1. Slide HALLD TAGGER MAGNET STRUCTURAL ANALYSIS Presented by William Crahen 6/10/09 Pole Plate analysis Vacuum chamber analysis Vacuum chamber tie rods and brackets 1

2. Slide POLE PLATE ANALYSIS Presented by William Crahen 6/10/09 Minimize fastener count (machining) and confirm that they meet the load sequence requirements. Confirm that plate deformation (and gaps!) are minimal. Check that tapped holes in 1006 will not strip, or distort to the point they create a problem. 2 gap Non-parallel Poles

3. Slide FASTENERS Presented by William Crahen 6/10/09 2” 4140 HT ROD THREADED BOTH ENDS 2-4.5. 1 ¼” Grade 8 bolt to help compress O-ring. 24” 12” 1 ¼” Grade 8 bolt to prevent pole bending ½”-13 threaded rod Grade 8 equiv. to compress O-ring and prevent bowing of the vacuum chamber. ¾” rod threaded both ends- 11L17 or high strength allthread 3 Top plate Bottom plate Lower pole plate Upper pole plate

4. Slide PULLING THE UPPER POLE DOWN COMPRESSING THE O-RING Presented by William Crahen 6/10/09 Pivot point Ignore contribution of 28 threaded rods 11 bolts to compress O-ring 34” 15” 79300# @ 35% squeeze Preload these bolts to twice this= 32680 lbf, which is 32% of proof load for 1 ¼” bolt of grade 8 specification. 4

5. Slide 2” MAIN TIE ROD FORCES Presented by William Crahen 6/10/09 Pivot point Ignore contribution of 11 bolts and O-ring force. Inner and outer tie rods carry 5500 lbf. There are 8 upper brackets. 15.1” 12.9” 31.6” 47.3” 25” 21 rods 2” dia. Vacuum load from edge of chamber (does not include O-ring force)=2388 lbf * 7 locations=16716 lbf <<2388 value from Ansys. Mag and vac force on pole face=312861 lbf For equilibrium: For specification (.5*proof): 3.1” Weight of upper plates= 82054 5

6. Slide FEA using specified forces: Loads Presented by William Crahen 6/10/09 131250 32688 gravity Magnetic and vacuum force:312861 131250 5500 32688 5500 2388 24” Note: 24” is ~1/10 th total plate length These forces actually repeat every 31”,not 24”- therefore this adds a safety factor. note: this is not the total load seen by the four ½”-13 tie rods. They also carry an O-ring compression force=4812, and a preload of 2000, for a total of 9200 lbf carried by the four tie rods. 6

7. Slide FEA using specified forces: Deformations Presented by William Crahen 6/10/09 Manufacturing tolerance equal to +/-.005” exceeds this! 7 Note: The Glasgow University analysis predicted about twice this deformation- I have more confidence in my analysis.

8. Slide FEA using specified forces: Deformations Presented by William Crahen 6/10/09 Noise level- machining tolerance issues 100 times greater. 8

9. Slide FEA using specified forces: Deformations Presented by William Crahen 6/10/09 Ansys reported zero gap. This is penetration. Once again, surface motion is insignificant with respect to flatness. 9

10. Slide Stress in tapped holes in the 1006 Plates: Length of engagement=2*D. Presented by William Crahen 6/10/09 Plate made of bubble gum- thread inserts all around? 10

11. Slide We plan to use thread inserts, but what length of engagement would carry the load without them? Presented by William Crahen 6/10/09 11

12. Slide Reality check on equations for A s and A n : A simplified look at shear area. Presented by William Crahen 6/10/09 12

13. Slide Calculation of tensile and shear areas Presented by William Crahen 6/10/09 I will use the reality check value, as it is the smallest. 13

14. Slide Thread load capacity of 1006 Plates and vacuum chamber attachments: Presented by William Crahen 6/10/09 Preload=32,688, but frictional forces from tightening are also significant. Insert needed. Both of these fasteners can be threaded into the vacuum chamber under no load, then held stationary while hardened nuts at the other end apply the load. As the working load is much lower (5500# for ¾, and 2300# for the ½), and friction is not an issue, no inserts are needed. 14 Bolts securing vacuum chamber bracket to the plates are preloaded to 6500#. Inserts not needed, but will be used in any case.

15. Slide VACUUM CHAMBER ANALYSIS Presented by William Crahen 6/10/09 Minimize the motion of the O-ring in contact with the poles Minimize the change in the opening width of the thin window flange to ~2mm Look at the overall plate motion and confirm that it isn’t much more than 2mm. Confirm that the stresses are acceptable Look at the effect of adding additional tie rods 15

16. Slide VACUUM CHAMBER ANALYSIS Presented by William Crahen 6/10/09 Minimize the motion of the O-ring in contact with the poles Minimize the change in the opening width of the thin window flange to ~2mm Look at the overall plate motion and confirm that it isn’t much more than 2mm. Confirm that the stresses are acceptable Look at the effect of adding additional tie rods 16

17. Slide Original configuration of the pole flange Presented by William Crahen 6/10/09 The O-ring was modeled as six linear springs to get a fair approximation of it’s loads, and added to the vacuum load. The midspan deflection was ~0.029”, even though outer tie rods were present. this seemed like an unacceptably large movement of a critical seal. 3/8” O-ring Outer tie rods 17

18. Slide The solution was to add the ½”-13 tie rods to the edge of the flange: Presented by William Crahen 6/10/09 18 O-ring motion reduced to ~.008”. We can now consider reducing the size of the O-ring from 3/8” to ¼”.

19. Slide The thin window flange had to much movement- the ‘C’ ribs were not stiff enough to limit the change in the opening width to 2mm. Presented by William Crahen 6/10/09 Motion of single flange! The lower flange also moves upward. 19 The original design:

20. Slide BRUTE FORCE SOLUTION- DOUBLE THE AREA MOMENT OF INERTIA FOR THE RIBS. Presented by William Crahen 6/10/09 Diameter =18.5” 20

21. Slide RESULTANT SKELETON DEFLECTION: Presented by William Crahen 6/10/09 CHANGE IN OPENING WIDTH=.018+.051=.069”=1.75mm Difference in values caused by gravity. Its effect is the difference from the average=.016” 21

22. Slide RESULTANT PLATE MOTION: Presented by William Crahen 6/10/09 Plates close together=.034+.062=.096”=2.4mm 22

23. Slide VON-MISES STRESSES: Presented by William Crahen 6/10/09 Ansys ‘hiccup’- presumably a small mesh problem. 23 Plate stresses well below the 16,700 psi limit as per ASME Boiler and Pressure vessel code

24. Slide VON-MISES STRESSES: Presented by William Crahen 6/10/09 Bogus stress here- edge attachment of tie rod Corner stress concentrator will yield locally. The structural skeleton is also comfortably below the 16,700 psi pressure vessel limit for 316L. 24

25. Slide REALITY CHECK ON ANSYS DEFLECTION: Presented by William Crahen 6/10/09 0.085” 20% DIFFERENCE. 25

26. Slide ADD A DIAGONAL TIE ROD? Presented by William Crahen 6/10/09 TIE ROD HERE? PROBABLY NOT. DEFLECTION=.027+.059=.086=2.2mm. Diagonal only buys us.43mm. 26

27. Slide BRACKET/TIE ROD ANALYSIS Presented by William Crahen 6/10/09 Look at the total bracket /tie rod deformation and stress. If the tie rod deformation is a significant portion, beef it up to reduce this. Modify the bracket as needed to reduce it’s total motion to ~0.5mm. 27

28. Slide ORIGIONAL BRACKET (8” x 4” x 3/8”wall): Presented by William Crahen 6/10/09 Rigid body tube motion (plate motion) Tube bending.0036” rod stretch- not worth improving. 28

29. Slide New bracket (10” x 4” x ½” with center bolt): Presented by William Crahen 6/10/09 Big improvement from.030” Bolt added inside tube holds plate flatter. 29

30. Slide Loads applied to bracket: Presented by William Crahen 6/10/09 5500# 8X 6500# 13799 x 1.077=14861#, and our preload is only 6500#. We still plan to use thread inserts here. 30

31. Slide Bracket stress: Presented by William Crahen 6/10/0931

32. Slide Summary: Presented by William Crahen 6/10/0932 The pole deflection is on the order of achievable machining tolerance, and gaps induced by bending are essentially zero. The fasteners and tapped holes have been appropriately sized to prevent tensile failure and thread stripping. The Vacuum chamber design meets the deflection criteria, stress levels are lower than allowed by ASME Pressure vessel code, and the critical O-ring seal will experience acceptable variation in “squeeze” (~.008”).

33. Slide Remaining tasks: Presented by William Crahen 6/10/0933 Investigate reducing the size of the O-rings from 3/8” to ¼” Analyze the coil attachments Analyze the thin window Analyze the Weldment that supports the main plates

34. Slide Additonal slides: Presented by William Crahen 6/10/0934

35. Slide CENTER OF GRAVITY OF CHAMBER: Presented by William Crahen 6/10/09 35