**Analysis of the NCSX Integrated Structure**

## Executive Summary

This report documents a nonlinear FEA model for NCSX coil support
structure and its analytic results for the four loading cases,
representing four stages during NCSX operation. The four stages are dead
load (DL) only at room temperature, dead loads plus cool-down to 85° K,
dead loads plus cool-down and electromagnetic (EM) loads at 85° K, and
dead loads and EM loads. The last load case assumes the thermal strain
during pulse will cancel the cool-down strain. The analyses do not
consist of seismic loads, the interacting loads from other components,
and the TF coil preloads.

As the previous nonlinear analysis \[1\] for the modular coil (MC) and
the modular coil winding form (MCWF) indicated the trouble areas at the
MCWF joints for the cool-down and EM loads, it is important to make
analyses with a model that includes the TF structure and loadings that
consider all governing load cases. Due to the physical memory of the
existing PC (32 bits with 1.5GB), the modeling efforts required to keep
the model size within a acceptable limit. Therefore, the element size
for most parts do not have fine mesh pattern. The parts that have few
contributions to the stiffness of the integrated system, such as the
vacuum vessel and the center stack, were disregarded in the model.
However, the load impact from those parts should be considered in the
analysis. The model did not contain the modular coil clamp assembly
because of its modeling complexity and less input to the modeling
stiffness. Alternatively, the modular coils were bonded to the winding
forms for stability. The model consists of MCWF system, TF structure
system, and all modular coils, TF coils, PF4, PF5 and PF6 in one field
period, which is a 120-degree sector.

The FEA model was formed using contact elements among all connecting
parts. All the contact surfaces are assumed to be bonded except the MCWF
wing interfaces that have frictionless unilateral contact behaviors. The
nonlinear property at the wing interfaces offers more rational
assessment of the forces across the MCWF toroidal joints. Using less
nonlinear elements will utilize less disk memory, reduce running time,
and minimize the difficulty for the solution convergence.

The highest MC conductor currents of the current waveforms at full
operating capability as shown in Section A.2.3.2 of Reference \[2\] were
selected as the governing case of EM loads. Additional load cases may be
run to verify whether the present case is the worst case or not. For the
vacuum-pressure impregnation (VPI) modular coils, the relative cooling
shrinkage of coil strain has been assumed to be 0.0004 m/m from the room
temperature to the operating temperature of 85K.

The NCSX structure will be supported at three locations, 120 degrees
apart at the C-C joints \[3\] to keep the EM loads from the support.
Each support offers only the vertical and toroidal restraints and let
the structure move freely in the radial direction. The design of base
support is not complete yet. For convenience, the base support was
located below the outboard stiffening leg.

The exact simulation of the integrated structure, which involves bolt
preloads, partial-bolted joints, sliding interfaces, and indefinite
orthotropic material properties of the modular coils, was very tedious
and may have difficulty of nonlinear convergence. This model shall be
treated as a basic model that provides the capability for further
modifications of the modeling assumptions. Because of time limit, no
further adjustments have been run. In order to obtain conservative
answers for particular areas, it is recommended that additional runs
should be carried out by modifying some contact surface behaviors or the
material properties. The following results are derived from the current
modeling assumptions.

-   For 2T high beta scenario, the maximum flux density is 4.901 Tesla
    on the MC Type B.

-   The net centering EM force Fr in one field period from MC is 5 MN.

-   Radial preloads for the TF coils is not considering in the analysis.
    Current design concept indicates that the preloads will be counter
    balanced by the ring tension of the inboard TF structure.

-   The impact of EM loads on the MCWF is much greater than the dead
    weight and the cooldown thermal strain.

-   The maxim displacement is 2.604 mm, occurred at the modular coil
    Type B from the DL and EM loads. The maximum displacement in the
    MCWF is 2.371 mm, located near the maximum coil displacement in the
    shell Type B.

-   The maximum von Mises stress in MCWF is 220 MPa (31.9 ksi), found at
    the inboard location of the shell Type A for dead load plus EM load.
    The allowable stress of stainless steel casting \[15\] for the
    membrane plus bending is 322.5 MPa (46.78 ksi).

-   The highest longitudinal stresses of the modular coil is 139MPa
    (20.1 ksi) in coil Type A from the load case of DL and EM with
    cool-down effects.

-   The PF4, PF5, and PF6 are constrained by the TF structure.
    Displacements of the integrated structure, especially the vertical
    displacements, have some impact on their stresses.

-   TF and PF currents are not the highest currents. The stresses in
    this EM load case do not stand for the critical load case for the TF
    and PF coils and possibly the TF structure.

-   No EM loads enter into the base support. All four load cases post
    the same vertical support reactions, which is 339.4 KN (76.3 kips).

-   The contact pressures on the wing bags are not very uniform. With
    modulus of elasticity at 13,750 MPa, the maximum contact pressure is
    128 MPa (18.6 ksi.), occurred on the wing bag Type B. The pressure
    could be improved if shape is changed to provide more uniform
    compression.

-   The TF structure will help carrying some loads to the base support,
    if the TF structure sections are fully bonded at the shim joints.

-   The thermal strain from the cool-down has only small impact on loads
    at flange joints in comparison with the EM loads.

-   Based on the net bolt preload of 45797 lbs for the 1 3/8" bolt,
    several locations along the toroidal flange joints have shear forces
    far exceeds the allowable value. That might cause the joints to
    slip.

-   In evaluating the bolt joint capacity, the selected areas for the
    bolt group shall be small enough that the centers of bolt groups
    match closely with the centers of bolt loads.

-   The worst location for the joint slip in the MCWF is at the inboard
    flanges joint B-C.

-   A complete design of the bolt joint should also consider the impact
    of preload change due to thermal variation and the creep of the
    insulation materials.

-   The model assumed all contact surfaces were bonded except for the
    wing interfaces that used frictionless contact elements through the
    wing bag shims. In the real case, the modular coils, TF coils, and
    PF coils are not exactly bonded to the structure. Some bolt joints
    may not be firmly connected. It is recommended that additional runs
    by changing contact behaviors or modifying the material properties
    shall be performed to assess the impact of modeling assumptions.

**2.0 Assumptions**

The following assumptions were applied in the analysis:

The model was built on the Pro/E model. All the part contact surfaces
are assumed to be bonded except the MCWF wing interfaces. The wing bag
shim was bond to shell on one side and had frictionless contact
behaviour to the adjacent shell on the other side. With primary interest
in the forces on the MCWF joints, the frictionless contact elements
properly imitate the forces that transfer through flange joints at
wings.

All material properties of coil conductors are based on the smeared
properties. As the MC conductor test programs have not yet established
many of the required data to form an orthotropic property, the model
utilized isotropic material properties for the winding packs. As the
coils are continuous in the axial direction, the isotropic material
properties are more suitable to be represented by the test data in the
longitudinal direction. The isotropic properties are also used for the
TF and PF coils.

The model did not contain the modular coil clamp assembly because of its
modeling complexity and less stiffness contribution. To ensure the
stability of the modular coils in the model, they were bonded to the
winding forms. Two longitudinal shear moduli in the coils were reduced
to limit the shear impact on the contact surfaces and lower the
composite action with the MCWF. The shear rigidities of shims for the TF
and PF coils are decreased for the intention of less resistance to the
coil movements. A description of the FEA model was given in a PowerPoint
document \[4\].

To minimize the size of the model, the model disregarded the parts that
have few contributions to the stiffness of the integrated system, such
as vacuum vessel and center stack. However, their load impacts were
added in the solution phase. For conservative reason, the weight of
center stack was supported at the upper TF structure and the weight of
vacuum vessel assemble was hung from the upper side of the shell Type A.

To make sure an adequate wedge action for the TF coil, all TF coils will
be preloaded by pulling in the radial direction against the TF
structure. As this assembling procedure will be carried out before the
TF structure is tied down to the MCWF, these preloads will not transfer
to MCWF and will not be considered in the analysis.

No bolt holes and bolt connections were simulated in the model and no
bolt preloads were applied in the analysis. The normal forces and shear
forces across the bolt joints shall be calculated after the analysis for
establishing the required bolt preloads that will make sure that the
bolt joints will not be opened up or sliding.

At the discussion meeting \[3\] of the stellarator support structure,
the notes showed that the structure will be supported at three
locations, 120 degrees apart at the C-C joints. The supports offer
cyclically symmetric restraints of weight and seismic loads, but no EM
loads. For this purpose, only the vertical and toroidal restraints exist
on each support.

As the design of base support structure is not completed yet, fictitious
base support blocks were added beneath the integrated model to keep high
local stress and deformation away from the structure.

3.  **Analysis Methodology and Inputs**

**3.1 Methodology**

The analysis uses the same mesh pattern for EM and stress analyses so
that it is able to avoid the errors of mapping applied loads from one
model to another model. The procedure will first solve the
electromagnetic (EM) analysis and review the results. Then applying the
EM loads obtained from the first analysis to the structural analysis for
evaluating the stresses and displacements.

Because of cyclic symmetry in the geometry and the loading, the model is
formed in a 120-degree sector to minimize the model size and the
computer running time. Figure 3.1.1 and 3.1.2 show the models elected
for the EM analysis and the structural analysis, respectively. The
geometric nonlinearity of the contact behavior, caused by the wing
interfaces, was solved using the ANSYS nonlinear method.

![](media/image1.png){width="2.313888888888889in"
height="3.411111111111111in"}

Fig. 3.1.1: EM model consists of MC, simplified plasma, PF coils, and TF
coils

![](media/image2.png){width="4.4847222222222225in"
height="3.6506944444444445in"}

Fig. 3.1.2: Integrated structural model

**3.2 Inputs of Models**

The geometric files of the MCWF and modular coils were developed by ORNL
while the geometric files of the TF structure and TF and PF coils were
provided by PPPL. Some small features, such as bolts, bolt holes,
chamfers, and fillers in the geometry were removed prior to the meshing.

In the EM model, the PF coils, TF coils, and the modular coils are
formed by ANSYS 8-node solid element SOLID5. For the current input, the
modular coils and TF coils were cut near the mid-height at the outboard
legs. The plasma current was simplified by SOURE36 current elements
along the center line of the plasma current.

After the EM analysis, the SOLID5 elements for the winding packs were
shifted to structural 3-D SOLID45 elements with identical number for the
nodal points and elements. The final structural model consists of the
following components:

1\) Modular coils

2\) MC winding form (MCWF)

3\) MCWF poloidal breaks

4\) MCWF toroidal shims

5\) MCWF wing bag shims

6\) PF coils No.4 to No.6

7\) PF coil brackets and shims

8\) TF coils

9\) TF coil shims at inboard, outboard, top and bottom

10\) TF inboard wedge spacers

11\) Inboard TF structure

12\) Outboard TF structure

13\) Tie bars for (11) and (12)

14\) TF structure toroidal shims

15\) Connecting blocks between TF structure and MCWF

16\) Fictitious base support blocks

The number of nodes and elements of the model was examined in order to
form a final model that can fit into the 3.2 bit PC with 1.5GB total
physical memory. All contact regions used the surface-to-surface contact
elements. Even with a total number of 163,090 elements and 283,750
nodes, the model does not have fine mesh size.

The model needs appropriate boundary conditions and support constraints
to simulate the structure in a stable and cyclically symmetric
condition. For parts with identical boundary nodes on θ=+60° and the
θ=-60°, such like MCWF and PF coils, coupled degrees of freedom were
defined for all degrees of freedom. For those without identical boundary
nodes in the TF wedges and TF structure, the constraint equations were
generated. Figure3.2.1 shows the model with boundary condition, in which
the green color and the pink color indicated the coupling and constraint
equation, respectively. To be able to achieve the cyclically boundary
condition, all nodes on the boundary surfaces shall be rotated into the
same global cylindrical coordinate system. The cyclically symmetric
conditions were also required for the wind bags located outside the end
boundaries on the shell Type C. The detail arrangement has been
explained in the previous report \[1\].

Fictitious base support blocks were added beneath the integrated model
to keep high local stress and deformation away from the structure. The
model was restrained by one-nodal support that has vertical and toroidal
constraints on the fictitious block. All the measuring units in the
model are in international MKS system.

![](media/image3.png){width="4.3805555555555555in"
height="3.689583333333333in"}

Fig. 3.2.1: Cyclic Symmetry Between θ=-60° and θ=+60°

**3.3 Applied Coil Currents for EM Analysis**

Reference \[2\] presents coil operating capability including turn per
coil and all current waveforms. The listed current is the current in
each turn, not the current in each conductor. Therefore, the modular
coil currents will be the currents multiplied by the number of conductor
turns. Table 3.3.1 lists the number of coil turns and turn currents at
the full operation capability for the 2T high beta scenario that was
selected in the EM analysis.

Table 3.3.1: Turn number of each coil set

Coil M1 M2 M3 PF1 PF2 PF3 PF4 PF5 PF6 TF Plasma

Turn No. 22 22 20 72 72 72 80 24 14 12 1

Turn Current 37190 37783 36538 -14615 -14615 -9054 -7498 460 453 -1301 0

For the current convention system, NCSX utilizes the cylindrical
coordinate system with the Z-axis as vertical. A positive PF or plasma
current is in the direction, which is counter-clockwise viewed from
above. A positive poloidal current, such as TF or modular coil current,
flows in the positive Z-direction in the inner leg.

**3.4 Applied Loads for Structural Analysis**

The individual loads are EM loads, cooling strain, and deal loads that
including interface dead load from vacuum vessel and center stack. The
cooling strain is due to temperature changes during the modular coil VPI
process and the initial cooling to the operating temperature of 85K. R &
D test has indicated that the winding pack cure shrinkage is very small
and negligible. The other test result shows that the CTE of the winging
pack is slightly higher than the winding form and when the modular coil
is cooled to 85K, the relative thermal strain between the modular coil
and the winding form is about -0.04%.

To simulate the load case of cool-down of the modular coils, the
equivalent temperature drop of 23.26K that is equivalent to coil strain
of 0.04%, should be applied to the WP only. The temperatures on the
other parts were kept unchanged.

To apply gravity load, specify gravity acceleration in a positive Z
direction by using ACEL command. As the model does not contain vacuum
vessel and center stack, the appropriate weight shall be added at the
part interfaces. One third of center stack weight \[5\] is 1288.4 lbs
(5731 N) and one third of vacuum vessel weight \[6\] is 4912.5 lbs. The
weight of inside vessel components was estimated about 2000 lbs.

The structural analysis shall consider all possible loading combinations
to determine the governing load case. Four load cases were defined in
the analysis. They are (1) dead load only at room temperature, (2) dead
loads plus cool-down to 85° K, (3) dead loads plus cool-down and EM
loads at 85° K, and (4) dead loads and EM loads. The last load case
assumes that the thermal strain during pulse will cancel cool-down
strain.

Radial preloads for the TF coils was not considering in the analysis.
Current design concept indicates that the preloads will be counter
balanced by the ring tension of the inboard TF structure. To accomplish
this condition, the TF coils shall be preloaded before the TF structure
attached to the MCWF.

**3.5 Material Properties**

The material properties are represented by isotropic materials with some
modifications on the shear modulus of elasticity to consider the parts
that are formed by the composite materials or possible surface sliding.
The modular coil R & D test results \[7\] illustrate the flexural
modulus of elasticity of the winding pact at 77K varies from 11.08Msi
(76.4GPa) for bare Cu specimens to 7.37Msi (50.8GPa) for glass wrapped
specimens. The longitudinal compressive test at room temperature \[8\]
shows the modulus of elasticity at an average value of 9.11Msi
(62.8GPa). As the test program has not yet established all of the
required data for forming an orthotropic property, the analysis employed
the smeared isotropic material property with a reduced longitudinal
shear modulus of elasticity to consider the impact of possible contact
sliding from the winding form.

The elastic modulus of MCWF casting alloy shall meet 145GPa at 77° K
\[9\]. The flange shim insulations placed between toroidal flange joints
are formed with a 3/8-in SS covered by 2 layers of 1/16-in G11. The
equivalent isotropic properties were calculated for their material
properties. The casting TF structure has not completed the design yet.
Its elastic modulus was assumed to be the same as the MCWF. Table 3.5.1
summarizes the material properties of all components. In the Table, the
shear modulus G with a sign of "\*" is calculated from the isotropic
material relationship. The shear rigidities of shims for the TF and PF
coils are decreased for the intention of less resistance to the coil
expansion movements. For the modular coils, the longitudinal direction
is Z for the element coordinate system. The 1st shear modulus is for Gxy
and the 2nd shear modulus is for Gyz and Gxz. The much small values for
the Gyz and Gxz intend to limit the shear impact on the contact surfaces
and lower the composite action with the MCWF.

Table 3.5.1: Material properties of components

![](media/image4.wmf){width="6.75in" height="3.8756944444444446in"}

4.  **Results and Interpretations**

**4.1 EM Analysis**

Figure 4.1-1 demonstrates the flux density contour plot, in which the
maximum flux density is 4.901 Tesla in the modular coil. The maximum
flux density equals to the value of the previous analysis \[1\] which
has same currents in the modular coils and the TF coils. The currents in
the PF coils have some variations.

![](media/image5.png){width="2.75in" height="3.9166666666666665in"}
![](media/image6.png){width="1.2291666666666667in"
height="3.1979166666666665in"}

Fig. 4.1-1: Flux density contour plot

Figure 4.1-2 displays the magnetic forces that show the magnetic forces
in the TF, PF5, and PF6 coils are very small in comparison with the
forces in the modular coils. Because of the stellarator stmmetry, the
net EM force components in the vertical and toroidal directions are
equal and opposite for the three right-hand-side modular coils and the
three left-hand-side modular coils that result in net zero forces.

![](media/image7.png){width="2.75in" height="3.9791666666666665in"}
![](media/image8.png){width="1.2291666666666667in" height="2.5in"}

Fig. 4.1-2: Element vector forces of Type B modular coils

**4.2 Structural Analyses**

Four load combination cases representing four stages during operation as
shown in Section 3.4 were run in the analyses. As the interest in the
analysis will be focus on the MCWF joints, the results will put emphasis
on the MCWF structure and the toroidal flange joints.

**4.2.1 Displacements**

The integrated structure is supported at the edge of the outboard leg
with vertical and toroidal constraints. The maximum displacements of the
four load cases are illustrated in Table 4.2.1.1. For the dead load, the
maximum displacement occurs at the mid-section between supports. During
the cool-down, modular coils shrink more than the MCWF that causes
bending moments in the combined section of MC and MCWF and yields
greatest displacement on the wings of MCWF. With the DL and EM loads,
the maxim displacement is 2.604 mm, occurred at the modular coil Type B.
The maximum displacement in the MCWF is 2.371 mm, located near the
maximum coil displacement in the shell Type B.

Table 4.2.1.1: Structural Displacements of Four Load Cases

Dmax (mm) Uz-max (mm) Uz-min (mm)

Dead load 0.384 0 -0.384

DL + Cooldown 0.595 0 -0.517

DL + Cooldown + EM 2.559 1.104 -1.318

DL + EM 2.604 1.091 -1.285

The vertical displacement contour plots for the dead load only and the
dead loads plus EM loads are illustrated in Fig. 4.2.1.1 and Fig.
4.2.1.2, respectively. The unit of displacement is meter. In the case of
only the dead loads (Fig. 4.2.1.1), the vertical displacements are
greater in the inboard region than the outboard region. If more evenly
distributed displacement is preferred, the location of the supports
shall be moved toward the inboard leg. In Fig. 4.2.1.2, the vertical
displacements in the right-hand side are opposite to the left-hand side
mainly due to stellarator symmetry of the EM loads.

![](media/image9.png){width="4.104166666666667in"
height="2.8020833333333335in"} ![](media/image10.png){width="1.28125in"
height="2.1979166666666665in"}

Fig. 4.2.1.1: Vertical displacement (Uz) for dead loads

![](media/image11.png){width="3.9270833333333335in"
height="2.7291666666666665in"} ![](media/image12.png){width="1.25in"
height="2.2291666666666665in"}

Fig. 4.2.1.2: Vertical displacement (Uz) for DL plus EM loads

**4.2.2 Stress in MCWF**

A review of the stress results demonstrates the Load Cases 3 and 4 are
the leading cases for the structural responses primarily due to the EM
loads. Examining stresses on all parts show that the maximum stress
takes place at the MCWF toroidal shim AA for the Load Case 4, as shown
in Fig. 4.2.2.1. The peak stress is confined locally at the corner of an
element and therefore it is not a great concern.

![](media/image13.png){width="2.7700787401574805in"
height="3.3633858267716534in"}![](media/image14.png){width="1.0862204724409448in"
height="2.3318897637795275in"}![](media/image15.png){width="2.1980314960629923in"
height="2.0200787401574805in"}

Fig. 4.2.2.1: Peak local stress from DL plus EM loads

For the dead load plus EM load, the von Mises contour stress of the
MCWF, which is the major load-carrying element, is shown in Fig.4.2.2.2.
The maximum stress of 220 MPa (31.9 ksi) was found at the inboard
location of the shell Type A, as shown in the Fig. 4.2.2.3. The peak
stress is limited to a small area, near the maximum stress spot on the
toroidal shim AA displayed in Fig. 4.2.2.1. The stresses in the other
areas are much smaller than the maximum value.

![](media/image16.png){width="4.114583333333333in"
height="2.986111111111111in"}
![](media/image17.png){width="1.0631944444444446in"
height="2.3361111111111112in"}

Fig. 4.2.2.2: MCWF von Mises stress from DL plus EM loads

![](media/image18.png){width="2.6763779527559057in"
height="2.311023622047244in"}![](media/image19.png){width="3.1598425196850393in"
height="2.027952755905512in"}

Fig. 4.2.2.3: Maximum von Mises stress from DL plus EM loads

The shell structure is made of stainless steel casting. According to the
NCSX design criteria (see Ref. \[12\]), the allowable stress for the
membrane plus bending will be 322.5 MPa or 46.78 ksi \[15\], which is
larger than the maximum stress.

**4.2.3 Stress in Coils and TF Structure**

On the base of the selected material properties and the assumed bonding
contact behavior, the longitudinal stresses contour plot for the modular
coil Type A, which have the highest stress, is illustrated in Fig.
4.2.3.1 from DL and EM with and without cool-down effects. The load case
with cooldown yields more tension in the coils than the load case
without cool-down because of additional shrinkage in the modular coils
than the winding form.

![](media/image20.png){width="2.6311023622047243in"
height="3.4366141732283464in"}![](media/image21.png){width="0.8397637795275591in"
height="1.9165354330708662in"}![](media/image22.png){width="2.697244094488189in"
height="3.5515748031496064in"}![](media/image23.png){width="0.8043307086614173in"
height="1.9165354330708662in"}

Fig. 4.2.3.1: Axial stress of coil Type A from DL and EM with and
without Cool-down

The currents used in the analysis for the PF coils and TF coils do not
represent the highest currents in the coils and, therefore, the stresses
in those coils are not considered to be the critical stresses. It is
noted that the PF coils are constrained on the TF structure. The
displacements of the integrated structure, especially the vertical
displacements, have more impact on the stresses in the PF5 and PF6.
Figure 4.2.3.2 exhibits the axial stress contour for the PF5 and PF6.

![](media/image24.png){width="3.7465277777777777in" height="2.725in"}
![](media/image25.png){width="1.16875in" height="2.5034722222222223in"}

Fig. 4.2.3.2 Axial stress of PF5 and PF6 from DL plus EM loads

The design of TF structure has not completed yet. From the applied DL
and EM load, stress contours of the lower TF structure are given in
Fig.4.2.3.3. The toroidal stresses are shown on the left side and the
von Mises stresses are shown on the right side. The results are not
necessary represent the critical load condition due to the input
currents. However, it indicated two structural behaviors: (1) the outer
TF structure subjected to bending in the toroidal direction under the
vertical deformation of the integrated structure, and (2) the maximum
stress will be at the lower TF structure near the base support.

![](media/image26.png){width="2.697244094488189in"
height="2.738976377952756in"}![](media/image27.png){width="1.0708661417322836in"
height="2.3326771653543306in"}![](media/image28.png){width="2.6251968503937007in"
height="2.7291338582677165in"}![](media/image29.png){width="0.989763779527559in"
height="2.1661417322834646in"}

Fig. 4.2.3.3: Axial stress of PF5 and PF6 from DL plus EM loads

**4.2.4 Base Support Reactions**

The support reactions from the four combined load cases are listed in
Table 4.2.4.1. They are only vertical and toroidal restraints at the
support. Because of the stellarator symmetry, the EM loads do not
transfer to the support. Neither the thermal strain from the cool-down
produces loading on the support. The only loading that transfers to the
support is the dead load, resulting a vertical reaction of 339.4 KN
(76.3 kips).

All four load cases post almost the same reactions. The small force
variations in the toroidal direction are caused by nonlinear convergence
and FEA model. The nodal points and elements in the model are not
totally symmetric with respect to the middle of the cross section,
although the CAD geometries are symmetry.

Table 4.2.4.1: Support Reactions for Four Load Cases

Fr (KN) Fθ (KN) Fz (KN)

Dead load 0 0.074 339.4

DL + Cooldown 0 0.077 339.4

DL + Cooldown + EM 0 0.280 339.4

DL + EM 0 0.283 339.4

**4.2.5 MCWF Toroidal flange Joints**

The model did not include any bolts or any bolt preloads in the toroidal
flange joints. An investigation of MCWF bolt joints \[10\] was performed
by A. Brooks based on the net bolt preload of 45797 lbs for the 1 3/8"
bolt. The flange was divided by several regions as shown in Figure
4.2.5.1 in according with the discontinuation in the flanges and at
inboard regions without bolt connection (green color). In each region,
the normal force and the shear force were evaluated from the FEA
results. The required coefficients of friction to prevent slip were then
calculated and plotted for all the flange regions.

![](media/image30.png){width="1.388976377952756in"
height="1.7255905511811023in"}![](media/image31.png){width="1.5in"
height="1.8507874015748031in"}![](media/image32.png){width="1.4311023622047243in"
height="1.698031496062992in"}![](media/image33.png){width="1.4807086614173228in"
height="1.6744094488188976in"}![](media/image34.png){width="1.3818897637795275in"
height="1.7645669291338584in"}![](media/image35.png){width="1.550787401574803in"
height="1.8188976377952757in"}![](media/image36.png){width="1.4590551181102362in"
height="1.7909448818897638in"}

Fig. 4.2.5.1 Designated names in flange regions for selected bolt groups

Figure 4.2.5.2 illustrates the coefficients of friction needed \[11\] to
prevent slips for EM load at the MCWF toroidal flange joints from two
FEA models, one with MCWF only (red color) and the other with integrated
model (blue color). The side-by-side result comparison shows the
influence of adding TF structure in the model. Some improvements are
found in most of regions. However, the shear forces in many regions are
much higher than the allowable coefficient of friction, 0.15, prescribed
by the design criteria \[12\]. The results indicate that the TF
structure can assist in carrying loads to the base support, if the TF
structure shim joints are fully bonded and good enough to maintain the
bending, torsional and shearing stiffness along the longitudinal
direction as assumed in the integrated model.

Figure 4.2.5.3 \[11\] illustrates the coefficient of friction needed to
prevent slips on the integrated model that subjected to the dead loads
and EM loads with or without cool-down strain. A comparison of the
required coefficients of friction shows that the thermal strain from the
cool-down has only small effects at flange joints. The worst location
for the joint slip is at the inboard flange joint B-C.

![](media/image37.wmf){width="5.997222222222222in"
height="3.5381944444444446in"}

Fig. 4.2.5.2 Comparison of required coefficient of friction at bolt
joints for two models with EM only load case

![](media/image38.wmf){width="5.997222222222222in"
height="3.5381944444444446in"}

Fig. 4.2.5.3 Comparison of required coefficient of friction for DL and
EM load with and without cooldowm.

The approach for calculating required coefficients of friction yields
accurate results only when the center of load matches the center of the
bolt group in each region. As the joint loads are not uniform along the
flanges, the resulting load centers and the bolt group centers, in
general, will not be coincident. To avoid obvious discrepancy, it is
suggested that some regions should be subdivided into smaller areas,
such as regions CCB, CC2B, CCT, and CC2T.

**4.2.6 Wing Bags**

Wing bag was designed to carry the loads from the wing to the next shell
segment. The amount of load transfer depends on the stiffness of the
wing bag, the contact behavior and the stiffness of wing. The model
assumed wing bag shim was bond to shell on one side and had frictionless
contact behaviour to the adjacent shell on the other side. This is the
only nonlinear action in the model in order to predict more appropriate
load-transferring mechanism. The analysis presumed that the modulus of
elasticity of wing bag was 13,750 MPa.

Figure 4.2.6.1 shows a contour plot of the wing bag contact pressure at
the shell Type A for the DL and EM loads. The unit of contact pressure
is Pascal. Positive pressure indicates load toward the surface and
therefore is in compression. The distribution of the contact pressure is
not very uniform on the contact surface. Most effective spot on the wing
bag locates near the cantilever end of the wing. The maximum contact
pressure is 128 MPa (18.6 ksi.), occurred on the wing bag at shell Types
B.

![](media/image39.png){width="3.53125in" height="2.1458333333333335in"}
![](media/image40.png){width="1.21875in" height="1.8645833333333333in"}

Figure 4.2.6.1: Contact pressure on wing bag at shell Types A

**4.2.7 Commands in Solution Phase**

The integrated FEA model database file "file6.db" includes the support
constraints and the EM loads for 2T high beta scenario at 0 seconds.
When the support location or the EM load changes, the corresponding
nodal constraints or the nodal forces should be removed and replaced.

The inputs of dead loads make use of the ANSYS acceleration command
"acel' and add in the proper weights from PF coil center stack \[13\]
and vacuum vessel \[14\]. For conservative, these additional weights are
supported on the upper structure. The input commands are:

> acel,,,9.806
>
> csw=-3865\*4.448/6 ! center stack weight/6
>
> f,278757,fz,csw
>
> f,299941,fz,csw
>
> esel,s,mat,,90 ! vacuum vessel
>
> nsle
>
> nsel,r,loc,z,nz(261533),nz(261533)
>
> f,all,fz,-6900\*4.448/32
>
> allsel

The relative thermal strain between the modular coils and the winding
form is about 0.04% when they are cooled to 85K. By setting up the
reference temperature at 0° K, the equivalent modular coil temperature
becomes -23.2558° K. The input commands are:

> tref,0
>
> esel,s,mat,,1,3 ! MC
>
> nsle
>
> bf,all,temp,-23.2558
>
> allsel

The displacement criterion was used for the nonlinear convergence
criteria. As the load case including EM load was more difficult to
converge due to coarse elements, a separate convergence tolerance value
was selected depending on the load case with or without EM loads

> cnvtol,u,,0.05 ! without EM loads

or

> cnvtol,u,,0.05\*2.1 ! with EM loads

**5.0 Discussions**

A FEA model of integrated structure was created with the main interest
in studying the MCWF joints during the operation stages. As previous
model did not include the TF structure, it is essential to understand
what will be the impact on the MCWF joints by adding the TF structure.

In order to run the ANSYS model in a PC with 32 bits and 1.5 GB memory,
it is necessary to keep the model within a proper size. For this,
fillers and chamfers in the Pro/E geometry were removed. Most of the
element sizes are not fine and those parts that have few contributions
to the model stiffness were eliminated, such as the PF coil center stack
and the vacuum vessel assembly. The complex clamp system for the modular
coil was removed, and instead, the modular coils were bonded to the MCWF
to assure a stable condition.

The model assumed all contact surfaces were bonded except for the wing
interfaces that used frictionless contact elements through the wing bag
shims. In the real case, the modular coils, TF coils, and PF coils are
not exactly bonded to the structure. Some bolt joints may not be firmly
connected on contact surfaces. It is recommended that additional runs by
changing contact behavior or by modifying the material properties shall
be performed to assess the impact of modeling assumptions.

Stress in the coil is derived from the displacement and the material
property. If the accurate stresses of coils are wanted, suitable
orthotropic material properties shall be provided and correct contact
assumptions shall be presented. To simulate the sliding condition on the
MC contact surfaces, an approximate approach may be used by distorting
the shear moduli of one of contact part to a very small value without
changing the bonded contact behavior. This may be useful for the TF coil
shims too.

The currents in the TF and PF coils do not have the highest currents.
The stresses in this EM load case do not stand for the critical load
case for the TF and PF coils and possibly the TF structure.

Bolt joint contact was assumed to be always bonded. If there was a
possibility of partial opening at the joint due to insufficient or
unevenly distributed bolts, a standard contact element shall be used.

The stellarator symmetry of the support system makes certain that there
are no EM loads transferring to the base support. The analysis did not
cover the seismic loads and some interacting forces from the attached
components. Therefore, the main load on the support is the dead weight.
The support location can be modified to test the best support location.

The selected EM loads from currents at 2T high beta current scenario
have the highest currents in the modular coils. Additional load cases
may be run to verify the present case is the worst case.

The investigation of the bolt joint was based on the net bolt preload of
45797 lbs. It considered neither the impact of preload variations due to
the temperate change, nor the loss of preload due to the creep of
insulation materials.

**6.0 References**

\[1\] H. Fan, "Nonlinear Analysis of Modular Coil and Shell Structure",
NCSX-CALC-14-001-001, February 3, 2006

\[2\] Engineering Technical Data "C08R00_C8_Ultimate.xls", January 14,
2006, PPPL NCSX web site

\[3\] B. Nelson, "Requirements for stellarator core support", March 14,
2006

\[4\] H. Fan, "Descriptions of the NCSX Integrated Model -- file6,db",
PPPL Email, July 18, 2006

\[5\] Drawing No. SE132-001 "Centerstack Assembly PF Coils 1, 2, & 3",

\[6\] F. Dahlgren, Nastran FEA model "model21bbe2a.dat"

\[7\] T. Kozub, "NCSX Composite Coil Tests", March 15, 2004, PPPL NCSX
web site

\[8\] T. Kozub, "NCSX Composite Coil Tests", April 5, 2004, PPPL NCSX
web site

\[9\] P. Heitzenroeder, "NCSX Product Specification Modular Coil Winding
Forms", NCSX-CSPEC-141-03, February, 7, 2006

\[10\] A. Brooks, "MCWF Toroidal Joint Concerns", PowerPoint
presentation attached in the email dated February 28, 2006

\[11\] A. Brooks, "Analysis of Coil Structure", PowerPoint presentation
attached in the email dated July 12, 2006

\[12\] I. Zatz, Editor, "NCSX Structural Design Criteria, Draft E", May
10, 2004, PPPL web site

\[13\] NCSX Drawing No. SE132-001 "Centerstack Assembly PF Coils 1, 2, &
3",

\[14\] F. Dahlgren, Nastran FEA model "model21bbe2a.dat"

\[15\] P. Heitzenroeder, "FEA Analyses Results of the A1 Casting with
Thin Wall Regions", E-Mail attachment, August 8, 2005