LOCAL MECHANICAL EFFECTS IN THE DESIGN OF THE SUPERCONDUCTING EUROPEAN LCT COIL

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LOCAL MECHANICAL EFFECTS IN THE DESIGN OF THE SUPERCONDUCTING EUROPEAN LCT

COIL

H. Zehlein

To cite this version:

H. Zehlein. LOCAL MECHANICAL EFFECTS IN THE DESIGN OF THE SUPERCONDUCT- ING EUROPEAN LCT COIL. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-905-C1-908.

�10.1051/jphyscol:19841185�. �jpa-00223661�

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JOURNAL DE PHYSIQUE

Colloque C1, suppl6ment au no 1, Tome 45, janvier 1984 page C1-905

L O C A L MECHANICAL EFFECTS I N THE D E S I G N OF THE SUPERCONDUCTING EUROPEAN L C T C O I L

H. Zehlein

Kernforschungszentrwn K a r Z s m h e GmbH, Institut fur ReaktorbaueZemente, Arbeitsgruppe ZuverZtlssigkeit und Schadenskunde, Postfach 36 40, 0-7500 K a r Z s m h e 2, F.R.G.

Resume

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On i l l u s t r e 2 s i t u a t i o n s d i f f e r e n t e s de contraintes mecaniques

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_{q u i}ont influence sensiblement l a construction de l'aimant Europeen

LCT.

Abstract

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The paper i l l u s t r a t e s 2 d i f f e r e n t mechanical s t r e s s s i t u a t i o n s which sensibly determined the European design of the LCT c o i l .

Both examples presented in t h i s paper deal with the avoidance of intolerable shear s t r e s s e s which may a r i s e

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between the superconductor layers within the winding pack of a toroidal f i e l d coil along the central support of a Tokamak reactor

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within an individual superconductor cable during the winding procedure.

Althoug the detailed analyses of these problemes /1,2/ were undertaken f o r the par- t i c u l a r design of the European LCT coil / 3 / the s i t u a t i o n s illuminated seem generic enough f o r the manufacture and operation of any d i s c r e t e toroidal f i e l d coil of fu- t u r e Tokamak reactors t o use them as a basis f o r carrying over t h e lessons learned /4,5/ t o the harder conditions met with b r i t t l e superconductors and/or vault- forming central supports /6/. Proposals t o a l l e v i a t e such more general and harder fabrication and working conditions a r e made.

T

( T R ) and a 30 f l n i t e elemnt model (3D).(Dimsnsionr ,n m)

asymmetric loading

Yo = 0.062 m , v7 = 0.066 nm

Fig. 1

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Exploded view of the LCT-coil (AE: A' support zones

EA

,

A'T f r e e bending zones) Fig. 2

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Axial displacements

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841185

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C1-906 JOURNAL DE PHYSIQUE

I . SUPPORT LOAD DIFFUSION EFFECTS ALONG THE INNER LEG OF A TF COIL UNDER ASYMMETRIC

LOADING

Fig. 1 shows t h e EURO-LCT-coil and i l l u s t r a t e s t h e asymmetric l o a d i n g due t o a f a u l t i n g neighbour c o i l . Our aim i s t o g i v e a s i m p l e ( l 0 ) d e s c r i p t i o n o f t h e a x i a l displacement o f c e n t r o i d o f t h e c o i l cross s e c t i o n as w e l l as i t s e l a s t i c d i s t o r - t i o n by superimposing t h e fundamental "deformation modes" 1 i ke bending, shear and t o r s i o n a l t w i s t . As a 3D f i n i t e element model ( l i k e t h a t i n / I / ) cannot g i v e t h i s breakdown, and as a simple r i g i d cross s e c t i o n beam model f o r t h e e n t i r e c o i l i s on p r i n c i p l e unable t o describe c o r r e c t l y t h e cross s e c t i o n deformation p r e v a i - l i n g i n t h e l o a d - d i f f u s i n g support regions (AE and A' i n f i g . l) i t was proposed p r e v i o u s l y /4/ t o subdivide t h e contour i n t o "support zones" w i t h l o c a l cross sec- t i o n deformations and "bending zones" w i t h r i g i d cross sections. This understand- i n g was o u t l i n e d i n /4/ f o r bucking post supports. The corresponding new thumb r u l e i s i n acceptable agreement w i t h 3D r e s u l t s /1/ (see f i g . 2). Here we o n l y p o i n t o u t t h e p a r t i c u l a r l y e x c e l l e n t agreement o f t h e support zone displacements (values vl and v2 v a l i d along nodes 1 t o 31 and 71 t o 81, resp. i n f i g . 2 ) which are g e n e r a l l y described by a 3 r d o r d e r power s e r i e s expansion o f t h e d i s t a n c e 1 between c o i l / b u c k i n g p o s t i n t e r f a c e and c r o s s s e c t i o n c e n t r o i d :

V/p = all

+

a21 2

+

a313 (P = l i n e l o a d ) (1 )

The c o e f f i c i e n t s al=l/AG, a2=t/GJ a3=1/3EI ( 2 ) (A-cross s e c t i o n area; E,G=shear, e l a s t i c modulus, I = ( ( 2 ) ) area moment, J = t o r s i o n a l s t i f f n e s f a c t o r , t = t o r s i o n a l t w i s t l e n g t h ) represent t h e shear, t o r s i o n a l and bending deformation. The superposi- t i o n e q . ( l ) i s confirmed by t h e 3D-results /1/ shown i n f i g . 3. The h i g h e s t absolute stresses of t h e whole l o a d case catalogue occurred i n corner C (see f i g . 3) o f t h e casing ( e q u i v a l e n t s t r e s s 400 t o 600 MPa i s r e l e v a n t ) as w e l l as i n t h e winding ( i n t e r l a y e r shear s t r e s s 30 t o 40 MPa and a x i a l s t r e s s 60 t o 80 MPa are r e l e v a n t ) / 1 , 2 / so t h a t f o r t h e EURO-LCT c o i l a forged r a t h e r t h a n r o l l e d f r o n t p l a t e had t o be cho- sen /3/ (see a l s o f i g . 1 ) . This c r i t i c a l f i n d i n g shows t h a t r i g o r o u s s c r u t i n y must be observed, when t h e understanding of eq. ( 1 ) i s t o be c a r r i e d over t o t h e s o f t e r cen- t r a l support provided by a v a u l t i n s t e a d o f a bucking post.

I I

E

sandwich beam behaviour wmagnif i c a t i o n f a c t o r : 500

F i g . 3

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Cross s e c t i o n deformation Fig-

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(3D f i n i t e element model) and surface f o r c e s

If t h e c e n t r a l support s t r u c t u r e i s b u i l t as a v a u l t as envisaged f o r t h e INTOR r e a c t o r study /6/ then t h e s i t u a t i o n becomes more complex because t h e r i g i d support by t h e bucking p o s t i s replaced by t h e e l a s t i c f o u n d a t i o n p r o v i d e d by t h e c l u s t e r o f i n n e r legs. These a r e themselves under asymmetrie magnetic body f o r c e s as w e l l as under s u r f a c e loads d i f f u s e d through t h e i r wedge s i d e faces by t h e s t a c k i n g e f f e c t . I f the d i s t r i b u t e d body and surface loads a r e approximated by t h e i r s i n g l e f o r c e r e s u l t a n t s , and i f s l i d i n g between t h e sidefaces i s prevented, then t h e r e a c t i o n f o r c e s shown i n f i g . 4 a r e a c t i n g on t h e cross section. The l o c a l cross s e c t i o n deformation i s expected t o c o n t r i b u t e o n l y p a r t i a l l y t o t h e i n n e r l e g d i s t o r t i o n whereas t h e accumulated deformation o f t h e unsymmetrically loaded v a u l t (gaps and displacements under stacked body and surface f o r c e s ) dominates. Due t o t h e wedge shape t h e r e a r e a l s o in-plane components which may deform t h e cross s e c t i o n

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(see f i g . 4). The s t i f f n e s s o f t h e v a u l t stack i s determined c o n s e c u t i v e l y s t a r t i n g w i t h t h e wedge opposite t o t h e f a u l t i n g c o i l . The c l u s t e r i s constructed by adding wedgeper wedge u s i n g t h e deformed shape ( w i t h p r e s t r e s s ) o f t h e already present stack as t h e support s t r u c t u r e t o be loaded by t h e c u r r e n t l y added wedge. The sum o f t h e t o t a l displacements o f v a u l t c l u s t e r and c o i l cross s e c t i o n i s found a f t e r a few e q u i l i b r i u m i t e r a t i o n s f o r each i n t e r m e d i a t e stack. I t i s azimuth-dependent and replaces eq. (1). The approximation o f t h e pure bending zone (see/4/ f o r d e t a i l s ) must be enhanced, however, t o i n c l u d e a gap and e l a s t i c r e s t r a i n t s a g a i n s t transverse and r o t a t i o n a l motion a t t h e i n n e r l e g t r a n s i t i o n . T h e purpose o f t h e procedure sket- ched here i s t o approximate t h e v a u l t response by a simple 1D beam f o r m u l a t i o n f o r t h e i n d i v i d u a l c o i l . The scheme should be as s i m i l a r as p o s s i b l e t o t h e one d e r i v e d f o r t h e bucking p o s t case. The simp1 i f i c a t i o n s behind the proposed approximation must o f course be corroborated by a thorough and more r e f i n e d 3D a n a l y s i s o f c o i l and v a u l t response. Work i n t h i s d i r e c t i o n i s under way and w i l l be r e p o r t e d i n a f u t u r e paper.

11. SHEAR RESULTANT WITHIN A SUPERCONDUCTOR CABLE DURING THE WINDING PROCEDURE Due t o t h e bending s t i f f n e s s o f t h e superconductor a boundary- 1 ayer-1 i ke concentrat- i o n o f s h a r p l y r i s i n g c u r v a t u r e as w e l l as bending and shear stresses must be expected near t h e touching p o i n t (see R 1 i n f i g . 5) a t t h e bobbin. This e f f e c t was appro- x i m a t e l y described by a d i s c r e t e "Simp1 i f i e d E l a s t i c a Conductor Model" (SECM) /5/

which was used t o study t h e combined i n f l u e n c e s o f t h e e l a s t o p l a s t i c metal forming, t h e geometric arrangement o f t h e winding equipment ( f i g . 5) and t h e model s i m p l i f i - cations. Whereas i n /5/ t h e numerical scheme p e r t a i n i n g t o t h e SECM as w e l l as t h e c i r c u m f e r e n t i a l d i s t r i b u t i o n o f t h e peak stresses around t h e bobbin contour were g i - ven, here we a r e more i n t e r e s t e d i n t h e shape o f these l o c a l peaks. Fig. 6 shows t h a t t h e i n f l u e n c e o f t h e p u l l i n g f o r c e i s marginal f o r t h e bending moment a t the end o f the conductor, b u t t h a t t h e shape o f t h e peak i s s e n s i b l y a f f e c t e d . The dependence o f t h e ensuing shear r e s u l t a n t (=bending moment g r a d i e n t ! ) on the p u l l i n g f o r c e i s almost l i n e a r ( f i g . 7 ) i n t h e f e a s i b l e p u l l i n g f o r c e range. P l a s t i c forming occurs every- where o u t s i d e o f the i n n e r l e g section. Experimental evidence i n d i c a t e d t h a t no damage should be expected below a bending moment o f 220 Nm. Even i n t h e small r a d i u s s e c t i o n s (Rl, R3 i n f i g . 5 ) t h i s s a f e l i m i t o f damage-free forming i s n o t exceeded.

Biegemomentverlauf entlang des Leiters

conductor l e n g t h Fig. 7

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Shear r e s u l t a n t d i s t r i - b u t i o n

;-

recommended

- -

~ u e e r

-

1 i m i t

-

0

freies Leitersttick' ~ c h w e n k b r u c k e ~ ^{- .}_00-⁰

-v -m

+-

^{RM= 15.5}^rn

Fig. 5

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Geometric arrangement o f t h e winding 3 .

equipment

2 zz-

1 superconductor 2 supply bridge L, ^L~

a

z:

x

Fig. 6

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Bending moment d i s t r i b u t i o n 250-

IHml 200

-

150- 100

-

50

-

0

R 1 = R 3 = 0 . 7 8 0 r n ^x^ul^a?-^wC

3 0

0 0

4 . 5 0 6:00 5 . 5 0 5 . 0 0

L E I T E R L R E N G E I N M conductor l e n g t h

RAOlUS NR. 1 Z ^9.SEKTURPUNKT

aZUGKRAFT= l O 0 0 0 . 0 WICKELRAOIU5= 0 . 7 8 0 AZUGKAAFT= 20000.0

+ZUGKRRFT= 3 0 0 0 0 . 0

XZIJGKRRFT= 400an.,

R1 = R3 = 0.780 m

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CI-908 JOURNAL D E PHYSIQUE

Overbending t e s t s have a l s o shown t h a t t h e forming l i m i t i s determined by the shear s t r e n g t h of t h e s o l d e r i n g seams w i t h i n t h e cable. Due t o measurements of t h e shear s t r e n g t h t o g e t h e r w i t h p r e l i m i n a r y assumptions on t h e d i s t r i b u t i o n o f shear s t r e s - ses over t h e cross s e c t i o n i t seems recommendable t o keep t h e shear r e s u l t a n t below 2500 N. This value i s nowhere reached i n the LCT-design (broken l i n e i n f i g . 7). For f u t u r e s t i f f e r superconductors l i k e Nb3Sn lower l i m i t s must be expected, however.

Therefore, i t seems reasonable t o consider t h e m i t i g a t i o n o f shear c o n c e n t r a t i o n e f - f e c t s near t h e touching p o i n t a t t h e bobbin contour by a b e t t e r arrangement o f t h e winding equipment. The shear-resul t a n t as t h e 1 im i t i n g parameter i n t h e forming pro- cess peaks over a l e n g t h o f about 1 m ( f i g . 7). I f i t i s p o s s i b l e t o p l a c e a r o l l e r ( o r r o l l e r s e t ) i n t h i s space near t h e bobbing then such a device would appear a t t r a c t i v e f o r t h i s purpose, because

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i t c o u l d impose a d e f i n e d i n t e r m e d i a t e bending moment thus l o w e r i n g t h e bending moment g r a d i e n t (= shear r e s u l t a n t ) a t t h e bobbin,

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t h e bending moment a t t h e bobbin contour must then no l o n g e r be provided by t h e p u l l i n g f o r c e alone, so t h a t t h e shear peak i n h e r e n t t o t h e f r e e SECM can be

"smoothed down".

a,b r o l l e r s e t c one r o l l e r d no r o l l e l

c o n d u c t o r a r c l e n g t h

F i g . 8

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M i t i g a t i o n o f t h e shear r e s u l t a n t by a r o l l e r gate

F i g u r e 8 g i v e s a schematic o f t h e envisaged arrangement. The r o l l e r gate R may be c u r - ved o r s t r a i g h t , staggered o r f a c e - t o face. An a d d i t i o n a l s u i t a b l y moving holddown r o l l e r H m i g h t h e l p f o r compaction ( e s p e c i a l l y near contour r a d i u s jumps!). To keep t h e r o l l e r s close enough t o t h e bobbin t h e y should be a b l e t o make a s i m p l e - s t ~ a i g h t motion (see arrows i n f i g . 8) which compensates f o r t h e change o f t h e d i s t a n c e t a b l e a x i s / t o u c h i n g p o i n t d u r i n g the winding (see arrows i n f i g . 8). Then t h e swivel of t h e supply b r i d g e may probably become unnecessary. Conductor branch b c o u l d be s t r a i g h t ( o r s u i t a b l y curved). The p r a c t i c a l importance of an improved arrangement l i e s i n t h e promise t o enhance t h e f e a s i b l e range o f p u l l i n g forces f o r t h e winding o f t h e f u t u r e s t i f f e r superconductors.

I I I. REFERENCES

/1/ MESSEMER, G., ZEHLEIN, H., Proc. 1 1 t h SOFT, EUR-7035EN (1981) 533 /2/ MAURER, A., t h i s conference MT-8, paper 4P1-03

/3/ KRAUTH, H. e t a l . IEEE-T.rans.Magnetics, MAG-17 (1981), 1726

/4/ ZEHLEIN, H., I n t . Conf. SMIRT7, Chicago, Aug--22-26, 1983, Paper N5/2, t o be published , i n Res Mechanica

/5/ MESSEMER, G., ZEHLEIN, H., I n t . Conf. SMIRT7, Chicago, Aug. 22-26, 1983, Paper N5/6, t o be published i n Res. Mechanica

/6/ ERB, J. e t al., IEEE-Trans.Magnetics, MAG-17 (1981), 1699