Results of LinearStress Analyses for Modular Coils

and Coil structure

For 2T High Beta Currents at 0 Seconds and Initial Coil Shrinkage of 0.0004 in/in

with Coil Equivalent E of 63,000 MPa

H.M. FanPPPL

March 15, 2005

FEA Model

• 120° sector model

• Appropriate boundary conditions

•Smeared property for modular coils.

• Pro/E geometry provided by ORNL

•Small features in the geometry were removed to improve meshing

• Model includes shells with tees and wings, wing bags, poloidal break spacers, toroidal flange spacers, and modular coils

• Bonded contact elements were assumed at the component interfaces

Upper shell C

Upper shell B

Upper shell A

Lower shell A

Lower shell B

Lower shell C

Boundary Conditions• Cyclic symmetry between edges at -60° and +60° (see Fig.A)

• Cyclic symmetry for wing bags outside the 120° range and their rotational images (see Fig.B)

• Displacement constraints at the bottom shell stiffeners in the vertical and toroidal directions

Figure AFigure B

Material Properties, Loading, and Assumptions• Use the following material properties:.

Tee/shell: modulus of elasticity = 193,000 MPa

Poissoin’s ratio = 0.31

Modular coil: modulus of elasticity = 63,000 MPa

Poissoin’s ratio = 0.20

Coef. of thermal expansion = 0.172e-4 / °C

Toroidal spacer: modulus of elasticity = 150,000 MPa

Poissoin’s ratio = 0.27 poloidal spacer: modulus of elasticity = 193,000 MPa

Poissoin’s ratio = 0.31 Wing bag: modulus of elasticity = 68,940 MPa

Poissoin’s ratio = 0.32 Wing bag image: modulus of elasticity = 689 MPa

Poissoin’s ratio = 0.32

• Magnetic loads are based on currents of 2T high beta scenario at 0.0 seconds.

• Initial cooling shrinkage of coil strain is 0.0004 in/in that is equivalent to a temperature difference of -23.2558 °C.

• No temperature change for the modular coil winding form.

• Contact elements are always bonded and the solution is a linearly elastic analysis.

Currents, Materials, and Element Type NumbersComponent Current Turn Material Elem. Type

(A/turn) Number Number

M1 40908 20 7 3 M2 41561 20 4 2 M3 40598 18 1 1 PF1 -15274 72 10 4 PF2 -15274 72 10 5 PF3 -5857 72 10 6 PF4 -9362 80 10 7 PF5 1080 24 10 8 PF6 -24 14 10 9 TF -1301 12 11 10 Plasma 0 1 11 11 Shell - - 10,13,16 10,13,16

19,22,25 19,22,25 Toroidal spacer - - 9 8 Poloidal spacer - - 11,15,17 11,15,17

20,24,26 20,24,26 Wing bag - - 12,14,18 12,14,18

21,23,27 21,23,27 Wing bag - - 69,70 18,27

Von Mises Stress Plots of Modular Coils

Maximum stressUnit of stress in pascal

Unit of displacement in meter

Shell Displacements

Total Displacement

Vertical Displacement

Von Mises Stress Plots of Shells

Unit of stress in pascal

Von Mises Stress Plots of Upper Shell A

Unit of stress in pascal

Unit of stress in pascal

Von Mises Stress Plots of Upper Shell B

Maximum stress

Von Mises Stress Plots of Upper Shell C

Unit of stress in pascal

Maximum stress

Von Mises Stress Plots of Lower Shell C

Maximum stress

Unit of stress in pascal

Contact Pressure on Wing Bag at Upper Shell A

Unit of pressure in pascal

Note – Positive pressure indicates load toward the surface and therefore is in compression

Unit of pressure in pascal

Contact Pressure on Wing Bags at Upper Shell B

Unit of pressure in pascal

Contact Pressure on Wing Bags at Upper Shell C

Rotational image of wing bag outside the 120° range in the upper shell C

Unit of pressure in pascal

Contact Pressure on Wing Bag at Lower Shell A

Unit of pressure in pascal

Contact Pressure on Wing Bags at Lower Shell B

Unit of pressure in pascal

Contact Pressure on Wing Bags at Upper Shell C

Rotational image of wing bag outside the 120° range in the lower shell C

1. Adding rotational images of the wing bags that locate outside the 120° section range provide correct cyclic symmetry boundary condition. The stiffness of the wing bag image was set at one percent of the material property of wing bag that should give negligible effects on the results.

2. Small features in the geometry such as chamfers and fillets were removed to improve the meshing and to minimize the node and element number.

3. Maximum stress occurs at coil lead opening corner in the shell type C, which will be reduced if the chamfer is provided. The higher stress level in the lead opening of lower shell C is because of its higher elevation that possess higher deformation.

4. Pressures on the wing bags are not uniform. The plots provide the informations for a most effective shim support location.

5. Because of bonding, the pressure on wing bags may yield tension. The nonliners contact elements are needed to eliminate tension.

6. The tension on the wing bag is of no use. It may be able to break the wing bag into several discontinuous pieces.

7. It should be noted that the stiffness of wing bags will affect the stresses of wing and the pressure on the wing bags.

Discussions