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Submitted on 1 Jan 1984
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A WATER-COOLED, COMPENSATED SOLENOID FOR HIGH GRADIENT MAGNETIC FILTRATION
TESTS
Aik Lua, R. Boucher
To cite this version:
Aik Lua, R. Boucher. A WATER-COOLED, COMPENSATED SOLENOID FOR HIGH GRADIENT
MAGNETIC FILTRATION TESTS. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-767-C1-
770. �10.1051/jphyscol:19841156�. �jpa-00223629�
JOURNAL DE PHYSIQUE
Colloque C1, supplCment a u no I, Tome 45, janvier 1984 page Cl-767
A WATER-COOLED, COMPENSATED SOLENOID FOR HIGH GRADIENT MAGNETIC FILTRATION TESTS
Aik Chong Lua and R.F. Boucher
Department of Mechanical Engineering, University of ~ h e f f i e ~ d , Sheffield S1 3JD, U.K.
R6sumb - Un s o l & n o i d e cornpens6 r e f r o i d i B l ' e a u a Q t 6 6 t b d i 6 e t c o n s t r u i t d a n s l e b u t d e p r o d u i r e un champ magngtique u n i f o r m e pour une experience d e f i l t r a - t i o n magngtique 3 h a u t g r a d i e n t . Le b o b i n a g e u t i l i s e un c o n d u c t e u r c r e u x e n c u i v r e d e s e c t i o n c a r r g e 6,35 x 6,35
mm2.Le s o l e n o y d e a un a l 6 s a g e d e 113 mm e t une l o n g u e u r d e 317 nun. Les composantes a x i a l e e t r a d i a l e du champ magngti- que o n t i5tg mesurges B l ' a i d e d e s o n d e s d e H a l l r e s p e c t i v e m e n t a x i a l e e t t r a n s - v e r s e . La d i s t r i b u t i o n d u champ a x i a l montre une bonne hornogCngit6, s e t r a d u i - s a n t p a r une v a r i a t i o n du champ s u r l ' a x e d e seulement 1 , 6 % s u r une l o n g u e u r d e 150 mm dans l a rBgion c e n t r a l e . L e s champs r a d i a u x s o n t t r S s f a i b l e s d a n s c e t t e r g g i o n .
A b s t r a c t - A w a t e r - c o o l e d , compensated s o l e n o i d was d e s i g n e d and c o n s t r u c t e d t o produce a uniform m a g n e t i c f i e l d f o r an HGMF i n v e s t i g a t i o n . C o i l s w e r e wound from 6.35 mm s q u a r e , hollow c o p p e r t u b e s . The s o l e n o i d h a s a
113mm b o r e and is 317 mm l o n g . A x i a l and r a d l a l m a g n e t i c f i e l d s were determined w i t h an a x i a l and a t r a n s v e r s e H a l l e f f e c t f i e l d p r o b e s r e s p e c t i v e l y . The a x i a l f i e l d d i s t r i b u t i o n o f t h e c o m p e n s a t e d s o l e n o i d s h o w s good h o m o g e n e i t y , g i v i n g a n o n - a x i s f i e l d v a r i a t i o n o f o n l y 1.6% o v e r a 150 mm l e n g t h o f t h e c e n t r a l r e g i o n . R a d i a l f i e l d s a r e v e r y weak i n t h i s r e g i o n .
INTRODUCTION
F o r c o n t r o l l e d High G r a d i e n t Magnetic F i l t r a t i o n (HGMF) i n v e s t i g a t i o n s , i t i s h i g h l y d e s i r a b l e t h a t t h e m a g n e t i c f i e l d t h r o u g h o u t t h e m a t r i x b e u n i - d i r e c t i o n a l a n d homogeneous e v e r y w h e r e . By i n c o r p o r a t i n g a n i n s i d e n o t c h e d c o i l a t t h e middle s e c t i o n o f t h e s o l e n o i d , t h e f i e l d u n i f o r m i t y c a n b e i m p r o v e d . The w a t e r - c o o l e d compensated s o l e n o i d d e s c r i b e d h e r e i n was developed f o r an HGMF p r o c e s s f o r c a p t u r i n g b a s i c oxygen f u r n a c e d u s t i n a i r s t r e a m s . It was d e s i g n e d t o p r o v i d e a n homogeneous a x i a l f i e l d o f up t o 0 . 8 T e s l a t h r o u g h o u t t h e b o r e . The b o r e h a s t o accommodate a f i l t e r c a n i s t e r o f e x t e r n a l d i a m e t e r 102 mm and f i l t e r l e n g t h s of up t o 0.25 m . SOLENOlD DESIGN
The c e n t r a l a x i a l m a g n e t i c f i e l d Ho (amps-turns/m) o f a s i m p l e s o l e n o i d ( F i g . 1 ) o f l e n g t h 2 b ( m ) is g i v e n by 113:
H o = {10/411}{NI/alj[ 1/2 @[l/(cr-1 ) l { F ( a , @ ) I ( 1 )
2 2 % 471B
l n ~ ~ + ( a +B
)1
and F ( a , B ) =
r+
( 1+82)P
w h e r e N : t o t a l number o f t u r n s ; I - c u P r e n t ( a m p s ) ; a l , a z = i n s i d e and o u t s i d e r a d i i r e s p e c t i v e l y ( m ) ; a = a 2 / a l , @ = b / a l . It c a n b e shown t h a t a s o l e n o i d o f a :3, 8 = 2 p r o d u c e s t h e m o s t f i e l d f o r t h e l e a s t power. The a x i a l f i e l d Hz a l o n g t h e z a x i s is a l s o g i v e n by [ I ] :
HZ = H ~ [ I + E ~ ( Z / ~ ~ ) ~ + E ~ ( ~ / ~ ~ ) ~ + E ~ ( Z / ~ ~ ) ~ + ... 1 ( 3 )
w h e r e En a r e c o e f f i c i e n t s i n a T a y l o r e x p a n s i o n . One of t h e methods o f i n c r e a s i n g t h e f i e l d homogeneity o f a s i m p l e s o l e n o i d i s by s u p e r i m p o s i n g a s u i t a b l e i n s i d e notched compensated c o i l on t h e main c o i l ( F i g . 2 ) . The a x i a l f i e l d o f t h i s s o l e n o i d w i t h a compensated c o i l ( s u f f i x c ) t h e n becomes:
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841156
(21-768 JOURNAL DE PHYSIQUE
HZ = Ho/F( a,B){F( ~ , B ) - F C ( ~ ~ , B C ) + [ F E ~ ( a , f 3 ) - ~ ~ ~ ~ ( a ~ , ~ ~ ) l [ z / a ~ l ~
+[FE4( a,@)-FcE4(ac,k)J[z/al14+. . . . . I ( 4 )
When F C E ~ ( ~ C , B C ) = F E ~ ( a,B) and FcE4(ac , B c ) = F E ~ ( a,B), t h e o r i g i n a l E2 and Eq t e r m s a r e c a n c e l l e d , t h u s c o m p e n s a t i n g t h e s o l e n o i d t o s i x t h o r d e r .
2 b 2 b
OIC =
-
0"
- -
a1
-
56.5 m, a2 = 123 m. 2b = 317 m, sc = 65 mm, 2bc = 116 mm.F i g . 1 . S c h e m a t i c diagram o f F i g . 2 . S c h e m a t i c d i a g r a m o f
s i m p l e s o l e n o i d compensated s o l e n o i d
D e s i g n v a l u e s o f a ~ 2 . 1 8 a n d 6 = 2 . 8 1 were used f o r t h e main c o i l i n o r d e r t o s a t i s f y t h e s p e c i f i e d s o l e n o i d d i m e n s i o n s , maximum f i e l d r e q u i r e d , s i z e o f c o n d u c t o r s u s e d , o u t p u t f r o m t h e power s u p p l y u n i t , e t c . For a.2.18 s n a f3=2.81, v a l u e s o f FE2(a ,B
)a n d FE4( a , B ) a r e o b t a i n e d by i n t e r p o l a t i o n s f r o m t a b u l a t e d v a l u e s o f F E 2 ( a , 8 ) , FE4( a , 8) v e r s u s a , B i n T a b l e 1 , g i v i n g FE2(a ,B)=-0.043 and FE4(a ,B )=-0.0038. A l l v a l u e s o f a , B t h a t a l s o s a t i s f y F c ~ 2 ( a c , B c ) = - 0 . 0 4 3 a n d F c E ~ ( a c , B c ) = - 0 . 0 0 3 8 a r e o b t a i n e d from F i g s . 3 and 4 r e s p e c t i v e l y . The two l o c i o f ( a , B ) p o i n t s a r e t h e n p l o t t e d i n F i g . 5 a n d t h e i r i n t e r s e c t i o n l o c a t e s t h e v a l u e s o f Uc=l. 15 and @,=I .08 f o r t h e compensated c o i l .
T a b l e 1. Values o f FE2( a,B) and FE4( a,B) v e r s u s a , B ( a f t e r Montgomery r e f . 1)
a FE2( a , @ ) FE4( a,B) a FE2( a , @ ) FE4( a,B)
2.00 2.80 -0.0355263 -0.00345390 2.20 2.80 -0.0443812 -0.00390020
2.00 2 - 9 0 -0.0321415 -0.00305147 2.20 2.90 -0.0403270 -0.00347537
* 2.18 2.81 -0.0430727 -0.00382249
- 0 ,
m
: - 0 z
.
B
F i g . 3 . FE2(a,B) v e r s u s 8 F i g . 4 . FE&(a,B) v e r s u s B ( a f t e r Montgomery r e f . 1 ) ( a f t e r Montgomery r e f . l ) The s o l e n o i d was b u i l t by c o m b i n i n g a s e r i e s of pancake c o i l s t o g e t h e r . Each was wound from a s q u a r e h o l l o w c o p p e r t u b e s ( 6 . 3 5 mm s q u a r e and 1.63 mm w a l l t h i c k n e s s ) i n t h e f o r m o f a d o u b l e - l a y e r e d c o i l a s shown i n F i g . 6. The c r o s s - o v e r o f t h e two l a y e r s is a t t h e i n n e r m o s t d i a m e t e r , l e a v i n g t h e two w a t e r t e r m i n a l s a c c e s s i b l e o n t h e o u t s i d e .
2.5
-
4
/I."
Fig'. 5 .
FE,: . ~ . 3 8 ~ * ' ~C o n t o u r s of
, (*,&)A
,k F i g . 6 .
FE2 = -0.0431 and
---*zA t y p i c a l
F E ~ = -0.00382.
0 5pancake c o i l
L,
0 0 5 1 15 2 2 5 3
COIL W I N D I N G AND SOLENOID CONSTRUCTION
A w i n d i n g r i g ( F i g . 7 ) was d e s i g n e d a n d c o n s t r u c t e d . B r i e f l y , i t c o n s i s t e d o f a w i n d i n g p l a t f o r m which was s l o w l y r o t a t e d by a d . c . m o t o r v i a r e d u c t i o n g e a r b o x e s . The f i r s t l a y e r o f a p a n c a k e c o i l was wound f r o m h a l f o f t h e c o p p e r t u b e l e n g t h , s t a r t i n g from t h e c r o s s - o v e r p o i n t and w i n d i n g o u t w a r d s a r o u n d a s t e e l f o r m e r . Epoxy i m p r e g n a t e d g l a s s f i b r e t a p e was u s e d f o r i n t e r - t u r n i n s u l a t i o n . The epoxy was c u r e d by s h i n i n g f o u r i n f r a - r e d l i g h t b u l b s a t t h e c o m p l e t e d l a y e r , f o r m i n g it i n t o a r i g i d c o i l . G l a s s backed m i c a p a p e r was u s e d f o r i n t e r - l a y e r i n s u l a t i o n . With t h e r o t a t i o n r e v e r s e d , t h e above p r o c e d u r e s were r e p e a t e d f o r t h e second l a y e r .
A l l t h e p a n c a k e c o i l s , s t a c k e d s i d e b y s i d e a n d i n s u l a t e d f r o m e a c h o t h e r b y m i c a p a p e r , were clamped t o g e t h e r between two c a s t i r o n p l a t e s by f o u r c a s t i r o n t i e b a r s ( F i g . 8 ) . Copper f l a g s which were b r a z e d o n t o t h e two r i m s o f e a c h pancake c o i l ( F i g . 6 ) p r o v i d e d s e r i e s e l e c t r i c a l c o n n e c t i o n s b e t w e e n a d j a c e n t p a n c a k e c o i l s b y s u r f a c e c o n t a c t . Due t o t h e l i m i t e d v o l t a g e o u t p u t f r o m t h e d . c . p o w e r s o u r c e (maximum 1 2 0 0 amps a t 4 5 v o l t s ) , t h e s e r i e s c o n n e c t i o n s w e r e b r o k e n o f f a t t h e m i d - p l a n e t o s p l i t t h e s o l e n o i d i n t o two i d e n t i c a l and p a r a l l e l e l e c t r i c a l c i r c u i t s . T h i s a l l o w s t h e f u l l 45 v o l t s t o be a p p l i e d e q u a l l y a c r o s s e a c h h a l f l e n g t h o f t h e s o l e n o i d , t h e r e b y r e d u c i n g t h e maximum p o s s i b l e s o l e n o i d c u r r e n t t o 600 amps. A l l t h e g a p s between t h e two c o p p e r f l a g s w i t h i n e a c h pancake c o i l and t h a t a t t h e m i d - p l a n e w e r e f i l l e d w i t h a h a r d m a t e r i a l , T u f f n o l , f o r p a c k i n g and i n s u l a t i o n . The f l a g s and T u f f n o l p a c k i n g s were clamped t o g e t h e r i n l i n e by two l o n g b o l t s .
F i g . 7 . C o i l w i n d i n g r i g F i g . 8 . G e n e r a l view o f compensated s o l e n o i d The c o m p e n s a t e d c o i l a t t h e m i d d l e s e c t i o n o f t h e s o l e n o i d i s made u p o f 8 d o u b l e - l a y e r e d pancake c o i l s which h a v e 9 t u r n s p e r l a y e r . They make u p t o a l e n g t h o f 1 1 6 m m , r e s u l t i n g i n a v a l u e
OfBe = 1 . 0 3 i n s t e a d o f 1 . 0 8 . The main c o i l i s made up o f 14 pancake c o i l s , s p l i t e q u a l l y a t e a c h e n d o f t h e s o l e n o i d , a n d h a v i n g 10 t u r n s p e r l a y e r . The c o m p e n s a t e d s o l e n o i d , o v e r a l l d i m e n s i o n s g i v e n i n F i g . 2 , c o n s i s t s o f 2 2 p a r a l l e l w a t e r p a t h s . U s i n g p l a s t i c t u b e s , o n e t e r m i n a l o f e a c h p a n c a k e c o i l i s c o n n e c t e d t o a common w a t e r i n l e t m a n i f o l d w h i l s t t h e o t h e r t e r m i n a l t o a common o u t l e t m a n i f o l d ( F i g . 8 ) . The w a t e r f l o w r a t e t h r o u g h t h e s o l e n o i d i s 2 8 l / m i n w h i c h l i m i t s t h e b u l k w a t e r t e m p e r a t u r e r i s e t o l e s s t h a n 300C a t f u l l power.
Magnetic s t r e s s e s i n t h e c o i l s were c a l c u l a t e d u s i n g e x p r e s s i o n s g i v e n i n r e f . [ I ] . Even a t maximum f i e l d , t h e y w e r e f o u n d t o b e s m a l l i n c o m p a r i s o n t o t h e y i e l d s t r e n g t h o f c o p p e r .
MAGNETIC FIELD MEASUREMENTS AND PROFILES
U s i n g a B e l l g a u s s m e t e r ( M o d e l 6 1 5 ) , t h e a x i a l and r a d i a l m a g n e t i c f l u x d e n s i t i e s
were measured w i t h a n a x i a l (Type SAB1-1802) and a t r a n s v e r s e ( T y p e S T G I - 0 2 0 4 ) H a l l
e f f e c t f i e l d p r o b e s r e s p e c t i v e l y . Each p r o b e was mounted on a j i g ( F i g . 8) and c o u l d
be s l i d e d a l o n g t h e l e n g t h o f t h e s o l e n o i d b o r e . The compensated s o l e n o i d p r o d u c e d a
maximum c e n t r a l a x i a l f l u x d e n s i t y o f 0.855 T e s l a f o r a c u r r e n t o f 580 amps. Using
e q n s . ( 1 ) and ( 4 ) , t h e same c u r r e n t would g i v e a t h e o r e t i c a l f l u x d e n s i t y o f o n l y
0 . 7 9 0 T e s l a . The m e a s u r e d v a l u e shows a n improvement o f 8 . 2 % o v e r t h e t h e o r e t i c a l
one. T h i s m u s t m o s t p r o b a b l y b e d u e t o t h e p r e s e n c e o f a m a g n e t i c r e t u r n p a t h
Cl-770 JOURNAL DE PHYSIQUE
p r o v i d e d by t h e c a s t i r o n e n d p l a t e s and t i e b a r s , t h u s r e d u c i n g s t r a y f i e l d s . The d i f f e r e n c e i n t h e c u r r e n t f l o w i n g t h r o u g h t h e two s o l e n o i d c i r c u i t s i s o n l y 0 . 8 6 $ , hence t h i s s h o u l d p r o d u c e good symmetry o f f i e l d p r o f i l e a b o u t t h e mid-plane.
0 4 8 12 16 20 21 28 32 Solenoid length, z (cm 1
050 82 L.4 ..6 ..8 ~ .ID ~"i2 '.Y. 'I S 5 ''' . , . . ~a 10 22 ,
. . .
a 26 28 a 3:r~ ~ knQlh t z ~ r m ) ~ ~ ~ d
Fig.10. Comparison o f a x i a l
F i g . 9 . A x i a l m a g n e t i c f i e l d p r o f i l e s f i e l d p r o f i l e s
F i g u r e 9 shows t h e a x i a l f i e l d p r o f i l e s a l o n g t h e p r i n c i p a l a x i s o f t h e s o l e n o i d a n d a t d i f f e r e n t r a d i i up t o r / a l = 0 . 8 8 5 . The f l a t p r o f i l e s w i t h i n t h e c e n t r a l r e g i o n i n d i c a t e good f i e l d homogeneity. An o v e r a l l f i e l d s y m m e t r y a b o u t t h e m i d - p o i n t i s a l s o shown. Over a l e n g t h o f 150 ma of t h e c e n t r a l r e g i o n , t h e f i e l d v a r i a t i o n a l o n g t h e p r i n c i p a l a x i s i s 1.6%. W i t h i n t h i s same l e n g t h , t h e maximum d i f f e r e n c e i n t h e f l u x d e n s i t y f r o m r / a l = O t o 0 . 8 8 5 i s 3 . 6 % . The f l u x d e n s i t i e s d e c r e a s e r a p i d l y t o w a r d s t h e two s o l e n o i d e n d s a s t h e E6 and h i g h e r o r d e r t e r m s i n eqn. ( 4 ) would t h e n become i n c r e a s i n g l y s i g n i f i c a n t . F i g u r e 10 s h o w s t w o a x i a l f i e l d m e a s u r e m e n t s c o m p a r e d t o t h e p r i n c i p a l a x i s p r o f i l e
o f a s i m p l e s o l e n o i d a s c a l c u l a t e d from eqn. ( 3 ) . It shows a p a r a b o l i c p r o f i l e f o r t h e s i m p l e s o l e n o i d . A g a i n , o v e r t h e 150 mm l e n g t h o f t h e c e n t r a l
=r e g i o n , t h e on-axib a x i a l f i e l d o f t h e io
c o m p e n s a t e d s o l e n o i d h a s d e c r e a s e d t o i o
o n l y 0 . 9 9 o f i t s c e n t r a l a x i a l f i e l d 2
w h i l s t f o r t h e s i m p l e s o l e n o i d , i t h a s f * d e c r e a s e d t o 0.93. The r e l a t i v e
$03m a g n i t u d e s o f t h e r a d i a l t o t h e a x i a l f i e l d s a t d i f f e r e n t r a d i i ( r / a l ) a r e shown i n F i g . 11. Over t h e same 150 mm l e n g t h o f t h e c e n t r a l r e g i o n , t h e
maximum r a t i o o f t h e r a d i a l t o t h e
Oo 2 6 1 8 io 12 s~~~~~~~ !L ss ~ I8 ~z ~ . m ) 20 ~ 12 ~ h2' 26 . 28 90 117a x i a l f i e l d s i s 0.016.
Fig.11. R a t i o o f r a d i a l t o a x i a l f i e l d s CONCLUSIONS
Good h o m o g e n e i t y o f t h e a x i a l m a g n e t i c f i e l d o f t h e c o m p e n s a t e d s o l e n o i d was o b t a i n e d . The o n - a x i s f i e l d v a r i a t i o n o v e r a 150 mm l e n g t h o f t h e c e n t r a l r e g i o n i s
la.6%. R a d i a l f l u x d e n s i t y is n e g l i g i b l e when compared t o t h e a x i a l f l u x d e n s i t y o v e r t h e working l e n g t h o f t h e compensated s o l e n o i d .
Acknowledgements - The work r e p o r t e d h e r e i n was funded by t h e S c i e n c e and E n g i n e e r i n g R e s e a r c h C o u n c i l . One o f t h e a u t h o r s ( A . C. L u a ) g r a t e f u l l y a c k n o w l e d g e d t h e f i n a n c i a l a s s i s t a n c e g i v e n by t h e U n i v e r s i t y o f S h e f f i e l d t h r o u g h t h e award o f a Frank Greaves Simpson P o s t g r a t i u a t e S c h o l a r s h i p . T h i s work was c a r r i e d o u t d u r i n g h i s Ph.D. s t u d y .
REFERENCE
1.