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 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)
Large deflection = On
Figure 5K – Single Lamination Nonlinear Results: Z-Deformations_FrontLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)
Large deflection = On
Figure 5L – Single Lamination Nonlinear Results: von Mises StressLoads: Emag Pressure (In Plane) Only
Large deflection = On
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
Large deflection = On
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
Large deflection = On
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
Large deflection = On
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)
Large deflection = On
Frictional contact (COF = .4)
Figure 6D – 3 Lamination Nonlinear Results: Z-Deformations_FrontLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)
Large deflection = On
Frictional contact (COF = .4)
Figure 6E – 3 Lamination Nonlinear Results: Contact StatusLoads: Combined Thermal Displacements, Emag Press. (In Plane) and Forces (OOP)
Large deflection = On
Frictional contact (COF = .4)
Figure 6F – 3 Lamination Results: Linear Buckling Mode MultiplierLoad Multiplier factor LMF applies to all Emag loads and thermal displacements
Large deflection = Off
Frictional contact (COF = .4)
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
Large deflection = Off
Frictional contact (COF = 0)
Fig. 7D –Laminated Strap Assembly FEA Results – Thermal Displacements Only: Total Deformation
Large deflection = Off
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