1. May 19-20, 2004NCSX FDRLeonard Myatt 1 Linear Structural Analysis of the NCSX Modular Coil & Shell Leonard Myatt NCSX Final Design Review May 19-20, 2004 PPPL Leonard Myatt NCSX Final Design Review May 19-20, 2004 PPPL

2. May 19-20, 2004NCSX FDRLeonard Myatt 2 Back-Up Documentation This work is captured more completely in the project memo entitled: Leonard Myatt, “Linear Structural Analysis of the NCSX Modular Coil & Shell,” 17-May, 2004

3. May 19-20, 2004NCSX FDRLeonard Myatt 3 Nomenclature CS = Central Solenoid CTE = Coefficient of Thermal Expansion E = Young’s Elastic Modulus EB = Electrical Breaks (insulated shims) EM = Electromagnetic EOP = End of Pulse FE = Finite Element MC = Modular Coils PF = Poloidal Field RT = Room Temperature R 0 = Major Radius S1 = 1 st Principal Stress (max tension) S3 = 3 rd Principal Stress (max compression) SI = Stress Intensity or Tresca Stress (S1 – S3) Sy = Yield Stress TF = Toroidal Field U = Displacements VPI = Vacuum-Pressure Impregnation WF = Winding Form and Integral Shell WP = Winding Pack

4. May 19-20, 2004NCSX FDRLeonard Myatt 4 Analysis Based on 3D ANSYS Multi-Field Model Electromagnetic-Structural FE Model 120 degree symmetry dictated by MCs Structural Elements: MC, WF & EB Field Elements: MC, CS, PF, TF, Simplified Plasma MC modeled with isotropic E & CTE MCWP U Constrained to MCWF

5. May 19-20, 2004NCSX FDRLeonard Myatt 5 Modular Coil & Winding Form (Tee) Interface MC conductor wound onto WF, VPI’d in- place and restrained by clamps. Simplistic modeling approach “glues” the WP to the Tee which eliminates contact converge issues at these surfaces. EM forces generally hold WP against Tee, making simplified approach OK over most of the coil. Module to Module bolted flanges are also modeled as “glued.” Linear model results in relatively fast run- times and allows many scoping studies where WP-Tee-Clamp interactions are not essential.

6. May 19-20, 2004NCSX FDRLeonard Myatt 6 Design-Basis Coil Loads (Currents & Temps) Coil Current Scenarios and resulting Temperature History are provided by the following project document: http://ncsx.pppl.gov/NCSX_Engineering/Requirements/Specs/GRD/Rev1/TDS_XL_C08R00_c3.pdf Turns out, 2T High-Beta is the most demanding EM & thermal loading.

7. May 19-20, 2004NCSX FDRLeonard Myatt 7 Linear Model Provides Some Insights Poloidal Breaks and Coil-to-Coil joints are exposed to tensile running loads of up to 9 kips/in and 3 kips/in, respectively. (Bolts must be sized accordingly.) Stiffness of MCWF to opening displacements at Poloidal Breaks is 22-57 kips/in. (Useful for MCWF manufacturing processes) Effects of MC Type C-C mechanical continuity in the inaccessible inboard region are studied and show that only toroidal continuity (produced by EM loads) provides any benefit. In-plane restraints (i.e., shear keys) provide essentially no benefit. An increase in the shell stiffness could result in a 20% reduction in the WP strain. However, only local changes to the shell are achievable, which would greatly diminish this expected benefit.

8. May 19-20, 2004NCSX FDRLeonard Myatt 8 Linear Model Provides Some Insights (cont’d) Providing support at the tips of the MCWF “wings” is critical to minimizing the WP bending stress. Wing supports must be capable of carrying about 0.6 MN (135 k-lb) in compression (or 20 MPa over a 300 cm 2 shim). Gaps from shrinkage of high CTE pillow- shim (~3 mils) are small compared to unsupported wing deflection (60 mils).

9. May 19-20, 2004NCSX FDRLeonard Myatt 9 Deformations Cause Departure from Ideal Coil Position Deformations of the MCWF from EM and CTE effects lead to non-ideal coil positions. This plot shows the deformations caused by energized coils. Maximum deformation ~1.6 mm. Displacements are calculated at each MC element center and provided as input to field error calculations.

10. May 19-20, 2004NCSX FDRLeonard Myatt 10 Linear Model Provides (Type-A) Shell Stresses Type-A shell stresses from 2T, High- Beta, t=0s time point (max MC current). Stress peaks at ~110 MPa. Max stress occurs in Tee web. Gradients signify bending stresses which are allowed to reach Sy. Away from the Tee, the shell stress is down to ~75 MPa. Materials testing is TBD, but a 500+MPa Sy seems likely (remember this number).

11. May 19-20, 2004NCSX FDRLeonard Myatt 11 Linear Model Provides (Type-B) Shell Stresses Type-B shell stresses from 2T, High- Beta, t=0s time point (max MC current). Stress peaks at ~190 MPa. Highly localized max stress occurs at a wing base, where there is a confluence of surfaces and a significant change in cross-section (i.e., stress concentration). Away from the stress concentration, the shell stress is down to ~70 MPa.

12. May 19-20, 2004NCSX FDRLeonard Myatt 12 Linear Model Provides (Type-C) Shell Stresses Type-B shell stresses from 2T, High-Beta, t=0s time point (max MC current). Primary Mem + Bend stresses are a maximum at the inboard leg: ~125 MPa. The static allowable (360 MPa) is almost a factor of three higher. Stress peaks at ~175 MPa. Max stress occurs at a vertical port knife-edge. The horizontal port is the next highest stress location (~100 MPa). Local peak stresses must be included in a fatigue analysis. Design-basis fatigue curve for casting is TBD. The stress ratio (max to yield) is ~0.5, which is close to a typical endurance limit level.

13. May 19-20, 2004NCSX FDRLeonard Myatt 13 Bounding Analysis Provides Upper Limits NCSX Structural Design Criteria requires analyzing a worst-case condition for establishing an upper bound for certain stress levels. Here, the MC WP is assigned a very soft modulus (0.8 GPa or ~2% of the experimental value). This puts all of the load on the structure. The plot contains a subset of WF elements and lists a maximum stress of 324 MPa. Since this stress is in the Tee adjacent to the WP, it can be converted to a WP strain: (324MPa/193GPa) or 0.167%. A RT fatigue test of 2x2 racetrack loaded to 0.2% strain for 130k cycles shows no apparent damage (consistent E & resistance before and after).

14. May 19-20, 2004NCSX FDRLeonard Myatt 14 Coil-to-Coil Flange Load Characteristics Contour plot of toroidal stresses in Intercoil Shims shows: Compression occurs everywhere inboard of ~R 0 A mix of tension and compression stresses occurs outboard of R 0 This confirms that the structure will not require fasteners at the inboard flange of C-to-C joints.

15. May 19-20, 2004NCSX FDRLeonard Myatt 15 Smeared MC WP Stresses, Wing Region The model is used to guide the conductor R&D test program by providing expected stress levels. Here, a Type-A wing flexes some, in spite of support from the adjacent shell, causing a max S1 of ~70 MPa.

16. May 19-20, 2004NCSX FDRLeonard Myatt 16 Smeared MC WP Stresses, Inboard Region In the congested Inboard region, the undercut Tee base of a Type-B WF provides little restraint to “weak-axis” bending. Here, S1 is reported to be 76 MPa. Improving connectivity (such as filled bladders) would stiffen this region and reduce the WP stress to some degree. This linear model indicates that a WP tensile strain of about 0.1% is typical in many regions.

17. May 19-20, 2004NCSX FDRLeonard Myatt 17 Stress History of Highest Stressed WP Element Focus on the max stress location. Determine the WP stress history. Stresses at intermediate time points lie between the extremes plotted here and do not contribute to cyclic damage. The maximum stress is determined by the 2T High-Beta scenario t=0 s time point (max MC currents). The minimum stress is determined by the compression at EOP (“warm” coil held by “cold” structure). The degree of compression at EOP could be overestimated based on assumed CTE.

18. May 19-20, 2004NCSX FDRLeonard Myatt 18 Shear Stresses in the Smeared WP Here is the Total shear stress (all components combined by SRSS). The SRSS operation eliminates the meaningless sign (similar to a von Mises or Tresca stress). The max stress is 26 MPa (3.8 ksi). There are more extensive regions at 20 MPa, and the volumetric average is 5 MPa. Preliminary RT shear tests have shown failures at 32 MPa (4.6 ksi).

19. May 19-20, 2004NCSX FDRLeonard Myatt 19 Linear Analysis Summary Linear model is used to study various design issues: Flange loads for bolting specs, Poloidal Break opening stiffness, Type C-C continuity effects, influence of shell stiffness, displacements for field error calculations, wing support specs, Shell stresses and smeared WP stresses/strains for conductor testing.

20. May 19-20, 2004NCSX FDRLeonard Myatt 20 Linear Analysis Summary (cont’d) Accepting its limitations (isotropic smeared WP, no clamps, contact surfaces or poloidal breaks) the Linear Model provides: Nominal & Upper Bound WP Tensile Strains: ~0.1% & 0.17% RT test specimen has survived 0.0 to 0.2% strain range for 130k cycles MC WP Shear stresses <26 MPa Close to 32 MPa failure from very preliminary RT shear stress tests Below more common epoxy-glass design goal of 30+ MPa (needs some work) Nominal, Max and Upper Bound Shell Stress: 75, 190 and 320 MPa Well below the 360 MPa Sy FYI: Upper Bound stress is very conservatively based on a dead-soft WP. MCWF Fatigue evaluation is TBD.