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Analysis of Narrow Support Element of The W7-X Magnet System
under Design Loads
Authors: J. Duhovnik, T. Kolsek, N. Mole, B. Stok, F. resman,
B. Jerman, J. Kramar
Introduction
In 1994 the building of a stellarator "Wendelstein W7-X" started in
Greifswald, East Germany. Stellarator is a device of toroidal shape,
basically consisting of a toroidal vacuum vessel and numerous magnets
embracing the vessel. During operation, the hydrogen as a fuel is heated
to several milions of degrees to become a very hot plasma. At certain conditions
the plasma particles fuse and the energy is released. Strong magnet field
keeps plasma away from the walls (Fig. 1).
Fig. 1: General layout of the W7-X device |
The magnet system of the Wendelstein 7-X (W7-X) stellarator device includes
50 non-planar coils (see Fig. 2). They are toroidally arranged
in 5 identical periods, and antisymmetrically within each period. The weight
of the coils and the electromagnetic loads occurring during operation are
taken by a central support ring. The loads from each coil are transferred to
the support ring via two central connection elements and to the neighbouring
coils through lateral, contact, planar and narrow support elements.
Narrow supports (NS) are one of the most critical components of the structure
due to extremely high loads to be transmitted with simultaneous relative
sliding and tilting between the coils, requirements for the cycle sliding
without stick-slip effect and inaccessibility for
checking/replacement (See Fig. 3).
Fig. 2: The geometry of the Wendelstein 3D coil system |
Global Finite Element (FE) analyses have been performed in the past
primarily for the purpose of understanding the structural behaviour of whole
magnet system, while preliminary local analysis has been carried out
separately. IPP Greifswald (IPPG) requested a Finite element analysis of
a Narrow Support Element NSE 1e7-2e4 of the Wendelstein stellarator
W7-X coil system and provided all necessary data in the form of 3D STEP
format models, 2D drawings and tabular material data.
Fig. 3: The "Half-Module" of the coil system, where the region
of interest, the NSE connection, is indicated |
The analysis assumed the load forces to cause the plastic deformation
of the materials. Therefore, the material stress-strain characteristics
for all relevant materials had to be taken into account. Additionaly, the
NSE connections are subject to operate at very low temperatures of 4K. A
highly nonlinear elastic-plastic contact analysis had to be performed in
order to obtain realistic results.
Analysis method
A finite element analysis of the selected NSE type has been performed
simultaneously with two popular engineering tools, ANSYS and ABAQUS. The
aim was to obtain the load-deformation characteristics of the NSE connection
in various directions and undervarious sliding conditions. The potential
damage to the components at a chosen force level should be indicated.
In the following, the analysis and the results are briefly reported.
Geometry
IPP requested a local analysis of the NSE connection and therefore supplied
only a portion of the relevant geometry, i.e. part of the touching coils
and the NSE components pad, and the pad frame. Since the target deformation
of the system had been prescribed, we selected only a portion of the geometry
to performthe detailed analysis, as shown on Figure 4. The cross section of
the relevant geometry is depicted on Figure 5.
Fig. 4: The geometry of the NSE and part of the coil casings;
orange color: The geometry provided by IPPG, blue coding: the geometry
entering analysis |
Fig. 5: The cross section of a NSE |
The main parameters of the analysis to follow are:
- the materials of the components:
Pad material - soft bronze alloy (AlBr1.0966)
Coil material -1.3960 steel
Frame material - 1.4429 steel
- the geometry of the Pad: Pad diameter is 73 mm and the Pad curvature on
both sides is 1100 mm
- The compression force on the assembly is up to 3 MN
- The analysis should involve cases with relative lateral shift of the coils
up to 2 mm
- The friction between the components can vary in the range 0.1-0.3
- the shrink fit between NPC-2/PadFrame 0.05 mm overlapping should be
taken into account, the initial gap between PadFrameCollar/NPC-2 is 0.03 mm
- The tilting of the surfaces in contact NPC-1/PadFrame should be up to 0.5 degree.
Material data
The analysis assumed the load forces to cause plastic deformation of the
materials. Therefore, the material stress-strain characteristics for all
relevant materials had to be taken into account. IPPG has provided necessary
data in a tabular form. The stress-strain characteristics of all materials
were highly nonlinear and temperature dependent.
Boundary conditions of the model
Since the model has been cut out of the whole non-planar coil system, we
have agreed to use simplified boundary conditions at the cut surfaces.
IPPG requested calculations of 6 distinctive computational cases, which
differ by the initial pad position, application of shear force, application
of the NC1 contact surface tilting and friction coefficient values (see Fig. 6).
Fig. 6: Parts in contact, position of the pad, and tilting |
- BC Case 1:
a) An initial Pad position is at the maximum possible positive
x-position with the respect to the Pad Frame, as shown on Fig 6;
b) The initial tilt of the part NPC-1 is 0 degree and is gradually increasing in
parallel to the compression force, until it reaches its maximum value of
0.5 degree, the final state shown on Fig 6;
c) A gradually increasing diplacement of NPC-1 in +x direction is applied
in parallel to the compression force, until it reaches its maximum
value of 2 mm; as a result, shear force Fx force is computed;
d) Friction coefficient Pad/PadFrame is 0.1 and Friction Coefficient
for Pad/NPC-1 is 0.3, see Fig 6;
- BC Case 2:
a) An initial Pad position is at the center;
b) No tilt of the part NPC-1 is applied;
c) No shear force is applied;
d) Friction coefficient Pad/PadFrame is 0.2 and Friction Coefficient for Pad/NPC-1 is 0.2;
- BC Case 3:
a) An initial Pad position is at the center;
b) No tilt of the part NPC-1 is applied;
c) A gradually increasing shear force Fx is applied in parallel to the
compression force in +x direction;
d) Friction coefficient Pad/PadFrame is 0.2 and Friction Coefficient for Pad/NPC-1 is 0.2;
- BC Case 4:
a) An initial Pad position is at the center;
b) No tilt of the part NPC-1 is applied;
c) A gradually increasing shear force Fx is applied in parallel to the
compression force in -x direction;
d) Friction coefficient Pad/PadFrame is 0.2 and Friction Coefficient for Pad/NPC-1 is 0.2;
- BC Case 5:
a) An initial Pad position is at the center;
b) No tilt of the part NPC-1 is applied;
c) A gradually increasing shear force Fy is applied in parallel to the
compression force in +y direction;
d) Friction coefficient Pad/PadFrame is 0.2 and Friction Coefficient for Pad/NPC-1 is 0.2;
- BC Case 6:
a) An initial Pad position is at the center;
b) No tilt of the part NPC-1 is applied;
c) A gradually increasing shear force Fy is applied in parallel to
the compression force in -y direction;
d) Friction coefficient Pad/PadFrame is 0.2 and Friction Coefficient for Pad/NPC-1 is 0.2;
We have run an initial BC Case 1 case by gradually increasing the displacement
of the NPC-2 in +normal-direction until the reaction force at the cutter
surfaces in normal-direction was 3.0 MN. The maximum value of the NPC-2
displacement in normal-direction was 2.56 mm. Aninitial overlapping between
the Pad Frame and NPC-2 of 0.05 mm was taken into account. The component's
contact has been modelled by surface to surface contact elements, which
were attached to all nodes, which could possibly be in contact. The contact
has been established between the following surfaces: NPC1-Pad, Pad-PadFrame,
PadFrame-NPC2 (see Figure 5).
Results
There were numerous results providing insight into the behaviour of
individual NSE components under design loads. A report comprising more
than 100 pages including details has been submitted to IPPG. Only a small
selection is provided here. Figures 7 and 8 show the equivalent plastic strain
of the components in contact, which indicate severe plastic deformation
both in pad and pad frame.
Fig. 7: Equivalent plastic strain at the PAD, and Pad Frame, F=3.0 MN |
Fig. 8: Equivalent plastic strain at the NPC-2, F=3.0 MN |
As the main result, the characteristic stiffness curves in multiple directions
have been calculated (see example on Fig. 9). There were some small
differences observed between ANSYS and ABAQUS results.
The difference between individual points on stiffness curves in all cases
were relatively small, in the vast majority of the points less than 10%.
Both tools yielded curves of the same characteristic nonlinear shape. There
were substantial differences in shear-stiffness characteristics in BC
Cases 3, 4, 5 and 6 (see example on Fig. 10). It turned out, that these
cases were handled with different boundary conditions as follows: ABAQUS
analysis used the following BC3: A gradually increasing shear force Fx
has been applied in parallel to the compression force in +x direction
as a consequence of the prescribed movement of the boundary faces of
the coil casing, until it reached 2mm in +x direction; Sliding has been
prevented by increasing friction; A preliminary calculation has been performed
to synchronize it with the vertical movement; ANSYS tool used the
following BC3: A gradually increasing shear force Fx has been applied in
parallel to the compression force in +x direction; Fx has been calcualted
as 0.199*Fz to avoid sliding; A preliminary calculation has been performed
to synchronize it with the vertical compression force; The analoguous
application of BC was performed for BC4, BC5, BC6;
The differences between the characteristics computed by ABAQUS and ANSYS
are attributed to the differences in the vendor code handling the
nonlinearities in terms of material behaviour, large deflections and
contact problems.
Fig. 9: Compression force versus vertical displacement, BC Case 1 |
Fig. 10: Shear force versus x-displacement, BC Case 3 |
Outlook for further research
The successful completion of the project initiated further collaboration
between IPP Greifswald and UNI-Ljubljana. A new 2006 project was defined
to evaluated the design of six different NSE and to determine the limit
and allowable forces during W7-X operation. Another project was defined
in order to perform cyclic loading simulation.
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