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Nr 6: Differential-Geometry Coilend Optimization

Goal

Optimize a cross-over turn using differential-geometry methods

Description

  • Block Data 2D: We wish to connect two conductors in a connection-side end. The left and right conductor are not symmetric. This situation is encountered with cross-over turns between blocks.
  • Block Data 3D: We provide start values for differential-geometry ends.
  • Block Groups: We are interested in only one semi-arc per cable.
  • Design Variables: For each block we use the following design variables. It is advisable to 'play' with the start values and use the 3D Preview to visualize the results in order to get a feeling of the design variables.
    • BOVERA ellipticity of the coil end
    • HORDER order of the hyper ellipse of the base-line (HORDER << 2: more triangular, HORDER >> 2: more rectangular)
    • TORS1-4 additional torsion applied in four points along the coil end to ease the conductor position. In between the four points a spline function is used.
    • The following design variables are applied to both semi-arcs alike:
    • BETA for the conductors to match they must have the same inclination angles at the apex.
    • CENTER this option allows to shift the angular position of the apex. For cross-over turns that need to bridge a large angular difference, this option can become important.
  • Objectives: The following objectives must be controlled
    • NORMA the max normal curvature or easy-way bend of the cable
    • GEODE the max geodesic curvature or hard-way bend
    • GEOSTR the integrated square of the geodesic curvature along the cables in the block, which is proportional to the strain energy in the cable
    • EREG the so-called edge-of-regression violation. This value should always be zero, which can usually be obtained by playing with TORS1-2.

The crucial part is to find the appropriate weights. We wish to controll the hard-way bend, most importantly the integrated square. However neglecting the control of normal curvature can lead to very rectangular coil ends. Rounder shapes can often be found with little cost on the side of hard-way bend by increasing the weight on the normal curvature. Sometimes an edge-of-regression violation can be eliminated manually after optimization by playing with TORS1 and TORS2 while controlling the other objectives.

More information on the theory can be found in

B. Auchmann and S. Russenschuck: Coil end design for superconducting magnets applying differential geometry methods. IEEE Transactions on Magnetics, 40(2):1208-1211, March 2003

For the optimization we use the cockpit view. The 'Optimization' option in the 'Main Options' must be selected. The cockpit is opened from the 'Run' menu.

The results of an optimization can be read into the data file from the 'Design Variables' widget. Click on the symbol in the top-right corner of the table and select 'Read in design set ...'. Select the .scan file with the same filename as the .data file. If you aborted the optimization, the .scan file is called 'roxie.scan'. Now you can load the last design set which should correspond to the best design.

Visualize the results in the 3D Preview.

Files

use_case_6.zip

  • diffGeomBlockOptim.data
  • roxie.bhdata
  • roxie.cadata