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Submitted on 1 Jan 1984
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FORCE DISTRIBUTIONS AND STRESS ANALYSIS OF THE INTOR-CH SUPERCONDUCTING COIL
C. Marinucci, L. Palladino, G. Pasotti, M. Ricci, G. Vécsey
To cite this version:
C. Marinucci, L. Palladino, G. Pasotti, M. Ricci, G. Vécsey. FORCE DISTRIBUTIONS AND STRESS
ANALYSIS OF THE INTOR-CH SUPERCONDUCTING COIL. Journal de Physique Colloques,
1984, 45 (C1), pp.C1-901-C1-904. �10.1051/jphyscol:19841184�. �jpa-00223660�
JOURNAL DE PHYSIQUE
Colloque C I , supplCment a u n o 1, T o m e 45, janvier 1984 p a g e C1-901
FORCE DISTRIBUTIONS AND STRESS ANALYSIS OF THE INTOR-CH SUPERCONDUCTING COIL
C. M a r i n u c c i , L . P a l l a d i n o r , G . p a s o t t i * , M.V. ~ i c c i * and G . Ve'csey Swiss I n s t i t u t e for PucZear Research (SIN), CH-5234 ViZZigen, SwitzerZand
*ENEA, 1-00044 Frascati, I t a l y
RQsum6
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Nous p r 6 s e n t o n s une r e v u e d e s c a l c u l s Qlectro-me'caniques a' c e j o u r , b a s e s s u r l e c o n c e p t du SIN, p o u r l e s b o b i n e s de champs t o r o T d a 1 INTOR/NEl'.S o n t p l u s e x p l i c i t e m e n t d i s c u t g s : l ' o p t i m a l i s a t i o n de l a forme e n D B t e n s i o n c o n s t a n t e , l e s c a l c u l s de f o r c e s ' e l e c t romagn8tiques e t l ' a n a l y s e d e s c o n t r a i n t e s dans l e c o n d u c t e u r , l e s e n r o u l e m e n t s e t l ' e n s e m b l e d e s b o b i n e s . A b s t r a c t
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The s t a t u s o f t h e e l e c t r o - m e c h a n i c a l c a l c u l a t i o n s of t h e SIN c o n c e p t f o r t h e INTOR/NET 1 1 T e s l a t o r o i d a l f i e l d c o i l s is p r e s e n t e d . 0 p t i m i . z a t i o n of t h e c o n s t a n t - t e n s i o n D-shape c u r v e , c a l c u l a t i o n s of e l e c t r o m a g n e t i c f o r c e s and s t r e s s a n a l y s i s of c o n d u c t o r , w i n d i n g a n d c o m p l e t e c o i l a r e d i s c u s s e d .INTRODUCTION
S e v e r e p r o b l e m s c o n c e r n i n g s t r u c t u r a l i n t e g r i t y a n d AC l o s s e s of t h e s t e e l c a s e r e f e r e n c e d e s i g n , a s d e f i n e d by t h e INTOR/NET M a g n e t i c Group, l e d SIN t o i n v e s t i g a t e a n a l t e r n a t e c o n c e p t . Main c h a r a c t e r i s t i c o f t h e SIN a p p r o a c h is t h e d i s t r i b u t i o n o f s t r u c t u r a l m a t e r i a l t o t h e i n d i v i d u a l c o n d u c t o r s w i t h t h e e l i m i n a t i o n , p a r t i a l o r c o m p l e t e , of t h e i n t e g r a l s t e e l c a s e / I / . T h i s c o n c e p t is b a s e d on a f o r c e d f l o w c o o l e d c o n d u c t o r w i t h Nb3Sn s t r a n d s c a b l e d a r o u n d a c e n t r a l c o o l i n g t u b e and e n c l o s e d t o g e t h e r w i t h c o p p e r s t a b i l i z i n g s t r i p s i n a s t a i n l e s s s t e e l j a c k e t . The p u r p o s e o f t h i s j a c k e t i s t o w i t h s t a n d a l l t h e i n - p l a n e f o r c e s and p a r t of t h e o u t - o f - p l a n e f o r c e s due t o t h e p o l o i d a l f i e l d .
A c c o r d i n g t o p r e l i m i n a r y e s t i m a t i o n s , based on t h e a s s u m p t i o n o f p u r e t e n s i o n , t h e s t r e s s e s i n t h e c o n d u c t o r s t e e l j a c k e t and i n t h e epoxy i n s u l a t i o n a r e s u c h t h a t t h e w i n d i n g package is s e l f - s u p p o r t i n g . To check t h i s r e s u l t , a n a c c u r a t e t h r e e - d i m e n s i o n a l f i n i t e - e l e m e n t s t r e s s a n a l y s i s i s i n p r o g r e s s . Mode 1 a n d p r e s e n t s t a t u s of t h e c a l c u l a t i o n s a r e r e p o r t e d i n t h i s p a p e r .
T h i s work was performed by ENEA-Italy and S I N - S w i t z e r l a n d a s p a r t o f t h e SULTAN c o o p e r a t i o n .
CONSTANT-TENSION D-SHAPE CURVE
I n o r d e r t o minimize t h e m e c h a n i c a l s t r e s s e s r e s u l t i n g from t h e e l e c t r o m a g n e t i c l o a d s ( i n - p l a n e f o r c e s ) , t h e s h a p e of t h e c o i l c e n t e r - l i n e was f i r s t o p t i m i z e d a s a c o n s t a n t - t e n s i o n c u r v e , c o r r e c t e d t o i n c l u d e t h e m a g n e t i c f i e l d d e v i a t i o n from t h e i d e a l t o r u s t o t h e 1 2 - c o i l s e c t o r e d a r r a y /2/. T h i s D-shape c u r v e h a s minimum a n d maximum b e n d i n g r a d i i o f 1 .95 m a n d 5.87 m r e s p e c t i v e l y . I n o r d e r t o p e r f o r m t h e t h r e e - d i m e n s i o n a l c a l c u l a t i o n s of f o r c e s and s t r e s s a n a l y s i s , t h e c o n s t a n t - t e n s i o n c o i l s h a p e was a p p r o x i m a t e d w i t h a f i n i t e number of c i r c u l a r a r c s . The e r r o r s i n t r o d u c e d by t h i s a p p r o x i m a t i o n do n o t exceed 0.25 $ i n t h e r a d i a l d i r e c t i o n . A two-dimensional beam model was u s e d t o v e r i f y t h a t t h e d i s t r i b u t i o n o f h o o p - s t r e s s e s a l o n g t h e p e r i m e t e r l e n g t h is c o n s t a n t . The c o i l c o n f i g u r a t i o n , s y m m e t r i c a l w i t h r e s p e c t t o t h e c o i l c e n t e r - l i n e , is shown i n Fig. 1 . I n s p i t e o f one minor d e v i a t i o n from t h e d i m e n s i o n s s e t u p by t h e INTOR/NET D e s i g n Group, t h e s h a p e o f t h e SIN c o i l i s deemed t o be a f e a s i b l e compromise between s t r u c t u r a l a n d g e o m e t r i c a l c o n s t r a i n t s .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841184
C1-902 JOURNAL
DE
PHYSIQUEF i g u r e 1
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C o i l c o n f i g u r a t i o n a n d t h r e e - d i m e n s ona 1 mesh ( s t r e s s - a n a l y s i s )ELECTROMAGNET1 C FORCES
The f o r c e s have b e e n c a l c u l a t e d by computing l o c a l v a l u e s o f t h e m a g n e t i c f i e l d i n s i d e t h e c o i l . The computer codes u s e d f o r t h e s e t h r e e - d i m e n s i o n a l c a l c u l a t i o n s a r e u p d a t e d v e r s i o n s of t h o s e u s e d f o r FINTOR /3/. F o r f i e l d c o m p u t a t i o n , t h e t o r o i d a l f i e l d c o i l s h a v e b e e n d i v i d e d i n t o 4 s u b c o i l s and t h e i r g e o m e t r i c a l s h a p e h a s been a p p r o x i m a t e d w i t h 11 c i r c u l a r a n d 1 s t r a i g h t segments.
The plasma, assumed t o be of u n i f o r m d e n s i t y , h a s been a p p r o x i m a t e d w i t h 5 0 c u r r e n t e l e m e n t s . R e s u l t s o f i n - p l a n e f o r c e s due t o t h e t o r o i d a l f i e l d a t e q u i l i b r i u m (12 c o i l s e n e r g i z e d ) a n d o u t - o f - p l a n e f o r c e s due t o t h e p o l o i d a l f i e l d a t d i f f e r e n t t i m e s of t h e b u r n c y c l e a r e shown, as a f u n c t i o n of p e r i m e t e r p e r c e n t a g e , i n F i g . 2 and 3 r e s p e c t i v e l y . The t o t a l o v e r t u r n i n g moment a r o u n d t h e X-axis i s 21 MN'm a t t - 0 s and -132 MN*m a t t=211 s.
F i g u r e 2
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F o r c e s a c t i n g t h e t o r o i d a l c o i l s , due t h e t o r o i d a l f i e l d e q u i l i b r i u m1
' I I I J0 50 100 150 200
PERIMETER I % 1
6
4
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E0 2
IT -2
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-4 -6 -8
0 50 103 I50 200
PERIMETER [ % 1
F i g u r e 3
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F o r c e s a c t i n g t h e t o r o i d a l c o i l s , due t h e p o l o i d a l f i e l dSTRESS ANALYSIS
B e f o r e s t r e s s and d e f o r m a t i o n of t h e e l e c t r o m a g n e t i c a l l y l o a d e d c o i l c a n be c a l c u l a t e d , a n a n a l y s i s was needed t o d e t e r m i n e t h e c h a r a c t e r i s t i c s of t h e m a t e r i a l which b e s t a p p r o x i m a t e t h e m e c h a n i c a l p r o p e r t i e s o f t h e components o f t h e w i n d i n g package. A l l c a l c u l a t i o n s were performed u s i n g t h e computer code SAP.
Conductor and w i n d i n g a n a l y s i s
S i n c e c o i l c o m p o s i t e m a t e r i a l s a r e h e t e r o g e n e o u s and a n i s o t r o p i c , it would be v e r y t i m e consuming t o p e r f o r m s t r e s s a n a l y s i s o f t h e c o i l c o n s i d e r i n g e a c h component m a t e r i a l s e p a r a t e l y . An a l t e r n a t i v e method i s t o r e p l a c e t h e o r i g i n a l component s y s t e m by a n e q u i v a l e n t homogeneous s o l i d which b e s t a p p r o x i m a t e t h e s t r u c t u r a l r e s p o n s e o f t h e c o i l . Such a n a p p r o a c h was f o l l o w e d , u s i n g t h e f i n i t e - e l e m e n t s t r e s s a n a l y s i s method, i n o r d e r t o p r o v i d e t h e m a t e r i a l d a t a f o r t h e s t r e s s a n a l y s i s of t h e INTOR-CH c o i l . E l a s t i c model a n d l a y e r i n g e f f e c t s were c o n s i d e r e d i n two s e p a r a t e s t a g e s , assuming p e r f e c t b o n d i n g between component m a t e r i a l s . F i r s t t h e c o n d u c t o r was modeled t o c a l c u l a t e t h e n i n e e n g i n e e r i n g c o n s t a n t s o f t h e o r t h o t r o p i c e q u i v a l e n t m a t e r i a l t o be u s e d i n t h e w i n d i n g model.
S e c o n d l y , t h e m e c h a n i c a l b e h a v i o u r o f t h e w i n d i n g package was s t u d i e d by a n a l y z i n g f o u r a d j a c e n t c o n d u c t o r s w i t h Epoxy l a y e r s i n between. D e t a i l s o f c o n d u c t o r and w i n d i n g a n a l y s i s w i l l be p u b l i s h e d soon.
C o i l a n a l y s i s
Only i n - p l a n e l o a d s due t o t o r o i d a l f i e l d a t e q u i l i b r i u m (12 c o i l s e n e r g i z e d ) and no t h e r m a l e f f e c t s were c o n s i d e r e d s o f a r . The c o i l was assumed t o be made o f t h e " e q u i v a l e n t w i n d i n g m a t e r i a l " whose e n g i n e e r i n g c o n s t a n t s were c a l c u l a t e d w i t h t h e w i n d i n g model. A p i c t u r e of t h e mesh, which i n c l u d e s 1088 nodes i n 136 e l e m e n t s , is shown i n F i g . 1
.
A s boundary c o n d i t i o n s , t h e d i s p l a c e m e n t s i n t h e X - d i r e c t i o n o f t h e s t r a i g h t s t u c t u r e ( b u c k i n g c y l i n d e r ) were f o r b i d d e n . The s i x s t r e s s components and t h e combined stress a c c o r d i n g t o von Mises t h e o r y were c a l c u l a t e d a t s e v e r a l l o c a t i o n s of e a c h element of t h e mesh.The d i s t r i b u t i o n o f hoop s t r e s s e s a l o n g t h e c o i l p e r i m e t e r i s shown i n F i g . 4 where, due t o symmetry, o n l y r e s u l t s i n t h e u p p e r h a l f o f t h e c o i l a r e p r e s e n t e d . The maximum r a d i a l d e f o r m a t i o n i s 25 mm a t a p p r o x i m a t e l y 50 $ a n d 150
%
o f , t h e p e r i m e t e r l e n g t h , r e s p e c t i v e l y . Bending d u e t o f i n i t e t h i c k n e s s of t h e c o i l i s l i k e l y t o be r e s p o n s i b l e f o r t h e l a r g e d e v i a t i o n f r o m a c o n s t a n t - t e n s i o n d i s t r i b u t i o n of h o o p - s t r e s s e s a t t h e c o i l c e n t e r l i n e . I n t h e u n s u p p o r t e d r e g i o n n e a r t h e e n d s of t h e c e n t r a l b u c k i n g c y l i n d e r , i n t h e i n n e r p a r t of t h e c o i l , t h e s e s t r e s s e s r e a c h u n t o l e r a b l e v a l u e s .C1-904 JOURNAL DE PHYSIQUE
However, r e m a r k a b l e r e d u c t i o n s of them c a n be a c h i e v e d i f s t r u c t u r a l r e i n f o r c e m e n t is added i n t h e c r i t i c a l a r e a s . T h i s a s p e c t was s t u d i e d by i n c l u d i n g t o t h e c o i l s t r u c t u r e boundary e l e m e n t s i n t h e f o r m o f r i g i d s u p p o r t s o r r a d i a l s p r i n g s u p p o r t s . D i s t r i b u t i o n o f hoop s t r e s s e s f o r t h e l a t t e r c a s e i s shown i n F i g . 5 . The maximum r a d i a l d e f o r m a t i o n i s reduced t o 15 mm.
NO I F I X E D SUPPORT -'1 SUPWRT
I I I I I
,
0 10 20 30 40 50 60 7 0
ELEMENT NO.
F i g u r e 4
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Hoop s t r e s s e s i n t h e c o i l , w i t h r i g i d s u p p o r t a t t h e b u c k i n g c y l i n d e r (AA of F i g . 1 )I 1 1 1 1 I I I
I I I
-
I2
m 200-
-
111 Ln W
n O - 1 I
I- I
Ln 0% I
F i g u r e 5
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Hoop s t r e s s e s i n t h e c o i l , w i t h r i g i d s u p p o r t a t t h e b u c k i n g c y l i n d e r (AA of F i g . 1 ) a n d w i t h a d d i t i o n a l r a d i a l s p r i n g s (AF of F i g . 1 ) -200T h e s e f i r s t r e s u l t s seem t o c o n f i r m t h e p r e d i c t i o n of t o l e r a b l e s t r e s s - l e v e l s i f a d e q u a t e s t r u c t u r a l r e i n f o r c e m e n t i s added. However, b e f o r e f i n a l c o n c l u s i o n s on t h e f e a s i b i l i t y of t h e SIN c o n c e p t c a n be drawn, t h e i m p a c t of t h i s s t r e s s a n a l y s i s on t h e d e s i g n of t h e INTOR/NET c o i l n e e d s t o be s t u d i e d a n d component s t r e s s e s have t o be r e - e v a l u a t e d i n g r e a t e r d e t a i l .
I I
I 100 %
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NOI
RADIAL I F I X E D-
SUPPORT
---j
SPRINGI
SUPPORTL I I 9 I I I
One of t h e a u t h o r s (CK) w i s h e s t o t h a n k C . H a u v i l l e r o f CERN f o r h i s h e l p f u l c r i t i c i s m and a s s i s t a n c e w i t h t h e code SAP. T h i s work was s u p p o r t e d by t h e S w i s s N a t i o n a l Energy R e s e a r c h F o u n d a t i o n (NEFF) a n d Euratom.
0 10 20 30 40 50 60 7 0
ELEMENT NO.
/ I / J.D.Elen, N . S a c c h e t t i , G,Vecsey
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INTOR P h a s e I I A , F i n a l Design R e p o r t by t h e SULTAN Group (1983)/2/ C.Marinucci
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A n a l y t i c a l s o l u t i o n of t h e c o n s t a n t t e n s i o n s h a p e o f t o r o i d a l f i e l d c o i l s-
SIN I n t e r n a l R e p o r t KRYO-82.6 (1982)/3/ G . P a s o t t i e t a l .
