E283C8.docx

E283C8.docx

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E283C8

CHAPTER8–DCMACHINERYFUNDAMENTALS

Summary:

1.ASimpleRotatingLoopbetweenCurvedPoleFaces

-TheVoltageInducedinaRotatingLoop

-GettingDCvoltageoutoftheRotatingLoop

-TheInducedTorqueintheRotatingLoop

2.CommutationinaSimpleFour-LoopDCMachine

3.ProblemswithCommutationinRealMachine

-ArmatureReaction

-Ldi/dtVoltages

-SolutionstotheProblemswithCommutation

4.TheInternalGeneratedVoltageandInducedTorqueEquationsofRealDCMachine

5.TheConstructionofDCMachine

6.PowerFlowandLossesinDCMachines

1.ASimpleRotatingLoopbetweenCurvedPoleFaces

Thesimplestrotatingdcmachineisshownbelow:

Itconsistsofasingleloopofwirerotatingaboutafixedaxis.Therotatingpartiscalledrotor,andthestationarypartisthestator.

Themagneticfieldforthemachineissuppliedbythemagneticnorthandsouthpoles.Sincetheairgapisofuniformwidth,thereluctanceisthesameeverywhereunderthepolefaces.

TheVoltageInducedinaRotatingLoop

Iftherotorisrotated,avoltagewillbeinducedinthewireloop.Todeterminethemagnitudeandshapeofthevoltage,examinethefigurebelow:

Todeterminethetotalvoltageetotontheloop,examineeachsegmentoftheloopseparatelyandsumalltheresultingvoltages.Thevoltageoneachsegmentisgivenbyeind=（vxB）l

Thus,thetotalinducedvoltageontheloopis:

eind=2vBl

Whenthelooprotatesthrough180°,segmentabisunderthenorthpolefaceinsteadofthesouthpoleface.Atthattime,thedirectionofthevoltageonthesegmentreverses,butitsmagnituderemainsconstant.Theresultingvoltageetotisshownbelow:

Thereisanalternativewaytoexpresstheeindequation,whichclearlyrelatesthebehaviourofthesinglelooptothebehaviouroflarger,realdcmachines.Examinethefigurebelow:

Thetangentialvelocityvoftheedgesoftheloopcanbeexpressedasv=rω.Substitutingthisexpressingintotheeindequationbeforegives:

eind=2rωBl

Therotorsurfaceisacylinder,sotheareaoftherotorsurfaceAisequalto2πrl.Sincethereare2poles,theareaundereachpoleisAp=πrl.Thus,

SincethefluxdensityBisconstanteverywhereintheairgapunderthepolefaces,thetotalfluxundereachpoleisφ=APB.Thus,thefinalformofthevoltageequationis:

Ingeneral,thevoltageinanyrealmachinewilldependonthesame3factors:

1.thefluxinthemachine

2.Thespeedofrotation

3.Aconstantrepresentingtheconstructionofthemachine.

GettingDCvoltageoutoftheRotatingLoop

Thevoltageoutoftheloopisalternatelyaconstantpositiveandaconstantnegativevalue.Howcanthismachinebemadetoproduceadcvoltageinsteadoftheacvoltage?

Thiscanbedonebyusingamechanismcalledcommutatorandbrushes,asshownbelow:

Here2semicircularconductingsegmentsareaddedtotheendoftheloop,and2fixedcontactsaresetupatananglesuchthatattheinstantwhenthevoltageintheloopiszero,thecontactsshort-circuitthetwosegments.

Thus,everytimethevoltageoftheloopswitchesdirection,thecontactsalsoswitchesconnections,andtheoutputofthecontactsisalwaysbuiltupinthesameway.Thisconnection-switchingprocessisknownascommutation.Therotatingsemicircularsegmentsarecalledcommutatorsegments,andthefixedcontactsarecalledbrushes.

TheInducedTorqueintheRotatingLoop

Supposeabatteryisnowconnectedtothemachineasshownhere,togetherwiththeresultingconfiguration:

Howmuchtorquewillbeproducedintheloopwhentheswitchisclosed?

Theapproachtotakeistoexamineonesegmentoftheloopatatimeandthensumtheeffectsofalltheindividualsegments.Theforceonasegmentoftheloopisgivenby:

F=i（lxB）,andthetorqueonthesegmentis=rFsinθ.

Theresultingtotalinducedtorqueintheloopis:

ind=2rilB

ByusingthefactthatAP=πrlandφ=APB,thetorqueexpressioncanbereducedto:

Ingeneral,thetorqueinanyrealmachinewilldependonthesame3factors:

1.Thefluxinthemachine

2.Thecurrentinthemachine

3.Aconstantrepresentingtheconstructionofthemachine.

2.CommutationinaSimpleFour-LoopDCMachine

Commutationistheprocessofconvertingtheacvoltagesandcurrentsintherotorofadcmachinetodcvoltagesandcurrentsatitsterminals.Asimple4loop,2poledcmachineisshownhere:

atωt=0°

Thismachinehas4completeloopsburiedinslotscarvedinthelaminatedsteelofitsrotor.Thepolefacesofthemachinearecurvedtoprovideauniformair-gapwidthandtogiveauniformfluxdensityeverywhereunderthefaces.

The4loopsofthismachinearelaidintotheslotsinaspecialmanner.The“unprimed”endofeachloopistheoutermostwireineachslot,whilethe“primed”endofeachloopistheinnermostwireintheslotdirectlyopposite.Thewinding’sconnectionstothemachine’scommutatorareshownbelow:

Noticethatloop1stretchesbetweencommutatorsegmentsaandb,loop2stretchesbetweensegmentsbandc,andsofortharoundtherotor.

Attheinstantshowninfigure（a）,the1,2,3’and4’endsoftheloopsareunderthenorthpoleface,whilethe1’,2’,3and4endsoftheloopsareunderthesouthpoleface.

Thevoltageineachofthe1,2,3’and4’endsoftheloopsisgivenby:

eind=（vxB）l

eind=vBl（positiveoutofpage）

Thevoltageineachofthe1’,2’,3and4endsoftheloopsisgivenby:

eind=（vxB）l

eind=vBl（positiveintothepage）

Theoverallresultisshowninfigure（b）.Eachcoilrepresentsoneside（orconductor）ofaloop.Iftheinducedvoltageonanyonesideofaloopiscallede=vBl,thenthetotalvoltageatthebrushesofthemachineisE=4e（ωt=0°）

Noticethattherearetwoparallelpathsforcurrentthroughthemachine.Theexistenceoftwoormoreparallelpathsforrotorcurrentisacommonfeatureofallcommutationschemes.

WhathappenstothevoltageEoftheterminalsastherotorcontinuestorotate?

Examinethefiguresbelow:

atωt=45°

Thisfigureshowsthemachineattimeωt=45°.Atthattime,loops1and3haverotatedintothegapbetweenthepoles,sothevoltageacrosseachofthemiszero.Noticethatatthisinstantthebrushesofthemachineareshortingoutcommutatorsegmentsabandcd.Thishappensjustatthetimewhentheloopsbetweenthesesegmentshave0Vacrossthem,soshortingoutthesegmentscreatesnoproblem.Atthistime,onlyloops2and4areunderthepolefaces,sotheterminalvoltageEisgivenby:

E=2e（ωt=45°）

Now,lettherotorcontinuetoturnanother45°.Theresultingsituationisshownbelow:

atωt=90°

Here,the1’,2,3,and4’endsoftheloopsareunderthenorthpoleface,andthe1,2’,3’and4endsoftheloopsareunderthesouthpoleface.Thevoltagesarestillbuiltupoutofthepagefortheendsunderthenorthpolefaceandintothepagefortheendsunderthesouthpoleface.Theresultingvoltagediagramisshownhere:

Therearenow4voltage-carryingendsineachparallelpaththroughthemachine,sotheterminalvoltageEisgivenby:

E=4e（ωt=90°）

Noticethatthevoltagesonloops1and3havereversedbetweenthe2pictures（fromωt=0°toωt=90°）,butsincetheirconnectionshavealsoreversed,thetotalvoltageisstillbeingbuiltupinthesamedirectionasbefore.Thisistheheartofeverycommutationscheme.

3.ProblemswithCommutationinRealMachine

Inpractice,therearetwomajoreffectsthatdisturbthecommutationprocess:

1.ArmatureReaction

2.Ldi/dtvoltages

ArmatureReaction

Ifthemagneticfieldwindingsofadcmachineareconnectedtoapowersupplyandtherotorofthemachineisturnedbyanexternalsourceofmechanicalpower,thenavoltagewillbeinducedintheconductorsoftherotor.Thisvoltagewillberectifiedintodcoutputbytheactionofthemachine’scommutator.

Now,connectaloadtotheterminalsofthemachine,andacurrentwillflowinitsarmaturewindings.Thiscurrentflowwillproduceamagneticfieldofitsown,whichwilldistorttheoriginalmagneticfieldfromthemachine’spoles.Thisdistortionofthefluxinamachineastheloadisincreasediscalledarmaturereaction.Itcauses2seriousproblemsinrealdcmachine.

Problem1:

Neutral-PlaneShift

Themagneticneutralplaneisdefinedastheplanewithinthemachinewherethevelocityoftherotorwiresisexactlyparalleltothemagneticfluxlines,sothateindintheconductorsintheplaneisexactlyzero.

Figure（a）showsatwopolesmachine.Noticethatthefluxisdistributeduniformlyunderthepolefaces.Therotorwindingsshownhavevoltagesbuiltupoutofthepageforwiresunderthenorthpoleandintothepageforwiresunderthesouthpoleface.Theneutralplaneinthismachineisexactlyvertical.

Now,supposealoadisconnectedtothismachinesothatitactsasagenerator.Currentwillflowoutofthepositiveterminalofthegenerator,socurrentwillbeflowingoutofthepageforwiresunderthenorthpolefaceandintothepageforwiresunderthesouthpoleface.Thiscurrentflowproducesamagneticfieldfromtherotorwindings,figure（c）.

Thisrotormagneticfieldaffectstheoriginalmagneticfieldfromthepolesthatproducedthegenerator’svoltageinthefirstplace.Insomeplacesunderthepolesurfaces,itsubtractsfromthepoleflux,andinotherplacesitaddstothepoleflux.Theoverallresultisthatthemagneticfluxintheairgapofthemachineisskewed,figure（d）and（e）.Noticethattheplaceontherotorwheretheinducedvoltageinaconductorwouldbezero（theneutralplane）hasshifted.

Forthegeneratorshownhe