Figure 1 – NSTX Upper Umbrella Assembly Upgrade Design: Version 3.

Figure 1 – NSTX Upper Umbrella Assembly Upgrade Design: Version 3

Figure 2 – Single Segment Strap Assembly Version 3 with G10/ 304 SS Supports

G10 Support

304 SS Support

Figure 3 – Single Segment Strap Assembly: Center Strap Only

B tor = 1 T

I = 130 kA

Bpol= .3 T

Urad thermal = .018 in

Uvert thermal = .3 in

38 Laminations: - .060” thk; .005” gapMat’l: CopperWtfull = 37.4 lb(Wtarch = 20.4 lb)

2”2.523”

7.5

”

Rin = 3.160”

Rout = 5.688”

5”

Figure 4 – Single Laminated Strap Assembly with Applied Fields and Current

x x x x x x x x x x xx x x x x x x

Out-of-Plane Load (z-direction)

Fop = 2*I*Bpol*R

Fop = 2 x 130,000 A/ 38 x .3 T x 5.688/39.37 m

Fop = 296.4 N = 66.6 lbf [per lamination]

In-Plane Load (y-direction)

Fip/ L = I*Btor

Fip/ L = 130,000 A/ 38 x 1 T [per lamination]

Fip/ L = 3,421 N/ m x .2248 lbf/ N x 1 m/ 39.37 in

Fip/ L = 19.53 lbf/ in

pressip = (Fip/ L)/ w

pressip = 19.53 lbf/in / 2 in

pressip = 9.77 lbf/ in2 (applied to inside cylindrical faces)

Calculated EMAG Loads

Bpol

Btor

I+

I+

R

w

Fop

pressip

Figure 5A – Single Lamination FEA Model: Mesh and Boundary Conditions

3 Elements thru Thickness

Ux = .018 inUy = .3 inUz = 0 Press =

9.7 psi

Force = 66.6 lbf

Fixed

Figure 5B – Single Lamination Linear Results: von Mises StressLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

Figure 5C – Single Lamination Linear Results: von Mises StressLoads: Thermal Displacements Only

Figure 5D – Single Lamination Linear Results: von Mises StressLoads: In-Plane (Pressure) Load Only

Figure 5E – Single Lamination Linear Results: von Mises StressLoads: Out-of-Plane (Force) Load Only

Large deflection = On

Figure 5F – Single Lamination Nonlinear Results: von Mises StressLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

Baseline Design

Proposed Design

ASM International, “Atlas of Stress-Strain Curves”, Electrolytic Tough-Pitch Copper (C11000)

Figure 5G – Copper Stress-Strain Curves versus % Cold Work Baseline Design and Proposed Design Combined-Load Stresses Shown

Baseline Design

Proposed Design

NIST Monograph 177, “Properties of Copper and Copper Alloys at Cryogenic Temperatures”

Figure 5H – Copper Fatigue S-N Curves versus % Cold Work Baseline Design and Proposed Design Combined-Load Stresses Shown

Figure 5J – Single Lamination Nonlinear Results: Z-DeformationsLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Figure 5K – Single Lamination Nonlinear Results: Z-Deformations_FrontLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Figure 5L – Single Lamination Nonlinear Results: von Mises StressLoads: Emag Pressure (In Plane) Only


σhoop = P*R/ t

= 9.77 psi x 5.688 in/ .060 in

= 924 psi

Figure 5M – Single Lamination Pre-Stressed Linear Buckling ResultsLoad multiplier LMF applies to all Emag loads and thermal displacements

1st ModeLoad Multiplier = 58.4

2nd ModeLoad Multiplier = 73.0

3rd ModeLoad Multiplier = 117.6

Large deflection = Off

1st ModeLoad Multiplier = 58.4

(Nonlinear 1st ModeLoad Multiplier = 50)

Figure 5N – Single Lamination Nonlinear Buckling: Y-Deformation at Onset (1)Load multiplier factor LMF applies only Out-of-Plane Emag load


Y

0 80

LMF = 14

Figure 5P – Single Lamination Nonlinear Buckling: Y-Deformation at Onset (2)Load multiplier factor LMF applies only to Out-of-Plane Emag load


LMF = 26

Y

0 80

Conclusions

• Buckling due mostly to out-of-plane load. In-plane load (pressure outward) reduces buckling; thermal displacements slightly increase buckling.

• Good agreement between linear and nonlinear buckling results with load multiplier factor applied to both Emag loads and to thermal displacements.

• Load multiplier factor over 14 for nonlinear analysis with constant in-plane load and increasing out-of-plane load (conservative).

Figure 6A – 3 Lamination FEA Model: Mesh

3 Elements / Lamination


Frictional contact (COF = .4)

Figure 6B – 3 Lamination Nonlinear Results: von Mises StressLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)

Figure 6C – 3 Lamination Nonlinear Results: Z-DeformationsLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)



Figure 6D – 3 Lamination Nonlinear Results: Z-Deformations_FrontLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)



Figure 6E – 3 Lamination Nonlinear Results: Contact StatusLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)



Figure 6F – 3 Lamination Results: Linear Buckling Mode MultiplierLoad Multiplier factor LMF applies to all Emag loads and thermal displacements



1st Mode Load Multiplier = 58.2

2nd Mode Load Multiplier = 60.7

3rd Mode Load Multiplier = 61.8

Figure 7A – Single Laminated Strap Assembly FEA Model: Bonded and Frictionless Contact Areas

3 elements/ lamination

Figure 7B – Single Laminated Strap Assembly FEA Model: Mesh

# Nodes = 850423

# Elements = 152895

Fig. 7C –Laminated Strap Assembly FEA Results - Thermal Displacements Only: von Mises Stress


Frictional contact (COF = 0)

Fig. 7D –Laminated Strap Assembly FEA Results – Thermal Displacements Only: Total Deformation


Frictional contact (COF = 0)

Tnodes

Heat Gen

JSFLorentz

By = .3T

Bz = 1 TI = 130 kA

Non-LinearLarge Deflection Non-Linear

Large Deflection

Fig. 8A – Upper Flex Strap ANSYS Multiphysics Analysis Work Flow Diagram

ux = .018”

uy = .30”

Figure 8B – Single Segment_Center Strap Assembly: Mesh

Fig. 9C – Single Segment_Center Strap Electric Model: Boundary Conditions

130,000 A

0 V

Figure 8D – Single Segment_Center Strap Electric Model Results: Voltage

Fig. 8E – Single Segment_Center Strap Electric Model Results: Current Density

Fig. 8F – Single Segment_Center Strap Electric Model Results: Joule Heat

Figure 1 – NSTX Upper Umbrella Assembly Upgrade Design: Version 3.

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