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FE-COMPUTATIONS OF A NONPLANAR COIL WITH DIFFERENT SUPPORT CONSIDERATIONS
U. Brossmann, H. Gorenflo, S. Mukherjee
To cite this version:
U. Brossmann, H. Gorenflo, S. Mukherjee. FE-COMPUTATIONS OF A NONPLANAR COIL WITH
DIFFERENT SUPPORT CONSIDERATIONS. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-
927-C1-931. �10.1051/jphyscol:19841189�. �jpa-00223665�
JOURNAL DE PHYSIQUE
Colloque C1, suppl6ment au no 1, Tome 45, janvier 1984 page Cl-927
FE-COMPUTATIONS OF A NONPLANAR C O I L W I T H DIFFERENT SUPPORT CONSIDERATIONS
U.B. Brossmann, H. Gorenflo and S.B. Mukherjee
Max-PZanck-Institut far PZasmaphysik, EURATOM-Association, 0-8046 Garehing, F.R. G.
Riesum6 - A cause de l e u r dkformation t o r o i d a l e l e s bobines non planes, en com-
- paralson avec des bobines planes, subissent une t e n s i o n mkcanique supplPmentaire.
Toutes l e s f o r c e s e t couples agissant sur chaque bobine i n d i v i d u e l l e e t l e s f o r c e s e n t r e bobines adjacentes sont contenues dans une s t r u c t u r e complexe dans l a q u e l l e l e s bobines sont soutenues par des coussins elastiques. Ces bobines non planes sont sensibles aux c o n d i t i o n s de f i x a t i o n . Les c o n t r a i n t e s mkcaniques dans l e s bobines d6pendent de l a faqon dont l e s bobines sont f i x P e s e t de l a r i g i d i r e de l a s t r u c t u r e . Le p r k s e n t r a p p o r t e s t un rksumk de l ' a n a l y s e des con- t r a i n t e s mPcaniques, de l ' o p t i m i s a t i o n de l a l o c a l i s a t i o n des supports e t des d i f y e r e n t e s s i m u l a t i o n s p a r klkments f i n i s .
A b s t r a c t - Because o f t h e i r t o r o i d a l d e v i a t i o n nonplanar c o i l s a r e subjected t o a d d i t i o n a l mechanical stresses by t h e magnetic f o r c e s when compared w i t h planar c o i l s . A l l three-dimensional forces and moments a c t i n g on an i n d i v i d u a l c o i l and a l l i n t e r a c t i v e f o r c e s and moments between adjacent c o i l s a r e supported w i t h i n a complex c o i l casing, i n which t h e c o i l s a r e embeded by e l a s t i c l a y e r s . These non- planar c o i l s a r e s e n s i t i v e t o support c o n d i t i o n s . The mechanical stresses i n t h e c o i l s response a c c o r d i n g l y on how t h e c o i l s a r e being supported and on t h e c o r - responding s t i f f n e s s o f t h e support system. The present r e p o r t summarizes t h e mechanical s t r e s s analyses w i t h optimized support regions and t h e survey o f d i f f e r e n t FE-simulations and t h e i r r e s u l t s .
1. INTRODUCTION
P r e l i m i n a r y design s t u d i e s o f l a r g e , nonplanar c o i l s f o r f u s i o n experiments have been aided by f i n i t e element analyses o f t h e c o i l s , i n c l u d i n g t h e support s t i f f n e s s .
hrutraJ / Beam In
Fig. 1 - The c o i l - s e t s o f t h e WENDELSTEIN VII-AS
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841189
C1-928 JOURNAL DE PHYSIQUE
Some works performed a t IPP are o u t l i n e d i n t h i s paper. The numerical r e s u l t s a r e intended as i l l u s t r a t i v e examples r a t h e r than f i n a l design data.
For t h e c o i l system, t h e v e r s i o n o f t h e c o i l - s e t s o f t h e WENDELSTEIN VII-AS /1/
advanced s t e l l a r a t o r (Fig. 1) a r e used. This c o n f i g u r a t i o n has f i v e f i e l d periods and each o f them contains n i n e d i f f e r e n t nonplanar c o i l s , w i t h one o f them having increased dimensions and c u r r e n t i n order t o p r o v i d e s u f f i c i e n t access ( F i g . 2).
The standard vacuum f i e l d c o n f i g u r a t i o n (Bo = 3T, t = 0.39) can be v a r i e d by an a d d i t i o n a l t o r o i d a l f i e l d (Bo = * 0.5 T). The present paper reviews t h e s t a t u s o f t h e mechanical s t r e s s analyses f o r t h e most unfavourably loaded nonplanar c o i l 1 w i t h d i f f e r e n t supports simulations.
2. MAGNETIC LOADS
The c a l c u l a t i o n s a r e made by u s i n g EFFI-code /2/. They i n c l u d e a magnetic f i e l d o f Bo = 3,5 T and as w e l l as t h e s e l f - f o r c e o f t h e i n d i v i d u a l c o i l s and t h e i n t e r - a c t i v e f o r c e between d i f f e r e n t c o i l s . The component f o r c e s a r e shown i n Fig. 3 as
f u n c t i o n o f t h e c o i l ' s circumferent- i a l coordinate. A1 1 components a c t a t the c e n t e r o f t h e r e s p e c t i v e f i n i t e macro-el ement o f t h e c o i 1. Typical maximum values o f t h e f o r c e s are -242 kN, 20 kN and 11 kN i n t h e x, y and z d i r e c t i o n s . Acted on by a l l t h r e e f o r c e components Fx, Fy and Fz each o f t h e nonplanar c o i l s tends t o s p r i n g back i n t o a plane.
3. COIL SUPPORT CONCEPT
Nonplanar c o i l s are u s u a l l y s e n s i t i v e t o support c o n d i t i o n s and t h e stresses response a c c o r d i n g l y on how t h e c o i l s a r e being supported /3/. I n t h i s con- c e p t t h e c o i l s a r e supported a t t h e f r o n t t o take up t h e c e n t e r i n g f o r c e and l a t e r a l l y t o t r a n s m i t t h e t o r o i d - Fig. 2 - Top view o f c o i l system o f a1 forces and t i l t i n g moments.
W VII-AS. One f i e l d p e r i o d c o n t a i n i n g
9 t w i s t e d c o i l s and 2 planar t o r o i d a l 4. FE-SIMULATION AND ANALYSIS f i e l d c o i l s
For t h e s t a t i ~ analyses o f t h e c o i l s -
M W L I I C F- (EiLO KYmo G580JaO) - C o i l # W11-15
t h e SAP V(2) /4/ code i s used. Three
d i f f e r e n t f i n i t e element models simulate t h e c o i l and t h e support s t r u c t u r e . Most FE-elements a r e t h r e e -
So
dimensional and isoparametric.
The FE c a l c u l a t i o n s a r e done w i t h t h e
O
nodal f o r c e s o f t h e above mentioned
values and u s i n g an i s o t r o p i c i d e a l - i z a t i o n w i t h Young's ypduli2EXx =
-50
= Ezz = 0.6 x 10 N/m (mixture
%copper and g l a s s epoxy). The poisson r a t i o s are%y = vxz = vyz = 0.3 and t h e shear moduj-i .
Fig. 3 - Global magnetic f o r c e s a c t i n g GXi : = GXz = Gyz = 0.23 xlOll n/mZ. The around t h e c o i l 1 s t ess values a t t h e c e n t r o i d o f an
element a r e obtained f o r comparison.
4.1 Boundary Support Concept
The FE-model a p p l i e d i s shown i n Fig. 4. A c o i l i s subdivided i n t o 288 elements and each element has 20 nodes. The support regions (hatched areas) a r e optimized by the simulated boundary s p r i n g elements, a c t i n g normally on t h e c o i l surface, i n a step by step method. Depending on t h e complex c o i l shape t h e c i r c u m f e r e n t i a l t e n s i o n s t r e s s spectrum ( F i g . 5) shows the i n f l u e n c e o f superimposed bending stresses. I t s maximum value o f oT = 76 MPa occurs a t element row 5.
4.2 2D -FE Support Concept
The cross-section o f t h e FE-model a p p l i e d i s shown i n F i g . 6. This model c o n s i s t s o f t h r e e main components: t h e c o i l , t h e padding and t h e casing. The c o i l and t h e casingare subdivided i n t o three-dimensional isoparametric FE elements and each element has 12 nodes. For t h e paddings 2 D elements, l a t e r a l l y d i r e c t e d , a r e being used. Those elements p r o v i d e a zero f r i c t i o n c o e f f i c i e n t and t r a n s f e r o n l y normal pressure. The paddings and t h e casing r i n g s can be modelized a t t h e r e a l support regions. The t e n s i o n s t r e s s u (Fig. 7) v a r i e s except a t t h e f r o n t support region, where a homogeneous s t r e s s varue o f 15 MPa occurs along t h i s r e g i o n . A peak v a l u e o f 42 MPa i s occured a t t h e l a t e r a l support r e g i o n because o f superimposed bending moments.
4.3 3D -FE Support Concept The cross-section o f t h e FE-model i s a l s o shown i n F i g . 6. The c o i l and t h e casina a r e subdivided i n t o
Fig. 4 - FE Model o f t h e c o i l 1
WIT-1S COIL1 .-4. LDUL
-a,
SN-FICLD-TO.P..mLS, II\.CPTthree-dimensional , isoparametric 12 node elements. Since t h e casing i s n o t closed around a nonplanar c o i l , s l i d i n g o f t h e c o i l r e l a t i v e t o t h e casing i s t o be considered.
The c u b i c elements a r e a p p l i e d i n t h e padding zone t o approximate f r i c t i o n a l behaviour. A low shear modulus i s given t o them i n order t o modelize t h i s behaviour. F i g . 8 shows t h e e n t i r e FE model. The r e s u l t s o f t h e t e n s i o n s t r e s s uT i s shown i n Fig. 9. I t s maximum value i s 50 MPa
F . . . . , . . . . , . . . . , . . . . , . . . . , . . . , . . . .
. , , ,, , .
0 5 10 15 20 25 30 35 10 45
F i g . 5 - T e n s i l e ( o r Hoop) s t r e s s w i t h
RRCboundary elements support
JOURNAL DE PHYSIQUE
F i g . 6 - Mesh o f t h e c o i l c r o s s - s e c t i o n
0 .
0
'- Y Y V 3.
F i g . 7 - T e n s i l e ( o r Hoop) s t r e s s w i t h 2D-padding elements
ARG
