Безрученко В.Н., Xотян А.С. Электрические машины

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CJIaooHaChllIJ.eHHbIe MaWHHbI OOJIa,ltaIOT JIytlWHMH peryJIH-

POOOtlHblMH CBOHCTBaMH, tleM CHJIbHOHaCbIm.eHHbIe. Ho MaWHHbI

' co CJIa60HaCbIm.eHHoH MarHHTHOH u.enblO, HMeSi OOJIbWHe nJIO-

m.a.IJ,HnOlIepetlHOrO CetleHHSI ytlacTKoB u.eDH, OOJIhWe no pern-

\ MepaM, TSl1KeJIee H .IJ,op01Ke.

. YMeHblIIHTb HaCbIm.eHHe MarHHTHoH u.enH MalIIHHbI M01KHO

sa CtIeT YBeJIHtleHHSI B03.IJ,YlIIHoro 3a30pa npH coxpaHeHHH BbI-

COKHX HH.IJ,YKUHHB CTaJIH. Ho npH 9TOM HeOOXO.IJ,HMOBbInOJIHHTb

MOm.HylO OOMOTKY B030YQeHHSI C 60JIblIIHM pacxo,Z{oM Me.IJ,H.

3aBHCHMOCTH OT yCJIOBHH paoOTbI, .IJ,JISIKOTOPbIX npe.n.-

Ha3HatleHa MalIIHHa, ee MarHHTHaSi uenb M01KeT ObITb: CJIaOO-

HacbIm.eHHoH

1,5),

Cpe.IJ,HeHacblm.eHHoH

1,6 -;-

-;- 1,8) H CHJIbHOHacbIm.eHHoH

1,9).

.llJISI nOJIYtleHHSI TaKHX 3HatleHHH Ko3<M>Hu.HeHToB HaCbIm.e-

HHSI B MalIIHHax nOCTOSlHHoro TOKa HH.IJ,yKU.HHHa OT,lteJIbHbIX

Ytl8CTKax MarHHTHOH uenH .IJ,OJI1KHbIHaXO,ltHTbCSI B npe,Z{eJIax:

BOS,lI,ymHblll sasop B", TJI

sy6Ub1 lIKOPlI

,TJI _ •

'I.

••••• 0,8-1,1

. ..•. 2,1-2,4

TeJI() JlXOpll

B.,

TJI •

IJQ/IJOCa

,T .II

» CTaHHHH "', TJI

• 1,2-1,6

• 1,3-1,7

• 1,1-1,4.

KOIITpO••••••••• Hnpocw

"311~

lITO H83b1BaeTCJI MarHRTHoA nenhlO? l(aKHe KOHCTpyxTHBHHe

9.11eMem1it

M8II1HH nOCTOJlHHOro TOKa 06P83Y1OT MarHRTHwe nenH? liTO TaKoe oc.

HOBHOI MarHRTHHI noroK?

Ha OCHOBaHHHKaKoro saKOHa H B KaKol nOCJIe.ll.OB8TeJlI>HOCTHBWnOJIHJI-

eTCJI pac'IeT MarHRTHHX nend?

liTO H83b1BaeTCJI KoscM>HIUleRToM nOJIIOCHOro nepeKpJ>ITHlI? Kall OH

Onpe,ll.eJIJleTCJI?

OcHOBHOI MarHRTHwA noroK B mecTHnOJIIOCHOM TJlroBOM .lUlHraTeJIe

9JIeKTpOB03a

fDo

0,12 B6; Ko3ljlcJlHIUleHT nOJIIOCHoro nepeKpJ>ITHJI

0,72 ; qHCJIO n830B B JlKOpe z

123; pac'IeTHJ>Ie mHpHHa H Bwcora

ay6na lIKOPll

zl/

•

0,01 M H

hz -

0,035 M; MHHa naKeTa JlKOPJI

l. =

••••0,38 M. lIeuy PaBHJ>I:

HH.lI.YKnHJIB sy6uax lIKOPll

;

M,llC

ay6.

. II.

nOB

(HCnOJII>SOB8TI>XapaKTepHCTHKY Ha pHC. 2.3)?

3.1.

YCTpoiicT80 O&MOTOK

COBpeMeHHbIe 3JIeKTpHqeCKHe MaWHHbI BbInOJIHHIOT B OCHOB-

HOM C 3y6qaTbIMH 15apa6aHHbIMH HKOpHMH, B na3bI KOTOpblX

yKJIa,lJ;blBaIOT

a8YXcIlOtlflble

ol5MOTKH.

OcHOBHbIM 3JIeMeHTOM ol5MoTKH HKOpH HBJIHeTCH

Ce"t4

KOTopaH COCTOHT H3 O,lJ;HOro HJIH HeCKOJIbKHX nOCJIe,lJ;oBaTeJIb-

HO COe,lJ;HHeHHblX BHTKOB.

Ka}l{)J;OM na3Y HaXO,lJ;HTCH, KaK

npaBHJIO, HecKOJIbKO ceKUHif (pHC.

3.1, a),

H30JIHpOBaHHbIx 015-

IlleR KopnycHoif H30JIHUHeR OT CTeHOK na3a H 015pa3ylOIllHx

KaTywKy HKOpH.

nOM cJIyqae rOBopHT,

qro

Ka}l{)J;OMy,lJ;Byx-

CJIOHHOMy

peaJlbflOMy

na3Y COOTBeTCTByeT HecKOJIbKO ABYx-

CJIOHHblX

8/1£MeHmapflblX

na30B.

CeKUHH HKOpH HMeeT ,lJ;BeaKTHBHble croPOHbl - BepxHIOIO

H HH1KHIOIO. nepexo,lJ; H3 aepxHero CJIOHB HHJKHHR BblnOJIHHIOT

nOMOIllblO

ZO/lOB"U

B 3aJJ;HeH JI0150BOH qaCTH ceKUHH. Koaubl

nepe,lJ;HeH JIoOOBOH qaCTH ceKUHH npHCOe,ZJ;HHHIOT(npHnaHBaIOT)

K KOJIJIeKTOpHblM nJIaCTHHaM (CM. pHC.

1.6),

npHqeM HallaJIO

nOCJIe,ZJ;YIOIlleHceKllHH nO,lJ;COe,lJ;HHHIOTK TOH JKe KOJlJIeKTOplJOH

nJI8CTHHe, liTO H KOHeu npe,lJ;bl,lJ;YIUeH.

3ro

C03,lJ;aeT HenpeplllB-

HOCTb ol5MOTKH. Ol5Illee KOJlHqeCTBO ceKUHR

BCer,lJ;a p8BHO

qHCJIY KOJIJIeKTOpHblX nJlaCTHH

H qHCJlY 3JIeMeHTapHblX na-

308

z,:

PBC.

3.1.

PaCUOJIO:IKeRBe npoBOABH-

EOB B nasax JlKOPlI CBa pe6po»

(a)

H CIIJI8JIDIJI»

(6):

1 -

ItlIBB:

:I -

npOItllIlAKB;

8 -

BJITo

KOBU.

4 _

KopnycRB..

5 -

nOKpOBBBJI

BBOJIlID.HlI

PHC. 3.2. 06JU11A BHA neTJIeBOA 06-

MOTKH

(a)

H CX,eMa coe.ll.HHeHHJI ee

ceKuHI

(6)

PHC.

3.3.

CxeMa' pacnOJIO:IKeHHJI

.lI.HaMeTpaJIbHOA, yxopOqeHHOA H

Y.lI.JIHHeHHOAceKUHI B MarHHTHOM

tlOJIe 9JIeKTpH'IecKol MaWHHW

r.n;e

un -

qHCJlO KOJlJleKTOpHbIX nJI8CTHH HJIH 3JIeMeHTapHblX

na30B, npHXO,lJ;HIllHXCH Ha O,lJ;HHpeaJlbHblH na3.

nOCKOJIbKY Ka:>K,lJ;bIHBHTOK ceKUHH o15pa30BaH ee ,lJ.ByMH

cropoHaMH (npOBO,lJ;HHKaMH), TO nOJlHoe qHCJlO npOBO,lJ;HHKOB

8 HKOpe

N =2Kw

2Sw

r,lJ;ew

qHCJIO BHTKOB B CeKu,HH.

nOCJltWIne ro.zu,r, oco6eHHO B TSlroBYX 9JleKTIUl'lecKRX

MaumH8X, IIIRpoKoe pacnpocrpaHeHRe nOJIyqHJl8.~

KOHCTpYKI{RSI nasa (PRC.

3.1, 6),

B KoiopoA 60JIbIIIee 3anOJl~

ReHRe Me~blO n JIYtIIIIaSl OT~atIa renJlOThI K81IC,AIiM npoBO~R.

KOM CTeHK8M nasa, XOTSI npHHI{HnHaJlbHoro paSJIHtIHSI MeQY

nas8MH Ha pHC.

3.1, a

HeT: BTOpOH MO>KHOnOJIytIHTb, pac~

nOJI01KHB npOBO~HKH nepBoro CnJIaWMSI»; y oOOHX

01:::

n09TOMY 06MOTKa, BhInOJIHeHHaSl KOHCTpyKTHBHO no

pHe.

3.1, 6,

TaK>Ke SlBJISleTCSI~BYXCJIOHHOH. '

HaBo~HMhIe B Ka>K,ZJ;oAH3 aKTHBHhIX CTOpOH CeKI{HH

3.llC

~OJI>KHhI CKJIa~hIBaTbcSI; n09TOMY croPOHhI CeKI{HA pacnoJIa-

raIOT no~ nOJIlOCaMH pa3HoH nOJISlpHOCTH H8 pacCToSlHHH Yl,

paBHOM HJIH npH6JIH3HTeJIbHO paBHOM ~JIHHe nOJIIOCHoro~e-

JIeHHSI ~ (pHC.

3.2).

06MOTKH, Y KOTOPhIX

~,T. e. £TOPOHbI

CeKI{HH HaXO~SlTCSIno~ yrJIOM

180°

3JI. no OTHOllIeHHIO ~pyr

K ~pyry, nOJIytIHJIH Ha3BaHHe

aUaMempa.JlbHblX,

B OTJIHtIHe

OT XOpa08blX,

r~e

+- ~.

Ha pHC.

3.3

nOKa3aHhI TpH CeKI{HH, y KOTOphIX: Yl

't'

(ceKI{HSI

ab);

't'

(ceKuHSI

ac)

't'

(ceKuHSI

ad).

KOHTyp

,l{HaMeTpaJIbHOH ceKUHH OXBaThIBaeT BeCb MarHHTHhIH nOTOK

<Do,

COOTBeTCTBYIOIII.HHnJIOIII.a;lH, OrpaHHtIeHHOH KpHBOH HH-

~KUHH B B03~YllIHOM 3a30pe: KOHTyp XOMOBOH yKopOtIeHHOH

ceKUHHac OXBaTblBaeT TOJIbKO tIaCTb 9TOro nOTOKa; n09TOMY

H8BO~HMaSl B HeH

3.llC

6Y~eT MeHbllIe, tIeM B ceKUHH

BeJIHtIHHy, npon,?PUHOHaJIbHYIO 3allITpHxoBaHHoii nJIOIII.~~H,

COOTBeTCTBYIOIII.eHyKopOtIeHHIO

be.

~JIHHeHHaSl ceKUHSI

nOJIyqaeT oTpHuaTeJIbHoe npHpaIII.eHHe nOTOKa, COOTBeTCTBYIO-

III.ee· sallITpHxoB8HHOH nJIOIII.a~H Ha paccTOSlHHH

bd.

ECJIH

yKopotleHHe

H y~JIHHeHHe

paBHhI MeJK,Zl;yco60ii, TO

~.llC

B ceKUHSlX

TaK>Ke 6Y~YT paBHbI; O,!{HaKO,!{JISI H3rotoB~

JIeHHSI y,!{JIHHeHHOH ceKUHH Tpe6yeTCSI 60JIbllIe Me,!{H H HaOJlH-

I{HH H8 BhInOJIHeHHe ee JI060BblX tIaCTeH. n03TOMY Ha npaK-

THKe y,!{JIHHeHHble 06MOTKH He npHM'eHHIOT. .

. . OCHOBHbIM THnOM 06MOTKH HBJIHeTCH yKopoIJ:eHHaH

(1/1

't),

H TOJIbKO Y He60JIltllIHX MallIHH MO:>KHOBCTpeTHTb ,!{H8-

MeTpaJIbHhIe 06MOTKH. He06xo.z(HMOCTb yKopOtIeHHH 06MOTOK

6y,!{eT oOOcHoBaHa B r JI.

3.2.

npOCT•• neTne••• o6MoTKa

PQCmo(J, netn.lle8o(J, 06MomKO(J,

Ha3hIBaeTCSI TaKaH, y KOTO-

pOH HatIaJIO H KOHeu ceKUHH npHcoe,!{HHeHl>l K pSl,!{OMJIe:>KaIII.HM

KOJIJIeKTOpHbIM nJIaCTHlfaM, T. e. ee waF no R:OJIJIeKTOpy

1. (3.2)

PHC.

3.4.

CxeM8 npOCTOA neTJIeBoA 06MOTKH

(2p

K =

18,

Ul =

-3,

= UK =

8 =

0,5)

CBoe H83BaHHe 3Ta 06MoTKa nOJIytIHJIa nOTOMY, qro ee ceKUHH

HanOMHHaeT neTJIIO (CM. pHC.

3.2).

PaccToHHHe Me:>K,!{yaKTHBHblMH CTopOHaMH O,!{HOHceKUHH,

Bblpa:>KeHHOetIepes tIHCJIO KOJIJIeKTOpHblx nJIaCTHH, Ha3b1BaeT-

CH·

nep8bl.M I/.QCmutUlblM UUl20M

Yl' TaK KaK Ha ,!{JIHHy O,!{HOro

nOJIIOCHOrO,!{eJIeHHSInpHxo,!{HTCH

K /(2p)

KOJIJIeKTOpHhIx nJIac-

THH, TO Y yKopOtIeHHOH 06MOTKH

2p -

(3.3)

r,!{e 8 - BeJIHtIHHa yKopOtIeHHH. QqeBH~Ho, BeJIHIJ:HHa8 ,!{OJI:>KHa

6b1Tb TaKOH, tIT06b1 3HatIeHHe llIara Yl 6b1JIO paDHO UeJIOMY

.IJ:HCJIy. KaK npaBHJIO, OHa MHHHMaJIbHa.

,!{HaMeTpaJIbHOH

06MOTKH 8

. BTopaH ceKUHH C,!{BHHyTa BnpaBO OT nepBOH Ha llIar

YK'

PaCCTOHHHe Me>K,!{y KOHeIJ:HOHcropOHOH npe,!{b1,!{YIII.eii ceKUHH

H HatIaJIbHOH CTOpOHoii CJIe,!{YIOIU.eH Ha3h1BaeTCH

8m.opbl.M

I/.QCmutt.Hbl.M UUl20M Y".

Ero OTCtIeT y neTJIeBOH 06MOTKH H,!{eT

cnpaBa HaJIeBO (npOTHB OTCtIeTa

Yl),

n03TOMY

HBJIHeTCSI

OTpHuaTeJIbHOH BeJIHtIHHoH.

PeaYllbmupylOUI,U(J, UUl2

neTJIeBoii 06MOTKH

I-, (3.4)

1- Ut. (3.4,a)

PaccMOTpHM npHMep npocroH neTJIeBoii 06MOTKH reHepa-

TOpa, cxeMa H OCHQBHble ,!{aHHhle KOTOPOH npHBe,!{eHhI Ha

pHC.

3.4.

[fOJIaraeM, tITO tIHCJIO3JIeMeHTapHblx na30B

=~,

-!!...-

T. e.

1; We

lUeTKR

Ha KOJlJleKTOpe OTCTOJITHa OAR-

HaKOBOM paCCTOHHRR APyr OT

Apyra R YCTaHOBJleHbI TOtIHO

no OCR nOJlIOCOB, 3aMbiKaH Ha-

KOpOTKO KOJlJleKTOpHble QJlaCTH-

Hbi ceKUHH, CTOPOHbI KOTOpblX

pacnOJlO1KeHbI CHMMeTpHtIHO OT-

HQCHTeJlbHO cepeAHHbI nOJlIOCa,

KorAa

a.llC

B HHX npH6J1H3H-

TeJIbHO paBHa HyJIIO (3TH ceK-

UHH

N!! 1

BbI)l.eJIeHbI Ha

pucyHKe 1KHpHbIMH JlUHHHMH).

ECJlu BeJiUtIHHa yKopoqeHuH

,JA

TO CTOpOHbI '!JfUX ceK--

UUH Jle1KaT TOtIHOlta reoMeTpU-

PHC. 3.S. Ynpo~eHHall cxeMa npo-

tIeCKOH HeHTpaJiU U ux

a.llC

CToli neTJIeBoli OOMOTKH

TOtIHO paBHa HyJIIO.

TaK KaK ceKUUU

'N!!

3a-

KOpOtIeHbI m.etKaMH

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B2,

OHU He yqaCTByIOT B C03,lJ;aHUU

a.llC

B 06MOTKe. OcTaJIbHbIe 1Ke

ceKuuH, pacnpe,lJ;eJleHHbIe paBHOMepHO Me1K,lI.y llieTK8MH,

06pa3yIOT tIeTbIpe O,lJ;HHaKOBbIXnapaJIJleJIbHblX BeTBH, B Ka1K-

,lJ;OHH3 KOTOpbIX C03,lJ;aeTCH

a.llC E

tIeTbIpbMH ceKUHHMH. Bepx-

HHe CTOPOHbI ceKUHH Ka1K.n.oHnapaJIJleJIbHOH BeTBH HaXO,ll,HTCH

no,lJ;O,lJ;HUMnOJlIOCOM, a HHJKHHe - no,lJ;,lI,pyrUM. ,YnpOIII.eHHaH

cxeMa npocroH neTJleBOH 06MOTKH, nOKa3aHHOH Ha pUC.

3.4,

u306paJKeHa Ha pUC.

3.5,

r,lJ;eKaJK,lJ;b1Hee BUTOK COOTBeTCTBY~

peaJlbHOH ceKUUU 06MOTKH. -

KaK BH,lI,HOU3 pHcyHKa, TOK HKOpH

COCTOUT H3 TOKOB

napaJIJIeJIbHbIX BeTBeH

BHyTpU 06MOTKH, npUtIeM K KaJK,lJ;OH

III.eTKe nO,ll,XO,lJ;HT(HJlU YXO,lJ;HT) TOK-

AByX napaJIJleJIbHbIX

BeTBeH. IlpH BpaIII.eHUU HKOpH ceKUUH nepeXO,lJ;UT H3 OAHOH

napaJlJIeJIbHOH BeTBU B ,lJ;pyryIO, 3aMblKaHCb HaKopOTKO III.eTKOH

B MOMeHT nepeXO,lJ;a. KaJK,lJ;OH nape nOJlIOCOB COOTBeTCTBYIOT

napa III.eTOK U napa napaJlJleJlbHhIX BeTBeH 06MOTKU.

113.paccMOTpeHHH cxeM npocTOH neTJleBOH 06MOTKU (puc.

3.4

3.5)

CJIe,ll,YeT, tITO y MaIlIHHbI C tIUCJIOM nOJlIOCOB

tIHCJlO napaJIJleJlbHblX BeTBeH 06MOTKU

Ho 3TO tIHCJlO

nOJlIOCOB 6bIJlO BbI6paHo B paccMoTpeHHoM npHMepe npou3-

BOJlbHO. CJIe,lJ;OBaTeJIbHO, B OOIII.eM CJlyqae tIUCJlO nap napaJl-

JleJIbHblX BeTBeH npocTOH neTJleBOH OOMOTKU paBHO tIHCJlY

nap nOJIIOCOB, T. e.

Iff

2ai

. (3.6)

OrMeTHM, tITO

a.llC

B OAHOH napaJlJleJIbHOA BeTHH

HB-

JlHeTCH TaK1Ke H

a.llC

BO Bcd ooMOTKe

tIHCJlO III.eTOK Ha KOJl-

JleKTOpe MaIlIHHbl C neTJleBOH OOMOTKOA BcerAa AOJlJKHO 6mb

paBHO tIHCJlY ee nOJlIOCOB.

npHMC!p pac'leT8 npocroA neT.lIeBOi 06MOTKH. HcXo~H1lIe ~aHH1lIe

(CM. pHC. 3.4): qHCJIOnOJlIOCOBMaWHHbI

= 4, qHCJIOnaSOB II

18, qHC-

JlO KOJIJIeKTOpHblXDJlaCTHH

= 18, qHCJIOBHTKOB B CeKnHH we =

nOCKOJIbKY

T. e. B K8JK,llOMpeaJIbHOM nasy

HaxO~TClI O~HH 9JIeMeHTapHblA, COCTOH~HA HX ~y~ cropOH (BepxHeA H

HH1KHeA) ceKUHA. '

CorJIaCHO (3.3), nepBblA qaCTHqHblA war

= ~8 - e. QT06b1

6b1JIOpaBHO UeJIOMy qHCJIY, MHHHMaJIbHall BeJIHqHH8 yKopo'leHHH e =

0,5;

ror~a

4 (npoBo~HHK, JIe1Ka~HH B nepBOM nasy, coe~HHlIeTClI Jlo6oBoA

'1aCTblOC npoBo~HHKOM nllToro nasa). nOJIHoe qHCJIOnpoBO,ll.HHKOB,COrJlaCHO

(3.1,

a),

2·18= 36. . .

nOCKOJIbKYYK

TO HS (3.4,

BropoA '1aCTH'IHblA war Ya = 1 - 4

-3 (ero OTC'IeTHa cxeMe H,lI.eT,B OTJlH'IHeOT nepBoro qaCTH'IHOro wara,

. He CJIeBa HanpaBO, a cnpaB8 HaJIeBO).

HaHeceM Ha '1epTe1K KOHTypbl nOJIIOCOB,YKa1KeM (npOHSBOJIbHO) HX

nOJIlIpHOCTb, a TaK1Ke npOHYMepyeM Bee nasbi (CM. pHC. 3.4). BepxHHA npo-

BO,ll.HHKB nasy npe,ll.CTaBJIeHCnJIOWHOH,a HH1KHHA- WTpHXOBOAJlHRHeA.

YCJIOBHMClIC'IKTaTb, lITO nOJIlOCbI,KOHTypbl KOTOPblXHaHeceHbI Ha '1epTe1Ke,

HaXO,ll.llTClIH8,lI.lIKOpHOA 06MOTKoA, T. e. MarHHTHbie CHJlOBbieJlHHHH, Ha-

npHMep ceeBepHoro» nOJIlOCa, BXO,ll.llTB nJIOCKOCTbqepTe1Ka.

38TeM He06xO,ll.HMOHs06pasHTb KOJIJleKTOpHble nJIaCTHHbI H npHcoe.u.H-

HHTb BepXHHA npOBO,ll.HHKnepBoro nasa K KOJIJIeKTOpHOAnJlaCTHHe, KOTO-

poA npHcBoHM

JIl'g

9TOT npOBO,ll.HHKs8,lI.HeAJIo6oBOA '18CTblOCoe,ll.HHlIeTClI

C HH1KHHMnpoBO,ll.HHKOMnllToro nasa. 06pasoBaJIacb nepBall ceKUHlI; ee

KOHeu no~coe~HHeH K KOJIJleKTOpHOAnJIaCTHHe

JIl'g

2, OT KOTOpoAHa'lHHaeTClI

Bropall ceKUHII (BepxHHA npOBO,ll.HHKBTOporo nasa) • .llaJIbHeAwee nocTpoe-

HHe cxeMbi BhinoJIHHeTCH aHaJIOrHqHO. nOCJIe,ll.HIIlI CeKUHlI (18-11) ,lI.OJI1KHa

SaMKHYTb o6MoTKy, T. e. eeKOHeu (HH1KHHH npOBO,ll.HHKqeTBepTOrO nasa)

no~coe.u.HHlIeTClI K KOJIJleKTOpHOAnJIaCTHHe

JIl't

.llaJIee CJI~YeT Hs06pasHTb Ha cxeMe ~eTKH. PacCTollHHe MeQY ~eT'

. KaMH npOTHBOnOJI01KHOAnOJlHpHOCTH

,lI.QJI1KHO6b1Tb paBHO

K/(2p)

18/

4,5

KOJIJleKTOpHblX nJlaCTHH; ~eTKH YCTaHaBJIHBalOTCHTO'lHO no

OCH nOJIIOCOB.nOCKOJlbKY 06MOTKa BblnOJlHlleTCH )l.JllI MaWHHbI C

lUeTOX ~OJl1KHO6b1Tb '1eTbipe. nOJIlIpHOCTb ~eTOK Onpe,ll.eJIHIOTHCXO,ll.lIHS

npe~nOJI01KeHHlI, lITO MaWHHa pa60TaeT B reHeparopHoM pe1KHMe, a ee lIKOPb

Bp8~aeTClI B HanpaBJIeHHH CTpeJIKH. BOCnOJlbSOB8BWHCb npaBHJIOM npa-

BoA pyKH, HaXO,ll.lIT HanpaBJIeHHe 3.llC (roKa) , HaBe~eHHoA B ceKUHllx, H

YKasbiBalOT ero CTpeJIKaMH. B HTOre OKaSaJIOCb, lITO ~eTKH

A2,

XOTOpblX TOK OTBO,lI.HTClIBO BHewHIOIO uenb, lIBJ1HlOTClI nOJI01KHTeJlbHblMH,

a ~eTKH

B2 -

OTpHuaTeJIbHblMH. lIJ.eTKH O~HHaKOBoA nOJIllpHOCTH

iJpHCoe.u.HHlllOTnapaJlJIeJIbHO K COOTBeTCTByro~HMBblBO,ll.aM.

, PaCCT8HOBKY ypaBHHTeJIbHblX coe.u.HHeHHA nepBoro po,ll.a CJIe,ll.YeT

BhlnOJlHHTb, DOJIb3yHCb Bblp81KeHHeM (3.18).

3.3.

"poeT •• IIOJIIIOU. o&MOTIC8

CeKIlHH BOJIHOBOiiOOMOTKH,npHCDeAHHeHHIlle K KOJIJleKTOpy,

HallOMHHalOT BOJlHY; OTCIO,na H Ha3BaHHe 06MOTKH -

8OJlH()(JQJl

(PHC.

3.6).

YCJIOBHe ee BblnOJIHeHHSI TaKOBO: HallaB C nepBOii KOJIJIeK-

ropHoii nJIaCTHHbI, HyJKHO COsepWHTb OJlHH 06xoJl SlKOpSl,

yJIOJKHB npH 9TOM p ceKIlHii; KOHell p-ii ceKIlHH CJIeJtYeT npH-

coeJlHHHTb K nJIaCTHHe, pacnOJIOJKeHHOii PSlJlOM c nepBOii. Ha

npaKTHKe OOJIbweii: lJaCTbIO BCTpelJaIOTCSI HenepeKpew,HBaIO-

w,HeCH oOMOTKH, y KOTOpblX oOXOJl HKOpSi 3aKaHlIHBaeTCH Ha

nJIaCTHHe, JIeJKaw,eii CJIeBa OT nepBoii, T. e. Ha K-ii nJIaCTHHe.

TaKoii: oOMoTKe ceKllHH npH YKJIaJlKe nOCJIeJlOBaTeJIbHO CJlBH-

raIOTCH Ha OJlHO KOJIJIeKTOpHoe JleJIeHHe, a nOCJIeJlHSISI ceKllHH

3aMKHyTa lJepea nepByIO KOJIJIeKTOpHyIO nJI3CTHHY C HallaJIOM

OOMoTKH.

B COOTBeTCTBHHco CKa3aHHblM, 3a OJlHH OOXOJl SlKOpH npo-

HCXOJlHT nepeMew,eHHe Ha

K -

KQJIJIeKTOpHblX nJIaCTHH,

HOTaK KaK npH 3TOMYKJIaJlblBaeTCSI p ceKIlHH, TO

K -

OTKy,lta

K-I

=-p-'

(3.7)

nOCKOJIbKY YK

Y,ltPOOHblM lIHCJIOMObITb He MOJKeT, lJHCJIO

,ltOJIJKHOOblTb CTporo COrJIaCOBaHO C

BTOpoii: lIaCTHlIHblii: war BOJIHOBOii OOMOTKHOTClIHTblBaeTCSI

B TOM >Ke HanpaBJieHHH, liTO H nepBblii; n09TOMY 3,lteCb

Y2-

nOJIOJKHTeJIbHaSi BeJIHIIHHa:

Y-

YK-

Yt·

03HaKOMHMCH CO cBoii:CTBaMHttpocToii: BOJIHOBOii: OOMOTKH

Ha npHMepe cxeMbI, nOKa3aHHoii Ha pHC. 3.7:

-1 17-1

YK=Y= --p-=

K 17 1

-2--

-4--

p .

CeKllHH N!! 1, 5, 9, 10 H 14, BbI,lteJIeHHble Ha pHC. 3.7 >KHp-

HblMH JIHHHSlMH, B OTJIHlIHe OT ceKllHii: neT,IIeBoii oOMOTKIt., 3a-

MblKalOTCSI HaKopOTKo lIepea JtBe W,eTKH o,ltHoii nOJISIpHOCTH H

COe,ltHHHTeJIbHble npOBO,lta Me>KJty HHMH.

npoCJIeJlHB Ha cxeMe oOMOTKH 3a HanpaBJIeHHeM 3IlC,

MOJKHO YBH,lteTb, liTO OHO cOXpaHSIeTCSI HeH3MeHHblM BO Bcex

cropoHax ceKIlHii, pacnOJIOJKeHHblX B npeJteJI8X nOJIIOcHoro

,neJIeHHSI, T. e. B K/(2p)

S/(2p) CTOpOHax ceKIlHii. 3a O,ltHH

OOXO,ltSIKOpSi npH HaMOTKe yKJIa,ltblBaeTCSI (cOe,ltHHSIeTCSInOCJIe-

,ltOBaTeJIbHo) 2p CTOpOH ceK~Hii; CJIe,ltOBaTeJIbHO, KOJIHlIeCTBO

PRC.

3.6.

061l{RH BHA BOJIHOBOHOOMOTKH

(a)

H cxeMa coeARHeHHlI ee ceK- .

" - IlHA

(6)

PRC.

3.7.

CxeMa npocroA BOJIHOBOA OOMOTKH

(2p

S =

17,

UK-

'8)

ceKIlHii B O,ltHoii napaJIJIeJIbHoii: BeTBH

S/2,

lIHCJIO napaJIJleJIbHblX BeTBeii: oOMOTKH He 3aBHCHT OT IIHCJI~

nOJIIOCOB MaWHHbl H paBHO

S/Sa

2, T. e.

1. (3.9)

3.llC B SlKope, KaK H B neTJIeBoii: 06MOTKe, onpeJteJISleTCSI

3IlC B o,ltHoii napaJIJIeJIbHOii BeTBH, a TOK SlKOPSI

2i..

(3.10)

Ha KOJIJIeKTOpe SlKOPSI c BOJIHOBOii OOMOTKOii MOJKHOYCTa-

HOBHTb TOJIbKO JtBe W,eTKH, HanpHMep

(CM. pHC.

3.7),

TaK KaK Bce W,eTKH JlaHHoii nOJISIpHOCTH COe,ltHHeHbl KOPOTKO-

38MKHyn.rMH CeKUHHMH Me1KJtY co6oA. 3TH .ABe IUeTKH npJIMYT

Bech TOK, a KOPOTK038MKHYTIlIX ceKUHA He 6YJJ;eT. OAHaKO

JJ;JIHcoxpaHeHHH nJIOTHOCTH TOKa nOJJ;IUeTKaMH npH 3l'OM nOTpe-

6yeTCH yJJ;JIHHHTh BJJ;BOeOCTaJIhHhle IUeTKH, 'ITO nOBJIe1JeT 3a

co6oA YBeJIH1JeHHe oceBOA JJ;JIHHhl KOJIJIeKTOpa.

KpOMe TOro, npH HenOJIHOM 1JHCJIeIUeTOK B03MOJKHa HeKO-

TOpaH HecHMMeTpHH napaJIJIeJIhHhlX BeTBeA OOMOTKH, Y KOTO-

phlX pa3Hoe 1JHCJIOceKUHA

KI(2a).

n03I'OMy 06hl1JHO CTaBHT

nOJIHhlA KOMnJIeKT

(2p)

IUeTOK, HMeH B BHJJ;y, 1JTO B CJIY1Jae

BhlXOJJ;a H3 CTpOH, HanpHMep, OJJ;Horo IUeTKOJJ;epJKaTeJIH B Ma-

WHHe, MOJKHO npoJJ;OJIJKHTh ee paoOTy c HenOJIHhlM 1JHCJIOM

IUeTOK, YMeHhWHB npH 3TOM TOKOBylO Harpy3Ky JJ;O3Ha1JeHHH,

JJ;onycTHMoro no nJIOTHOCTH TOKa ,nJIH OCTaBWHXCH IUeTOK.

PHe.

3.9.

CxeMa «JlHrYllle'lbeib 06MoTKH

(a)

H lfloPMa ee lIKOP-

HoA KaTywKH

(6)

BpeMeHHO. PaCCMOTpeHHaH oOMOTKa Ha3bIBaeTCH

iJ8yxxoiJ08Oa

iJ8YKpamJt03aMKHymoa.

ECJIH 1JHCJIOKOJIJIeKTOpHbIX nJIaCTHH B MaWHHe He1JeTHOe,

TO, 3aK'oH1JHB nepBbIR 06xoJJ; KOJIJIeKTOpa Ha

K-R

nJIaCTHHe

H He npepblBaH HaMOTKH, BbInOJIHHM BTOPOR 06xoJJ; no 1JeTHbIM

nJIaCTHHaM. B HTOre nOJIy1JHM OOMOTKY, Ha3blBaeMYlO

iJ8YXX~

iJ080a OOHOKpORl.flO8(lMKHymoa. .

CJlOlKlUlH BOJIHOBaSlOOMOTKa. ECJIH, BbInOJIHHH BOJIHOBylO 06·

MOTKy, nOCJIe OJJ;Horo ooxoJJ;a KOJIJIeKTOpa npHRTH K nJIaCTHHe,

OTCTOHIUeA OT HCXOJJ;HORHa

JJ;eJIeHHR, TO MOJKHO nOJIY1JHTb

caMOCTOHTeJIbHblX BOJIHOBbIX OOMOTOK, KOTopbIe oopa3ylOT

O)1,Hy CJIO:lKHYIO BOJIHOBylO. B HeR war no KOJIJIeKTopy

K-m

= --

(3.13)

a 1JHCJIOnap napaJIJIeJIbHbIX BeTBeR

m. (3.14)

KOMOHHHpoBaHHaJI (<<JlJlrywellbSllt) OOMOTKa. npe)1,CTaBJIH-

eT c060R KOM6HHaUHIO npoCTOR neTJIeBOR H CJIOJKHoA BOJI-

HOBOR OOMOTOK, oOIUaH ceKUHH KOTOPblX HanOMHHaeT JIHrywKy

(PHC.

3.9).

06e OOMOTKH npHcOe)1,HHHIOTCHK O)1,HOMy H TOMyJKe

KOJIJIeKTOpy, JIeJKaT B O)1,HHXna3ax H COCTOHl: H3 O)1,HHaKoBOro

1JHCJIaceKUHR. ,UJIH paBeHcTBa 3,UC B napaJIJIeJIbHblX BeTBHX,

00pa3yeMblx neTJIeBOR H BOJIHOBOR ooMOTKaMH, 1JHCJIOnapaJI-

JIeJIbHblX BeTBeR HX )1,OJIJKHOObITb O)1,HHaKOBO. n03TOMY eCJIH

y neTJIeBOR OOMOTKH

tln

TO BOJIHOBaH OOMOTKa )1,OJIJKHa

HMeTb 1JHCJIO XO)1,OB m

TOr)1,a, COrJIaCHO BblpaJKeHHIO

(3.14),

tln

aa.

llIar no KOJIJIeKTOpy )1,OJIJKeHCOOTBeTCTBOBaTb

pe3YJIbTHpYIOIUeMY, T. e.

YK.n

YK.B

KIp.

3.4.

CnoHCHwe 06MOTH"

C/103ICHble,

HJIH

MHOeoxoiJOOble,

OOMOTKH MO>KHO paccMaTpa-

BaTb KaK C01JeTaHHe HeCKOJIbKHX

2, 3, ... )

npocTblx 00-

MOTOK. qHCJIO napaJIJIeJIbHbIX BeTBeR B TaKHX oOMOTKax COOT-

BeTCTBeHHO B

pa3 OoJIbWe 1JHCJIaBeTBeR B npocTbIX oOMoTKax.

CJIOlKHaJI neTJIeBaSl oOMoTKa. qHCJIO nap napaJIJIeJIbHblX

BeTBeR B TaKoR oOMOTKe

m. (3.12)

Ha pHC.

3.8

H300paJKeH 3JIeMeHT OOMOTKH npH

ECJIH MaWHHa HMeeT 1JeTHOe1JHCJIOKOJIJIeKTOpHblX nJIaCTHH,

TO TaKaH OOMOTKa npe)1,CTaBJIHeT COOOR cOBoKynHocTb )1,ByX

OT)1,eJIbHbIX npocTbIx OOMO-

TOK, COBMeIUeHHbIX Ha HKO-

pe H paooTalOIUHx napaJI-

JIeJIhHO. Ha pHC.

3.8,

1JTa-

ObI no,n1JepKHyTb caMOCTOSl-

TeJIbHOCTb ooeHX 06MOTOK,

OHH nOKa3aHbI no 06e CTa-

POHbI OT KOJIJIeKTopa. O)1,Ha

oOMoTKa 3aMblKaeTCSI TOJIbKO

no He1JeTHbIM, a )1,pyraSl - no

1JeTHbIM nJIaCTHHaM. qHCJIO

IUeTOK OCTaeTCSIpaBHbIM 1JHC-

JIy nOJIIOCOB

2p,

HO wHpHHa

KaJK,AORIUeTKH )1,OJIJKHaObITb

yBeJIH1JeHa, 1JTb6b1 ooe 06-

MOTKH MOrJIH pa60TaTb O)1,Ha-

PHC.

3.8.

CxeMa CJIo)l(HoA neTJleBOA

06MOTKH C ypaBHHTeJIlIMH TpeTberO

pO,Aa

3.5. YCnoBNJI cNMMeTpNN o&MOTOIC

Ka:H<,lJ.aSlnapa napaJlJleJIbHblX BeTBeA 06MOTKH 06pasyeT

KaK 6b1 npocreAIUylO MalliHHY, pa6OTalOIIJ.YIO napaJlJleJlbHO

C ,lJ,pyrHMH. Cne,lJ,OBaTeJlbHO, 3.llC B Ka:H<,lJ.oAnape napaJlJleJIb-

HbiX BeTBeA ,lJ.omKHbI 6b1Tb paBHbI Me:H<,lJ.yco6oA, qTO ,lJ,OCTH-

raeTCSI npH BblnOJlHeHHH CJIe,lJ,YIOIIJ.HXYCJlOBHA:

1) K8:H<,lJ.aHnapa BeTBeA ,lJ.OJl:lKHa6b1Tb 06pa30BaHa H3 O,IJ.H-

HaKOBoro lIHCJIa CeKu.HA, T. e.

S.la

KIa

u.. q. (u.eJloe qHCJlO); (3.15)

2) napaJlJleJIbHbIe BeTBH ,lJ.OJl:lKHbIpa3MeIIJ.aTbCSI B O,IJ.HHa-

KOBOM lIHCJle na30B, T. e.

zla=u..

q.;

(3.16)

3) napaJlJIeJIbHble BeTBH ,lJ.OJl:lKHbICHMMeTpHqHO pacnoJla-

raTbCH B MarHHTJIOM nOJIe nOJlIOCOB, T. e.

2pla

u..

(3.17)

KaK BH,lJ.HO, H3 CJIOJKHbIX neTJIeBbiX 06MOTOK YCJIOhHSlM

CHMMeTpHH OTBeqaeT TOJlbKO ,lJ.ByxXO,IJ.OBaSi,lJ.ByKparH03aMKHy-

TaSi. Bce OCTaJIbHbIe ~MOTKH, y KOTOpbIX

2, HBJIHIOTCSI

HecHMMeTPHqHbIMH H npHMeHHlOTcSI J1Hllib B HCKJIlOqHTeJlbHblX

CJlYlIaHx.

3.6. YpaBHNTenltHWe coeANHeHNJI

TeopeTHqecKH npH CHMMeTpHqHOR 06MOTKe H paBeHcTBe

MarHHTHbIX nOTOKOB BCex nOJIIOCOB 3.llC BO Bcex BeTBHX 06-

MOTKH ,lJ,OJI:lKHbI6bITb O,IJ.HHaKOBbI, a BeTBH - paBHoMepHo 3a-

rpY:lKeHbI TOKaMH. OnbIT nOKa3bIBaeT, O,lJ,HaKO,lITO no II,eJlOMY

pH,lJ.Y npHlIHH B03HHKaeT aCHMMeTpHjJ OOMOTKH: B03,lJ,YlliHbIe

3a30pbI no,lJ, nOJIlOCaMH H3-3a HeTOlIHOCTH COopKH HJlH eCTecT-

BeHHOrO nporHoa BaJla MalliHHbI nOJIYlIalOTCH pa3HbIMH, IIJ.eTKH

CMeIIJ.aIOTCH Ha KOJIJleKTOpe, MaTepHaJI MarHHTOnpOBO,lJ,a CTa-

HHHbI HJIH Cep,IJ.elIHHKOB nOJlIOCOB Heo,lJ,HOp0,lJ,eHH T. ,lJ,.

HepaBeHCTBO 3.llC B O~,lJ,eJIbHbIXBeTBHX npHBO,lJ,HT K nOSlB-

.u,eHHIOBHYTPH 06MOTKH ypaBHHTeJlbHbIX TOKOB, npOTeKalOIIJ.HX

siepe3 IIJ.~KY OT TOqeK C OOJlblliHM nOTeHII,HaJlOM K TOlIKaM C

MeHblliHM nOTeHII,HaJlOM.

Y~BHHTeJJH nepBOro pO,lJ,a• .llJIH npHMepa paCCMOTpHM

OOM9TKY, nOKa3aHHYlO Ha pHC. 3.4 H 3.5. Ee CeKII,HH

.N'!!

1 H 10,

KOTopble 6epyT HaqaJlO y nJlaCTHH TaKHX :lKe HOMepOB, Teope-

THqeCKH ,lJ,OJl>KHbIHMeTb paBHbIR nOTeHII,HaJl. ECJIH no npHlIH-

HaM, YKa3aHHbIM BbIllie, nJIaCTHHa

.N'!!

10oY,lJ.eT HMeTb 60JIblliHH

nOTeHIJ.HaJI, OT Hee K nJlaCTHHe

.N'!!

1 naTeqeT ypaBHHTeJlbHLIA

TOK, ,lJ,OOaaolIHO HarpY:lK8IOIIJ.HH 06MOTKY H IIJ.eTKH.

TaK KaK COnpOTHBJIeHHe II,enH ,lJ.J1S1ypaBHHTeJlbHOrO TOKa

HeBeJlHKO, TO ,lJ.a:lKe npH HeOOJlblliOH pa3HoCTH nOTeHII,HaJlOB

ypaBHHTeJlbHblH TOK MO:lKeT ,lJ,OCTHrHYTb 60JlblliOrO 3HalIeHHH.

He06xo,IJ.HMO OTBecTH ypaBHHTeJlbHhIe TOKH no HHOMy, He3a-

BHCHMOMY nyTH. .llJlSl 3THX II,eJleH CJIy:lKaT. ypaBHHTeJlH, co-

e,IJ.HHHIOIIJ.HeBHYTPH neTJIeBOH 06MOTKH paBHOnOTeHII,HaJlbHbIe

TOlIKH (CM. pHC. 3.4) H nOJlYlIHBlliHe Ha3BaHHe

ypa8ftutn£.Ilea

nep80eo poiJa. '

PaCCTOHHHe Me:H<,lJ.ypaBHOnOTeHII,HaJIbHhIMH TOlIKaMH onpe-

,lJ.eJlHeT lliar ypaBHHTeJIbHhIX COe,IJ.HHeHHH

Yyp

KIa

KIp.

(3.18)

YpaBHHTeJIH MO:lKHOpacnOJIaraTb J1H60 Ha CTopOHe KOJlJIeK-

Topa, COe,lJ,HHHHHenOCpe,lJ,CTBeHHo KOJIJIeKTOpHbIe nJlaCTHHbI,

J1HOOco CTOpOHbI 3a,lJ,HHX J1000BbIX lIaCTeH. nepBoe no MHorHM

co06pa>KeHHHM HBJIHeTCjJ npe,IJ.nOlITHTeJlbHhIM.

TeopeTHlIeCKH MalliHHY CJIe,IJ.YeTCHao,lJ,HTb nOJIHbIM qHCJIOM

ypaBHHTeJIeH, HO npaKTHlIecKH 3TQro HHKOr,IJ.a He ,lJ.eJIalOT.

OnhIT nOKa3bIBaeT, lITO ,lJ,OCTaTOlIHOHMeTb O,lJ,HH,a y KpynHbIX

MalliHH C TH:lKeJIbIMH yCJIOBHHMH pa60TbI - ,lJ.Ba ypaBHHTeJlSI

Ha O,IJ.HHpeaJlbHbIH na3. nJIOIIJ.a,lJ,bnOnepeqHOrO CeqeHHSI ypaB-

HHTeJIbHOrO npOBO,IJ.aoepyT paBHOH npHMepHo 25

nJIOIIJ.a,lJ,H

nonepelIHoro celIeHHSI npOBO,lJ,a OOMOTKH HKOPjJ.

npOTeKalOIIJ.He ypaBHHTeJIbHbIe TOKH, nOCKOJlbKY 3T0 TOKH

. SlKOpH, HBJlHIOTCH nepeMeHHhIMH H no 3aKoHy JIeHII,a C03,lJ,alOT

MarHHTHOe nOJIe TaKoro HanpaBJIeHHH, qT06hI CrJIa,lJ,HTb He-

CHMMeTpHIO OCHOBHoro nOJlSl MalliHHbI, no,IJ.,lJ.eHCTBHeMKOTOpOH

OHH B03HHKJIH, lITO, B CBOIO Oqepe,IJ.b, cnocoocTByeT oCJlcr6JIe-

HHIO ypaBHHTeJIbHbIX TOKOB.

Y npOCTbIX BOJIHOBbIX OOMOTOK

1) B Ka:lK,lJ.YIOnapaJI-

J1eJIbHYIO BeTBb BXO,lJ,HTCeKII,HH, CTOpOHbI KOTOPbIX pacnoJlo-

:lKeHbI no,IJ. BceMH nOJIIOCaMH, n03ToMY HepaBeHcTBo nOTOKOS

OT,lJ,eJlbHbIXnOJIIOCOB He BbI3bIBaeT HepaBeHCTBa 3.llC B napaJI-

J1eJIbHhIX BeTBHX. CJIe,lJ,OBaTeJlbHO, 3TH OOMOTKH He HY>K,lJ,aIOTCjJ

B ypaBHHTeJIbHbIX COe,lJ,HHeHHSlX•

YpaBHHTeJlH BToporo po,lJ,a. CJIO:lKHhIe OOMOTKH, HMelOIIJ.He

qHCJIO nap napaJlJIeJIbHbIX BeTBeH

1, npe,IJ.CTaBJlHIOTCO'OOH

ep8KTHlIecKH HeCKOJIbKO npOCTbIX OOMOTOK.M eCJIH ,lJ.8:lKenOJI-

Hoe paBeHCTBO 3.llC BO Bcex BeTBHX TaKOH OOMOTKH 06ecne-

lIeHO, Bce >Ke B ·pe3yJIbTaTe HeCTaOHJlbHOCTH cOnpOTkBJIeHHjJ

.KOHT8KTa IIJ.eTKa - KOJIJIeKTOp TOKH Me:H<,lJ.yOT,lJ,eJIbHbIMH xo-

,lJ.8MHOOMOTKHMoryT pacnpe,IJ.eJIHTbCH HepaBHOMepHO, BCJIe,lJ,CT"

BHe lIero p8BHoMepHoe pacnpe,IJ.eJIeHHe nOTeHIJ.H8JI8 no KOJl-

, J1eKTopy Hapylli8eTCH.