With the aim of selecting the most suitable design for the series production of the LHC main dipoles, several possible configurations were analysed with respect to admissible component tolerances and structural stability, field level, field quality, number and weight of parts. Two alternatives designs, featuring common collars made out of aluminium alloy and austenitic steel, respectively, were finally compared in detail. Although both designs are almost equivalent at nominal conditions, the austenitic steel collar structure turned out to be far less sensitive to components dimensional variations. This paper reports the main results of the above evaluations, which lead to the choice of austenitic steel collars for the LHC main dipoles

Fessia, P

Perini, D

Russenschuck, Stephan

Vuillermet, R

Völlinger, C

Wyss, C

CERN Document Server

IEEE TRANSACIIONS ON APPLIED SUl'EnCONDIJCTIVI'rY, VOL. 10, NO. 1, MARCH ZMU 65 Selection of the Cross-Section Design for the LHC Main Dipole P. Fessia, D. Perini, S. Russenschuck,:Ch. Voellinger, R. Vuillermet and C. Wyss CERN Gerieva. Swidzerland Absh-dct - With the aim of sclecling tIie must suitribIe design for the series production of tlic LHC ninin dipoles, several possllile configurations were wnnlysed with respect to admissible component tolerances and structural stability, field level, field quality, nambcr and weight of parts. T w o  alternatives designs, Featuring common collars made nut of aluminium alloy and austenitic stccI, respectively, were finally compared in detail. Although botlr designs are almost cquivalent nt nominal conditions, the austenitic stccl colIar structure turned aut to be h r  less scnsitivc to components dimensional varlationa. This papcr reports the mniii results of the above evaluations, which lend to the choice of austcnitic stcel collars For the LHC muin dipoles. I. INTRODUCTION The design of the LHC two-in-one main dipolc magnets [ I ]  has to satisfy stringciil requirements in view of their successful series manufaacturc and subsequent operation in the LHC. Their structure must, up to above the ultimate field of 9 T and in spite of electroniagnetic forces reaching 400 t/m, prevent any systematic coil movcincnt causing quenches. This aspcct i s  particularly important for magnets opcratcd at 1.9 K, whcrc matcrinls show no practicnl heat capacity and any energy dissipated musl bc ~wnoved via tlie superfluid helium. A predictable and controllahlc structtlrc is required nlso, to achieve the requircd lolcranccs on field quality of B few I O 4 .  The coinponent design and assembty must nevertheless allow fur tmleranccs achievable in a cost effective way, to bc suitable for magnet series production at an affordahle price. We evaluntcd ~ h c  behaviour of  four diffcrcnt dipole cross-section designs in terms of: a) coil pre- stress during and after collaring, after welding of the shrinking cylinder, after cool-down IO 1.8 K and during operation up to 9 T; b) strength and distribution of the mating forces within thc dipole structural elements; c) sensitivity Lo Lhc tolcranccs or the geometry of collars and laminations, and their assemblics; d) scnsitivity to variations of cui1 pre-stress; e) dcrorrnation nl' the collar cavity after asscmhly, cool-down,. and during magnet operation; f] field quality; g) rluaiitities or materials and components. As result of this evaluation, a dcsign was selected for series manufacture. 11. POSSIULEMAGNET CROSS-SECTIONS Four different two-in-one dipolc cross-scction designs, with tlie innin features hclow, wcrc considered: A. double racclrack aluminum alloy (AA) collars, fitted with n magnetic iiiscrt (Fig. I )  B .  double AA collar. without magnelic insert (Fig. 2) C. as above, bul with nusteniric steel (AS) collars D. AS separated collars (Fig. 3) lnsc~t - Pig. 1 ,  Design A,  -~ MBPlT Mid yoke - Id" Id1 d l  nlo Pig. 2. Designs R (AA collars) and C (AS collars). Id0 Ikli Fig.?, Design D. 1051-R223/00$10.00 0 2CMl IEEE 66 Thesc structures present essciitially four main components, the behaviour of which must remain matched from assembly at room temperature (RT) to cool-down at 1.9 K and opera- tion up to a magnctic induction of 9 T: 1) the coils; thcir assembly pre-stress at RT, inter remaved by thc action o f  Ihc electromagnetic forccs at cold, causes the vertical dimensions of the collared coils to vary from 0.3 mm to 0.15 mm, depending 011 collar material and design prc- stress; 2) the collars; the difference in thermal contraction of their material with respect to [hat of the coils determines tho values of coil pre-stress during collaring and after collaring necessary to achieve the design pre-stress at 1 .Y K, 3) tlie vertically split yoke, always showing a gap before the assembly 01‘ tlie cold mass; the s i x  of this gap and its presence or absence after tlie welding of thc shrinking cylinder, depcnd on thc difference in thermal contraction between thc yoke and thc collar inakrial; 4) the shrinking cylinder, which assures, by its dil‘rcrence in thermal contraction with respect to that of the yokc, the presencc of the mating Ibrccs between (he yoke halvcs necessary to take up the e m  I‘orces transmitted via the collars and to guarantec the mechanical stabilily of the siructure, mid hcnce limit coil defonnations. 111. FINITE ELEMENT MODELS, OPTIMIZATION, RESULTS Four, 2-D models were meshed and the plane-sti<ess option was used Tor the elenlents. It is possible to siinulatc the collar Structures by crcaling two layers of a 0.5-mm thick mesh. FOF thc coils, iron yokc, cylinder, insert and lacking rods n 1- mm thick laycr was meshcd. The pre-strcss of the coils is imposed by giving an interfercnce at the interfaces betwcen the collars and thc coil. The extcrnal cylinder pre-stress i s  also simulated by giving an intcrhence betwceii thc iron yoke and cylindcr. Thc geometry is modeled at room temperature and in  non- defarmed conditions, i.e. the dimension uscd in the model arc for parts at their nominal size. The areas were meshed using two-dimensional lincar elements (plane 42) and contact surfaces with thrcc-dimensional contact clcments (contac 52). Further information concerning these eleinents is availablc from the ANSYS manuals [2]. Magnet operation is simulated by loading the coils with the clcctro-magnetic forces computed with the same code. Iron saturation was taken into account. No friction was considered between the different components in caw of relative displacernenls. The effect of friction was later computed for the B and C designs only [3]. The incsh considers a one-quartcr srructure (with appropriate boundary conditions for the simulation of two layers of colIars). Each of the abovc cross-sections was optimised, so as to: a) provide thc dcsign coil pre-stress at cold, avoiding at the same time unsafe stresses during collaring, welding of the shrinking cylinder undcr the assembly press and after assembly. Average compressive values above 130 MPa maintained for more than a few minutes can be dangerous for the coil insulation (creep); b) provide between the yoke halves balanced mating forces larger than the e.m. forces generated during magnet excitation, so as to avoid displaccments and instabilities of the mechanical structure; c) maintain contact between thc collared ‘coils and the yoke, in the vertical plane for the whnlc cxcitation range, so as to stiffen the dipole. structure, and in the horizontal plane preferably also for the whole excitation rangc, so as to avoid coil deformations during magnet excitation. The detailed description of the behaviour of tho designs A, R, C and D from assembly to high field operation is given in [4]. For thc four designs, Tablc I, provides a summary of the layer pre-stresses; Table I1 gives the size of the open vertical yokc gaps prior to wclding of the shrinking cylinder; Tables 111 and IV show tlie level of the mating forces. It can be seen from the 2”d column for each desing of Table I, that with doucle collars, the layers “ccntral” sides (Ido, Idi in Fig. 1) are less prestressed than the layers “lateral” sides ( d o ,  rdi i n  Fig. 1). This effect stcms from the different width (and hence inechanical strength) available for the collars central and lateral legs, fixed by the choicc of the 194 mm distance between beam axis and by the iron yokc optimisation (ficld level and quality). A 5 MPa prestress unbalance leads to a leftlrigth asymmetry of‘ thc layers azimuthal lengths of about 0.025 mm. This cffect is less pronounced far AS collars and does not occur with separate AS collars. Table I1 shows that prior to thc welding of the shrinking cylinder, AS collars require a vcrtical yoke gap 3 to 4 times smaller then AA collars. Tbis smaIler gap can be safely closed, without dnninging the coils, by the forcc applied by lhc cotd mass assembly press first and subsequently by h e  weldments of the shrinking cylinder half-shells. From Table 111 i t  can be seen that for dcsign B, with respect to the A onc: a) the vertical “inclined force” (or “shr5” far design A) bctween yoke laminatio’n and insert is at cold and during powering (hrce times higher, Ieading to an enhanced stiffness o f  the whole structure; b) the “yokc bottom” Force at 9 T is also about three times higher. Comparing the figures in Tables I11 and IV, it can be seen that, for a same stress level in  the shrinking cylinder after its weIding, h e  yoke gap is dosed (presence of mating f o r m  “yoke top” and “yoke bottom”) Cor designs C and D, featuring AS collars. As a consequcncc, at 2 K the azimuthal stress in rho cylinder is 65% higher than in designs A and B with AA collars, leading to high horizontal and vertical mating forces between yokc elements up to 9 T, TARLE I AVeRACBCOlLPRRSTRUSS(MPA) (i1’TME INNER AND OUTER LAYER5 (nR?,rCOL”) AND PRB- STRESS DIFFERENCB(ASYMMEIRY) BETWEEN T IE  INNER ANU OUCH WIYERSCBNTRAL AND LATERALSIDES (SECClNOCOLUMN). FORDESIGNS A ANDB. AFTERCYLINDER WELDING, THEPRE- S~bSSINTIIeIN~RLAY~R~(MI h l P A ~ l S H ~ O l ~ ~ ~ ~ I N T ~ O l ~ U ~ ~ E R ( ~ ~ M ~ A ~  Design A. C n At collaring 90 0 87 0 100 0 After wclding 60155 S ’ 70 2 60 0 T = 2 K , B = O T  45 5 40 2 30 0 T = Z K , l I = S . 3 T  5 1 5 0 2 0  After collaring 45 5 65 2 55 0 T = Z  K, B =9T 0 0 0 0  o b  67 U 0.085 0.08s Cylinder IS91 154 2061 185 206/ I 8 5  2071184 Yokc top O i O  109314G9 10971480 1071 1468 Yoke bottolll 010  81811102 208/421 1141300 ShrSllnclincd 607 1 594 83 / 460 167 1.581 210 / 616 Shr I 4101287 5 2 / 6  4181382 693/604 Shr 2 602/607 1141215 374/521 303/423 Shr 3 13421 1544 010 010  0 1 0  TABLE IV PlRST RV\V CYLINDER STRCSS IN MFAFOlt DES1GY.S CID FOLLOWING ROWS- MATlNtiFOlCE (N/MMOPTHICKKRSS) ATTHESTRUCTURE INTERFACES SlIUWMONFlOS. 2 AN0 3 FOR DES[ONSCID Location T = 2 9 3 K  T = 2 K  T=2K T = 2 K  B = O T  B = O T  l3=8.37’ l3=9,0T Cylinder 151/144 3201322 3211.126 3291326 Yoke top 102/358 [d49/1645 1 xW1492 157111491 Yoke bottom $7/7$ 140811340 9371716 8881716 Inclincd 62W22 39616SI S31/985 5571985 Shr 1 I671228 015 7 200l.152 282l577 Shr 2 689/ I44 28/0 3561325 4391224 Shr 3 6061225 010 on5 010 Slir 4 014s 9 o/o 010 o/o TABLE V Design Horizontal axis Vertical axis A / p * 0. I Inin f 0.1 Inin Act hPThB1.E CnhTWNehTTUMRANCE KANG6 c i u  lt 0,2 Il l I l l  * 0.3 rllnl IV. SENSWVtTY ANALYSIS Calculations wcre madc to ASSCSS which structure is inost robust with regard to componcnls and asscmbly lolcrances (hence tnorc apprapriatc for. sccics innnul‘acturc), and to assess thc stability of the gcoinetry of the collar cavity. A. Effect of Diniensional Tiilerarices The mechanical hcbaviour of a dipole structuie is goveined by the geometry of its components (precise to I 0.02 mm at best) and their subassemblies (precise to f 0.04 mm at bcsl). Thc dctcrminant factors are the tolerances of the dimensions of the fine-blanked collars, laminations and inserts and of thc colfal.cd coils. The dimcnsions of the latter depend on coil prestress (a variation of * 5 MPa coil pre-stress changes the vertical dimcnsions of AA and AS collars by f 0.05 and f 0.02 mm. respectively). In the course of asscmbly, tolerances add up and result in a gap or an intcrfcrcnce ninang coInponents. Tolerances along the horizontal axis lead Lo an overall tolcrance of the vertical yoke gap. The sizc of this gap govcrns the strength ol‘ the maliiig forces “yoke lop”, yoke bortom” and “Shr 1”. Tolerances along the vcrtical axis lead to an overall tolerance of the match between yoke halves and the insert (”inclined force”). The presciicc of vertical mating forces is essential to inaintain the structural stiffness, espccially at high field, where the vertical dimensions of thc collared coil decrease (depending on collar material) because of the unloading of the coil prc-stress by the electro-magnetic forces. The ovcrall horizontal and vcrrical tolerances along the cross-section axis were scanned systematically by varying one dimension at a time, the dlowablc range being defined as the one wilhin which the various mating forces are always positive up lo 9 T. The results arc given in Table V, showing that the higher strength (and heiicc smaller delormation) and smaller ihcrmal contraction of AS collars with respect to AA ones, allow for a wide1 tolerance band for components and their asscmbly. Following the work presenkd in this paper, rurthcr FEM computations wcrc carried out [ 5 ] ,  exploring nt a same time the impact on slructtiral behaviour of the tolerances of several components, as actually observed in the course of model and prototype work, using a statistical approach. The outcomc clearly skowcd that for a large series production, only AS collars can reliably provide the necessary structural stability of the two-in-one LHC niain dipole magnet, R. Deformation of the Collar Cavity The horizonlal inward displacement of the dipolc apcrlurc centre at asscmbly, caoldown and operation at 8.3 T was also computed with the FE models, the results is shown in Tablc VI. It can be sccii that the relative collar movements are miniinum for the dcsigns with AS collars. Other results reported in [4] show that Lhc radial and azimuthal deformation of a collar with respect to its ihcorelical circular shapc arc minimum with AS collars, providing a better stabilily of field quality. TABLE VI Design T=2’33K T = 2 K  T = 2 K  IIOR1zONTAL INWARD DISPLACZMfiNT (MM) UP T IE  APER’IURh CENTIXL B = O T  R = O T  l3=8,3T A 0.09 0.42 0.39 I3 0.06 0.40 0.37 C 0.02 0.23 0.24 . D  0.04 0.26 0.24 68 TABLE VI1 CIIYP4RISOh. OPMAlNPAT(AhiETEW, IDEAL CEI)MEIRIES (NO MECIIANICAI. STRESSES A N 0  TIERMAT. S H n l A X A W .  MULTlPUI-ARCOh~PONB~liIN I e U N r l X  ATR= 17MM Design C Design U Yoke radius 265.5 iiim 270 mm I (A) at 8.36 11772 A 11500 A Bss 9,68 T 9.75 T Field qualily inj  noin inj nam Qundnlpole 0.64 -0.82 -0.06 0.03 Scxtupole 5.78 6.18 11.00 11.44 Octupvlc 0.22 0.06 0.00 -0.18 De c a p o I c -0.91 -0.91 -1.14 -1.02 v. FIELD LEVEL AND QUALITY Following the results presented so far, AS collars were selectcd as baseline dcsign. To chosc between designs C and D, they wcrc optimised [ 6 ]  from the point of view .of field level and quality. The coil geometry considered was the 6- block geometry alrcady validated by extensive model work [7] and for which 15-m-long tooling was being manufactured by thrcc firms in charge of prototypc work. The optimisation objectivcs were: a) maximum short-sample field Bss; b) small quadrupole and octupole field components at injection field Icvcl; c) low variation of quadrupole, scxtupole and octupolc components kom injection to nominal Iicld level d) low sensitivity to tolerances of the yoke geomctry e) small yoke outer radius. The optimisation led ror design D to an insert shape slightly diKcrcnt from the one shown in Fig. 3, featuring a drop-shaped hole instead ofa  round one, to rcduce the quadrupole coinponcnt at high ficld. Main parainelcrs are shown in Tahlc VII. It can be scen from thc above that, with rcspect to design C, design D requires a marginally larger yokc radius, achievcs noinifial field at 2.3% smaller currcnt (thanks to thc larger contribution of the yoke), has to within 0.7% thc samc short saniplc field, presents a sextupole component higher by about 5 units (requiring a coil redesign 10 satisfy LHC hcarn optics) and finally shows (for an ideal geometry) at injection field practically no quadrupolc and octupole components (the iron insert acts as a perfectly symmetric scrccn between the two apertures). Concerning field quality, it is to be notcd, however, that thc’ quadrupole and octupole camponcnts prcscnt at injection ficld with the C dcsign do not constitutc a difficulty 181. VI. QUANTITIES OF MATEKIAL AND COLLARS Designs C and D are compared in TabIc VI11 concerning quantity of collar raw material and collar number per magnet unit. TABLE VI11 AUSTENITIC STKLQ~AWITY AND COLMRNUMOER WK oimcc UNIT Design C ’Design D For design I), thc largcr number of collars to be .fine- blanked partially compensates the lower cost of the ruw material. This cost difference is estimated at below 2% or  ihc cold mass value. Cost variations resulting frotii the further handling of different. numbers of collars are not considcrcd here. VII. CONCLUDING REMARKS The considerations made in Scctions 111 and IV l e d  to the choice of AS ns collar material. Tho mcrits ofthis choice are: a) the required structural bchaviour can bc achieved with realistic components tolerances, making scries production possible at affordable conditions; b) the yoke halves can be made to mate (no gap) after assembly at room temperaturc. (Experience with AA collars has shown that such a gap is difficult to control within the required tolerancc of f 0,05 IWI). The comparison in tcrms of magnetic performancc and cost of collars shows a marginal advantage for design D (separalc collars). The implementation of thc latter would however rcquirc the redesign of already available 6-block coil dcsign, of winding, curing and collaring tooling, with its inherent costs and time schedules. It was thereforc chosen not to depart from tho combined collar design. Slrong AS- combined collars c n t d  only minor changes LO existing tooling and drawings. Moreover, they ininimisc the coupling between collared coils and cold mass assembly, so as to make field quality and cold mass bchaviour only weakly dependcnt on assembly history, which is a positive feature Ibr a large scrics production. REFERENCES The Large Hndron Coilidcr CEKN/AU95-05 (LHC), October 1995 Ansys User’s Mnnual for Rcvision 5.4, Muston 1997. Swanson Analysis Systc Inc. M. Bajko, P.Pessia, D.Pt?rini, “FEM computations about the effcct of friction in two LHC main dipole structures”, this Confcrcnce. DPerini, R.Vuillcrtuct, C.Wyss, “Comparative study OF different designs of the mcchanicnl structure of the LHC innin dipoles”, LHC Report, unpublishcd. M. Bnjko, P.Fessia, D.Pcrini, “StatisticnI studies of the robustness of the LHC innin dipole mechanical structiire”, this Conf. S,Itussenschuck, “ROXIE: the routine for the optimiznrion of inngiict X- scctions, Inverse field culculalion and coil end dcsign”, Proc. of (he 1st Int. Roxic Uscrs Meeting nnd Workshop, Yellow Kcport CERN 99-01, ISBN 92-9083-140-5, N.Andreev et nl, “Pcrforninoce of five and six block coil gcoinetries in short superconducting dipole models for the LHC”. PAC 99. Ncw York. J.P.Koutcbouk. ‘The LHC dynamic apciturc”, PAC99. New York. Austenitic stccl 8770 kg 6355 kg Number of collars 8400 18800 

Selection of the Cross-Section Design for the LHC Main Dipole

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