# Presentation: 934383

## Analysis of TF Load Paths and Vacuum Vessel Loading

- H. M. Fan
- Jan. 22, 2009

## TF and PF Coils

## Outer TF Coil Supports

-   Outer TF leg is supported by umbrella structure, tie rod, ring bar and vacuum vessel
-   The ring bars and tie rods may reduce the in-plane and out-of-plane forces at the umbrella structure

## Max. and Min. Upgraded PF Coil Currents

| Coil | Turns | Fill | Min Curr | Min Curr | Max Curr | Max Curr | Usage | Worst Case Current |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
|   |   |   | (kA) | (kA-Turn) | (kA) | (kA-Turn) |   | (kA) |
| OH | 515 | 0.6283 | -24.0 | -12348.0 | 24.0 | 12348.0 | -1 | -24 |
| PF1a | 28 | 0.7000 | -4.0 | -112.0 | 28.0 | 784.0 | 1 | 28 |
| PF1b | 10 | 0.7000 | -8.0 | -80.0 | 12.0 | 120.0 | 1 | 12 |
| PF1c | 10 | 0.7000 | -12.0 | -120.0 | 20.0 | 200.0 | 1 | 20 |
| PF2a | 14 | 0.7409 | 0.0 | 0.0 | 20.0 | 280.0 | 1 | 20 |
| PF2b | 14 | 0.7409 | 0.0 | 0.0 | 20.0 | 280.0 | 1 | 20 |
| PF3a | 15 | 0.6928 | -16.0 | -240.0 | 8.0 | 120.0 | -1 | -16 |
| PF3b | 15 | 0.6928 | -16.0 | -240.0 | 8.0 | 120.0 | -1 | -16 |
| PF4b | 8 | 0.7525 | -20.0 | -160.0 | 8.0 | 64.0 | -1 | -20 |
| PF4c | 9 | 0.6723 | -20.0 | -180.0 | 8.0 | 72.0 | -1 | -20 |
| PF5a | 12 | 0.7689 | -32.0 | -384.0 | 0.0 | 0.0 | -1 | -32 |
| PF5b | 12 | 0.7689 | -32.0 | -384.0 | 0.0 | 0.0 | -1 | -32 |
| PFAB1 | 48 | 0.5613 | -1.0 | -48.0 | 1.0 | 48.0 | 1 | 1 |
| PFAB2 | 48 | 0.5613 | -1.0 | -48.0 | 1.0 | 48.0 | 1 | 1 |

## Reactions of Outer TF Leg w/wo Upgrade

**TF=71.16,  OH=-20,  PF1a=-11.35,  PF2=-16.93,  PF3=-18.83,  PF4=-10.73,  PL=1000**

**TF=130,    OH=-24,   PF1a=-4,   PF1b=-8,   PF1c=-10,   PF2=0,    PF3=-16,   PF4=-20,   PF5=-32,   PL=0**

**F******** = 12177 lbs**

**6285 lbs**

**6285 lbs**

**Note: For the upgrade coil currents, forces in the ring becomes compression.**

**compression**

**tension**

**No PF5**

## Radial Displacement of Ring Bar Decides the Ring Force – For Currents without Upgrade

**At ring, the radial displacement**** ****is 0.114 mm**

## Radial Displacement of Ring Bar Decides the Ring Force – For Currents with Upgrade

**At ring, the radial displacement is -0.613 mm**

## Structural Responses to Ring and Tie Rod Variations

| Item | Force |   | Without current upgrade | Upgrade A - with tension-only tie rods | Upgrade A - w/o rings and tie rods | Upgrade A - w/o rings | Upgrade A - move ring 7” toward midheight | Upgrade B - tension and comp. tie rods |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Reactions at | Fr | lb | -13,969 | -42,628 | -66,248 | -30,638 | -46,778 | -47,352 |
| Al block | F | lb | -12,177 | -48,793 | -80,169 | -52,817 | -52,228 | -45,929 |
|   | Fz | lb | -11,617 | -42,664 | -22,504 | -55,081 | -41,558 | -38,548 |
| Ratios of | Fr | lb | 1.00 | 3.05 | 4.74 | 2.19 | 3.35 | 3.39 |
| Reactions | F | lb | 1.00 | 4.01 | 6.58 | 4.34 | 4.29 | 3.77 |
|   | Fz | lb | 1.00 | 3.67 | 1.94 | 4.74 | 3.58 | 3.32 |
| Reactions at | Fr | lb | -1,199 | -28,354 |   | -24,685 | -33,008 | -1,827 |
| tie-rods | F | lb | -1,678 | -39,672 |   | -34,539 | -41,661 | -43,354 |
|   | Fz | lb | -530 | -12,530 |   | -10,909 | -511 | -807 |
|   | Total | lb | 2,130 | 50,347 | N/A | 43,833 | 53,155 | 43,400 |
| Axial forces | Fr | lb | 0 | 0 |   |   | 0 | 0 |
| at ring bar | F | lb | 6,285 | -32,615 |   |   | -50,146 | 25,946 |
|   | Fz | lb | 0 | 0 |   |   | 0 | 0 |
|   | Total | lb | 6,285 | 32,615 | N/A | N/A | 50,146 | 25,946 |

**Negative force mean compression**

**Force is mainly in vessel plane**

**Note – The results above are responses of upper Aluminum block, ring bar and tie rod.**

## Vertical Reactions of PF2 to PF5 Coils

| PF2a | Fz | lb | 0 | 0 |
| --- | --- | --- | --- | --- |
| PF2b | Fz | lb | 0 | 0 |
| PF2 total |   | lb | 0 | 0 |
| PF3a | Fz | lb | 80,904 | 80,904 |
| PF3b | Fz | lb | -13,248 | -13,248 |
| PF3 total |   | lb | 67,655 | 67,655 |
| PF4c | Fz | lb | 83,602 | 83,602 |
| PF4b | Fz | lb | 10,130 | 10,130 |
| PF4 total |   | lb | 93,732 | 93,732 |
| PF5a | Fz | lb | 161,783 | 161,783 |
| PF5b | Fz | lb | -193,781 | -193,781 |
| PF5 total |   | lb | -31,999 | -31,999 |

## Vacuum Vessel  Model

-  90° cyclically symmetric model
-  All ports with covers
-  Not include TF coils, but the TF loadings were applied on the umbrella structure and the vacuum vessel
-  Not include PF coils, but the PF loadings were applied on the PF support brackets
-  Weight of TF and PF coils are also included.

## Von Mises Stress Plots excluding Umbrella Structure

**Dead Loads**

**Vacuum Loads**

**Max. stress in support leg**

**Max. stress**

## Von Mises Stress Plots excluding Umbrella Structure

**EM Loads**

**EM, Vacuum and Dead loads**

**Max. stress**

**Max. stress**

## Summary of Vacuum Vessel for Upgraded Loads

| Loads | Dmax.        (m) | Max. Seqv  (Pa) | Dmax.        (in) | Max. Seqv (ksi) | Max. stress location |
| --- | --- | --- | --- | --- | --- |
| EM | 0.00400 | 5.94E+08 | 0.157 | 86.16 | near mid-height |
| Vacuum | 0.00053 | 7.47E+07 | 0.021 | 10.84 | NB port |
| DL | 0.00033 | 2.68E+07 | 0.013 | 3.89 | near leg support |
| EM, Vac., DL | 0.00419 | 5.81E+08 | 0.165 | 84.28 | near mid-height |

**Max. stress was found at the edge of port opening**

## Summary

-  EM load is the most crucial load case in the vacuum vessel design.
-  Because of symmetry in the EM load, ring bar can be used to reduce the in-plane load caused by the outer TF legs.
-  Tie rod can minimize the deformation of the ring bar and take the out-of-plane loading without causing bending moment in the vacuum vessel.
-  Provide struts between upper and lower PF4 and PF5 coils will effectively restrain the PF vertical force to the vacuum vessel.
-  The highest stress was found at the welded joint area between vacuum vessel and port, the allowable stress for welding should also be checked.
-  In the FEA model, the cross-sectional area of ring bar and  tie rod is 4.0 in2 and 1.0 in2, respectively.
-  Other design considerations may include but not limit to:

- Modify dimension and location of the ring bar and tie rod
- Improve the outer TF leg stiffness
- Reinforce the vacuum vessel
- And ...........