at starting(n : O) hearmaturecurrent s | 'limitedsolelyby the armaturecircuit resistance. Hence, f fullterminal-..-..' ; Ivoltage s applied,excessivermature currents will fl ow. This isespecially o Iwhere argemachiles are nvolvedbecause he armature esistance etssmall- |er as the rating increases.n addition to limitingthe armature current,con-

*-

trollers fulfillotherusefulfunctions as describedn Sec.4-10.Depictedin Fig. 6-23 is a simpleline starter whichis used for small

d-c motors. The operationis straightforward. Pushing thestart button Fis. 6-2s. Linestarte r v D .p uwur u_ c r no [ o r /r3ll

Speed-regulationor characteristic

(% )

Va' 'ing,dependingor'.degreeof com-pounding-up to25-30

Widelyvariable,high at noJoad

Speedcontrol(%)

Increase up to 200by6eld control; de-crease y armature-voltage control

6:1 rangeby fieldcon-trol, loweredbelowbasespeedby arma-ture-voltagecontrol

Not usually used butmay be up to 125byfieldcontrol

Shuntieldwinding


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318 DtREcr-cuRRENTAcHtNEs , chop. ehop. PR,OBTEMS19


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Fig. 6-25. Definiteime-limitcontrolleror a d_cmotor.

delay)contactorscloseanyway. This allorvsan increased tarting torqueto bedeveloped. Thus the motor is made to "work harder,, if it does not start onthe first step. Accordingly, whenever a controiler must be selected for ageneral-purposemotor, it is wiser to prescribethe definite timeJimit type.The reason s that as a rule for general-purposeapprieations he startingcon-ditionsare not wellknown.

(b) Directingattentionsolely o the undamental omponentfthe flux densityin the air-gap, compule hevoltage value appearingat the brushes.

6-3 RepeatProb.6-2 or the case vhere lot 1 liesto the left ofthe interpolar axisby 15".

6-4 I'orthe machine f Prob.6-2draw hevariaion f thearmaturenduced oltagemeasuredat the brushesas a function of c,r,fwherec,.,s the angular rotor velocity.Dealingonly withthe fundamentalcomponent fthe flux densitycurve, show hevariation of eachcoil voltageas wellas hat of the total. Compute hemaximumandminimumvaluesof the coil and total voltages.

6-5 RepeatProb.6-1 or a d-cmachinewith thefollowingspecifications:-poles,6 slots, ull-pitch, wave-woundarmaturewindinghaving twocoil sidesper slot.

6-6 For the machine f Prob. 6-l sketch hevariationoflhe emf nduced n eachcoilvoltageas wellas between rushes s a function ofco"l,where o"s the rotor angularvelocity.Directattention solely o ihefundamentalcomponent f the air-gap luxdensity. Indicate the maximum and minimum valuesof coil and brush voltages.

6-7 Explainyour answer o eachpart:(a) Can a separately xcited -cgenerator perate elow he knee of its mag-

netization urve?(b) Cana d-c shuntgeneratoroperatebelow he kneeof its magnetizationcurve?

6-8 The magnetization urveor ad-cshuntgeneratorrivenat a constant peed f1000 pm is shorvnn Fig.&16. Eachverticaldivisionepresents0 volts; eachhori-zontal divisionepresents .2amp.

(a) Computehe criticalield resistance.(b) Whatvoitages inducedby theresidual lux ofthismachine?(c) \Yhat must be theresistancef the field cirtuit inorderthat the no-Ioad

terminalvoltagebe 240voltsat a speed f 1000 pm?(d) Determinehe field currentproduced y the esiduai lux voltagewhen he

field circuit resistanceas he value ound n part (c).(e) At what speedmust thegeneratorbe drivenin orderthat it wouldfail to

buildup whenoperatingwith thefield circuit resistance fpart (c)?

6-9 Ad-c shuntgeneratorasa magnetizationurvegivenby Fig.6-16,whereeachordinateunit is madeequal o 20 voltsand eachabscissa nit is set equal o 0.2 ampand the speed f rotations 1000 pm. Thefield circuit resistances 156ohms.

Determine hevoltagenducedbetween rusheswhen hegenerators operatedat aeduced peed f 800 pm.

6-f0 It isdesiredo reversehe terminalvoltagepolarityqfa generatorhat hasbeenoperatingproprlys a

-cumulativecompoundgenerator.The rnachine s stopped.

Residualmagnetisms reversed y ternporarily isconnectinghe shuntfield andsepa-rately excitingt with reversedcurrent. The connectionsre hen restoredexactly asthey werebefore.

(a) Does he terminalvoltage uild up? Explain.(b) If answer o(a) is yes,willthe compoundingbe cumuiativeor differential?

Explain.

PROBI.EA,IS

6-l rhe rotor of a 2-poled-c machinehas 12 slots. The wave-wound,uil-pitcharm-aturewindinghas two coilsidesper slot. Thereare 12 commutatorsegments.showa planviewofthe windingayout. cleariyidentifyhe positionof he brusheson he commutatornd elativeo the poles.Alsoshow he directionfthe nduced mfn the coilsidesor a counterclockwiseotationof the rotor-6'2 Therotorofa 2-poled-cmachine arriesa wave-woundrmaturewindinghavingtwocoilsides er slot n its 12slots.The windings fuli_pitch.(a) Drawthe schematiciagram hat shows he two armature pathsexistingbetweenhe two brushes. Representeachsuitablymarkedcoilvortageb|

, smalld-csouces ith properlydentifiedpolarities.consider hat instantwhenslots1 and Zare ocated xactlybetweenhe poles.

320 orncr.cuRRENTAcHINES chop. chop. PROBLEMS21


21/24

rt 6-rr A 2-poled-c machine s equippedwith a wavewindinghaving 240armatureconductors.The pole aces pan70per centof a polepicharidthe netwindinghas210 urns. This machineperatesvitha fixed ierdcurrentof 1.6amp.Themagnetizationurves depictedn Fig.6-16wheneach rdinatunitrepresents

0.1 veber ndeach bseissanit represents.2amp.Assume : 120,,/ 10b0At ratedoad hc armaturecurrents 40 amu.

(a) Determinehe emountof demagnetizationf the fieldfluxcaused v thealmaturcmm[.(b) Whatis the valueof the air_gaplux under oad.?(c) \Yhat s the valueol fluxat the eadingpole ip?

6'12 In a lap-wound'armatureindinghereare as manybrushes s hereare poles.Hence, or a 4-poled-c machinet is customaryo use our brushes,witheachpairofbushes eing esponsibleor conductingne-halfof the totalu.-uir.. current.Show he distributionof currentn the coilsundergoingommutationor two in-stances:ust before ndergoingommutationnd ive+ighthshrough he commutationperiod.Assumeesistanceommutationhroughout,

{ 6-13 The noJoadcharacteristic fa 1O-kw,250-volt,d-e self-excitedhunt generatordrivenat 1000pm s shon'nn Fig.6-16. Eachverticalunitdenotes 0 volts,and eachhoizontalnit represents.2amp. Thearmaturecircuitesistances 0.8ohm,and hefieldcircuitresistances set at 157ohms. Determine:(a) The oiticalresistancef the shuntfieldcircuit.(b) The change n voltagerom no-load o full-load.I.{eglectarmaturede-magnetization.(c) The shunt fieldcurrentunderrated load conditions.

6'14 RepeatProb.6-13(b)and (c)for the casewhere he armaturedemagnetizingefrect s knowno be 0.2a,mp xpressedn termsof equivalentieldcurrent.6-15 The machinef Prob.6-18 perates ith a fieldwindingesistancef 148ohms.(a) \Yhatis the no-loadvoltase?

(b) When he generatordeliverspower o a specifiedoad, the terminalvoltageis ound o dropto 220voltsancl he correspondingemagnetizationffectof thearmaturemmfis knowno be 0.2bequivalentield. mperes.Deter-mine he armaturewindinecurrent.

(c) what is the valueof the ierdcurrentat the oadconditionof (b)?(d) find the armaturewindingemfunder oad.

Y 9-1.6 The noJoadcharacteristicofa 5-kw, 125-voltshuntgenerator rivenat 1000pmis shownn Fig.6-16.Eachordinate nit represents 0volts,and eachabscissanitrepresents'1amp. The armature ircuitesistances 0.2ohm,and he fieldcircuite-sistances 157ohms.\\'hen the generatordelivers ated armaturecurrent,the armature nducedemfis

p

6-L7 ThenoJoadcharacteristicof a d-cshuntgeneratordriven at aspeedof 800 pmis approximated n itsusefulrangeby the equation

o - 300IZ * I t

where E sarmaturenducedemf and 1 s the fieldcurrent. The armaturecircuit e-sistances 0.1ohm. The fieldwinding esistances 20 ohms.The demagnetizingffectof armature eacLionay be neglected,

(a) The terminal voltage sto be 225 volts whenhe armature current s 150amp. The generators drivenat 800 pm. Findthe resistance fthe fieldrheostat orthiscondition.

(b) Change he field rheostatettingo l0 ohms.Let the oad be disconnectedand he speed educed o 720 pm. Findthe terminalvoltage.

(c) Returnto the conditionsf part (a). Assumehe rotational osseso be2 kw. Fiqd the outputporver,he efficiency,nd heshaft inpu orquefromthe primemover ofthe generator.

6-f8 The noJoadcharacteristicof a d-c machine n itsuseful operating range anddriven at 1500pm maybe approximatedy

fz o

400 E"_ 4Q0Itl7a : l--,-i Or 1 :o -T rl

ll 6 volts.(a)(b )

(c)(d)

Findthe terminalvoltaEe.\\hatis the valueofthe demagnetizationf the armaturemmf expressed.nequivalentieldamperes?Whatis the fieldcurrent?Howmuchpowers deliveredo the oad?

This machine soperatedas a d-c shuntgeneratorwhose ieldcircuit resistances

50 ohms.(a) Computethe no-loadterminalvoltage when.the generator is driven at1,500pm, indicatingany necessaryssumptions.

(b) What wilibe the terminal voltage at no-loadwhen he speed s reduced o750 pm? Accountor the argedifference.

d 6-19 The magnetizationurve ofa d-c shuntgenerators representedn tr'ig.6-16,provided hat eachordinateunit is multipliedby 40 voltsand eachabscissa nit by0.5amp. lb.earmaturecircuit resistances 0.4ohm,and he ieldwinding resistances

(a) This machines made o deliveran armaturecurrentof 60 amp. Findtheresistance f the field rheostatin series viththe fieldwinding) sohat theterminalvoitagewillbe 520voltsat a speed f 1000 pm.

(b) Withthe fieldrheostatsetas n part (a)findthe terminal voltage atno-load

and 1000 pm.S 6-20 A cumulative-compoundenerator riven at 1000 pm has he magnetization

curveshorvnn Fig.6-16,providedhat eachunit of the ordinateaxis s multiplied by20voltsand eachabscissa nit is multipliedby 1 amp. The armature circuit resistanc eis 0.06 ohm. In addition:

Series urnsper pole (N"): 20Shuntturnsper pole (Nr): 1000Armature-reactiondemagnetizingeffectat

1" of 100amp : 600at per poleThe fieldcircuit resistances 45 ohms.

(a) Deterrninehe no-load erminal voltage.

322 DIRECr-cURRENTMAcHtNEs chop.thop. PROBTEMS23


22/24

(b)

(c)(d )

Find the terminalvoltagewhenthe loadis such hat it causes 00amp toflowthroughthe armaturewinding.Findthe newvalueof the fieldcurrent.wha,tis the valueof thearmature nducedemfat the specifiedoad.

6-21 RepeatProb. 6-20 or the casewherethe fieldcircuitresistances reduced o31.5ohrns nd he numberof seriesieldturnsper pole s ncreasedo 40. The arma-ture currentemains t 100amp.-z6'22 A cumulative-compoundeneratorhas the magnetization,,.r" .ho*n in Fig.

6-16,where achordinateunit is 20voltsand eachabscissanit isI amp. Determinet'he equiredieldcircuitresistancehat allows he generatoro operate

at a terminalvoltageof 240voltswhen he armaturecurrent s 100amp. In adition:Armaturecircuit esistancerop : 10voltsSeries ield urnsper pole: 2bShunt ield urnsper pole : 1000Armaturedemagnetizingt per pole: g00

6'23 A 10-hp,230-voltshunt'motorhas an armaturecircuitresistance f0.5ohmanda fieldresistancef 1i5ohms.At noloadand atedvoltagehe speed s 1200pm andthe armature unent s 2amp. If loads applied,he spee rops o 1100 pm. Deter-mine:

(a) The armaturecurrentand the linecurrent.(b) Thedevelopedorque.(c) The horsepowerutputassuminghe rotationalosses re 500watts.

Neglectarmatureeaction.

6-24 A 230-volt,50-hp,d-c shunt motordeliversporvero a load drawingan armature currentof 200ampand runningat a speed f t ioorpm. The magnetizationurveis givenby Fig.6-16'whereeach erticalunit represents0 voltsand eachhorizontalunit representsamp. Neglectarmatureeaction.AlsoB, : 0.02ohrr.

(a) Findthe valueof the armaturenducedemfat this oadcondition.(b) Computehe motor ieldcurrent.(c) Computehe valueofthe oad orque. The rotationalosses re j00watts.(d) At whatefficiencys the motoroperating?(e) At whatpercentagef rated powers it operating?

6-25 Refer o Prob.6-24,and assumehe oad is reduced ohatan armatufecurrentof 75amp lows.

' (a) Findthe newvalueof speed.(b) \4'hats the nervhorsepowereingdeliveredo the oad?t' 6:26 The magnetizationurveof Fig.6-16applies o a ?80_vqlLl*b.:bp_optor,hereeachordinate nit represents0voltsand eachabseissaiil r"p..r"ni,0.2amp. At

no-load,he fieldcircuitdrarvs currentof 1.9amp fromthe line,while he armaturecurrentis negligiblysmall. !$pged a-b o-log,d,_s_000 pm.A mechanicaload is the;pplid to ihe motorshaft. The measuredarmaturecurrents found o be40 amp,causiug n armaturecircuitesistancerop of 16volts.Moreover,he demagnetizingffectof the armaturemmfis foundto beQrlgguive+eqfieldamperes.

(a) computethe loadspeed n rpm,neglectinghe demagnetizingeffectof thearmature eaction.

{ (b) Findthe speed or the specifiedoad when he demagnetizingffects ac-i countedor. (['Iint:The procedures similaro that outlined or generator' behavior,except hat norv he voltageequation orthe moior isused n

place f that for the generator.Also,keep n mindthat the magnetizationcurve s valid onlyfor a singlespeed, o that adjustmerttsare needed.)

(c) Compute he percentage f change n speed rom no-loadto full-loadforparts (a) and (b); compare ndexplainthe difference

6-27 A 230-volt,5-hp,d-c shunt motorhas he magnetizationurveshown n Fig.6-16,whereeach rdinateunit represents0volts andeach bscissani epresents.2amp. Thiscurve s.valid or operation t 1000pm.(a) Ratedvoltage s appiiedo this motor, and at no-loadhe speed s found o

be 900 pm. Negligiblermature urrent lo'ws his condition. Findthetotalfieldcircuit resislanceor this pointof operation.

(b) Load s appliedo thismotor,correspondingo an armature currentof 40amp. Ifthe armature ircuit esistancerop s 16volts andthe demagnetiz-ingeffectofthe armaturemmf is0.3 equivalent ieldamperes, eterminehenerv peedn rpm.

6-2B A 115-volt,15-hp, d-c cumulative-compound otor hasthe magnetizationcurveshownn Fig.6-16,whereeach rdinate nit represents0volts andeaqh bscissaui represents1 amp. The mtor speed at ntr-loadand rated voltageapplied is_{00j&*:''---.-*--:-""-(a) Assumingegligiblearmaturecurrent at noJoad, indthe fieldcircuit re-

sistanceor this operatingoint.(b) The motordeliverspor,veronsistent ith an armatureurrent of 100amp,which s alsomade o flow hroughhe seriesield vinding.The magnetiza-tion effectof the seriesield srepresentedy 3 equivalentielda,mperes.Thedemagnetizingffect f the armaure vinding sdenotedby 0.7equiva-lent fieldamperes. The armatwe circuit resistancerop (includingheseriesield) is6 volts. Findthe speedunder load.

6-29 A 20-hp,230-volt,1150-rpm, -pole,d-c shunt molorhas a total of620 con-ductorsarrangedn trvoparallelpathsand yieldingan armaturecircuit resistancef0.2 ohm..-'WFnildelivers ated porverat ratedspeed, he motor drawsa linecurrentof 74.8amp and a fieldcurrent of3 amp. Compute:

(a) The fluxper pole.V(b) The developedorque(c) The rotational osses.(d) l'he totai losses xpressed s apercentage f the ratedpower.

Assumenegligiblearmature reaction.

6-30 A 230-vol, 0-hp,d-c seiesmotoldrarvs linecurrentof 36amp rvhen eliver-ing ratedpowerat tsrated speed f 1200 pm. The armatureircuit resistances 0.2-'ohm, andthe seriesieldwinding esistances 0.1ohm. The magnetizationurvemaV/be consiileredinear. Effectsof armature eactionmaybe neglected. /

(a) Findthe speedof this motor rvhen t dran's a linecurrent of20 amp. [,/(b) What s the developedorqueat the new conditions? ,(c) How doeshis 'iorquecomparewith the originalvalue? Why? V

6-31 A 250-volt,50-hp, 1000-rpm,d-c shunt motor drives aload tha requires a

/

324 DtREcr-cURRENTAcHtNES chop. chop. ROBTEMS 25


23/24

(b) Specify the nameplate holscporvel and steed r.atingsof the individunlmotorsto be purclg!-e4_too these obs. ,\ssunie hat at 500 rpm the torquefor both load.llsJEsame, andequal to 1050 b-ft.

6-37 Figurc l'6-37sho*'s a d-c selics notor', vith a rheostat in palallel with the fieldwinding. The lesistance ofthis rheostat s equal to tn'o-thildsof the fieldwindingre-

Fig.P6-37

sistance.The motor sopelatingn the steady-state.viththe lheostatsrvitchopen.The te rminl voltage s250 voits,he almature cunent40 amp, the speed700 pm.

When he oad olque s tttglgglgd_by0pel cent andthe rheostat wiich s closed,findthe nerv teady-state aluesof speed nd armatur,e urrent.Given values:

Armatureesistance.2 ohm,seriesield resistance.15ohm,Neglectsaturation, rmatulereaction, ndrotationalpolverosses.

V O-gA -\ d-cseliesmolorrunsat 300 prn,and dras'sa currentof75arnp rom he 500-volt line. Thetotal resistancef thearmalureand ficldcicuitss 0.4 ohm.

Find the nerv teady-state aiuesfarmatureculrent andspeedf the linevoltageis increasedrom 500 o 600 volts.Assumehat the developedorque is to remainconstant.

fJ O-S Read he followingsentence arefully,and correctany wrongstatementhatyou may findn it:

A d-c shunt motor operatesndel oad n the steady-state.At the time I: 0,the field rheostatesistances reduced; his increaseshe flux andtherebyhetorque. So he motor acceleratesnd reaches nerv teady-statepeedwhich shigherthan it rvasbefore.

6-40 Ad-cshuntnotol dl'aws10.0 rnprom ts 220-voltupplyine. The resistanceof ts armature ircuitincludingbrushes, rushcontacts nd nterpoles)s ?" : 1ohm.The fieldwinding esistances R : 300ohms. (There s no ield heostat.)The rota-tional losseshysteresis,ddy currents, liction and rvindage)re l0 per cent of theoutpupo\Yer.

Find the efficiency,as accurately asthe giveninformationand the use of a sliderulepelmit.

6-41 Ad-cshuntmotors ated at 3 hp, 115 voits, 1000 pm. At raedperating on-ditions, the elTiciencys 82.5per cent. The armature resisanceincludingbrushcontact) s0.44ohm, he field circuit esistances 145ohms.

constatorque egardlessfthe speed f operation.Thearmaturecircuitesistances0.04ohm. \\Ihenhis motordeliversated power, he armaturecurrent s 160amp.(a) If the lux s reducedo 70per centof itsoriginalvalue, ind the nerv alueof armatulecurrent.

(b) \\hat s the nervspeed?6'32 \\rhena 250-volt,0-hp, 000-r1rn.r,-cshuntmotors used o supply atedout-put po\4ero a constant-torqueoad, t drarvsan armaturecurlentof 160amp. Thearmaturecircuithas a resistancef 0.04ohrn,and the rotationalosses re equal o2 kw' Anexternalesistancef0.5ohn'rs nsertedn seriesvithhe armaturevinding.For thiscondilionompute:

(a) The speed.(b) The developedower.(c ) The elciencyssuminghe fieldoss s 1.6kw.

Armatureeactions negligible.6-33 A d-c shuntmotorhas he magnetizationurveshownn Fig. 6-16, vhere neverticalunitrepresents0voltsandonehorizontalunitlepresents fi"eldmperes. hearmafurecircui tresistanceis0.0bohni .\ tasPecif ieci loadandaspeedofl000rr, , . , ,

'thefieldcurrents ound o be 12amp vhen terminalvoltage f 245 ,oltss appliecloth e motor'The otationalosses 'e 2. 5krr., nd a.'ratu'e.eaction-s egligible.(a) Findthe arrnalulecurrent.(b) Computehe developedorque.(c) l\'hatis the efficiency?

6-34 A 230-volt,-c shuntmotors usedas an adjustable peed .iveovera range fzeroto2400pm . Speedsro mzeroo r600 pm a' e obtained y adjustinghe arma-ture terminalvoltagerom zero o 280vorts, viththe fieldculrentept fixedat fullfieldvalue. speeds rom 1600 pm to 2-100'pma'e obtainedby incr.singhe fieidcurrent,withtheafnaturetelminalvoltagemaintained t zaO nlts. Ignoremachinelosses nd armatureeactioneffects.

(a) The torque requiredby the loadremainsconstantover the entirespeedrange. Show he generalorm of the culr.e or armaturecurrentrersusspeed, ver the fullspeedange.

(b) Insteadof keeping he roadtorqueconstant, uppose hat rhe armatur.ecurrents not to exceed specifiedalue. show the generalorm of thecurveor allou'ableoa d orqueve'sus peec, 'e r thelntirespeeclange.

6-35 Acustomers nterestedn buyirrgd-cshuntmotol o supplya oarl equiringconstanorque of 525 b-ft continuously,ver a speed angeof 500 o 2000 pm.(a) Listthree vayshat this ob can be done.

. (b) Iioreachmethodof part (a),specifyhe base peed nd horsepoweratingof the motor.

(c) Listlhe outstandingdvantage ssociatedvitheachmethodof control.6'36 Tlvoadjustabie-speed,-c shuntmotorshave maximumspeeds f 2000 pmand minimuurpeedsf500 pm. llotor i\ clrives oaclequilingcinstanthorsepo*-erover he speedange.JfotorR drives ne equiringconstantorque. Neglect ll ossesand armatureection.

(a) If speed djustments.obtainedy fielcicontlolan


24/24

(a ) Calculatethe valueof the induced voltage,0"at r.atedoperating conditions.(b) If this motor istested at no-Ioatl,,vith the supply voitage adjusted to the

valuecalculatedunder'(a)and the specdkept at 1000 pm (so hat therota-tonal lossesemain the sar'e as al full load), horv much is the armatureculrent under this condition? (AolerThe loro drop at noload can bencglcctcd.)

6-42 Trvo identicald- c machinesare tested in "orposition"as shorvn (armaturesinparallel,shaftscoupled, osses upplieclrom an erectlicalsource). The lettersG and, Istand for generator nd ntotor.

(a) \\'hich machine has the higher annatul.e copper osses?(b ) \\'hich machine has the higher. ield copper

osses?(c) \\'hich machine has the higher core losses?To each nswer,add a blief explanation.

Fig. P6-42

6-43 The magnetizationcurve of Fig. 6-16 showsthe no-ioadcharaeteristic or a d-cshunt generatorat 900 rpm, rvhereeach abscissa unit represents 0.b amp and eachordinate unit represents20 volts.

The armaturecircuit rcsistance s 0.2 ohm, the fieldcircuitresistance rvithoutfieldrheostat) 30 ohms. The effectof armaturereaction is equivalentto fourdemagnetizingampere-turns perpole for every ampere of armatul'e current. The fieldrvindinshas1250 urns per pole.

(a) Find the resistanceof the fieldrheosta (in serieswith the fieldwinding)forthe machine operatingas a generator driven at g00 rpni and carrying anarmature c'rrent of 12bamp at a terminal vortageof 220vorts.

(b) The fieldrheostat remainsas for part (a). The load is now disconnected.The speed remai's unchanged. what is the new value of the terminal

voltage?(c) Find the fieldrheostat t'esistanceor a noloadvoltage of 420r,oltsat a speed

of I800rpm.

9'44 Depictc'dn Fig. P6-44 s the reversingcontrollercircuitryfor a cl-e hunt motor.Identify the unrnal'kedarmature eontactsand explainthe leversingoperation. Explain,too, rvhythe auxiliaryinterlockcontactsro nd 8. arerlacedn seriei with the Rev andFrvd switches.

y-45 A current-limit type controller for a cl-c shunt motor is shorvn in Fig. p6-45.The accelerating relays (AR) respond to armature current. These relays havc a light-

weight armatureso ha hey easilypickup andopen heircontacts vheneverhe arma-ture currentexceedshe rated value. By meansof a step-by-steprocedure,describethe operation ofthis controlier. Be carefulo identifythe properclosiagand openingsequencewhenever wo or more contactorsa,ppea,rn series.

*b tFuse Armolurr

R3

1A9"3AR

Shunt ield

OL R lstort

StopMo

\,./

M 1AR f.1y't \72^F ) 1l'------"|---t7-t# 6^t--r--L

Fig. P6-45

R1 R2 R3

Fig. P6-44

vincent del toro - chap 06

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