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 Flex Strap Assembly EMAG and Thermal Displacement Stresses, OOP EMAG Force, and Deflection Force vs Lamination Radius

0.000E+00

5.000E+03

1.000E+04

1.500E+04

2.000E+04

2.500E+04

3.000E+04

3.500E+04

3.15 3.65 4.15 4.65 5.15 5.65

Lamination Outside Radius - Ro (inches)

von

Mis

es S

tres

s -

psi

0.000

1.000

2.000

3.000

4.000

5.000

6.000

7.000

0 5 10 15 20 25 30 35 40

Def

lect

ion

Fo

rce

- W

(lb

f)

Total Combined Stress

OOP Emag Stress

IP Emag Stress

Therm Disp. Stress

Deflection Force

OOP Emag Force

Lamination Number - n

0.00

30.00

20.00

10.00

40.00

50.00

60.00

70.00

Ou

t-o

f-P

lan

e E

mag

Fo

rce

- F

op (

lbf)

Baseline-Design MathCAD Flex Strap Lamination Analysis: Conclusions/ Recommendations

• ~3/4 overall stiffness due to Inner Strap Assy• OOP torsional stress dominates in Outer Strap Assy;

thermal displacement bending dominates in Inner Strap Assy

• OOP force proportional to radius• Thermal displacement bending stress inversely

proportional to radius• Deflection force inversely proportional to radius• Proposed Design:

– Outer Assy: 12X .090” thick, 2.0” wide laminations– Inner Assy: 19X .060” thick, 2.0” wide laminations– Mat’l: Fully-hardened Cu-Zr

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. 8C – Single Segment_Center Strap Assembly: von Mises Stress_Iso-View

Fig. 8D – Single Segment_Center Strap Assembly: von Mises Stress_Side View

Figure 8E – Single Segment_Center Strap Assembly: Joint Contact Pressure

Figure 8F – Single Segment_Center Strap Assembly: Thread Stress

Figure 9A – Strap-to-E Beam Joint Analysis: Solid Model

Figure 9B – Strap-to-E Beam Joint Analysis: Full-Load von Mises Stress

Figure 9C– Strap-to-E Beam Joint Analysis: Maximum Shear Stress

Full-Load Pretension

Figure 9D – Strap-to-E Beam Joint Analysis: Contact Pressure

Full Load Pressure Bolt Pretension-Only Pressure

Figure 9E – Strap-to-E Beam Joint Analysis: Contact Status

Bolt Pretension-Only Status

Full Load Status

Figure 10A – Strap-to-TF Coil Outer Leg Joint: Solid Model

Figure 10B – Strap-to-TF Coil Outer Leg Joint Analysis: Full-Load Stress

Figure 10C – Strap-to-TF Coil Outer Leg Joint Analysis: Contact Pressure


Fig. 10D – Strap-to-TF Coil Outer Leg Joint: TF Leg-Only Contact Pressure


Figure 10E – Strap-to-TF Coil Outer Leg Joint Analysis: Contact Status

Bolt Pretension-Only StatusFull Load Status

Fig. 11A – Single Segment_Center Strap Electric Model: Boundary Conditions

130,000 A

0 V

Figure 11B – Single Segment_Center Strap Electric Model Results: Voltage

Fig. 11C – Single Segment_Center Strap Electric Model Results: Current Density

Fig. 11D – Single Segment_Center Strap Electric Model Results: Joule Heat

Shear Key Copper Threads, Static Results (cont.)

A-1 12,500lbs peak, 8 Threads A-2 12,620lbs peak, 8.5 Threads

A-3 13,120lbs peak, 9 Threads A-4 12,500lbs peak, 8 Threads A-5 10,880lbs peak, 7 Threads A-6 12,380lbs peak, 8 Threads

• Correlation between pull out force and the number of threads pulled explains scatter

• By design shear key bolt will catch 8-9 threads

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

Documents