1. Stress and cool-down analysis of the cryomodule
Yun He

2. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

9. 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

10. 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

11. 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
MPa
200K – 100K
260 MPa
1.8 – 2.4
150K – 50K
119 GPa
ΔY= 0.35mm
186 MPa
MPa
100K – 2K
125 GPa
ΔY= 0.15mm
94 MPa
MPa 10
30K – 2K
ΔY= 0
28 MPa
1193 MPa 43
10/3/2012
Yun HE, MLC External Review

12. Cavity flexible support
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

13. 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

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

15. Cool-down analysis of thermal shield
Boundary steady state
1.25 W/m2 radiation flux rate from room steady state
Experimental data from CERN
Heat transfer coefficient 1100 W/m2-K of He gas in extruded 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

16. 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

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

18. Cool-down analysis of 40K shieldhr
Temperature 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

19. Cool-down analysis of 40K shieldhr
Max. 60 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

20. 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

21. 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
10/3/2012
Yun HE, MLC External Review