Coil EM Loads and Stresses Analyzed with ANSYS

Coil EM Loads and Stresses Analyzed with ANSYS NCSX Analysis documented in project memo: L. Myatt, “Electromagnetic Stress Analysis of the NCSX TF and PF Coil Systems, ” 09/24/03. 1

Analysis focuses on (5) Important Load Cases NCSX 1. 2. 3. 4. 5. 0. 5 T TF Only, t=0. 0 s (Max TF coil current) 1. 7 T Ohmic Scenario, t=0. 0 s (Max ~PF 5 & PF 6 coil currents) 2. 0 T High Beta Scenario, t=0. 0 s (Max Modular coil currents) 320 k. A Ohmic Scenario, t=0. 206 s (Max PF 4 coil current) 320 k. A Ohmic Scenario, t=0. 506 s (Max PF 1 & 2 coil and Plasma currents) NCSX Preliminary Design Review 2

Maximum TF Coil Stresses Produced when BTF = 0. 5 T NCSX • This relatively coarse mesh results in a Smeared winding pack (WP) stress of 130 MPa. • Results in a Safety Factor (SF, Allowable/Actual) of 230/130=1. 8. • Maximum stress occurs in the Wedge/De-Wedge transition region. NCSX Preliminary Design Review 3

Modeling Approximation in Wedged Region Suspect NCSX • (Left) The design has the top and bottom of the wedged surfaces extending beyond the straight part of the inboard legs. • (Right) The model has the wedged surfaces limited to the straight part of the inboard legs. NCSX Preliminary Design Review 4

TF Coil Displacements at BTF=0. 5 T NCSX • Outboard legs move 12. 2 mm (1/2”) towards the machine axis. • Abrupt stiffness transition in dewedged region produces bending stresses shown previously. • Plans in-place to refine the model and possibly to re-design this region to reduce this local bending stress. NCSX Preliminary Design Review 5

Stress in TF Shelf-Structure at BTF=0. 5 T NCSX • By design, the TF Coil Shelf-Structure carries no load when just the TF Coils are energized. • This plot shows essentially zero-stress (23 Pa) for this load case, indicating that the coupled-field model is working correctly. NCSX Preliminary Design Review 6

Smeared Stress Summary for (5) Important Load Cases NCSX • • • LC 2 (1. 7 T Ohmic, 0. 0 s) Produces Max Stress in CS, PF 5, PF 6 and Support Structure. LC 4 (320 k. A Ohmic, 0. 206 s) Produces Max Stress in PF 4, and Max Vertical Tension in CS. Smeared WP and Structure stresses can be compared to PM+PB limits: – TF WP: 1. 5 x 165/1. 06 = 230 MPa – PF WP: 1. 5 x 165/1. 47 = 170 MPa – Structure: 1. 5 x 435/1. 00 = 520 MPa • So…these coarse-mesh model results look OK. NCSX Preliminary Design Review 7

TF Stresses from 1. 7 T Ohmic Scenario NCSX • 3. 5 k. A TF current much less than 16. 2 k. A for BTF = 0. 5 T. • Max smeared stress of 42 MPa still occurs in Transition Region of Inboard Leg. • Results in a SF of 230/42=5. • Away from peak, stresses < 25 MPa. Solenoid at 1. 7 T Ohmic scenario; t=0 NCSX Preliminary Design Review 8

Stress in TF Shelf-Structure from 1. 7 T Ohmic Scenario NCSX • Max stress of 45 MPa occurs in PF 5/6 Support Hardware. • Results in a SF of 520/44. 4=12. • Feedback from budgetary estimates will lead to cost-reduction measures (i. e. , a lighter structure with less machining). NCSX Preliminary Design Review 9

CS Stresses from 1. 7 T Ohmic Scenario NCSX • 25 k. A in PF 1/2 result in Max Stress • 31. 5 MPa Smeared, 46 MPa Unsmeared • Results in a SF of 170/31. 5=5 • Note that this model does not include vertical compression from a Tie Rod structure. NCSX Preliminary Design Review 10

PF 4 Stresses from 320 k. A Ohmic Scenario NCSX • PF 4/5/6 tied to TF Shelves in Vertical & Toroidal Directions (free in R). • 14 k. A PF 4 current results in Max Stress • 12 MPa Smeared, 18 MPa Unsmeared • Results in a Safety Factor of 170/12=14 NCSX Preliminary Design Review 11

PF 6 Stresses from 1. 7 T Ohmic Scenario NCSX • 9 k. A PF 6 current results in Max Stress. • 12 MPa Smeared, 18 MPa Unsmeared. • Results in a Safety Factor of 170/12=14. • Stresses in PF 5 are lower by 20%. NCSX Preliminary Design Review 12

Effects of Radial Freedom on Ring Coil Displacements NCSX • High Currents in PF 5/6 during 1. 7 T Ohmic Scenario produce maximum deformations. • Radial displacement contour plot on greatly exaggerated deformed shape shows how PF 5/6 change shape. • Max relative motion at supports is <0. 6 mm for PF 6. NCSX Preliminary Design Review 13

Max Vertical Tension in CS (No Preload Structure) NCSX • At t=0. 206 s of 320 k. A Ohmic Scenario, Polarity of PF 3 opposes that of PF 1/2. • Un-Preloaded CS experiences vertical tensile stresses of 4 MPa. • This load case will help determine the preload required to maintain vertical compression in CS. (Details TBD) NCSX Preliminary Design Review 14

TF/PF Coil Stress Analysis Summary NCSX • • Reference Scenarios produce TF Coil stresses well below stress limit (SF>5). TF Coils can produce 0. 5 T, but SF drops to 1. 8. Re-working the model and/or design in the Wedge/De-Wedge region should improve the SF for this 0. 5 T operating condition. Reference Scenarios produce PF Coil stresses well below stress limit (SF>5 in CS not including Tie Rod Preload, SF>14 in PF 4/5/6). Reference Scenarios produce Structure stresses well below limit (SF>12). Plan to “cost reduce” the structure by making it lighter and minimizing machining. CS Pre-Load structure is TBD, but critical load cases are identified. Relative motion in R at the Ring Coil supports is <0. 6 mm (manageable). Winding pack models too crude to determine insulation stresses. (TBD) NCSX Preliminary Design Review 15