f Fermilab Fermi National Accelerator Laboratory

P.O. Box 500 • Batavia, Illinois • 60510

TD-99-022

April 19, 1999

## Design and Fabrication of End Parts for the 

## First High Field Magnet Mechanical Model[^1]

S. Yadav[^2] and I. Terechkine[^3]^+^

#### MS 316, PO Box 500

# *Fermi National Accelerator Laboratory, Batavia, IL, USA*

1.  **Introduction**

Fermilab, in collaboration with LBNL and KEK, is working on the design
of a high field Nb~3~Sn dipole magnet (of field strength 11 T) for use
in future Very Large Hadron Collider (VLHC) machine. The conceptual
design for the first magnet is provided in \[[^4]\]. This design is
based on a 2-layer cosθ coil structure with a cold iron yoke. It was
decided to build a mechanical model before building an actual magnet to
verify our production technology. Since Nb~3~Sn cable was not available
initially, it was decided to build this first HFM mechanical model using
NbTi cable from LHC project. This note provides a brief summary of the
design and manufacturing aspects of the coil end parts for the first
mechanical model magnet. The goals for this first mechanical model are
as follows:

-   to check ROXIE \[[^5]\] code for design of cross section and magnet
    end parts,

-   to select CAD-CAM software for end parts design and manufacturing,

-   to find cheap technology to fabricate end parts,

-   to set up the equipment and tooling necessary for coil fabrication,

-   to get experience with handling insulation and to study insulation
    properties at different production steps,

-   to verify the coil impregnation procedures and to check the quality
    of the impregnated coils,

-   to verify the chosen assembly technique, and

-   to measure mechanical properties of the wound and impregnated coils.

2.  **End Parts Design**

*2.1 Cross-section optimization*

Fig. 1 shows the cross section of the dipole model magnet, which is
based on a 5-block design. The geometric position of coil block
arrangements in the cross section was calculated from given input data
such as the number of blocks, number of conductors per block, cable
dimensions, radius of the winding mandrel, and positioning and
inclination angle of the blocks. Table 1 provides the relevant input
geometrical data for the model magnet cross-section, whereas cable
dimensions and properties are provided in Table 2. The magnet
cross-section and the coil ends could be optimized using program ROXIE,
which utilizes both deterministic and stochastic (genetic algorithms)
methods for solving the constraint vector-optimization problem
associated with the design of superconducting magnets. ROXIE also allows
optimization of the cross-section by an appropriate placement of the
coil blocks to find a coil cross-section with a part compensation of the
persistent current effects. However, since the goals for this first
mechanical model were to verify our production technology and assembly
techniques, it was decided not to spend further resources in optimizing
the magnetic field within the bore of the mechanical model.

*2.2 Coil end geometry and field optimization*

The coil ends were designed with the objectives of maximizing the radius
of curvature in the end and to apply as little '*hard-way*' strain as
possible to the cable. ROXIE also allows shifting of the relative
positions of the coil blocks to optimize the integrated multipole field.
However, this feature was not used for the first mechanical model due to
the reason already mentioned before. The input parameters which were
used for the generation of the coil ends are the *z* position of the
first conductor of each coil block and its inclination angle. The
conductors were aligned on the winding mandrel and not to the outer
radius of the end-spacers.

ROXIE uses a constant perimeter approach to define the coil ends. The
upper edge of the conductor is assumed to be of elliptical or
hyper-elliptical shape, in the developed plane defined by its radial
position in the straight section. The position of the lower edge is then
computed by assuming constant perimeter. Fig.2 shows a graphical
representation of the inner and outer lead end coils for this model
magnet obtained from ROXIE.

As part of the coil end design process, it was made sure that the
parameter *bulge* (maximum/middle width) does not get larger than 1.1.
Since the cable does not deform a lot, a *bulge* of more than 1.1 gives
rulings which make sense mathematically but not physically. A large
value of the parameter *bulge* can be corrected by inclining the blocks
more or by adding additional spacers or inter-turn fillings. Also a
*bulge* of more than 1.1 can cause lifting off the cable from the
mandrel, after winding. ROXIE also outputs the values of '*hard-way*'
strain and '*easy-way*' strain for all the conductors. Care should be
exercised in keeping these values below a certain critical value, which
depends on the

![](media/image1.png)

Figure 1: Cross-section of the HFM mechanical model obtained from ROXIE.

  --------------- ------------- -------------- -------------- --------------
  Block Number    No. of        Positioning    Inclination    Inner Radius
                  Conductors    Angle          Angle          (mm)
                                (degrees)      (degrees)      

  1               13            0.78           0.0            41.06

  2               10            29.90          39.0           41.06

  3               7             1.28           0.0            25.0

  4               6             27.50          39.5           25.0

  5               4             51.25          62.0           25.0
  --------------- ------------- -------------- -------------- --------------

Table 1: Geometrical data for the model magnet cross-section.

  ----------------------------------- -----------------------------------
  Insulated Cable Height (mm)         15.62

  Insulated Cable Inner Width (mm)    1.5231

  Insulated Cable Outer Width (mm)    1.7899

  Bare Cable Height (mm)              15.40

  Bare Cable Inner Width (mm)         1.325

  Bare Cable Outer Width (mm)         1.588

  Number of strands                   38

  Diameter of strands (mm)            0.8080

  Cu/Superconductor Ratio             1.3

  Cabling Angle (degree)              16
  ----------------------------------- -----------------------------------

Table 2: Cable (NbTi) dimensions and properties for the model magnet.

![](media/image2.png){width="6.8in" height="4.8in"}

Figure 2: Lead ends of the inner and outer coils of the model magnet.

type of conductor used, mechanical properties of the cable and prior
user's experience in coil winding with the same cable. It is claimed
that a de-keystoning factor can also be defined in ROXIE to account for
the change in shape of the cable at the ends, caused by the winding
process. However, the only way we found in ROXIE to account for cable
de-keystoning was by the introduction of inter-turn spacers in between
the conductors.

*2.3 End parts positioning*

To avoid using spliced joints, it was decided to wind both the inner and
outer layers from the same cable. This required winding of the outer
layer coil on top of a pre-wound inner layer coil on the mandrel. Thus,
it was necessary to fix the outer layer parts to the mandrel through the
holes on the inner layer end parts. Therefore, holes needed to mount the
parts on the mandrel were aligned together for the inner layer and outer
layer end parts to lie on top of one other as shown in Fig. 3.

![](media/image3.png){width="10.3in" height="7.0in"}

3.  **End Parts Manufacturing**

The shape and position of the coil blocks obtained from ROXIE's
optimization techniques determine the shape of the end-parts. ROXIE
outputs the surfaces to be machined in terms of 9 polygons, which
describe the end-part surfaces. Three different ways of sectioning these
polygons are provided in ROXIE:

-   Equiangular slicing of the ellipses in the sz planes (Etype 10).

-   Equidistant slicing of the ellipses (Etype 11).

-   Equitangential slicing of the upper and lower ellipses (Etype 12).

Both the equiangular and equidistant slicing of the ellipses requires
the use of a spherical cutter to cut end part surfaces, which are
defined by the 9 polygon surfaces. This makes the machining process to
be very time-consuming and expensive. On the other hand, an
equitangential slicing of the ellipses offers the opportunity of using a
cylindrical cutter, whereby only the upper and lower polygon surfaces
could be used for the machining of the end-parts. This makes machining
to be less time consuming and relatively less expensive. Therefore,
equitangential slicing (Etype 12) of the ellipses was performed to
define the rulings for end parts manufacturing. A set of 72 rulings was
used to define the tool path for machining of the end parts.

The end parts were made out of 6061 T-651 aluminum tubes, which were
machined to the appropriate inside and outside diameters corresponding
to the inner and outer coil cross-section. The end parts were then cut
out of these machined tubes by a wire EDM process. It should be
mentioned that the residual stresses in the machined tubes could cause
changes in the dimensions of the end parts, after electric discharge
machining process. To prevent any dimension changes due to the residual
stresses, the machined tubes were given a stress-relieve annealing
treatment. This was achieved by heating the tubes in a furnace at 343 °C
for 1 hour followed by an overnight cool in the furnace.

Fig. 4 shows a schematic of the end parts manufacturing process. ROXIE
provided output data in an ASCII format giving the X, Y and Z
coordinates for the 72 points on the rulings for 9 different polygon
surfaces. A program was written by V. Kashikin to extract the 72 ruling
points on the upper and lower polygons only, and to read them in AutoCAD
in a DXF format. Thus, a set of 72 rulings for surfaces defining the end
parts could be obtained. These data were transmitted electronically to
Lawrence Berkeley National Lab (LBNL) for the machining of the end parts
via a 6-axis wire EDM (electric discharge machining). EDM of the end
parts was chosen for parts manufacturing rather than conventional 5-axis
machining techniques due to the substantial savings in cost offered by
the EDM technique. For a comparison, it was found that the electric
discharge machining of the end parts was approximately three times
cheaper than conventional machining. An alternative methodology for end
parts manufacturing can use IDEAS instead of AutoCAD as the intermediate
step.

Figure 4: Schematic of the methodology followed for end parts
manufacturing.

Note that if it is not required to make and archive drawings for the end
parts, and if the end parts are not put through a very thorough
inspection process, then the above methodology presented in Fig. 4 for
end parts manufacturing is self-sufficient by itself. This would require
conveying information (such as location of the holes) to the machinist
in terms of hand-made sketches. Otherwise, Fig. 5 shows a schematic of
the methodology followed for generating end parts drawings from the
ROXIE output. Note that the same process is required if BEND is used
instead of ROXIE for designing the end parts. Due to the complex
3-dimensional shape of the end parts (as seen in Fig. 6 and Fig. 7), it
is necessary to make a 3-D solid model of the end parts before
generating the 2-D drawings. This is a very time consuming process and
takes significant efforts and resources of the personnel involved in the
project. Note that to shorten the process shown in Fig. 5, one of the
intermediate steps of going through ANVIL can be bypassed. It should be
mentioned here that the '*gen*' files made in ANVIL are used at Fermilab
for both the machining and inspection of the end parts. However, it is
still possible to bypass this extra intermediate step of going through
ANVIL. This would be helpful because there are more personnel at
Fermilab who are trained to use IDEAS software than those who are
trained to use ANVIL. Achieving of this goal would require a combined
effort on part of the part designer, machinist and the inspection crew.
Note that even after elimination of this intermediate step, producing of
drawings for archival purposes is still a very time consuming process.

Figure 5: Schematic of the methodology used to produce end parts
drawings.

### ![](media/image5.png){width="6.1in" height="5.782638888888889in"}

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Figure 6: 3-D solid model for the outer layer end parts for the first
mechanical model magnet.

![](media/image6.png)

Figure 7: Photograph of a partially wound inner coil.

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### Acknowledgements

The authors would like to specially thank J. Brandt for several useful
discussions during the design phase and for being very supportive and
helpful during all times. Thanks are also due to S. Russenschuck and R.
Bossert for their valuable input. The authors would also like to thank
T. Arkan, V. Kashikin, T. Lee, J. Jablonski, G. Zielbauer, L. Aslip, J.
Zweibohmer, S. Caspi, E. Hagler from the machine shop, and R. Rylan from
the inspection group for their contributions to this project.

### Appendix

The drawings for the end parts for the first mechanical model magnet can
be found in the XDCS system. There are 18 drawings with part numbers
ranging from 376031 to 376048. The drawings for all other parts such as
transition, pole pieces and wedges are archived and can be obtained from
L. Aslip as sketch numbers ranging from SY012599-1 to SY012599-8.

### References

[^1]: ^^ Work supported by the U.S. Department of Energy

[^2]: ^^ Email: syadav@fnal.gov

[^3]: ^++^ Email: terechki@fnal.gov

[^4]: T. Arkan et al., "Conceptual design of the Fermilab Nb~3~Sn high
    field dipole model," PAC-99, New York, 1999.

[^5]: ROXIE, Routine for the optimization of magnet X-sections, inverse
    field computation and coil end design, Proceedings of the First
    International Roxie Workshop, Geneva, March 1998.