stress and cool-down analysis of the cryomodule yun he mlc external review october 03, 2012

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


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


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


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


Structural analysis of HGRPStresses

Max. stress: 26 MPa

Material yield strength: •276 MPa @room temperature•834 MPa @cryo temperature

Conclusion: •Plenty safety margin


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


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


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

11

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

12

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


13

Max stress caused by weight of cavity

Vertical displacement caused by weight of cavity <0.001 mm

Cavity flexible support stress @ normal operations



Cool-down thermal analysis

•Asymmetric cooling on 40K shield •Material properties as a function of temperatures•40K thermal shield temperature/stress during cool-down


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


Material properties as a function of temperature

Used material data from NIST for calculations


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


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


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


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


Max. shear stress 30 MPa @ fingers

Conclusion:Shield safe for normal cool-down operations

Material strength

Max. 60 MPa @ finger corners, safe


Cool-down analysis of 40K shieldStress @faster cooldown rate 20K/hr

Conclusion:Shield safe still safe

Prototype testing Accidental faster 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

5K

40KG-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

Compared with ENS’s back-of-the envelope calculation

WL

AkQ eg 4.12*int

1.569 W/cm @300K-40K

25

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


5K 6.5K

26

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

stress and cool-down analysis of the cryomodule yun he mlc external review october 03, 2012

Documents

mlc external review1032012yun

wall x

vertical position

x 2hgrp0

lhe vessel

portsmax vertical displacement

coldmass weight vacuumstress

cavity flexible support