Stress and cool-down analysis of the cryomodule Yun He MLC external review October 03, 2012.
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Stress and cool-down analysisof the cryomodule
Yun He
MLC external reviewOctober 03, 2012
10/3/2012 Yun HE, MLC External Review 2
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
10/3/2012 Yun HE, MLC External Review 3
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
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 0.5 Ton
Cooling pipes 0.5 Ton
Support post 0.5 Ton
Vacuum vessel 3 Ton
Intermodule 0.5 Ton
Misc. items 0.5 Ton
Weight of module and its sub-assemblies
Cold mass3 Ton
Cryomodule7 Ton
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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 6
Structural analysis of HGRPDeformation 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
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Structural analysis of HGRPStresses
Max. stress: 26 MPa
Material yield strength: •276 MPa @room temperature•834 MPa @cryo temperature
Conclusion: •Plenty safety margin
10/3/2012 Yun HE, MLC External Review 8
Structural analysis of vacuum vesselDeformation
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
10/3/2012 Yun HE, MLC External Review 9
Structural analysis of vacuum vesselDeformation 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 Before After Before After
0° 0.31 0.01 0.28 0.09 0.24 0.06
90° 0.37 0.11 0.34 0.20 0.28 0.12
180° 0.35 0.24 0.32 0.31 0.26 0.23
270° 0.37 0.12 0.34 0.20 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 10
Structural analysis of vacuum vesselBuckling 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)1st mode deformation
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A: FZ=100 NB: ΔZ=0C: 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
10/3/2012 Yun HE, MLC External Review
ΔT Modulus Displacement
300K – 2K 105 GPa ΔY= 1mm
300K – 200K 105 GPa ΔY= 0.5mm
250K – 150K 111 GPa ΔY= 0.6mm
200K – 100K 111 GPa ΔY= 0.5mm
150K – 50K 119 GPa ΔY= 0.35mm
100K – 2K 125 GPa ΔY= 0.15mm
30K – 2K 125 GPa ΔY= 0
Displacement under different temperature differentials/ranges between cavity and HGRP
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ΔT Modulus Displacement σmax Yield Strength Safety factor
300K – 2K 105 GPa ΔY= 1mm 460 MPa
300K – 200K 105 GPa 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 111 GPa ΔY= 0.5mm 260 MPa 466-615 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 125 GPa ΔY= 0 28 MPa 1193 MPa 43
In reality, the temperature differentials are controlled within 20K, hence the stress would be much lower
At low temperatureDifferential displacement smallYield 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
10/3/2012 Yun HE, MLC External Review
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Max stress caused by weight of cavity
Vertical displacement caused by weight of cavity <0.001 mm
Cavity flexible support stress @ normal operations
10/3/2012 Yun HE, MLC External Review
10/3/2012 Yun HE, MLC External Review 14
Cool-down thermal analysis
•Asymmetric cooling on 40K shield •Material properties as a function of temperatures•40K thermal shield temperature/stress during cool-down
10/3/2012 Yun HE, MLC External Review 15
Cool-down analysis of 40K shieldModel & 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 300KHe gas
He gas
Conduction300K
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Material properties as a function of temperature
Used material data from NIST for calculations
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Cool-down analysis of thermal shieldBoundary conditions @ steady state
Heat transfer coefficient 1100 W/m2-K of He gas in extruded pipe @ steady state
1.25 W/m2 radiation flux rate from room temperature @ steady stateExperimental 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
10/3/2012 Yun HE, MLC External Review 18
Cool-down analysis of 40K shieldBoundary conditions for transient analysis
Radiation heat flux rate set differently in 3 zones depends on their temperatureswith a lapse of time delay - colder, top/bottom, far end
)( 44ch TTQ
He gas heat transfer coefficient is a function of temperature, hence a function of time
2.0
8.0**004.0
D
GCh p
Max. ∆T=55 oC @7 hr
Cool-down analysis of 40K shieldTemperature distributions and trends
10/3/2012 Yun HE, MLC External Review 19
Temperature @15hr, when temperature gradient reaches max. ∆T=13oC, for a duration of ~30 hrs
Temperature @75hr, when temperature reaches equilibrium, ∆T=3oC
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 shieldDeformation @15hr
10/3/2012 Yun HE, MLC External Review 20
Max. von-Mises stress 45 MPa @ fingers
Cool-down analysis of 40K shieldStress @15hr
AL 1100-H14 AL 6063-T52
Tensile strength Yield strength Shear strength Tensile strength Yield strength Shear strength
77 K 205 MPa 140 MPa 255 MPa 165 MPa
300 K 125 MPa 115 MPa 75 MPa 186 MPa 145 MPa 117 MPa
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Max. shear stress 30 MPa @ fingers
Conclusion:Shield safe for normal cool-down operations
Material strength
Max. 60 MPa @ finger corners, safe
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Cool-down analysis of 40K shieldStress @faster cooldown rate 20K/hr
Conclusion:Shield safe still safe
Prototype testing Accidental faster cool-down
10/3/2012 Yun HE, MLC External Review 23
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
5K
40KG-10 tube
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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
Compared with ENS’s back-of-the envelope calculation
WL
AkQ eg 4.12*int
1.569 W/cm @300K-40K
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Heat loads on middle section, 1/3 of the shield
In Out
Radiation heat 9.2 W
Heat from 300 K flange 11.13 W
Heat leak to 2K pipe 0.046 W
Heat leak to 5K-6.5K pipes 0.38 W
Heat loads @ steady state
10/3/2012 Yun HE, MLC External Review
5K 6.5K
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Beamline warm-cold transitions for prototype – Heat inleaks
Gate valves will be at 80 K
Warm-cold transition, wall 1.65mmWill 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
300K80K
Heat leak from 300K to 80K: 5 W
80K300K
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