1. Stress and Cool-down Analysis Yun HE MLC Internal Review 9/5/2012Yun HE, MLC Internal Review1

2. 9/5/2012Yun HE, MLC Internal Review2 Outline 1). Deformation/stress of HGRP under 1 ton beamline weight 2). Deformation/stress of vacuum vessel with 4 ton cold mass weight on 3 support posts 3). 40K thermal shield temperature/stress during cool-down process

3. 9/5/2012Yun HE, MLC Internal Review3 Structural analysis of HGRP Boundary conditions w/ 1 ton beamline string hanging under the HGRP Material: Ti, 11” ID, 3/8” wall, 383” length Total force applied: 10000 N Cavity – 120 lb x 6 = 720 lb. HOM – 60 lb x 7 = 420 lb. SC magnets – 180 lb Gate valve – 150 lb x 2 = 300 lb. Tuner – 40 lb x 6 = 240 lb. Coupler w/ pump – 60 lb x 6 = 360 lb 1 ton  The original HGRP design had two sections connected by bellows, with 4-posts  It has been decided to use a single pipe without a bellows section, supported w/ 3-posts Reduce heat leak, easy for alignment, more reliable, reduce cost

4. 9/5/2012Yun HE, MLC Internal Review4 Structural analysis of HGRP Deformation and natural frequency Max. 0.1 mm displacement Natural frequency ~ 89.1 Hz > 60 Hz Conclusion: Acceptable vertical displacement Vibration safe

5. 9/5/2012Yun HE, MLC Internal Review5 Structural analysis of HGRP Stresses Max. stress: 26 MPa Material yield strength: 276 Mpa @room temperature 834 Mpa @cryo temperature Conclusion: Plenty safety margin

6. 9/5/2012Yun HE, MLC Internal Review6 Structural analysis of vacuum vessel Boundary conditions  w/ 4 ton (over-estimated, 3 ton actually) cold mass weight on 3 posts  150 N on each of coupler support

7. 9/5/2012Yun HE, MLC Internal Review7 Structural analysis of vacuum vessel Deformation Cross-section of top middle port Max vertical displacement : 0.3 mm Distortion due to ports being on one side No blank-off flanges in the FEA model

8. 9/5/2012Yun HE, MLC Internal Review8 Structural analysis of vacuum vessel Deformation before/after pump-down Before pump-down After pump-down (1 atm external pressure applied) Post 1Post 2Post 3 BeforeAfterBeforeAfterBeforeAfter 0°0.370.310.240.30 0.29 90°0.450.350.300.320.370.30 180°0.440.330.300.290.370.30 270°0.450.290.31 0.380.30 Change in vertical position after pump-down would cause to slightly tilt In this model, no stiffening rings on the left/right ports yet

9. 9/5/2012Yun HE, MLC Internal Review9 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 (4 ton load + 1 atm external pressure) 1 st mode deformation

10. 9/5/2012Yun HE, MLC Internal Review10 Cool-down analysis of thermal shield Model & thermal interfaces  w/ He gas cooling rate 20 K/hr Simulate:  Temperature profile  Thermo-mechanical stresses and distortion Radiation from 300K He gas Conduction 300K

11. 9/5/2012Yun HE, MLC Internal Review11 Cool-down analysis of thermal shield Boundary conditions @ steady state Heat transfer coefficient of He gas in extruded pipe @ steady state 1.25 W/m 2 radiation from room temperature @ steady state Experimental data from CERN 1 W/panel (over-estimated) heat load from semi-rigid cables

12. 9/5/2012Yun HE, MLC Internal Review12 Cool-down analysis of thermal 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

13. 9/5/2012Yun HE, MLC Internal Review13 Cool-down analysis of thermal shield Material properties SS 304L Al 6061 T6 Al 1100 G10 Cu OFHC Ti grade 2 For data @2K- 4K, used the value @ 4K

14. 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 Cool-down analysis of thermal shield Temperature distributions and trends 9/5/2012Yun HE, MLC Internal Review14

15. Compare to ENS’s back-of-the envelope calculation 1.569 W/cm @300K-40K 300K 40K 15 Heat loads on middle section, 1/3 of the shield InOut Total radiation heat9.2 W Heat taken by extruded pipe23.27 W Heat from 300 K flange11.13 W Heat leak to 2K pipe0.046 W Heat leak to 5K pipe0.31 W Heat leak to 6.5K pipe0.069 W Heat leak to 40K pipe0.018 W Heat from 80K pipe0.73W Heat from semi-rigid cables2 W Cool-down analysis of thermal shield Heat loads on shield @steady state 9/5/2012Yun HE, MLC Internal Review

16. Temperature profile @7hr was loaded X axis Z axis Y axisTotal X+8.5 mm, -5.3 mm Y±4.1 mm Z±11.7 mm Cool-down analysis of thermal shield Deformation @7 hr 9/5/2012Yun HE, MLC Internal Review16

17. Max. 60 MPa @ finger corners Cool-down analysis of thermal shield Stress @7 hr Tensile strength (MPa) Yield strength (MPa) 1100-O80 K17041 300 K9034 1100-H1480 K205140 300 K125115 1100-H1880 K180160 300 K165150 Material strength: 9/5/2012Yun HE, MLC Internal Review17