1. Stress and cool-down analysis of the cryomodule Yun He MLC external review October 03, 2012

2. 10/3/2012Yun HE, MLC External Review2 Outline  Structural analysis Weight of module and its sub-assemblies Deformation/stress/frequency of HGRP under beamline weight Deformation/stress/buckling of vacuum vessel under coldmass weight & vacuum Stress on cavity flexible support due to differential thermal contractions  Cool-down thermal analysis Asymmetric cooling on 40K shield Material properties as a function of temperatures 40K thermal shield temperature/stress during cool-down  Heat loads from conduction and radiation Heat loads from conduction and radiation on posts and shield Heat inleak from conduction through warm-cold transition beampipes

3. 10/3/2012Yun HE, MLC External Review3 Structural analysis Weight of module and its sub-assemblies Deformation/stress/frequency of HGRP under beamline weight Deformation/stress/buckling of vacuum vessel under coldmass weight & vacuum Stress on cavity flexible support due to differential thermal contractions

4. Beamline cavity120 lb x6 1 Ton HOM absorber60 lb x7 Coupler w/pump60 lb x6 Tuner40 lb x6 SC magnets180 lb Gate valve150 lb x 2 HGRP0.5 Ton 40K shield, MLI, magnetic shield0.5 Ton Cooling pipes0.5 Ton Support post0.5 Ton Vacuum vessel3 Ton Intermodule0.5 Ton Misc. items0.5 Ton Weight of module and its sub- assemblies Cold mass 3 Ton Cryomodule 7 Ton

5. 10/3/2012Yun HE, MLC External Review5 Outline of structural analysis  Deformation/stress of HGRP under 1 ton beamline weight Material: Ti grade 2, Ф 0.28 m ID x 9.5 mm wall x 9.65 m L  Deformation/stress of vacuum vessel under 3 ton cold mass weight & vacuum Material: Carbon steel, Ф 0.96 m ID x 9.5 mm wall x 9.15 m L  LHe vessel cooled faster than HGRP, causing differential thermal contraction Material: Ti grade 2

6. 10/3/2012Yun HE, MLC External Review6 Structural analysis of HGRP Deformation and natural frequency Max. 0.1 mm displacement Natural frequency ~ 89.1 Hz > 60 Hz Conclusion: Acceptable vertical displacement May use shims to compensate the different vertical displacement at various locations Vibration safe; may add stiffening rings if needed

7. 10/3/2012Yun HE, MLC External Review7 Structural analysis of HGRP Stresses Max. stress: 26 MPa Material yield strength: 276 MPa @room temperature 834 MPa @cryo temperature Conclusion: Plenty safety margin

8. 10/3/2012Yun HE, MLC External Review8 Structural analysis of vacuum vessel Deformation Cross-section of top ports Max vertical displacement : 0.38 mm Adjustment on suspension brackets will compensate these vertical displacements Right port Middle port Left port

9. 10/3/2012Yun HE, MLC External Review9 Structural analysis of vacuum vessel Deformation before/after pump-down Before pump-down After pump-down (1 atm external pressure applied) Unit (mm)Post 1Post 2Post 3 BeforeAfterBeforeAfterBeforeAfter 0°0.310.010.280.090.240.06 90°0.370.110.340.200.280.12 180°0.350.240.320.310.260.23 270°0.370.120.340.200.290.15 Change in vertical position after pump-down would cause cavity to shift horizontally by 0.3 mm

10. 10/3/2012Yun HE, MLC External Review10 Structural analysis of vacuum vessel Buckling analysis Critical load for the onset of buckling: 6.2 X applied loads So, buckling unlikely - safe Pre-stress from structural analysis (3 ton load + 1 atm external pressure) 1 st mode deformation

11. 11 A: F Z =100 N B: ΔZ=0 C: ΔY=1 mm Weightforce of 20 kg cavity shared by 2 supports Displacement caused by 300K to 2K temperature differential between cavity and HGRP, though it is an unlikely case Fixed top surface on HGRP In reality, cool-down is well controlled to maintain temperature differential less than 20 K, see Eric’s talk Thermal expansion rate of Ti Cavity flexible support model, boundary conditions 10/3/2012Yun HE, MLC External Review ΔTΔTModulusDisplacement 300K – 2K105 GPaΔ Y = 1mm 300K – 200K105 GPaΔ Y = 0.5mm 250K – 150K111 GPaΔ Y = 0.6mm 200K – 100K111 GPaΔ Y = 0.5mm 150K – 50K119 GPaΔ Y = 0.35mm 100K – 2K125 GPaΔ Y = 0.15mm 30K – 2K125 GPaΔ Y = 0 Displacement under different temperature differentials/ranges between cavity and HGRP

12. 12 ΔTΔTModulusDisplacementσ max Yield StrengthSafety factor 300K – 2K105 GPaΔ Y = 1mm460 MPa 300K – 200K105 GPaΔ Y = 0.5mm230 MPa466 MPa2 250K – 150K111 GPaΔ Y = 0.6mm304 MPa466-615 MPa1.5 - 2 200K – 100K111 GPaΔ Y = 0.5mm 260 MPa466-615 MPa1.8 – 2.4 150K – 50K119 GPaΔ Y = 0.35mm 186 MPa615-938 MPa3.3 - 5 100K – 2K125 GPaΔ Y = 0.15mm 94 MPa938-1193 MPa10 30K – 2K125 GPaΔ Y = 028 MPa1193 MPa43 In reality, the temperature differentials are controlled within 20K, hence the stress would be much lower At low temperature  Differential displacement small  Yield strength high Case studies of stresses under different temperature differentials/ranges between cavity and HGRP Max stress 460 MPa, caused by 1 mm displacement Cavity flexible support sensitivity check of stress vs. cool-down rate 10/3/2012Yun HE, MLC External Review

13. 13 Max stress caused by weight of cavity Vertical displacement caused by weight of cavity <0.001 mm Cavity flexible support stress @ normal operations 10/3/2012Yun HE, MLC External Review

14. 10/3/2012Yun HE, MLC External Review14 Cool-down thermal analysis Asymmetric cooling on 40K shield Material properties as a function of temperatures 40K thermal shield temperature/stress during cool-down

15. 10/3/2012Yun HE, MLC External Review15 Cool-down analysis of 40K shield Model & thermal interfaces  He gas cooling being on one side causes thermal gradient and shield distortion  He gas cooling rate 4 K/hr for normal cool-down procedure Simulate:  With a cooling rate of 4K/hr  Temperature profile  Thermo-mechanical stresses and distortion  Scenario w/ faster cool-down rate @20K/hr Radiation from 300K He gas Conduction 300K

16. 10/3/2012Yun HE, MLC External Review16 Material properties as a function of temperature Used material data from NIST for calculations

17. 10/3/2012Yun HE, MLC External Review17 Cool-down analysis of thermal shield Boundary conditions @ steady state Heat transfer coefficient 1100 W/m 2 -K of He gas in extruded pipe @ steady state 1.25 W/m 2 radiation flux rate from room temperature @ steady state Experimental data from CERN 1 W/panel (over-estimated) heat load from semi-rigid cables Cu OFHC G10 SS 304L Al 6061 T6 Al 1100-H14 Ti grade 2 5K

18. 10/3/2012Yun HE, MLC External Review18 Cool-down analysis of 40K shield Boundary conditions for transient analysis Radiation heat flux rate set differently in 3 zones depends on their temperatures with a lapse of time delay - colder, top/bottom, far end He gas heat transfer coefficient is a function of temperature, hence a function of time

19. Max. ∆T=55 o C @7 hr Cool-down analysis of 40K shield Temperature distributions and trends 10/3/2012Yun HE, MLC External Review19 Temperature @15hr, when temperature gradient reaches max. ∆T=13 o C, for a duration of ~30 hrs Temperature @75hr, when temperature reaches equilibrium, ∆T=3 o C

20. Temperature profile @15hr was loaded X axis Z axis Y axis X+2.3 mm, -1.3 mm Y+2.31 mm, -2.8 mm Z±5.2 mm Cool-down analysis of 40K shield Deformation @15hr 10/3/2012Yun HE, MLC External Review20

21. Max. von-Mises stress 45 MPa @ fingers Cool-down analysis of 40K shield Stress @15hr AL 1100-H14AL 6063-T52 Tensile strengthYield strengthShear strengthTensile strengthYield strengthShear strength 77 K205 MPa140 MPa255 MPa165 MPa 300 K125 MPa115 MPa75 MPa186 MPa145 MPa117 MPa 10/3/2012Yun HE, MLC External Review21 Max. shear stress 30 MPa @ fingers Conclusion: Shield safe for normal cool-down operations Material strength

22. Max. 60 MPa @ finger corners, safe 10/3/2012Yun HE, MLC External Review22 Cool-down analysis of 40K shield Stress @faster cooldown rate 20K/hr Conclusion: Shield safe still safe  Prototype testing  Accidental faster cool-down

23. 10/3/2012Yun HE, MLC External Review23 Heat loads from conduction and radiation Heat loads from conduction and radiation on posts and shield Heat inleak from conduction through warm-cold transition beampipes

24. 5K 40K G-10 tube 24  Conduction via G10 tube  Radiation from 300K to 40K shield Conduction 300K 2K Yun HE, MLC External Review Heat transfer from room temperature Radiation 10/3/2012

25. Compared with ENS’s back-of-the envelope calculation 1.569 W/cm @300K-40K 25 Heat loads on middle section, 1/3 of the shield InOut Radiation heat9.2 W Heat from 300 K flange11.13 W Heat leak to 2K pipe0.046 W Heat leak to 5K-6.5K pipes0.38 W Heat loads @ steady state 10/3/2012Yun HE, MLC External Review 5K 6.5K

26. 26 Beamline warm-cold transitions for prototype – Heat inleaks Gate valves will be at 80 K Warm-cold transition, wall 1.65mm Will have sliding joints on beamline outside module to accommodate beamline shifts at cold Yun HE, MLC External Review10/3/2012 Heat leak from 300K to 80K: 1.3 W 300K 80K Heat leak from 300K to 80K: 5 W 80K 300K