Perin, R

Perini, D

Salminen, J

Soini, J

CERN Document Server

9 November 1995 OCR OutputGeneva, SwitzerlandMagnet Technology Conference (MT14), 11-16 june 1995, Tainpere, Finland*Picl<er Nordstar Oy, Helsinki, Finlandabout the influence of the tolerances on the behaviour of the structure.assembly procedure were also modelled. Considerations are also madetemperature and at 1.8 K both energized and non—energized. Collaring andand a vertically split yoke. The structure has been studied at roomsuperconducting LHC dipole prototype with aluminium common collarFE-calculations have been carried out for the cross-section of the 56 mmR. Perin, D. Perini, j. Salminen, ]. Soini*Finite Element Structural Analysis of LHC Bending MagnetSd 3 TM YCERN-AT-95-19 LHC Note 32SH I lCERN »·—T/M <MA>/llllllllllllllllllllllllllllllllllllCERN LIBRARIES, GENEVAEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHL4_,..!·‘¢//»»ANSYS is trademark of Swanson Analysis lnc. OCR OutputDiego Perini, e—mail perini@cemvm.cem.d1salmi1¤@parcb.c¤·n.di, phone +41-22-767 3291, fax +41-22-767 63w:Manusuip received June 13, 1995. Jukka Salminen, e-mailprocess. This is obtained by pushing on the slots in the colnecessary to elongate the collar legs during the collaringtube, 7. SC his-ban, 8. Shritking qlhde: / He Il—ves•el ln order to limit the stresses in the coils under the press, it iscoils, 4. Non-mapuic wllan, S. lion yoke, 6. Heat exdungefomiation of the collars.Hg.1.Cr0s»•cctior1d'LllCdip0|e¤ugri¤. 1.Beam—screen,?. Bemipipe,3.released, part of the compression is lost, because of the deinsertion of the pins. Once the pins are in, and the pressure isreaches the maximum value under the press just before theinterference around the coils. The compression of the coils*‘/R ® T @During the collaring, the collars are assembled with a given• AA •sa I IMA. General,,,,r\• •\7\ E " 4IH. COLLARINGthe model are for parts in their nominal size, as produced.; ‘*‘ "‘ 1 ‘°\ defonned conditions. That is to say the dimensions used inmrs The geometry is modeled at room temperature and in noncylinder.interference at the interface between the iron yoke andThe extemal cylinder prestress is also simulated by giving an1560ence at the interfaces between the collars and the coil heads.The prestress of the coils is imposed by giving an interferconditions manuals.tween the nominal size of the adjacent pieces in undeformed ceming these elements are available from the ANSYSrywhere in this paper we call "gap size" the difference be sional type 52-contac [4] elements. Further information conpresent anywhere in the coils in all working conditions. Eve type 42 [4] elements and contact surfaces with three dimenobtained under all load cases. Compressive stresses must be The areas have been meshed using two dimensional linearfine the nominal dimensions so that favorable stresses can be inder and pins a one lmm thick layer is meshed.The aim of the present analysis and optimization was to de mm thick mesh for the collars. For the coils, iron yoke, cylmm and a new cross-section (Fig. 1). ble to simulate such a structure by creating two layers of 0.5ture. These magnets will have a coil aperture diameter of 56 keeping the forces that are exerted by the coils. It was possi(1 m, 10 m, 15 m) for the LHC will be builtin the near fu magnet’s longitudinal section, every second collar only isA number of model and prototype dipoles of different lengths stress option has been used in the elements. Through theA two dimensional model has been meshed and the planeI.lr~mzoDucr1oN has been considered.the stresses and strains present in the structure. No frictionstructure. tion. From this the same fmite element package calculatedabout the influence of the tolerances on the behaviour of the at 9.7 T have been computed taking into accotmt iron saturaprocedure were also modeled. Considerations are also made ANSYSI fmite element package. The electro-magnetic forcesboth energized and non-energized. Collarlng and wmbly sign of the structure, which was studied by means of thestructure has been studied at room temperature and at 1.8 KA central field of 9.7 T was assumed for the mechanical dewith aluminium common collar and a verdully split yoke. Thesection of the 56 mm superconducting LHC dipole prototypeH. FINITE-EUEMENT Monet.Abstmct FE-calculations have been carried out for the crosPicker Nordstar Oy, Helsinki, FinlandJouko SoiniCERN, 12ll Gcncvu 23, SwitzerlandRomeo Pcrin, Diego Pcrini, Jukka SalmincnFinite Element Structural Analysis of LHC Bending Magnetshown in the Table I. The relaxation is: coils. On the other hand to avoid the deterioration of the coil OCR Outputcase where only the top of the collar is pressed. This is ensure that no cracks or sudden displacements occur in theadvantage of pre-pulling the collar legs, we have calculated a mum field some azimuthal compression is still needed toconsequently higher deformation at this point. To show the and the first tum of the coil. When the magnet is at maxiis higher stress concentration near the central key pin and e.m. forces will unload the pressure between the central postported when the magnet is energized. During excitation thethan that for the lateral side. This is due to the fact that thereelectro—magnetic forces the conductors should be well supcentral side (nearer to the magnet central axis) coil is lowerFrom Table I it can be seen that the relaxation ratio of the To avoid any conductor movement under the influence of theFm 2541.5 + 2658.3 A. GeneralF 131 .6 1139.3 —@= ——L;——>< 100 ~ 47.2% (3)V. COMPIEIE MAGNET(Fyls2) and before (Fylsl) the press is released.between yoke and the collar appears.cal forces on the horizontal median plane of the coils afterfinal stages of the assembly a small interference of 0.07 mmWe can defme a relaxation ratio as a ratio betwwn the vertithe collar assembly can be placed into the yoke, only in thecollars.The gap size between x0-x38 is 0.2 mm (Fig. 3). ln this waysary to apply part of the collaring force at the top of theenough surface area to apply the forces. Therefore it is neces gives rise to 100 MPa tensile stress at the point E Fig. 3).cessive (i.e. 0.23 mm vertical displacement of the point x0might become excessive due to the fact that there is notmuthal tensile stresses near the horizontal plane become exto push only at the extreme edges of the collars, since stressesof about 0.2 mm from the symmetry plane before the azipress close to the horizontal axis. However, it is not possibleIt is possible to open the ‘C’ shaped half-yoke by a maximum'I`herefore relaxation of the stress in the coil is smaller if weaccount the deformed shape of the collars after collaring.compression force in the coil is taken by the length ‘l2’for special tooling the shape of the iron yoke takes intothe press is released and the locking pins are placed, thetop of the fixed collars are 0.14-0.18mm. To avoid the needdeformation of the local defonnation around the pins. Whenthe iron insert (Fig. 3). Elsewhere the displacements at themost of the spring back eKect is the result of the leg elasticlared coil pack occurs at the vertical symmetry plane abovethe central post of the collar is much stiffer than the legs,The maximum vertical displacement (0.268mm) in the colWhere kun., is the spring coefticient of the collar legs. SincekmtzaIV. ASSEMBLY OF THE MAGNET1 +F2 = _m2-u · km! (2)Allforceaareforor1ecoil(balfacollar)permm.-7.3x1O`3 ‘ -3.8><10`3 ·the force that is needed will be:Rishi_1-lXl0—3 —If the collaring force is applied only on the side of the collarsV¤‘LOK$C£Of10Cki!1g!OdO¤l8£!fY(I!1h0f.lXlS[HH!l](1)F1 = 2 - u - kwu 0 om¤ mil ldt 82.1 36.6 90.4 37.10 outa coil right 79.2 43.7 83.8 42.3kmu, the force needed to insert the rods is therefore: 37.3c ima coil left 90.5 37.4 104.5c ima coil right 85.8 41.6 86.8 40.3locking rods. If the spring constant of the coil is marked withcaverage 84.4 39.8 91.4 39.2coils have to deform by length u, to allow the insertion of theCoil atruaea along\heooilmidpIme{Wa]If the collaring force is applied at the top of the collars, theTotal Fy 2417.15199.8 2452.9 5627.8Coil lm (hor plme) 2658.3 1139.3 3®1.l 1145.31271.8Coil right(hor pim) 2541.5 1313.6 2626.7Hg.2Coils¤ndoolhrp•u¤nedurpri¤gs.At top of the tool -5199.8 - -5627.8F<>f¤¤ [N/mm/V: wllnrlreleasedreleasedU& Prua UndaCollarConPreferredpoeedum PreuureoncollartopSruovm Tm Couiuzmo PnomssTABLE!SHE £ E>>Em{] ,Eelongating the collar legs during the collaring process.l F;/2F1/2 lThis means that the relaxation can be reduced by 4.3% bybc simulated using springs (Fig. 2). F M 2626.7 + 3001.1 yarc ignorcd thc coil-collar structure of a single aperture can F 27 . 45.3 2 Z i1JL.X100 z 42.9% tolars. If for thc sakc of simplicity all non-linear phcnomcnabeen cut out in the middle of the collar post. OCR OutputMP;4 -62 -58 -24 reduce these stresses a 3.8 mm deep and 4 mm wide slot hasMP;-60 -61 -98 nermost comer of the top of the inner coil layer. In order toMP;-81 ·Tl -42to the coils. This increases the azimuthal stresses at the inMP;-71 -70 -94are taken by the collars. Part of this force is then transmittedPoint 293K UI` 1.8K OT 1.8K 9.7'l`A¤Mun-w,&·nmsasmsoMaS|oNmcANrP0nnsoP1rnC0u.s all the horizontal forces coming from the shrinking cylinderTABLE IV the vertical gap is completely open at room temperature andinnermost comer of the top of the inner coil layer. MoreoverCollars are divi% into two laym: fixed (Mu') and floating (Mf') value at room temperature. The compression is higher at the-0.035 0.227 -0.413 -0.212 -0.4% -0.262 During collaring the stress in the coils reaches its maximum-0.037 0.236 -0.413 4).201 -0.4M -0.252 collars have line to line tit from -5° to 25°0.002 4).250 0282 collars shrink more than the surrounding yoke. At 9.7T the-0.190 -0.444Kriglu -0.531 sulting force decreases due to the fact that the aluminium-0.189 -0.819 -0 768 tween collars and yoke (Table V). At 1.8K the normal re-0.237 4).404-0.052 -0.47 -0.380 -0.470At room temperature a relatively strong contact exists be-0.276 -0.073 -0.6w 4).6N -0.7564).72.5-0.823-0.079 -0.793 gap remains closed.-1.04-0.199 -0.995 completely closed at 1.8K. When the magnet is energized thePoints The vertical iron yoke gap is open at room temperature and9.7TOT 1.8K 1.8KLoad Stq 293K OT the assembly (Fig. 3).Drsi=umm1·s lu Som Sncmvicam Ponrrspoint x38 to the point x59 in order to avoid contact duringTABLE HI0.04 mm at 25°. A gap of 0.2 mm has been left from the-0.43 rmsndius intufetmce horizontal plane (0°) and increases linearly to a size ofYoke-dirinkhg cylinder creases as a function ofthe angle. The gap is zero at the4x3.8 umThe nominal gap between yoke and collar quadrants inCollaruose slot0.33out¤ coil i=62.9inn lavu -8230.3outa coil r=45.7B(wL layer) -1940.3irmer coil #5.222480.28immr coil r=28Lotmz force in right coil quadr. (9.71)lntufcsunce buwm wllan md coilsx$ 0.2WaMax. ahr&ing cyl& mus on bonz 156 230 2260.2x=38F3(0Sx§8)0.3xé9 1044 658S130.3at 38° F2(38°$x§9)0.04a 25° F1(0°-25°) 1673 1626552bottom ¤t0° Collar-yoke interface@1Iar-yoke gp sim Sin I botxmn 0.230.47at the bottom (Q) Sim at top 0.340.62it me wp (D-) 1738 713Veniul gy ¤iMalf gp Veniml gapWQ Paumtms Or Tm Maunmcn. Dasiuu 0T OT 9.7T293K 1.8K 1.8KTABLE 11Owutcmxsnc DATA W ’h~m Mucuuncu. DasnouTABLE VTables H·V and Fig. 3.in the considered different load steps are reported in the Fig. 3.P;rmxetc¤forthemed1mit¤l iz.;tion nd sigtifncmt points.The parameters, stresses and displacements of the structure . < I €.¤wt3l rw 1E lkture,at l.8K,B0=0Tandat 1.8 K,B0=9.7T.The assembled magnet has been analyzed at room tempera \ x [AIT y\’ H 4\ . 1 A / ¤:—sV‘L) \l\w \\B. Discussion ofthe Results\\M·~·*>%,F2rigid structure.mating force between the iron yoke halves can warrant a\ \contact between collars and iron yoke as well as a stronggap permits the iron to follow the collars contraction. A gooddifferent conuactions, there is a vertical gap in the iron. ’l`l1is >`\ \\ / `\ `conuacts much less than the collars. To compensate for the Q . ( \\.\\\\During cool down from room temperature to 1.8 K the irontoo high [5]. 6; §.\\Pthrough crccp, thc room temperature prestress should not beaccuracy of the estimation. We can see reasonable corre127.tively. Results have been compared with ANSYS to check theanalysis ofLHC bmding mag1et,” Geneva 1995, CERN, Internal note 95and F, are 713 N/mm, 552 N/mm and 513 N/mm respec{6] MaEe121oli A., Perini D., Salminen J., Soini I. “F`tnite-dement structuralbeen minimized. It is recalled that the nominal forces F,. F.erator school.able way. In the second case the vertical mating force F. has omductiviy ii particle aocelerators," Geneva 1989, CAS CERN Accel[5] Md} K. H, Sdmilser P., “SIQ¤¤X$\1d.iDg Accelerator magnets, Superbeen minimized by choosing all the tolerances in a unfavorAnalysis Sysuns lnethe normal contact force F, between collars and yoke has[4] "ANSYS User's Maura] for Revision 5.0," Houston 1992, SwmsonIn table VI two ‘limit cases’ are presented. In the first case 1990, GERN, LHC Note 120.magnet for the large hadron oollide.r," Geneva[3] Bona M., Perini D., "Finite dana: suutxural analysis ofthe twin apertureAre-¤·>c¤» I lmby Perin, R. Geneva 1994, CERN, Internal Note 94-103{2] 'Design features dtbe new LHC dipole long models (prototypes),” Edited(X0-¤38)G¤p |+| 513 e¤.," Gureva 1993, CERN, CERNlACJ93·03(L1·1C).V¢r!G¤p I I 713 I1) The LHC Study Group, 'LHC The Large Hadron Collider Aocelator Proj(8)1Q0¤_25¤)G,,,, I L 6625 -2500 -7875 Rrzrazxswcms2I0.I38)Gap I = IFv,,,G,p { [-10150 1675 6450 .4. Normal man forces betwm rurfms vs. vmiul yoke gm shiftHalf vertical yoke gap shift (mm)and the complete equation:-0.06 -0.02 0.02 0.06 0.16625 -2600 -7875[S]=| 1525 —6825 ~2525 I (7)N Q """10150 1675 6450 § 450be evaluated using the following matrix: —)€—F31.8K(T1`(x0-x38) gap shifts on the corresponding mating foroes can —i—F1 1.8KUI`g_ 900gap values. ’l`he influence of vertical gap, (0°-25°) gap and —.—Fg l.8K9.7Tthese shifts and [Fo] the forces [N/mm] due to the nominalwhere [u] are the shifts [mm], [F] the forces [N/mm] due to1350<6>lFl= [Sl·[¤l+[F¤]Error -1.2 %-11.9 % -1.8 %We can therefore defme a matrix of the slopes [S]:Total force by ANSYS 839145 1069matrix [F] (8)nominal dimensions, forces behave linmrly with tolerances.829.2Total animated 127.8 1049.5force i vs. the gap j shift. If the variations are small around+204.7¤0x38 (F5) 4)-03 ··50.2 +75be evaluated as the "slope" of the curve representing the+50.50·-z5° sm (Fr) 0.02 -129 +1575where FD is the nominal force and every differential term can +61Vertical gap G,) 0.04 -406 +265Nominal force (F.] 513713 552-105%Error 0.3 % -515%219.9Tmal form by ANSYS 1294 112.5(5)}T=Eo+Z5·§·dGd.v, ¤¤~¤ix {Fl (8)BFTuul eaimated 196.71298.2 54.5-204.7+50.2 -75for a certain force Fi:-50.5O°-E° gp 0.02 10-x38 0.03 +129 -157.5For small shifts around the nominal dimensions, we can get,-61+406 -265513Nominal form [F,] Vertiul gg -0.04 713 552(1.8K)Half vertical pp size between yoke-halves from Di to D., [mm] (1.8K, 9.TD (1.8K)Shih F. IN/mm] Fr [N/nm] F¤[N/mm]Gap size between collar and yoke hom x0 to x38BwOro® Svurum MmmmF. Am>F.Gap size between collar and yoke from 0° to 25°Ranma CwrAcrFonms Wim Au.Dn»rm~rsro1rrtr.T0t.rart4tra<:ras HavsGap size between collar and yoke at 25° TABLE VI'I`he following parameters have been studied (Fig. 3):are less interesting.only one parameter per time has been changed. is the reason why far from the nominal conditions low forcescausalities and km the number of the analysis reasonable, model a reasonable safety margin has to be considered. Thisbehaviour of the magnet have been studied. To understand low force levels (Fig. 4). Due to the approximations of theThe influcnccs of manufacturing tolerances on mechanical explained by the fact that the forces behave unlinearly withwhere the simplified model is over pessimistic. This can beV1. Tommuczs spondence, except for the force F. with very low values,

Finite element structural analysis of LHC bending magnet

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