Figure 1 – NSTX Upper Umbrella Assembly Upgrade Design: Version 3
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Figure 1 – NSTX Upper Umbrella Assembly Upgrade Design: Version 3. 304 SS Support. G10 Support. Figure 2 – Single Segment Strap Assembly Version 3 with G10/ 304 SS Supports. Figure 3 – Single Segment Strap Assembly: Center Strap Only. R out = 5.688”. 38 Laminations: - .060” thk; .005” gap

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

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Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

304 SS Support

G10 Support

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Figure 3 – Single Segment Strap Assembly: Center Strap Only


Figure 1 nstx upper umbrella assembly upgrade design version 3

Rout = 5.688”

38 Laminations:

- .060” thk; .005” gap

Mat’l: Copper

Wtfull = 37.4 lb

(Wtarch = 20.4 lb)

Rin = 3.160”

7.5”

Bpol= .3 T

5”

I = 130 kA

Uvertthermal = .3 in

Btor = 1 T

Uradthermal = .018 in

2.523”

2”

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Calculated EMAG Loads

Fop

Out-of-Plane Load (z-direction)

I+

R

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]

Bpol

In-Plane Load (y-direction)

pressip

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)

x x x x x

x x x x x x

x x x x x x x

I+

w

Btor


Figure 1 nstx upper umbrella assembly upgrade design version 3

Force = 66.6 lbf

Ux = .018 in

Uy = .3 in

Uz = 0

Press = 9.7 psi

Fixed

3 Elements thru Thickness

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Figure 5B – Single Lamination Linear Results: von Mises Stress

Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Figure 1 nstx upper umbrella assembly upgrade design version 3

Figure 5C – Single Lamination Linear Results: von Mises Stress

Loads: Thermal Displacements Only


Figure 1 nstx upper umbrella assembly upgrade design version 3

Figure 5D – Single Lamination Linear Results: von Mises Stress

Loads: In-Plane (Pressure) Load Only


Figure 1 nstx upper umbrella assembly upgrade design version 3

Figure 5E – Single Lamination Linear Results: von Mises Stress

Loads: Out-of-Plane (Force) Load Only


Figure 1 nstx upper umbrella assembly upgrade design version 3

Large deflection = On

Figure 5F – Single Lamination Nonlinear Results: von Mises Stress

Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Baseline design mathcad flex strap lamination analysis conclusions recommendations

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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 1 nstx upper umbrella assembly upgrade design version 3

Large deflection = On

Figure 5J – Single Lamination Nonlinear Results: Z-Deformations

Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Figure 1 nstx upper umbrella assembly upgrade design version 3

Large deflection = On

Figure 5K – Single Lamination Nonlinear Results: Z-Deformations_Front

Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Figure 1 nstx upper umbrella assembly upgrade design version 3

σhoop = P*R/ t

= 9.77 psi x 5.688 in/ .060 in

= 924 psi

Large deflection = On

Figure 5L – Single Lamination Nonlinear Results: von Mises Stress

Loads: Emag Pressure (In Plane) Only


Figure 1 nstx upper umbrella assembly upgrade design version 3

1st Mode

Load Multiplier = 58.4

1st Mode

Load Multiplier = 58.4

3rd Mode

Load Multiplier = 117.6

(Nonlinear 1st Mode

Load Multiplier = 50)

Large deflection = Off

2nd Mode

Load Multiplier = 73.0

Figure 5M – Single Lamination Pre-Stressed Linear Buckling Results

Load multiplier LMF applies to all Emag loads and thermal displacements


Figure 1 nstx upper umbrella assembly upgrade design version 3

Y

LMF = 14

0

80

Large deflection = On

Figure 5N – Single Lamination Nonlinear Buckling: Y-Deformation at Onset (1)

Load multiplier factor LMF applies only Out-of-Plane Emag load


Figure 1 nstx upper umbrella assembly upgrade design version 3

Y

LMF = 26

0

80

Large deflection = On

Figure 5P – Single Lamination Nonlinear Buckling: Y-Deformation at Onset (2)

Load multiplier factor LMF applies only to Out-of-Plane Emag load


Conclusions

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 1 nstx upper umbrella assembly upgrade design version 3

3 Elements / Lamination

Figure 6A – 3 Lamination FEA Model: Mesh


Figure 1 nstx upper umbrella assembly upgrade design version 3

Large deflection = On

Frictional contact (COF = .4)

Figure 6B – 3 Lamination Nonlinear Results: von Mises Stress

Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Figure 1 nstx upper umbrella assembly upgrade design version 3

Large deflection = On

Frictional contact (COF = .4)

Figure 6C – 3 Lamination Nonlinear Results: Z-Deformations

Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Figure 1 nstx upper umbrella assembly upgrade design version 3

Large deflection = On

Frictional contact (COF = .4)

Figure 6D – 3 Lamination Nonlinear Results: Z-Deformations_Front

Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Figure 1 nstx upper umbrella assembly upgrade design version 3

Large deflection = On

Frictional contact (COF = .4)

Figure 6E – 3 Lamination Nonlinear Results: Contact Status

Loads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)


Figure 1 nstx upper umbrella assembly upgrade design version 3

3rd Mode

Load Multiplier = 61.8

1st Mode

Load Multiplier = 58.2

Large deflection = Off

Frictional contact (COF = .4)

2nd Mode

Load Multiplier = 60.7

Figure 6F – 3 Lamination Results: Linear Buckling Mode Multiplier

Load Multiplier factor LMF applies to all Emag loads and thermal displacements


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

3 elements/ lamination

# Nodes = 850423

# Elements = 152895

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Large deflection = Off

Frictional contact (COF = 0)

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Large deflection = Off

Frictional contact (COF = 0)

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

By = .3T

Bz = 1 T

ux = .018”

uy = .30”

I = 130 kA

JS

FLorentz

Non-Linear

Large Deflection

Non-Linear

Large Deflection

Heat Gen

Tnodes

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Figure 8B – Single Segment_Center Strap Assembly: Mesh


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Figure 8F – Single Segment_Center Strap Assembly: Thread Stress


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Full-Load

Pretension

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Full Load Pressure

Bolt Pretension-Only Pressure

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Full Load Status

Bolt Pretension-Only Status

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Full Load Pressure

Bolt Pretension-Only Pressure

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Full Load Pressure

Bolt Pretension-Only Pressure

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

Full Load Status

Bolt Pretension-Only Status

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

0 V

130,000 A

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Figure 1 nstx upper umbrella assembly upgrade design version 3

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


Shear key copper threads static results cont

Shear Key Copper Threads, Static Results (cont.)

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

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

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


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