Analysis of TF Load Paths and Vacuum Vessel Loading

H. M. Fan

Jan. 22, 2009

Upper PF1A

Lower PF2

Upper PF1B

Lower PF1B

Upper PF1C

Lower PF5

Upper PF3

Lower PF4

Upper PF2

Lower PF3

Upper PF5

Lower PF1C

Upper PF4

Lower PF1A

OH

Outer TF coil

Inner TF coil

TF and PF Coils

Outer TF Coil Supports

Tension only tie rod

Tension only tie rod

Flexible TF coil

Ring bar

Ring bar

Al block assembly

Flexible TF coilAl block assembly

• 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

Coil Turns Fill Min Curr Min Curr Max Curr Max Curr UsageWorst 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

Max. and Min. Upgraded PF Coil Currents

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

Reactions of Outer TF Leg w/wo Upgrade

Fz = 42664 lbs

F = 48793 lbs Fr = 42628 lbs

50347 lbs

50347 lbs

32615 lbs

0 lbs

32615 lbs

32615 lbs

32615 lbs

0 lbs

6285 lbs

6285 lbs

Fz = 11617 lbs

Fr = 13969 lbs

2130 lbs

2130 lbs

6285 lbs

0 lbs

6285 lbs

0 lbs

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

compressiontension

No PF5

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

At ring, the radial displacement is 0.114 mm

At ring, the radial displacement is -0.613 mm

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

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

Structural Responses to Ring and Tie Rod Variations

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

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

Vertical Reactions of PF2 to PF5 Coils

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.

Dead LoadsVacuum Loads

Max. stress in support leg

Max. stress

Von Mises Stress Plots excluding Umbrella Structure

Von Mises Stress Plots excluding Umbrella Structure

EM LoadsEM, Vacuum and Dead loads

Max. stress

Max. stress

Summary of Vacuum Vessel for Upgraded Loads

LoadsDmax.

(m)

Max. Seqv (Pa)

Dmax. (in)

Max. Seqv (ksi)

Max. stress location

EM 0.00400 5.94E+08 0.157 86.16near mid-

height

Vacuum 0.00053 7.47E+07 0.021 10.84NB port

DL 0.00033 2.68E+07 0.013 3.89near leg support

EM, Vac., DL 0.00419 5.81E+08 0.165 84.28near 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:1. Modify dimension and location of the ring bar and tie rod2. Improve the outer TF leg stiffness3. Reinforce the vacuum vessel4. And ………..