# Presentation: 880039

## NSTX TF outer leg analysis

**Because the stress on umbrella structure is too high, there are some ideas to reduce it, ****like adding a case to enhance the stiffness of TF coil, ****adding a ring to constrain the expansion**** and ****adding tie bars to constrain the movement****.  **

**(KA)**

**Parameters:**

**ss case**

**ring**

**Tie bar**

## NSTX Coil Model

**ss**

**Al 6061 blocks are fixed, the reaction force is calculated to approximate the force to umbrella structure.**

**Welded ****solid bar (5*5”), tube may be better.**

**1. Materials of case, ring and tie bar are all ss.**
**2. Different lengths, positions and orientations are calculated.**

## Result 1 (plasma curr=0A)  

**r: radius direction; theta: out-of-plane direction; z: center stack direction**

| case | no case (plasma curr=0A) | adding case (0.5" thick ss, 12" wide) | Additionally, adding ring (0.5*12" in rect, welded) | Additionally, adding tie bar (3*3” rect, pin connected) |
| --- | --- | --- | --- | --- |
| Total end reaction force (kN)
(the ends of Al6061 blocks are fixed and reaction force is here) | 297 | 296 | 275 | 253 |
| End reaction force r (kN) | 245.71 | 246.08 | 237.88 | 215.33 |
| End reaction force theta (kN) out-of-plane | 166.49 | 164.18 | 137.52 | 127.95 |
| End reaction force z (kN) | 11.956 | 8.5121 | 2.937 | 34.467 |
| coil stress Von Mises (Mpa) | 187 | 169 | 111 | 103 |
| S r (Mpa) | 159 | 143 | 94.6 | 92.4 |
| S theta (Mpa) out-of-plane | 50 | 44.6 | 30.7 | 33.2 |
| S z (Mpa) | 89.2 | 89 | 88.3 | 87.8 |

**Old parameters:**

**1. ss case doesn’t help to reduce the force.**
**2. Rings and tie bars have some effect on force reduction. Then different positions of rings and different orientations of tie bars are further studied.**

## Result 2 (plasma curr=0A)  

**r: radius direction; theta: out-of-plane direction; z: center stack direction**

| Ring at height of PF4 |  |  |  | link to vacuum vessel |
| --- | --- | --- | --- | --- |
| case | no case (plasma curr=0A) | adding case (0.5" thick ss, 12" wide) | adding straight ring (0.5*12" in rect, welded) | adding tie bar (3*3 in rect, pin connected) |
| Total end reaction force (kN) | 297 | 296 | 260 | 257 |
| End reaction force r (kN) | 245.71 | 246.08 | 218.75 | 218.71 |
| End reaction force theta (kN) | 166.49 | 164.18 | 137.65 | 130.58 |
| End reaction force z (kN) | 11.956 | 8.5121 | 29.676 | 31.391 |
| max coil stress Von Mises (Mpa) | 187 | 169 | 117 | 103 |
| S r (Mpa) | 159 | 143 | 102 | 92.6 |
| S theta (Mpa) out-of-plane | 50 | 44.6 | 36.7 | 33.3 |
| S z (Mpa) | 89.2 | 89 | 88 | 87.7 |
| max shear stress between coil and case |   |   |   |   |
| S r-theta (Mpa) |  |  | 35.8 | 26.4 |
| S theta-z (Mpa) |  |  | 57.9 | 20.3 |
| S r-z (Mpa): coil length direction |   |   | 65.3 | 25.2 |

**Old parameters:**

## r: radius direction; theta: out-of-plane direction; z: center stack direction

| Ring at height of PF3 |  |  |  | link to vacuum vessel: bar1, 2 and 3 have different directions, see following pictures. |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| case | no case (plasma curr=0A) | adding case (0.5" thick ss, 12" wide) | adding straight ring (0.5*12" in rect, welded) | adding bar1 (3*3 in rect, pin connected) | adding bar2 (3*3 in rect, pin connected) | adding bar3 (3*3 in rect, pin connected) |
| Total end reaction force (kN) | 297 | 294 | 269 | 239 | 249 | 224 |
| End reaction force r (kN) | 245.71 | 245.96 | 223.2 | 212.98 | 225 | 192.09 |
| End reaction force theta (kN) | 166.49 | 161.03 | 149.95 | 105.98 | 105.95 | 106.05 |
| End reaction force z (kN) | 11.956 | 10.3 | 10.155 | 19.366 | 9.2544 | 44.565 |
| max coil stress Von Mises (Mpa) | 187 | 160 | 137 | 86.3 | 86.3 | 86 |
| S r (Mpa) | 159 | 137 | 118 | 60.5 | 63.5 | 51.7 |
| S theta (Mpa) out-of-plane | 50 | 43.8 | 37.6 | 25.9 | 25.9 | 25.8 |
| S z (Mpa) | 89.2 | 89 | 88.7 | 87.8 | 87.8 | 87.6 |
| max shear stress between coil and case |   |   |   |   |  |   |
| S r-theta (Mpa) |  | 8.5 | 26.3 | 28.4 | 18 | 51.8 |
| S theta-z (Mpa) |  | 16.6 | 26.7 | 16.7 | 18.6 | 16.7 |
| S r-z (Mpa): coil length direction |   | 43.5 | 45.4 | 33.3 | 29.9 | 29 |

## Ring at height of PF3 with different tie bar orientations

**0.1m (~4”)**

**0.1m (~4”)**

**bar 1**

**bar 2**

**bar 3**

## Result 3 (plasma curr=0A)  

**r: radius direction; theta: out-of-plane direction; z: center stack direction**

| case | no additional support (plasma curr=0A) | middle ring | 2 rings | 2 rings and horizontal bar | 1 middle ring and -25o oriented bar | welding bar |   |
| --- | --- | --- | --- | --- | --- | --- | --- |
| Total end reaction force (kN) | 297 | 274 | 237 | 225 | 212 | 186 |   |
| End reaction force r (kN) | 245.71 | -230.49 | -177.57 | -148.25 | -155.65 | -126.6 |   |
| End reaction force theta (kN) Out-of-plane force | 166.49 | -146.87 | -143.77 | -143.52 | -120.91 | -92.256 |   |
| End reaction force z (kN) | 11.956 | -18.119 | -64.298 | -89.967 | -78.6 | -100.87 |   |
| Total bar end reaction force (kN) |  |  |  | 65.377 | 70 | 34 | bending moment (N-m) |
| bar end reaction force r (kN) |  |  |  | -65.377 | -55.822 | 15.883 | 539.61 |
| bar end reaction force theta (kN) |  |  |  | 0.00 | -33.054 | -16.805 | -2415.1 |
| bar end reaction force z (kN) |  |  |  | 0 | -25.158 | 24.543 | -1029.9 |

**See following pages for these cases.**

**Significant reduction in the force.**

**Old parameters:**

## Coil deflection without additional support

**Coil deflection at this position is not very high and thus adding rings here will not help very much.**

**Adding ring in the middle will change the deflection shape and then adding another ring to further constrain the coil.**

## Adding ring in the middle will change the deflection shape and then adding another ring to further constrain the coil.(2nd and 3rd column in the result 3 table)

**Adding ring in the middle**
** ****(2****nd**** column in the result table)**

**Coil deflection**

**Adding 2 rings to constrain the coil**
-  **(3rd column in the result table)**

## Adding 2 rings and some pinned bars to further constrain the coil.(4th and 5th column in the result 3 table

- Adding 2 rings and some pinned bars to further constrain the coil.(4th and 5th column in the result 3 table

**Adding pinned bars to constrain the coil**
** ****(4****th**** column in the result table)**

**Adding pinned bars to constrain the coil**
-  **(5th column in the result table)**

**Horizontal bar**

**25o oriented bar**

## Result 4 (plasma curr=0A): similar to result 3 but with updated parameters  

**r: radius direction; theta: out-of-plane direction; z: center stack direction**

| min current (extreme negative current) |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| case | no case (plasma curr=0A) | middle ring | 2 rings | 2 rings and straight bar | welding bar |   |
| Total end reaction force (kN) | 411 | 345 | 325 | 315 | 210 |   |
| End reaction force r (kN) | -253.71 | -230.49 | -183.13 | -152.85 | -130.34 |   |
| End reaction force theta (kN) Out-of-plane force | -322.77 | -256.61 | -260.75 | -260.05 | -128.34 |   |
| End reaction force z (kN) | 13.63 | -17.851 | -65.538 | -92.048 | -103.55 |   |
| bar end reaction force (kN) |  |  |  | 67.517 | 88 | bending moment (N-m) |
| bar end reaction force r (kN) |  |  |  | -67.517 | 16.68 | 2736.1 |
| bar end reaction force theta (kN) |  |  |  | 0.00 | -82.127 | -2494 |
| bar end reaction force z (kN) |   |   |   | 0 | 25.527 | -5212.8 |

**See last page for the position of rings and bars.**

**Significant reduction in the force.**

- Updated parameters: TF=129.7,OH=-24,PF1a=-4, PF1b=-8, PF1c=-12, PF2a=0, PF2b=0, PF3a=-16, PF3b=-16, PF4b=-20, PF4c=-20, PF5a=-32, PF5b=-32,PFab1=-1, PFab2=-1,plasma=0   unit: KA

## Welding bar  

**ss**

**Al 6061 blocks are fixed**

**Welded ****solid bar (5*5”), tube may be better.**

**Coil deflection**

**Fixing a section of the coil tightly will help to reduce the force at the Aluminum block, the closer the fixed point to the Aluminum block, the more reduction on the force.**

- Welding bar