Fixes J. Kerby For my many colleagues who have contributed to this effort (Ranko Ostojic, Cedric Garion, Tom Page, Thierry Renaglia, Herve Prin, Bob Wands, Frederic Gicquel, Ingrid Fang, Juan Carlos Perez, Tom Nicol, Sandor Feher, Tatsu Nakamoto, Peter Limon, Glyn Kirby, Paul Olderr, Tom Peterson, Jim Strait, Vadim Kashikin…and anyone else I have inadvertently forgotten…)

24-25 Inner Triplet Review - J Kerby2 Outline  Review of event  Requirements for a fix  Proposal  Supporting Calculations  Vacuum Loading  Alternative Restraint Design

24-25 Inner Triplet Review - J Kerby3 Non IP end of Q1, looking toward IP The Xb, XBt, V EE and FF lines, and beam screen lines were not pressurized during the 27 Mar test

24-25 Inner Triplet Review - J Kerby4  Tables are the full load cases IF all lines were pressurized to MAWP  27 March test the pumping and shield lines were not pressurized, and failure was at 20 bar Q1 load 115kN Q3 load 93kN

24-25 Inner Triplet Review - J Kerby5 Q1 115kN Q3 94kN

24-25 Inner Triplet Review - J Kerby6 Cold Mass Support  A ‘fixed’ and ‘free’ spider support  Invar rod connecting the two to share support

24-25 Inner Triplet Review - J Kerby7 Geometry was drawn directly from the CAD model. The bellows at the interconnections between cold masses were simulated with spring elements having a total stiffness of 5500 lbs/in at each interconnection. Moments due to the L line bellows were estimated, and are reacted w/ much longer lever arm of the spacing of the supports, so are a small effect in these analyses. Elements are second-order hexahedral and tetrahedral solids. A total of 500 thousand elements and nodes were used.

24-25 Inner Triplet Review - J Kerby8 Meshing of the supports was refined to include three elements through the half-inch thickness of the G11. The G11 was treated as orthotropic; in the plane of the support (the xy plane in the analysis) bending is resisted primarily by the tension or compression of the relatively stiff glass fibers; the Young's modulus is dominated by the glass, and was set to 3e6 psi in both the x and y directions. For the z-direction (through the thickness), loads are perpendicular to the glass fibers, and the stiffness is influenced more strongly by the epoxy matrix; a reduced modulus of 1e6 psi was used for this direction. Note that while this is technically "orthotropic", it really assumes isotropy in the xy plane.

24-25 Inner Triplet Review - J Kerby9 Q1- Q2 - full 20 bar load (all lines) sliding support lbs Q1 fixed support lbs IP bellows lbs lbs Q2 sliding support - 55 lbs fixed support lbs sliding support - 65 lbs IP bellows – 1920 lbs bellows lbs

24-25 Inner Triplet Review - J Kerby10 Q3 – full 20 bar load (all lines) fixed support lbs Q3 sliding support lbs IP bellows lbs lbs

24-25 Inner Triplet Review - J Kerby11 Pressure Test Summary  With Shield and Xb lines empty, actual loads 84% of 20 bar load in model…results linearly scaled for now: Q1 fixed support fails at 16,950lbs/75.4kN (7.5mm); then propagates to Q1 free support Q3 fixed support being checked at 14250lbs/63.3kN (6.4mm); Q3 free support shows no signs of damage Q2 appears unaffected  DFBX damage not from interaction with Q3

24-25 Inner Triplet Review - J Kerby12 Requirements for a Fix  In Situ  Does not move fix point of the assemblies  React loads with sufficient stiffness to limit deflection – 150kN design load (slide 4)  Acts at any temperature 300K to 2K  Focus on implementation in Q1—Q3 solution tuned for length will then accommodate

24-25 Inner Triplet Review - J Kerby13 Fix Points MQXAMQXBMQXAMQXB Q3Q2AQ1 DFBX Q2B MQXB LBX D1 External heat exchanger (HX) Fixed Point HX-Cold Mass FP Cold Mass- Vacuum Vessel Fixed Point Triplet- Tunnel Floor Tie Rods Linking Vacuum Vessels Jacks (longitudinal) Internal heat exchanger

24-25 Inner Triplet Review - J Kerby14 Q1

24-25 Inner Triplet Review - J Kerby15 Q1 MQXA Corrector Containment

24-25 Inner Triplet Review - J Kerby16 Q3

24-25 Inner Triplet Review - J Kerby17 Q3 MQXA Corrector Containment

24-25 Inner Triplet Review - J Kerby18

24-25 Inner Triplet Review - J Kerby19 Allowable Deflection of Support  From failure analysis support fails at deflection of 7.5mm (6.4mm borderline)  System Analysis from Q1-Q2-Q3  Cooldown deflection 1.8mm in Q2 free spiders (all tested, ok)  Current ongoing tests

24-25 Inner Triplet Review - J Kerby20 Cooldown / 20 bar loads – Q1/Q2 Q2 sliding support lbs (2300 lbs) fixed support - 60 lbs (-86 lbs) sliding support lbs (2195 lbs) IP bellows – 7940 lbs (6000 lbs) bellows lbs (6115 lbs) sliding support lbs (-3190 lbs) Q1 fixed support lbs (-2840 lbs) IP bellows lbs (6000 lbs) lbs (0 lbs) 137kN (0kN) 35kN (27kN) 77kN (-13kN) 25kN (-14kN) 35kN (27kN) 10kN (10kN) 0kN (0kN) 35kN (27kN) 10kN (10kN)

24-25 Inner Triplet Review - J Kerby21 Cooldown / 20 bar loads – Q3 fixed support lbs (-2826 lbs) Q3 sliding support lbs (-3230 lbs) IP bellows lbs (6115 lbs) lbs (0 lbs)  Contraction of cold mass interconnect bellows Q1-Q2 and Q2-Q3 reacts portion of quench load  Further models move from full triplet to Q1 only w/ load of interconnect bellows included  W/ cooldown, free support pulled toward fixed support by Invar tie rod (Q1/Q3 = ~0.8mm, Q2 = 1.8mm) 35kN (27kN) 62kN (-13kN) 18kN (-14kN) 115kN (0kN)

24-25 Inner Triplet Review - J Kerby22 Allowable Deflection of Support  Continued longitudinal studies of supports Push tests in Bat 181 of Q1 / Q2 / Q3  System stiffness of 14.2/18.0/14.2 kN/mm by calculation  Measured 14.8/23.3/20.0 kN/mm (Herve, tuesday)  Material properties in model stiffer than directly measured in  Note load sharing between fixed and free support is a weak function of this modulus—failure load of Q1 fixed support changes <10%

24-25 Inner Triplet Review - J Kerby23 Allowable Deflection of Support  Testing / modeling to failure of individual supports ongoing The cold mass provides a rotational constraint on the support and lug which does not exist in the test fixture (currently) Initial tests allowed rotation, deflection without failure or delamination of 6mm at 8kN load applied to lug, but deflection shape not same as installed Initial modeling results ongoing to understand result before proceeding to failure tests  Deflection of 2mm used as allowable, not including ‘slip’ of fixed support

24-25 Inner Triplet Review - J Kerby24 Cartouche / Cartridge  Affixed at Q1 non-IP end; Q3 IP end  Transfer load at all temperatures  Limits support deflections

24-25 Inner Triplet Review - J Kerby25 Pieces…. Cold Mass Bracket, mechanically and thermally attaches AL cylinder to cold mass volume Vacuum vessel bracket, transfers Invar load to Vacuum Vessel Cartridge, Invar rod centered in Al tube

24-25 Inner Triplet Review - J Kerby26  Four cartridges  +/- 331mm horizontally; +174/-89mm vertically  Utilizes open areas in Cryostat volumes  Bracket analysis to vacuum vessel continuing, optimization for heat load, assembly and bending of flange

24-25 Inner Triplet Review - J Kerby27  m thickwall Al Tube, 60mmOD 40mmID Polished or plated for lower emissivity Captured by cold mass bracket for load transfer and thermalization In compression when loaded  ~1.6m Invar rod, 30mm diameter necked at warm end for thermalization to shield Torqued at assembly for load distribution Could include GRP spacer to cut heat load to vacuum vessel bracket Connected to Al tube through SS shoulder threaded joint at far end Centered 2 places along length

24-25 Inner Triplet Review - J Kerby28  Two mechanical models created; optimization ongoing but looks very promising  Bracket to cold beefed up in this iteration; increase thermal coupling and reduces deflections Q1 Cartridge Modeling

24-25 Inner Triplet Review - J Kerby29 Q1 Cartridge Modeling  Cartridge applied to Q1 model including bellows for: Warm 25 bar pressure test load Cold Cold, 20 bar quench load Figure 1. Finite Element Model of Q1 with Cartridge

24-25 Inner Triplet Review - J Kerby30

24-25 Inner Triplet Review - J Kerby31 Q1 Cartridge, 25 bar pressure test sliding support lbs Q1 fixed support lbs IP bellows lbs lbs cartridge lbs Figure 2. Forces on Components due to 25 Bar Warm Pressure Test Load 171kN 8kN18kN 144kN 2kN

24-25 Inner Triplet Review - J Kerby32 Q1 Cartridge, Cooldown sliding support lbs Q1 fixed support lbs IP bellows lbs 0 lbs cartridge lbs Figure 3. Forces on Components due to Cooldown 0kN 13kN 9kN 5kN 27kN

24-25 Inner Triplet Review - J Kerby33 Q1 Cartridge, cooldown + 20 bar sliding support lbs Q1 fixed support lbs IP bellows lbs lbs cartridge lbs Figure 4. Forces on Components due to Cooldown and 20 Bar Pressure Load 137kN 6kN5kN 109kN 28kN

24-25 Inner Triplet Review - J Kerby34 Q1 Cartridge, Deflections  Load per cartridge: 36kN (warm test, 25 bar evenly split)  Al tube stress (3300 psi / 8600 psi ASME allowable) (22.7MPa/59MPa allowable)  Invar peak cross section (16600 psi / psi) (114MPa / 148MPa) (Allowable – 3 to ultimate or 2 to yield of annealed Invar)

24-25 Inner Triplet Review - J Kerby35 Cartridge Initial Thermal Analysis  Cold mass at 2K  50K Heat intercept at the end of the invar rod  50K Radiation of invar on inner surface of Al tube  Thermal connection of the cold end of the Al tube with the cold mass (SS support too resistive otherwise)  Vacuum vessel at K  Radiation to the cold mass from the brackets welded to the vacuum vessel  All interior surfaces with radiation condition have an emmissivity of.05 which is standard with silver plating  Al6061 used instead of 6082 because material properties were not available

24-25 Inner Triplet Review - J Kerby36 Boundary Conditions

24-25 Inner Triplet Review - J Kerby37 Steady 2K  Loads per magnet 11.72W to the vacuum vessel.23W to the cold mass 10.5W at the 50K heat intercept 1W radiation cooling on the brackets  Revised (larger at warm end) Invar rod diameter gives 29 W to 50K heat intercept Vacuum flange cooled to 14.3 C

24-25 Inner Triplet Review - J Kerby38 longitudinal deformation

24-25 Inner Triplet Review - J Kerby39 Aluminum tube temperature

24-25 Inner Triplet Review - J Kerby40 Invar rod temperature

24-25 Inner Triplet Review - J Kerby41 Vacuum vessel flange temperature

24-25 Inner Triplet Review - J Kerby42 Cooldown  Hypothesis: 4 50K/day, then 4 days stable Uniform temperature of cold mass No thermal radiation taken into account No heat intercept on the invar rod  Need to confirm the cartridge is well enough thermalized to the cold mass at all times and upset conditions

24-25 Inner Triplet Review - J Kerby43 Cooldown Initial Results  Results for first 200K of cooldown  Length optimization ongoing  Results still being checked  Real wave smoothed w/ cartridge located at opposite end of Q1 or Q3 from cryo entry

24-25 Inner Triplet Review - J Kerby44 Magnetic Model settings The same low-carbon steel properties for MQXA and MCBX yokes; The rods, 34mm in diameter also have properties of low- carbon steel; Nominal current in MQXA coil (I=7149A, G=215T/m); Nominal current in both MCBX coils (I=550A, Bx=By ≈ 3.3T); No planes of symmetry within the model.

24-25 Inner Triplet Review - J Kerby45 Magnetic field in the iron

24-25 Inner Triplet Review - J Kerby46 Total forces on the rods Rod #F x, NF y, NF z, N Rod numbering corresponds to quadrant numbering in XY (transverse) plane; Z longitundal here

24-25 Inner Triplet Review - J Kerby47 Magnetic field distortions Calculated as the field difference between two models - with and without iron rods. Identical meshes, boundary conditions and material properties (except for the rods). Harmonics are presented at 17mm reference radius in absolute units (T).

24-25 Inner Triplet Review - J Kerby48 Field distortions: dipole

24-25 Inner Triplet Review - J Kerby49 Field distortions: integral n A n, T  mB n, T  m 11.04E E E E E E E E E E E E E E E E E E E E E E-12

24-25 Inner Triplet Review - J Kerby50 Cartridge Initial Analysis Cartridge looks very promising, and is the proposed solution  Worst case Q1 spider support longitudinal deflection < 2mm limit  Worst case Q1 spider load < ¼ load that caused failure during recent pressure test  Does not move magnet fix point In fact fixes Q1 / Q3 better than currently  Magnetic effect negligible  Design is ongoing to look at: Length; diameter of rod (not 10% effect in various models) Steady state thermalization BC’s Thermal performance under upset / transient conditions Attachment details to cold mass (corrector containment volume shell) Attachment details to vacuum vessel, including effect on O ring groove due to  Cartridge bracket / tie rod ear deflections  Cooling of the Vacuum Vessel due to additional heat leak Q3 attachment Consolidation of design variants and anlayses

24-25 Inner Triplet Review - J Kerby51 Vacuum Loads to Ground

24-25 Inner Triplet Review - J Kerby52 25 Bar load; no transverse load on jacks  Vacuum Vessel Deflections V1 8.4mm to IP V2 4.6mm to IP V3 0.4mm to IP V1V1 IPIP tot rod force = lbs lbs V2V2 IPIP tot rod force = lbs V3V3 IPIP lbs tot rod force = lbs tot rod force = 8100 lbs 171kN 135kN 171kN 36kN

24-25 Inner Triplet Review - J Kerby53 25 bar load; transverse load ok on jacks  Jacks assumed = 64kN/mm, IP end each vessel only  Vacuum Vessel Deflections V1 2.5mm to IP V2 0.8mm to IP V3 0.6mm from IP V2V2 IPIP tot rod force = lbs tot rod force = lbs V1V1 IPIP tot rod force = lbs lbs V3V3 IPIP lbs tot rod force = lbs tot rod force = lbs jack force = lbs jack force = 4250 lbs jack force = 5730 lbs 171kN 88kN 83kN 88kN62kN 26kN 62kN 19kN 135kN 54kN

V2V2 IPIP tot rod force = lbs bellows force = 500 lbs V3V3 IPIP lbs tot rod force = lbs tot rod force = 7100 lbs bellows force = 500 lbs bellows force = 100 lbs V1V1 IPIP tot rod force = lbs lbs bellows force = 500 lbs 25 bar load + Vacuum load (+bellows); no transverse load on jacks  Vacuum Vessel Deflections V1 4.3mm to IP V2 2.0mm to IP V3 0.4mm from IP  Vac Bellows makes ~5% change in deflections in 2 previous cases 100kN 171kN 100kN 1kN 2kN 100kN 2kN 100kN 135kN 32kN

V2V2 IPIP tot rod force = lbs tot rod force = lbs bellows force = 300 lbs bellows force = 220 lbs V3V3 IPIP lbs tot rod force = lbs tot rod force = lbs bellows force = 220 lbs bellows force = 150 lbs V1V1 IPIP tot rod force = lbs lbs bellows force = 300 lbs 25 bar load + Vacuum load; transverse load ok on jacks  Jacks assumed = 64kN/mm, IP end each vessel only  Vacuum Vessel Deflections V1 1.5mm to IP V2 0.3mm to IP V3 0.7mm from IP 171kN 1kN 56kN 1kN 10kN 46kN 19kN 135kN 64kN jack force = lbs jack force = 2280 lbs jack force = 5080 lbs 45kN 1kN 46kN 1kN 23kN 1kN

24-25 Inner Triplet Review - J Kerby56 Tie Bar / Tunnel Jacks  A model exists that can be used to predict load sharing  The transverse stiffness and load carrying capability of the jacks is in parallel w/ the stiffness of the tie rods and ears Vacuum vessels are effectively rigid bodies by comparison

LHC Inner Triplet CERN Hook Design April 24-25, 2007 T. Page - Fermilab

24-25 Inner Triplet Review - J Kerby58  Outline  Design Overview  Analysis Results  Component Testing

24-25 Inner Triplet Review - J Kerby59  Hook Design  Purpose is to react the axial bellows thrust load on the Q1 and Q3 cold masses.  Can be installed from one end of the magnet.  Current design only reacts loads in one direction Q1: force towards the IP Q3: force away from the IP  Does not work for Q2 magnets.  Proposed variations on design include features to react loads (i.e. vacuum load) in opposite direction.

24-25 Inner Triplet Review - J Kerby60 Hook Design The hook wraps around and grabs the fixed point cold mass block. The tie rods are fixed to the end of the vacuum vessel.

24-25 Inner Triplet Review - J Kerby61 Hook Design Hook needs to be inserted beyond the cold mass block.

24-25 Inner Triplet Review - J Kerby62 Hook Design Hook brought into place on the cold mass block.

24-25 Inner Triplet Review - J Kerby63 Hook Design Lower tie bar installed on hook.

24-25 Inner Triplet Review - J Kerby64 Hook Design 25 mm nominal gap.

24-25 Inner Triplet Review - J Kerby65 Hook Design (4) tie bar design, mm (5/8”) diameter rod, 1/2”thread. (2) tie bar design, 19 mm (3/4”) diameter rod, 5/8” thread.

24-25 Inner Triplet Review - J Kerby66 Hook Design

24-25 Inner Triplet Review - J Kerby67  Analysis

24-25 Inner Triplet Review - J Kerby68 Hook Deformations - Summary Component Deformation (2) Rods Deformation (4) Rods [in][mm][in][mm] Vacuum Flange Restraint tie rod connection Hook under load

24-25 Inner Triplet Review - J Kerby69 Hook Stresses - Summary Component Stresses (2) RodsStresses (4) Rods [psi][MPa][psi][MPa] Invar Tie rods 22, , S.S. Hook (Max.) 14, ,500148

24-25 Inner Triplet Review - J Kerby70 Hook Deformations: (2) rods, ANSYS Vacuum flange only.Complete hook system.

24-25 Inner Triplet Review - J Kerby71 Hook Deformations: (4) rods, ANSYS Vacuum flange only.Complete hook system.

24-25 Inner Triplet Review - J Kerby72 Hook Design - Stresses

24-25 Inner Triplet Review - J Kerby73 Hook Design - Stresses

24-25 Inner Triplet Review - J Kerby74  Testing

24-25 Inner Triplet Review - J Kerby75 Component Tests – Invar Raw Material Yield strength ~ MPa (48,970 psi) Ultimate ~ MPa (75,500 psi)

24-25 Inner Triplet Review - J Kerby76 Component Tests – Threaded Connection Linear to ~66,720 N (15,000 lb). Load at 20 bar: 33,350 N (7,500 lb.)

24-25 Inner Triplet Review - J Kerby77 Component Tests – Single Hook (2) Rods Test load: 88,964 N (20,000 lb).

24-25 Inner Triplet Review - J Kerby78 Component Tests – Thread Test 2 Tested (4) samples of 1/2-13 threaded connection. (2) Samples tested to break. (2) Samples cycled 20 times to 5,000 lb, then to break. One set of this data was missing the break test data.

24-25 Inner Triplet Review - J Kerby79 Component Tests – Thread Cycle Data Cycle data as measured. Cycled 20 times to 5,000 lb.

24-25 Inner Triplet Review - J Kerby80  End