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Input files
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MagLevScan.BAT, MagLevScan.MIN, MagLevScan.NIN, nelson_force.cfg, MagLev.SCR, MagLev.MIN, MagLev.NIN, MagLev.SCR, MagLevBound.MIN, MagLevBound.NIN, MagLevForce.png, FieldLineComparison.png, MagLevJPlot.png, MagneticLevitationTEAM.pdf
MagneticLevitationA.zip
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Description
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The example illustrates force calculations in the Nelson program for AC/RF magnetic fields. New entries were added to the standard Nelson configuration file to calculate magnetic forces integrated over the volume of material objects. The geometry and parameters follow a benchmark example created by the TEAM (Testing Electromagnetic Analysis Methods) project. A paper describing the example is included with the input files and is available at CompuMag.org. An aluminum plate is levitated by a 50 Hz AC magnet coil assembly. The plate is in axial equilibrium and is assumed to be constrained transversely. This example determines the final equilibrium position. The dynamic behavior described in the paper is determined by air resistance and other damping factors in combination with the magnetic force.
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Results
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The calculations described in the TEAM report were performed with boundary element methods with infinite space boundary conditions. Initial calculations with Nelson using a finite-element method indicated that finite boundary conditions could significantly affect quantitative results. The main Nelson calculations were performed with a large solution volume surrounding the assembly. The outer volume at reduced resolution was inside a flux-conserving boundary. The top section of the second figure shows the geometry with field lines: two concentric coils with opposing polarity act on an aluminum disk. Note that the UP direction is to the right.
The run files MagLevScan.bat, MagLev.scr, MagLevScan.MIN and MagLevScan.NIN controlled the initial runs, a determination of force as a function of distance between the top of the coil and the bottom of the disk. The force was calculated by a volume integral of the time-average of Sigma*ETheta*Br. The first figure is a plot of the results. The dashed red line is the force of gravity on the disk (1.05 N). The calculated long-term equilibrium distance is 11.37 mm, in agreement with the TEAM experimental measurements that show a small amplitude oscillation between 11.3 and 11.4 mm. A Nelson calculation at the equilibium position gives a vertical force of 1.051 N. An additional calculation was performed with a reduced solution volume to gauge the effect of the boundaries (bottom section of the second figure). The calculated force is Fz = 1.336 N, 27% higher than the open-space value.
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Comments
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The example is a rigourous test of accuracy. The skin depth is much larger than the plate thickness (the skin depth in aluminum at 50 Hz is 11.6 mm) and there is considerable spatial variation of the induced current density (third figure). For comparison, a PerMag example with a pulsed magnetic field or with a superconducting disk gives a much large force, 29.381 N.
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