Stress and cool-down analysis of the cryomodule Yun He

Yun HE, MLC External Review 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 10/3/2012 Yun HE, MLC External Review

Weight of module and its sub-assemblies Beamline cavity 120 lb x6 1 Ton HOM absorber 60 lb x7 Coupler w/pump 60 lb x6 Tuner 40 lb x6 SC magnets 180 lb Gate valve 150 lb x 2 HGRP 0.5 Ton 40K shield, MLI, magnetic shield Cooling pipes Support post Vacuum vessel 3 Ton Intermodule Misc. items Cold mass 3 Ton Cryomodule 7 Ton

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 10/3/2012 Yun HE, MLC External Review

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 10/3/2012 Yun HE, MLC External Review

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

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

Structural analysis of vacuum vessel Deformation before/after pump-down Before pump-down After pump-down (1 atm external pressure applied) Unit (mm) Post 1 Post 2 Post 3 Before After 0° 0.31 0.01 0.28 0.09 0.24 0.06 90° 0.37 0.11 0.34 0.20 0.12 180° 0.35 0.32 0.26 0.23 270° 0.29 0.15 Change in vertical position after pump-down would cause cavity to shift horizontally by 0.3 mm 10/3/2012 Yun HE, MLC External Review

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

Cavity flexible support model, boundary conditions A: FZ=100 N B: ΔZ=0 C: ΔY=1 mm Weightforce of 20 kg cavity shared by 2 supports Fixed top surface on HGRP Displacement caused by 300K to 2K temperature differential between cavity and HGRP, though it is an unlikely case In reality, cool-down is well controlled to maintain temperature differential less than 20 K, see Eric’s talk Displacement under different temperature differentials/ranges between cavity and HGRP ΔT Modulus Displacement 300K – 2K 105 GPa ΔY= 1mm 300K – 200K ΔY= 0.5mm 250K – 150K 111 GPa ΔY= 0.6mm 200K – 100K 150K – 50K 119 GPa ΔY= 0.35mm 100K – 2K 125 GPa ΔY= 0.15mm 30K – 2K ΔY= 0 Thermal expansion rate of Ti 10/3/2012 Yun HE, MLC External Review

Cavity flexible support sensitivity check of stress vs. cool-down rate Max stress 460 MPa, caused by 1 mm displacement 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 ΔT Modulus Displacement σmax Yield Strength Safety factor 300K – 2K 105 GPa ΔY= 1mm 460 MPa 300K – 200K ΔY= 0.5mm 230 MPa 466 MPa 2 250K – 150K 111 GPa ΔY= 0.6mm 304 MPa 466-615 MPa 1.5 - 2 200K – 100K 260 MPa 1.8 – 2.4 150K – 50K 119 GPa ΔY= 0.35mm 186 MPa 615-938 MPa 3.3 - 5 100K – 2K 125 GPa ΔY= 0.15mm 94 MPa 938-1193 MPa 10 30K – 2K ΔY= 0 28 MPa 1193 MPa 43 10/3/2012 Yun HE, MLC External Review

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

Cool-down analysis of 40K shield Model & thermal interfaces He gas cooling being on one side causes large thermal gradient He gas cooling rate 4 K/hr for normal cool-down procedure, 20K/hr for test (worst) Simulate: With a cooling rate of 20K/hr Temperature profile Thermo-mechanical stresses and distortion Conduction 300K He gas Radiation from 300K He gas 10/3/2012 Yun HE, MLC External Review

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

Cool-down analysis of thermal shield Boundary conditions @ steady state 1.25 W/m2 radiation flux rate from room temperature @ steady state Experimental data from CERN Heat transfer coefficient 1100 W/m2-K of He gas in extruded pipe @ steady state 1 W/panel (over-estimated) heat load from semi-rigid cables SS 304L G10 Al 6061 T6 Cu OFHC Al 1100-H14 5K Ti grade 2 10/3/2012 Yun HE, MLC External Review

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 10/3/2012 Yun HE, MLC External Review

Cool-down analysis of 40K shield Temperature distributions and trends Temperature @7hr, when temperature gradient reaches max.=55 °C Temperature @15hr, when temperature reaches equilibrium, ∆T=3 °C Max. temperature gradient = 55 °C @7 hr 10/3/2012 Yun HE, MLC External Review

Cool-down analysis of 40K shield Deformation @7 hr Temperature profile @7hr was loaded X +8.5 mm, -5.3 mm Y ±4.1 mm Z ±11.7 mm Z axis Total X axis Y axis 10/3/2012 Yun HE, MLC External Review

Cool-down analysis of 40K shield Stress @7 hr Max. 60 MPa @ finger corners, safe Material strength of AL 1100-H14: Tensile strength (MPa) Yield strength (MPa) 4 K 345 160 77 K 205 140 300 K 125 115 10/3/2012 Yun HE, MLC External Review

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

Heat loads @ steady state Heat loads on middle section, 1/3 of the shield In Out Total radiation heat 9.2 W Heat taken by extruded pipe 23.27 W Heat from 300 K flange 11.13 W Heat leak to 2K pipe 0.046 W Heat leak to 5K pipe 0.31 W Heat leak to 6.5K pipe 0.069 W Heat leak to 40K pipe 0.018 W Heat from 80K pipe 0.73W Heat from semi-rigid cables 2 W Compare to ENS’s back-of-the envelope calculation 300K 40K 1.569 W/cm @300K-40K 10/3/2012 Yun HE, MLC External Review