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86791_319015271.pdf BAR.C.-1362
3 9 h i STUD Y O F TW O MEDIU M SIZ E "C " COR E ELECTROMAGNET S GENERATIN G LO W MAGNETI C FIELD S by M. S . Bhati a an d S . Das sMuliidisciplinar
y Researc h Schem e and U . K . Chatterje e Lase r Divisio n 1987
B.A.R.C. - 1352
GOVERNMEN
T O F INDI A ATOMI C ENERG Y COMMISSIO N ua:BOMBAY
, INDI A 1987
BARC-1352
INI S Subjec t Categor y : A14 . 2 2Descriptor
sELECTROMAGNET
S MAGNE T CORE SMAGNETI
C FIELD S FLU X DENSIT YMAGNETI
C FLU X SHAP E LEAK S MAGNE T CCIL S AI RMAGNETIZATIO
NABSTRACT
Magneti
c fiel d requirement s o f laboratorie s ma y impos e constraint s tha t ofte n cal l fo r s variet y o f non-standar d designs * Th e designe r ha s t o fulfi l thes e demand s withou t lettin g th e desig n t o becom e to o inefficient . Sinc e n o read y desig n procedure s ar e availabl e h e ha s t o resor t t o intution , calculatio n an d modelling . Inspit e o f thi s ther e ma y b e wid e discrepanc y betwee n th e desig n value s an d th e actua l results . Thi s repor t describe s th e experienc e gaine d o n tw o "C " cor e electromagnet s bein g use d i n ou r laboratory . Thes e magnet s generat e lo w magneti c field s ove r reasonabl y larg e volumes , a requiremen t tha t run s opposit e t o tha t o f mos t othe r magnets . Th e stud y reveal s th e dependenc e o f overal l performanc e efficiency , fiel d uniformit y etc . o n th e desig n parameters .CONTENTS
Pag e Wo . I . INTRODUCTIO N 1 II . FIRS T ELECTROMAGNE T . 3 2. 1 Magneti c fiel d requiremen t 3 2. 2 Yoke/Cor e cissig n an d fabricatio n 3 2. 3 Stan d desig n an d fabricatio n 4 2. 4 Ampere-tur n calculation s 4 2. 5 Magne t parameter s 7 III . FIRS T MAGNE T EXCITATIO N 8 3. 1 Coi l positio n 8 3. 2 Excitatio n b y coi l o n yok e 9 3. 3 Leakag e flu x a s a functio n o f ai r ga p 1 2 3. 4 Fiel d uniformit y an d symmetr y 1 3 3. 5 Firs t magne t excitatio n b y cor e coil s 1 4 3. 6 Uniformit y an d symmetr y wit h cor e coil s 1 5 3. 7 Coi l combination s 1 5 3. 8 Efficienc y o f coil s 1 5 3. 9 Effec t o f shar p bend s an d edge s 1 6 IV . SECON D ELECTROMAGNE T 1 7 4. 1 Secon d magne t detail s 1 7 4. 2 Magne t excitatio n 1 7 4. 3 Fiel d uniformit y an d symmetr y 1 7 V . DISCUSSIO N 1 8 STUDY OF TWO PlEOIUPl SIZE "C" CORE ELECTROMAGNETS GENERATING LO W MAGNETI C FIELD S b y ri.S . Bhat.ia , S . Oas s an d U.K . Chatterje e 1 . INTRODUCTIO N I n principl e lo w magneti c field s (10 0 - 500 guasa ) ca n b e generate d ove r reasonabl e volume s (upt o 0* 5 m ) b y permanen t magnets . However , i t i s no t eas y t o var y th e magneti c Fiel d conti - nuousl y ove r a wid e range . Wher e continuou s variatio n o f magneti c fiel d i s require d ove r a wid e range, electromagnet s ar e th e onl y answer . A n electromagne t ca n consis t o f a coil , a pai r o f coil s o r a n iro n yok e an d cor e magne t wit h suitabl e energisin g coil * B y us e o f iro n th e magneti c fiel d ca n b e generate d a t a considerabl y lowe r power . Thi s make s th e desig n o f powe r suppl y quit e easy . Th e overal l weigh t an d cos t o f th e iro n cor e magnet s i s lowe r tha n thei r coi l counte r parts . Howeve r whe n hig h flu x densitie s ar e t o b e generate d (» 2 Tesla) , iro n ha s bu t limite d us e a s i t contribute s onl y a smal l fractio n o f th e tota l field . Thu s fo r generatin g highe r field s onl y coil s ar e used . Fig. 1 give s th e magnetisatio n characteristic s o f som e commo n magne t materials . Fig. 2 illustrate s som e o f th e shape s i n whic h laborator y magnet s ar e available . Th e yoke-cor e combinatio n ca n tak e th e shap e o f a n "H " o r "C" . O f th e tw o "H " shape d electromagnet s ar e mor e efficien t an d generat e a symmetri c field . However , economi c an d physica l constraint s ma y mak e th e us e o f "C " shape d magne t inevitable . -2- FO T generatin g hig h field s (1 T t o abou t 2.5T ) th e cor e an d pol e cap s ar e tapered . Thi s result s i n som e concentratio n o f flu x i n th e ga p an d als o improve s th e uniformity . Fo r suc h magnet s th e flu x densit y i s hig h i n th e pol e an d cor e bu t i s kep t lowe r i n yok e t o avoi d los s o f amper e turns . Th e yok e cros s sectio n i s thu s kep t highB r tha n tha t o f core . Fo r suc h magnet s desig n dat a i s availabl e (1 )along with an easy design procedure % Th e desig n o f magnet s generatin g lo w magneti c field s (10 0 t o 50
0 guass ) ove r larg e volume s i s a littl e differen t tha n tha t discusse d above * Her e ther e i s n o sens e i n makin g th e cor e an d yok e stalkie r throughou t a s i t woul d lea d t o gros s underusag e o f th e iron , " i on e use s a n invers e tapere d cor e an d a slende r yoke . Thi s make s th e flu x densit y i n yok e highe r tha n tha t i n core . Howeve r th e yok e cros s sectio n canno t b e mad e s o smal l tha t i t begin s t o saturate . Th e magnet s describe d i n thi s repor t fal l int o thi s category * T o star t wit h n o desig n dat a wa s availabl e fo r suc h typ e o f magnet . Th e stra y flu x cal - culatio n fo r larg e ai r gap s (larg e ai r gap/pol e diamete r ratio ) i s difficul t t o perform . Thu s a reasonabl e valu e ma s assume d an d th e magne t wa s designe d wit h a hop e tha t an y discrepanc y woul d b e compensate d fo r b y som e extr a ampere-turns . Th e actua l result s ar e describe d i n subsequen t sections * (1 ) 0.3 . Kroo n - "Laborator y Magnets " - Nort h Hollan d Publishin g C o (1572) . -3- II . FIRS T ELECTROMAGNE T 2. 1 Magneti c Fiel d Requiremen t A unifor m magneti c fiel d variabl e fro m a fe u guas s (1 0 guass ) t o 10 0 guas s wa s require d insid e a vacuu m chambe r i n whic h a n electro n bea m heate d vapou r generatin g sourc e wa s located * Th e fiel d uniformit y an d steadines s (freedo m fro m lo w frequenc y ripple ) ensure s tha t electro n bea m qualit y doe s no t deteriorate * Th e presenc e o f magneti c fiel d al l ove r th e chambe r ensure s tha t th e ioni c specie s i n th e vapou r strea m mov e i n curve d trajectorie s an d thu s ge t trappe d b y th e colli - mators . Th e neutra l vapou r passe s unimpede d throug h th e aligne d slits * Th e coil s an d iro n coul d no t b e pu t insid e th e vacuu m chambe r a s thi s woul d increas e th e complexit y an d severel y loa d th e vacuu m system . Als o sinc e th e chambe r wa s t o b e frequentl y opene d fro m th e side s fo r th e purpos e o f loadin g fres h charg e an d subsequen t cleaning ^ th e magne t whos e pol e piece s surroun d th e chambe r (Fig.3) , i n norma l operations , ha s t o b e move d awa y durin g suc h a n operation . Thi s requiremen t compel s on e t o us ; a "C " shape d magnet . Th e yok e i s kep t thi n t o minimis e th e weigh t o f magne t thereb y enablin g it' s eas y movement . 2* 2 Yoke/Cor e Desig n an d Fabricatio n A s outline d abov e th e desig n o f yok e an d cor e wa s don e wit h th e ide a tha t minimu m iro n b e used . Th e detail s o f th e magne t ar e show n i n Fig.4 . Practicall y th e entir e magne t i s mad e ou t o f mil d stee l plat e o f appropriat e thicknes s ( 2 inches) . Th e bolt s an d nut s wer e mad e fro m mil d stee l bar s o f appropriat e diameters * Th e tota l weigh t o f iro n i s abou t 20 0 K g correspondin g t o a n iro n volum e o f 0*02 5 m . -A- Th e ai r ga p o f th e magne t ca n b e varie d betwee n 2 5 c m 4od4 0 c m b y suitabl e manipulatio n o f positio n o f disc s o n th e bolt . Fo r large r ai r gap s th e ring s ar e place d o n oute r sid e o f yoke . Thi s provisio n t ohad to be kept/make it suitable for any chamber whose width falls in th e rang e o f 2 5 t o 4 0 cm * 2* 3 Stan d Desig n an d Fabricatio n A suitabl e stan d wa s designe d t o hol d th e magne t firml y a t th e correc t height * Th e stan d als o help s i n eas y movemen t o f th e magne t a s th e bas e i s provide d wit h fou r mil d stee l castors * Car e wa s take n i n th e desig n t o preven t flu x dilutio n i n th e ai r ga p du e t o possibl e "shortin g effect " cause d b y proximit y o f mil d stee l part s o f th e stand . Fo r thi s aluminiu m support s wer e use d abov e a certai n heigh t i n eac h o f th e fou r legs * Th e sam e argumen t applie d t o th e stan d o f th e vacuu m chamber * Th e stan d ha s a wid e bas e (1. 2 m b y 1. 2 m ) fo r stabilit y reason s an d weigh s abou t 25
0 Kg . Th e magne t bas e ha s thre e bolt s whic h ar e use d t o ancho r i t firml y a t a place . Thes e bolt s ar e tightene d o n t o th e rest - block s enablin g th e castor s t o han g free . Woode n rest s ar e use d ato p th e aluminiu m support s wit h th e ide a tha t woo d bein g softe r wil l giv e wa y t o enabl e large r contac t are a betwee n i t an d th e magne t lim b thereb y ensurin g unifor m stressin g o f th e support * 2. 4 Ampere-Tur n Calculation s Th e calculatio n o f require d ampere-turn s t o generat e a fiel d o f -5- 10 0 guas s (maximu m require d field ) fo r a n ai r ga p o f 4 0 c m (maximu m ai r gap ) wa s don e usin g th e Ampere' s circuita l le u a T c star t wit h i t i s assume d tha t ther e i s n o fringin g an d leakag e flux , an d als o th e magnitisatio n an d th e flu x densit y i s assume d constan t ove r an y cros s section . Th e amper e turn s calculate d wit h abov e assumptio n represent s th e theoreticall y minimu m of ampere-turn s tha t ar e necessar y fo r th e presen t geometry * Th e Ampere' s la w state s tha t < D H.Calculatin g th e amper e turn s usin g relatio n (2 ) yield s u y\\ t s ) 4- n • io~ 7 Mir - *"T 7 x \f c Th e actua l requiremen t wil l b e highe r tha n tha t calculate d abov e abov e du e t o th e followin g reasons . Th e demagnetisin g fiel d creste d du e t o uncompensate d pole s o n th e pol e piec e surfac e ten d t o mak e th e flu x fring e ou t o f th e ga p (se e Fig.£") . I n additio n t o thi s fringin g flu x ther e wil l b e leakag e alon g th e yok e a s well . Al l thi s leakag e flu x ha s t o pas s throug h th e iro n alon g wit h th e usefu l flux * Thi s increase s th e iro n drop , tha t i s th e secon d ter m i n equatio n 2 . Th e flu x line s wil l no t b e perpendicula r t o th e pol e fac e especiall y nea r th e edg e o f pole s an d thu s averag e ga p distanc e fo r thes e flu x line s i s mor e tha n th e pol e separation . Furthe r th e flu x densit y ove r th e cros s sectio n wil l no t b e uniform . Th e flu x densit y wil l b e mor e i n th e centra l section s o f th e yok e an d core * Thi s i s s o becaus e suc h line s se e th e minimu m ai r gap * T o accoun t fo r al l thes e effect s i t wa s decide d t o doubl e th e figur e obtaine d fo r th e idea l cas e whic h o n roundin g o f yield s 7 00 0 amper e turns . -7- 2. 5 Magne t parameter s Th e importan t parameter s o f th e magne t ca n b e summafisa d a s follows : 1 . Flu x densit y i n air-ga p : 2 * Ai r ga p o r pole-separatio n : 3 . Diamete r o f pol e fac e : 4 . Fiel d uniformit y j S o Rippl e i n magneti c fiel d : 6 . Ampere-turi s requiremen t : 7 . Powe r supp.L y sContinuously variable between 3 0 guas s upt o 10 0 guass *
Adjustabl
e betwee n 2 5 c m t o 4 0 cm * 3 0 c m 5% i n abou t 30%o f th e ga p volum e Les s tha n A% r*m"s * 700
0 Amper e turn s Th e coi l shoul d b e chose n suc h tha t it' s energ y requiremen t fall s belo w 50
0 watt s (3 5 volt s an d 1 5 amperes ) thereb y enablin g on e t o us 6 a n I.e . 72
3 regulate d suppl y havin g serie s pas s transistor s wit h commensurat e voltag e an d curren t ratings * -8- II . FIRS T MAGNE T EXCITATIO N 3. 1 Coi l positio n I f th e reluctarw e o f th e ai r ga p i s lo w (smal l ga p an d l a rg e po t diamete r t o ga p ratio) , th e excitatio n coi l ca n b e locate d anywher e o n th e yoke-cor e fram e withou t an y los s i n efficienc y i n regar d t o th e ampere-tur n requirement . Howeve r a s th e air-ga p i s increase d th e situatio n change s drastically . Fo r larg e ai r gap s th e leakag e o r fringin g flu x become s considerable . A s a consequenc e onl y a fractio n o f amper e turn s ar e actuall y utilize d fo r th e ai r ga p flux . Thi s happen s du e t o increas e i n th e iro n dro p - sinc e no w th e iro n ha s t o carr y bot h th e ga p flu x an d th e stra y flux . Fro m efficienc y poin t o f vie w i t i s the n bes t fo r suc h case s t o locat e th e coi l a s nea r th e air-ga p a 3 possibl e a s thi s minimise s th e lengt h o f iro n i n whic h th e tota l flu x i s carrie d befor e th e pol e fac e i s reached . Wherea s i t i s bas t t o locat e th e coil s nea r th e ai r ga p fro m th e poin t o f vie w o f efficiency , i t ma y no t b e s o fro m th e poin t o f vie w o f uniformit y o f flu x densit y i n th e ai r gap . I n s o doin g i t i s ensure d tha t onl y axia l an d para-axia l flu x line s reac h th e air-ga p o r i n othe r word s th e alignmen t o f th e uncompensate d dipole s o n th e pol e surfac e i s mor e o r lea s perpendicula r t o th e pol e face . Th e non-para-axia l line s generate d nea r th e coi l en d wil l pas s ou t o f th e iro n fram e a s leakag e flux . Th e tw o possibl e position s i n whic h th e coi l (o r coi l pair ) ca n b e locate d ar e show n i n Fig.6 . Bot h th e position s wer e trie d an d th e result s ar e describe d i n th e subsequen t sections . -9- 3. 2 Excitatio n b y coi l o n yok e Base d o n th e parameter s liste d i n Chapte r 2 a coi l ua s designed . Th e coi l {COI L 1 ) detail s ar e show n i n Fig.7 a alon g wit h th e plo t o f th e fiel d measure d alon g certai n indicate d lin6 S (Fig.7b) . Thes e plot s giv e u s a n ide a o f th e natur e o f fiel d generate d b y th e coi l an d ca n hel p u s i n analysi s o f th 6 performanc e o f th e magnet . Th e excitatio n curv e (flu x densit y a t air-ga p mi d poin t v s amper e turns ) obtaine d b y th e COI L 1 i s show n i n Fig.8 . Th e ai r ga p wa s 36.
5 c m whic h ua s th e minimu m ga p require d fo r th e experimen t chamber . Th e curv e start s fro m a minimu m fiel d o f 1 0 guas s whic h i s th e fiel d du e t o residua l magnetis m i n th e magnet . Als o show n o n th e grap h i s th e idea l excitatio n curv e (curv e 1 ) i n whic h al l th e amper e turn s appea r acros s th e ai r gap , tha t i s zer o iro n drop * Comparin g initia l portio n o f curv e 2 wit h curv e 1 w e se e tha t onl y 40.
7 percen t o f th e amper e turn s ar e utilise d fo r th e ai r gap . Th e res t ar e los t i n conductin g th e flu x i n iron . Thi s continue s til l 300
0 amper e turn s ar e reache d wher e th e flu x densit y i n th e air-gap-mid-poin t i s 5 0 guass . Afte r thi s saturatio n o f th e yok e occur s an d thu s ther e i s practicall y n o gai n i n th e flu x densit y fo r an y appreciabl e increas e i n ampere-turns . Th e portio n o f iro n enclose d withi n th e coi l ha s t o carr y th e entir e flu x tha t i s generate d an d s o saturatio n o f iro n occur s her e firs t o f all . T o eas e th e proble m somewha t i t ua s decide d t o distribut e th e Amper e turn s ove r a greate r lengt h o r i n othe r word s us e a longe r coil . A secon d coi l (coi l 2 ) ua s designe d an d it s detail s ar e show n i n Fig-9 a an d th e plot s o f fiel d i t generate s i n ai r i s snow n i n Fig.9b . O n comparin g th e field s -10- o f th e coil s i t i s apparen t tha t coi l 2 generate s a unifor m fiel d i n it s centr e fo r a greate r lengt h tha n COI L 1 . Als o tii e leakag e fiel d o f COI L 2 i s les s tha n tha t o f COI L 1 * Th e excitatio n curv e obtaine d wit h thi s coi l i s als o show n i n Fig.8 . I t i s apparen t tha t COI L 2 perform s slightl y bette r tha n CCI L 1 * Th e ampere-tur n utilisatio n i s 45*
7 percen t i n compariso n t o 4 3 percen t o f COI L 1 * Als o i t reache s a slightl y highe r flu x densit y o f 5 6 guas s befor e saturatio n set s in *
Howeve
r th e performanc e o f th e magne t fall s shor t o f th e requiremen t i n bot h th e cases . Th e caus e o f discrepanc y i s th e assum - ptio n tha t wa s mad e namel y tha t leakag e flu x i s negligibl e o r smal l enoug h s o tha t th e yok e wil l no t saturate . T o examin e wha t i s happenin g th e leakag e flu x wa s monitored . Thi s wa s don e b y measurin g th e flu x densit y al l ove r th e surfac e o f th e iron . Averag e flu x densit y fo r certai n part s wer e obtained . Th e averag e flu x densit y ove r a certai n par t sa y sid e limb* * wa s multiplie d b y th e tota l expose d surfac e are a o f th e sid e lim b t o arriv e a t th e leakag e flu x fro m th e sid e limb * Base d o n suc h measurement s th e tota l flu x generate d an d it' s distributio n wa s obtained * Fig.1 0 show s th e tota l flu x generate d a s a functio n o f ampere - turn s fo r bot h COIL' 1 an d COI L 2 . COI L 1 generate s onl y slightl y highe r flu x a t an y give n ampere-tur n value . Thi s i s s o becaus e i t ha s highe r inductanc e tha n tha t o f COI L 2 . Th e flu x rise s faste r initiall y til l saturatio n set s i n a t 3000 ampere-turn s afte r whic h i t rise s e t progre - ssivel y lowe r rate . Th e iro n whic h ha s hig h premeabilit y a t lo w flu x densitie s ha s poore r an d poore r permeabilit y a s flu x densit y increase s til l a t complet e saturatio n it s permeabilit y i s equa l t o tha t o f ai r (JU. V
»1)
, -11- A s excitatio n i s increased ) greate r amoun t o f iro n i n an d aroun d th e coi l i s drive n int o saturation . Th e distributio n o f th e flu x alon g th e differen t part s o f th e magne t i s show n i n Fig.11 . A t lo w excitatio n (200 0 AT ) fo r COI L 2 approxiniatel y 16. 5 percen t flu x reache s th e pol e fac e an d onl y 8 percen t reache s th e mi d plane . Th e figure s fo r 6500 A T an d 1000
0 A T ar e 13. 5 an d 6*3 4 pe r cen t an d 12. 6 an d 6 percen t respectively * Figur e 1 2 als o show s th e outlin e o f th e flu x tub e tha t i s actuall y responsibl e fo r th e flu x i n th e mi d plane . Thi s clearl y point s a t th e poo r flu x utilizatio n an d th e pric e w * hav e t o pa y fo r it . Th e flu x utilizatio n wit h COI L 1 i s a littl e poore r tha n COI L 2 . Thi s i s s o becaus e COI L 1 produce s mor e divergen t flu x tube s an d s o th e contributin g flu x tub e i s narrowe r tha n tha t o f COI L 2 * A t 360
0 Aape r turn s excitatio n th e portio n o f flu x reachin g pol e fac e an d od d plan e expreese d a s percentag e ar e 14* 5 an d 6.3 7 percen t wherea s fo r excitatio n leve l 11,52 0 amper e turn s they ar e 10*2 2 an d 5 percent .
Theoretica
l predictio n o f th e flu x distributio n ca n b e attempte d b y simplisti c mode l show n i n FigJ2 . Her e i t i s assume d tha t flu x distri - bute s itsel f ove r th e variou s part s .i th e invers e rati o o f th e reluctance s o f th e variou s parts . Thi a pictur e applie s til l saturatio n set s in * Afte r saturatio n th e part s awa y fro m th e coi l se e les s I W du e t o los s o f ampere-turn s i n th e iron . Eve n thoug h ther e i s difficult y i n E xac t calculatio n o f th e reluctances , th e value s closel y matc h wit h experimenta l results * -12- 3. 3 Leakag e flu x 3 3 a functio n t f ai r ga p Th e magne t wa s assemble d t o giv e thre e distinc t ai r gap s (24 , 3 0 an d 36.5 cm ) b y manipulatio n o f th e positio n o f rings . Th e flu x wa s monitore d alon g th e magne t surfac e fo r eac h ai r gap . Th e invers e o f rati o o f flu x passin g throug h air-ga p mid-plan e t o th e res t o f flu x expresse d a s percentag e i s define d a s leakag e an d i s plotte d i n curv e 1 o f Fig.1 3 a s a functio n o f air-gap . Curv e 2 i s plo t wit h flu x emergin g fro m pol e fac e a s th e bas e i n plac e o f mid - plan e flux . Curv e 3 give s th e mi d poin t fiel d a s a functio n o f air-gap . Fo r al l th e abov e reading s th e ampere-turn s wer e fixe d a t 10,000 . A t smalle r air-gap s highe r mi d poin t field s wer e possible . Thi s happen s becaus e o f thre e reasons . On e ther e i s bette r utilizatio n becaus e no w th e reluctanc e o f ai r ga p i s smaller . Houevbr , th e flu x measure d i s highe r tha n tha t expecte d fro m reluctanc e considerations . Thi s i s du e t o th e fac t tha t whe n ai r ga p i s reduce d th e overal l reluctanc e face d b y th e coi l i s les s an d s o i t generate s marginall y highe r flu x fo r th e sam e amper e turns . I n fac t th e gain i n tota l flu x generate d i s o f th e orde r o f 1 percen t pe r c m reductio n i n ai r ga p i n th e rang e o f variatio n (2 5 c m t o 36.
5 cm) . Takin g bot h thes e fact s int o accoun t w e fin d th e measure d flu x i s highe r i n th e mid-plan e tha n wha t th e calculatio n shows . Thi s i s attribute d t o a highe r percentag e o f th e flu x leavin g th e pol e fac e tha t i s no w abl e t o reac h th e mi d plan e a t lowe r air-gaps . Thi s i s du e t o a mor e paralle l alignmen t o f th e pole s o n th e pol e fac e a t smalle r ai r gaps * -13- Thi s als o result s i n smalle r leakag e aroun d th e air-gap * Thi s ca n b e verifie d fro m tfie Fig.3 . Th e spacin g betwee n th e curv e 1 an d curv e 2 increase s a s th e air-ga p increase s indicatin g tha t a lesse r an d lesse r percentag e o f th e flu x leavin g th e pol e fac e reache s th e mid-plane * 3. 4 Fiel d uniformit y an d symmetr y Fig.1 4 give s th e graph s o f th e flu x densit y measure d alon g th e vertica l axi s i n th e mi d plan e an d alon g th e pol e fac e fo r thre e differen t excitatio n level s usin g COI L 2 fo r a n ai r ga p o f 36.
5 cm . I t i s apparen t tha t th e uniformit y i s bette r a t lowe r excitations . Thi s i s s o becaus e onc e saturatio n occur s i n th e centra l regio n o f th e yok e an d core , furthe r excitatio n wil l strengthe n th e flu x densit y i n th e periphera l region s only . Th e ^"n r tha t i s radiu s i n whic h th e fiel d doe s no t var y 17 b b y mor e tha n 1 percen t i s equa l t o 4* 5 c m at . mi d plane , an d 4* 5 c m a t th e pol e fac e fo r excitatio n leve l o f 200
0 amper e turns . Th e valu e a t 10,00 0 Amper e turn s i s 2. 5 c m an d 2. 3 cm . Similarl y V_ g i s 8* 5 c m an d 8. 5 c m a t 200
0 amper e turn s an d 8. 5 c m an d 6. 5 c m a t 10,00 0 amper e turns . Base d o n abov e measurement s w e ca n sa y tha t th e fiel d i s unifor m t o withi n 5 percen t i n 2 5 percen t o f th e volum e a t s n ai r ga p o f 36.
5 cm . Th e uniformit y attaine d wit h COI L 1 i s marginall y bette r tha t fo r COI L 2 (Fig.15) . Als o th e uniformit y improve s whe n th e ai r ga p i s reduce d Fig.1 6 • Thi s i s agai n attribute d t o a mor e paralle l alignmen t o f pole s o n th e peripher y o f pol e a t smalle r ai r gaps . Th e fiel d whic h i s symmetri c i n th e vertica l axi s i s no t s o i n th e horizonta l axis . Th e reaso n bein g crowdin g o f th e flu x i n th e regio n betwee n yok e containin g coi l an d th e cor e leakag e flux . Fig.1 6 give s th e -Id- plo t o f th e flu x densit y i n th e mi d plan e an d pol e fac e alon g th e tw o axe s (vertica l an d horizontal ) obtaine d wit h COI L 2 a t a n excitatio n lev/e l o f 1 0 amperes . Th e symmetr y i s bette r a t lowe r excitatio n an d als o improve s whe n th e air-ga p i s reduced . 3* 5 Fira t magne t excitatio n b y cor e coil s Th e detail s o f th e coi l pai r (COI L 3 ) use d fo r excitatio n o f magne t ar e show n i n Fig.17 . Thi 3 coi l wa a late r modifie d b y additio n o f 25
0 turns/coi l t o for m COI L 4 . Th e coil s discusse d abov e ar e al l shor t coil s a s thei r lengt h t o diamete r rati o i s small . I n thi s respec t COI C 4 i s marginall y bette r tha n COI L 3 an d s o COI L 4 i s expecte d t o perfor m a littl e bette r tha n COI L 3 . Fig.1 8 show s th e excitatio n curv e o f th e magne t usin g thes e coils . Th e ampere-tur n utilizatio n fo r COI L 3 i s 50.
7 percent . Fo r COI L 4 i s a littl e highe r 53.
3 percent . Th e utilizatio n o f ampere - turn s i s bette r tha n fo r th e previou s coils . Th e reason s fo r tha t i s tha t no w th e leakag e flu x aroun d th e coi l caus e saturatio n o f th e iro n i n it' s bore . Thes e point s wer e les s stresse d i n th e cas e whe n coi l th e wa s place d on/yoke . Fig.1 9 show s th e distributio n o f th e tota l flux , alon g th e different , part s o f th e magnet . Th e flu x tub e responsibl e fo r generatio n o f flu x i n th e mid-plan e i s als o shown * Th e flu x densit y a t variou s point s i n thi s flu x tub e ar e atos o shown . Wit h bette r ampere-tur n utilization , highe r air-ga p field s ar e possible . Thi s i s becaus e th e coi l i s nea r t o th e pol e fac e an d thu s th e flu x tub e contributin g t o pol e fac e magnetisatio n ha s large r are a -15- tha n i n th e previou s case * However , th e saturatio n i s expecte d a t field s greate r tha n 20 0 guass . 3. 6 Uniformit y an d Symmetr y wit h cor e coil s Th e symmetr y wit h thes e coil s i s ver y good . Thi s i s becaus e ther e i s les s crowin g o f flu x lik e i n th e previou s cas e (Fig.20) . Th e uniformit y i s howeve r poore r thoug h marginall y (Fig.21) . Thi s i s partl y du e t o th e proximit y o f th e coil . Th e Y * ~* radiu s i s equa l t o 8 c m a t 120
0 amper e turn s an d become s 7 c m a t 840
0 amper e turns . 3. 7 Coi l combination s Th 6 dat a fo r th e tao form s o f excitatio n show s tha t eac h for m ha s it s merit s an d demerits . Th e ampere-tur n utilizatio n an d uniformit y i s slightl y bette r fo r th e firs t case * Howeve r wit h secon d for m o f excitation , highe r flu x densitie s ca n b e achieved . Thu s i t wa s decide d t o explor e th e advantage s o f excitatio n o f bot h th e coils . Th e relativ e distributio n o f ampere-turn s ca n b e change d b y variou s serie s paralle l connection s betwee n th e coils . Th e excitatio n curve s o f som e o f combinatio n coil s i s show n i n
Fig.22
. Th e curve s hav e feature s o f bot h th e coils . I n tha t sens e the y ar e mea n o f th e tw o extrem e represente d b y th e cor e an d yok e excitatio n methods . Simila r trend s ar e see n i n tine uniformit y curve s Fig.23 . 3. 8 efficienc y o f coil s Fig.2 4 give s th e mid-poin t fiel d a s a functio n o f ampere-turns . Fig.2 5 give s fiel d a s a functio n o f inpu t power . Th e yok e coi l ha s bette r amper e tur n utilizatio n an d als o efficien t upt o th e poin t o f saturatio n beyon d whic h it' s utilizatio n an d efficienc y fall s of f rapidly . Th e cor e coi l ha s poore r ampere-tur n utilizatio n an d efficienc y initially , bu t doe s -16- no t suffe r s o muc h o n th e saturatio n front * Th e combinatio n coil s hav e characteristic s tha t li e i n betwee n thes e tw o extremes * 3. 9 Effec t o f shar p bend s an d edg.6 9 Th e edge s i n th e yok e fram e produc e a non-unifor m flu x densit y distributio n ove r th e cros s section . Thi s i s show n schematicall y i nFig.25
. Typicall y th e edge s hav e 1. 5 t o 2 time s mor e flu x densit y tha n a t th e cente r o f th e surface . Thi s lead s t o poore r utilizatio n o f iro n becaus e ther e i s unequa l distributio n o f flu x density . Fo r a give n flu x densit y a t th e centr e ther e i s mor e leakag e wit h edge s tha n withou t it . Th e affec t o f shar p bend s i s agai n similar . Par t o f th e flu x i n th e peripher y i s drive n ou t i n air * Thi s agai n lead s t o non-unifor m distributio n o f flu x densit y i n iro n a s th e oute r flu x tube s se e mor e ai r ga p lengt h tha n th e inne r ones * A s explaine d earlie r th e non-unifor m flu x densit y distributio n drive s th e inne r sectio n o f th e iro n yok e an d cor e furthe r toward s saturatio n fo r a give n wante d flu x i n th e ai r gap . -17- IV . SECON D ELECTRONGNE T 4. 1 Fo r anothe r experimen t ther e ua s a nee d t o maintai n a large r flu x densit y 400 guas s ove r simila r volum e an d geometry . Th e previou s magne t wa s limite d t o lea s tha n 20 0 guass . S o a secon d magne t ua s designe d whic h ua s differen t i n it' s cor e shap e an d coi l volume . Th e desig n o f yok e an d th e stan d ar e mor e o r les s th e san e wit h mino r changes . Th e magnet' s dimension s ar e show n i n Fig.27 . Th e coi l detail s ar 6 show n i n Fig.28 . Her e th e coppe r t o iro n rati o i s 1:2 0 i n compariso n t o 1: 3 fo r th e firs t magnet . Cor e excitatio n i s use d t o ge t bette r flu x utilization . 4. 2 Waqns t excitatio n Fig.2 9 ehow s th e excitatio n curv e obtaine d wit h thi s geometr y wit h an d withou t iron . Curv e 1 i s th e excitatio n curv e wit h n o iro n wherea s curv e 2 give s the excitatio n curv e whe n cor e wit h pol e ca p i s adde d an d curv e 3 whe n th e entir e magn6 t wit h yoke/cor e an d pol e ca p i s added . Th e effec t o f constrictio n o f yok e (don e b y removin g circula r piece s fro m yoke ) result s i n reductio n o f mid-poin t flu x densit y an d thi s i s show n i n curv e 4 . Th e pre-saturatio n iro n contributio n ca n clearl y b e seen . Afte r saturatio n th e gai n come s onl y fro m th e coi l contribution * Her e th e slop e o f th e excitatio n curv e equal s th e no-iro n case . Th e powe r efficienc y curv e fo r th e thre e case s ar e show n i n Fig.30 . 4. 3 Fiel d uniformit y an d symmetr y Th e mid-plan e an d pol e fac e flu x densit y profile s ar e show n i n
Fig.31
. Th e V ^ fo r th e full y assemble d magne t i s 8. 5 c m a t 1. 5 Amper e excitatio n current . Th e field s ar e symmetri c du e t o tiie for m o f excitatio n use d here * -18- V . DISCUSSIO N I n th e conventiona l design , tha t is , tapere d pole s an d lo w ai r ga p length s (lo w i n compariso n t o othe r dimension s i n th e magnet ) th e leakag e flu x alon g th e yok e an d coi l i s negligible . S o on e ha s t o conside r onl y th e pol e an d cor 6 leakag e flux . Th e pol e desig n whic h give s th e leas t leakag e whil e meetin g th e uniformit y th e requiremen t wil l be/bes t choice . Fo r larg e air-gap s (larg e i n compariso n t o othe r dimensions ) th e yok e an d coi l leakag e i s considerable . I n thi s cas e on e ha s t o pa y attentio n t o th e desig n o f yok e an d coi l an d als o th e locatio n o f th e coil . Th e cor e coil s performanc e i s therefor e superio r i n term s o f ampere-turn s utilisatio n an d powe r efficiency . Th e uniformit y i s onl y marginall y poo r fo r th e univers e tapere d poles . Th e uniformit y i n th e magne t wit h invers e tapere d pole s i s no t a stron g functio n o f excitatio n an d i t improve s slightl y a s th e excitatio n i s increased . Fo r th e pol e desig n wit h n o taper , th e uniformit y i s goo d a t lo w excitatio n an d i t become s poore r a s th e excita - tio n i s raised . Thu s her e w e hav e a ivaAe-o W betwee n th e rang e ove r whic h th e uniformit y ca n b e maintaine d an d th e coi l inne r diamete r whic h determine s th e amoun t o f coppe r an d als o th e electrica l power . Th e tapere d pol e constructio n give s bette r flu x utilizatio n an d als o a lower - mea n tur n - lengt h fo r it s coil * Thu s i t i s desirabl e fro m powe r econom y poin t t o tape r th e poles . Howeve r whe n th e ampere-turn s require d ar e ver y tapere d pole s wit h hig h the n th e differenc e betwee n / ' pol e and/n o tape r ma y onl y b e margina l an d thu s th e straigh t poles , bein g simple r t o fabricate , ma y b e used . - 19 -ACKNOWLEDGEMEN
T Th e author s ar e thankfu l t o Shr i T.P . Davi d o f Nuclea rPhysic
s Divisio n fo r hi s valuabl e suggestion s fo r th e desig n o f th e firs t electromagnet . The y ar e als o indebte d t o Shr i A.V . Thaku r an d Dr . G.D . Sakaen a fo r thei r uorksho p hel p an d finall y Dr . P.R.K . Rao , Head , MDR S fo r hi s valuabl e suggestion s an d encouragement * 100t "£20to 00 5 2
1I i I I ii' > I I 11!lmrT 1-
8=23 i' I '"L 1 . MIL D STEE L 2 . ELECTROLYTI C IRO N 3 34% CO-IRON . < , 50
% C O IRO N SHEET S VACUU M CAS T " • 1 I I 1 I I I I i I I i lll l I i I I 1 il l 5 1 0 2 0 5 0 10 0 20 0 50
0 100
0 H (OERSTEDS) - • FIG. I MAGNETIZATIO N CURVE S O F SOM E SOF T MAGNETI C MATERIAL S ABOV E
SATURATIO
N TH E FLU X DENSIT Y B CA N B E WRITTE N A S B = 4 JJ M Q + H . (a) C-CORE WITH TAPERED POLES(b) H-CORE WITH TAPERED POLES . (c)C-COR E WIT H INVERS E TAPERE D (d ) H-COR E WIT H INVERS E TAPERE D POLES . POLES . FIG . 2 SOM E SHAPE S O F LABORATOR Y MAGNETS .EXPERIMENTAL
CHAMBE
R (S.S. ) VACUU M CHAMBE R (S.S. ) WOODE N BAS E , ALUMINIU MSUPPOR
T STAN D (l-2M x 1- 2 M ) M.S . FIG. 3 POSITIONIN G O F MAGNE T AROUN D TH E CHAMBER . 23013FIG . 4 MAGNE T ASSEMBLY . AL L DIMENSION S AR E I N MM .
MATERIAL
- M.S .FLUX LINES
(a ) N O LEAKAG E FLU X LINE S tb ) WtT H LEAKAG E FIG. 5 FLU X PROFIL E WIT H AN D WITHOU T LEAKAGE . \ l ( I ) YOK E COI L (I I ) COR E COI L -PAI R FIG. 6 COI L POSITION SFLUX DENSITY ( GUASS)FLUX DENSITY(GUASS)
DENSIT
Y (GUASS )80/(CURVE 3)
IDEA L CURV E 60COIL I
( CURV E 2 ) C O C O C O U J a x3 2 0 ii 4 5 6 AMPER E TURN S x1073810II FIG . 8EXCITATION CURVEFLUX DENSITY (GUASS)FLUX DENSITY (GUASS)
Oeno o FLU X DENSIT Y ( GUASS ) 0 0 o_roo_ orooororooooCM r oo 73 4 5 6 7 8
AMPERE-TURN
S x 1 0 *• FIG.I O TOTA L FLU X GENERATE D101216-34 %
21-16% \ ^7-48 % 6*92 %
CONTRIBUTIN
G FLU X TUBE . 2 4-78 % I 1 i <-7-09 %16-22%EXCITATIO
N - 200 0 A T 12*6216-51%
6'28 % - 115-29%2301
% ^21-76 %
EXCITATIO
N - 10,00 0 A T FIG . I I DISTRIBUTIO N O F FLU XCENTRAL PLANE
O F COIL . EAC H FLU X TUB E REPRESENT S TH E TOTA L FLU X EMERGIN G FRO M A GIVE N PART . 1 COI L LEAKAG E FLU X 2 BAC K LIM B LEAKAG E FLU X 3 SID E LIM B LEAKAG E FLU X 4 POL E SURFAC E LEAKAG E FLU X 5 POL E FAC E FLU X TH E RELUCTANC E ASSUME D I S TH E AVERAG E FO R A GIVE N FLU X TUBE . FIG . 1 2 FLU X DISTRIBUTIO N MODE L I N TH E MAGNET .LEAKAGE FACTOR
P C O -r j H O zoro m> am r ~cX >3o r oo o "D -o o o o §MID POINT FIELD (GUASS) - •FLUX DENSITY tSUASS)
I o o * o " o o oFLUX DENSITY (GUASS)IN)i\>oA1ISN3Q XO"1J
O 04o00ogioID
U J ou.tUi - J o0.Ul_J l l oQ.a. <00 e © (ssvno ) A±ISN3 Q xn uCOIL SIDE
AIR-GA
P 3 0 c mHORIZONTAL PLANEVERTICA
L PLAN E 1 6 2 0 2 4 2 8 3 0 FRO M POL E EDG E (cm ) F1G.I 6 FIEL D SYMMETR Y I N MID-PLAN E WIT H C0IL 2 .KC0IL3
SCAL E 10 ! I TURNS : 600 ( 300
T/COIL
)WEIGHT
! 4 K g ( COI L PAI R )RESISTANCE
:(COIL PAIR) COI L 4 FORME D B Y ADDIN G 250T/C0IL O N TH E SAM E FORME R TURN S : 110
0
WEIGHT
! 9' 5 Kg . ( COI L PAIR )RESISTANCE
: 4-2- ^ (COI L PAIR ) FIG.1 7 DETAIL S O F COR E COILS . 160 r4 5 6 AMPER E TURN S 26-9%
47-2
% 19-2 % (a ) EXCITATIO N 120
0 A T ,17-5 % r 45-
5 % ^7- 4 % Ib ) EXCITATIO N 8,,40 0 AT FIG.I 9 FLU X DISTRIBUTIO N ( CO I L 3 )4-2
HORIZONTAL
AN DVERTICA
L 3 0 3 7DISTANC
E (CM ) - FIG.2 0 FIEL D SYMMETR Y WIT H COR E COI L (COI L 3 )POLE FACEPROFILE
MI D PLAN EPROFIL
Er500 400 30
0© zLU 1-20 0 °x 10 0 1 0 1 5
DISTANC
E FRO M CENTR E (CM ) FIG.2 1 UNIFORMIT Y WIT H COI L 4 .AM! ERE-TURN
DIVISIO
N (COI L 21COI L 3 ) 1401
- F1G . 2
23 4 5 6 7AMPERE-TURNS x I03 - *"EXCITATION CURVES OF COIL COMBINATIONS8910II
(IJO-3) FIG . 2310 IS
DISTANC
E FRO M CENTR E (CM )UNIFORMIT
Y WIT H COI L COMBINATIO N20160 r-
140'- t120 v>v> 3 OI0 0 wz.uo80 6 0 4 0 2 0 J _JL_L108910
AMPERE
- TURN S x 1 0 FIG . 2 4 EXCITATION-CURV E O F COIL SII !60r /C0IL 2 40160 200 240 280
POWE R ( Watts ) ~320 360 400 FIG.2 5 POWE R EFFICIENC Y O F COIL S .ISOFIELD LINES
(a ) EFFEC T O F EDGE S FLU X LINE S lb ) EFFEC T O F SHAR P BEND S FIG . 2 6 EFFEC T O F EDGE S AN D BEND S oin o o IT )ALL DIMENSIONS IN MM oin 1A 0 FIG . 2 7 SECON D MAGNE T ASSEMBL YALL DIMENSIONS IN CM.
TURNS : 4000 TURNS/COI L
RESISTANCE
: 25(COIL PAIR)
WEIGHT
: 5 6 K G PE R COI L FIG . 2 8 COI L DIMENSION S AN D DETAIL SCURVE 4
o WIT H COR E 8 YOKECURVES
WIT H COR E a YOKE(HAVING 5cm 0
HOLE ) CURV E 2 WIT H COR E N O COR E AMPER E TURN S x | 0 FIG.2 9 EXCITATIO N CURVE S 40035
0 3 2 25
0 in 5 20 0 Q X 3 . 15 0 10 0 5
0CURVE I
±1-75 2-00-25 " 0.5 0-75 1-0 1-25 1-5
POWE R ( K Watts ) FIG.3 0 POWE R EFFICIENC Y CURVE S .2-25 2-5 3208 0 4