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Linear Structural Analysis of the NCSX Modular Coil & Shell

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Linear Structural Analysisof the NCSX Modular Coil & Shell

- Leonard Myatt
- NCSX Final Design Review
- May 19-20, 2004
- PPPL

NCSX FDR

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

NCSX FDR

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

R0 = Major Radius

S1 = 1st Principal Stress (max tension)

S3 = 3rd 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

NomenclatureNCSX FDR

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

NCSX FDR

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.

NCSX FDR

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.

NCSX FDR

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.

NCSX FDR

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 cm2 shim).
- Gaps from shrinkage of high CTE pillow-shim (~3 mils) are small compared to unsupported wing deflection (60 mils).

NCSX FDR

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.

NCSX FDR

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).

NCSX FDR

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.

NCSX FDR

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.

NCSX FDR

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).

NCSX FDR

Coil-to-Coil Flange Load Characteristics

- Contour plot of toroidal stresses in Intercoil Shims shows:
- Compression occurs everywhere inboard of ~R0
- A mix of tension and compression stresses occurs outboard of R0
- This confirms that the structure will not require fasteners at the inboard flange of C-to-C joints.

NCSX FDR

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.

NCSX FDR

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.

NCSX FDR

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.

NCSX FDR

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).

NCSX FDR

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.

NCSX FDR

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.

NCSX FDR

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