1. 1 Target Geometry: End view of airgap. Only 2 magnets and two axial coils modeled for simplicity NSNS SNSN Gap to minimize circulating Flux Neodymium magnet (attached to rotor)

2. 2 Model used to simulate target Geometry - bend/split circular gap into two rectangular gaps and provided low-reluctance return path on right to simulate axial return. Rotor Stator This is low reluctance return path for flux. The flux returns axially in the actual device, but cannot be be modeled that way in 2D F.E.A. => provide “in-plane” flux return path NSNS SNSN

3. 3 Model Parameters Conductors. 1000 series turns 24AWG carrying 1A encircling stator core axially at two locations with polarities shown. The cross section envelope for these 1000 conductors is 4”x 0.25” Perm Magnet cross section 0.25” x 2”. The 2” dimension is centered on the 4” dimension of the conductor block. Neo N40 magnet Depth is 1” deep into paper (result is force per inch of length) Frequency is DC. Grid coordinates 0.1” per dot. 4 dots per square (0.4” x 0.4” gridlines) 0.05” airgap between rotor/PM; PM/Conductors; Conductors/Stator * 0.1” airgap between sections of return path on RHS. * * Note that an airgap is required surrounding a part to calculate force on it. Also mesh must be fine for small airgaps to give accurate force results

4. 4 Mesh. High density mesh (0.02” max triangle side) used in critical airgap areas.

5. 5 Mesh zoom-in

6. 6 Simulation Results - flux lines and flux densities (color shows density)

7. 7 Simulation results - arrow- plot showing direction of flux

8. 8 Fconductor=-5.5 Fpm=-7.1 Frotor_iron=-2.3 Fconductor=6.7 Fpm=7.5 Fstator_iron = 1.4 Fstator_iron=-0.9 Summary of force results from simulation (these are x-directed forces where x corresdponds to tangential direction): Force on conductor is as predicted by right-hand rule. Force on P.M. is in the ballpark equal/opposite for this particular geometry. Screen shots showing force on individual components are at the end of ppt.

9. 9 Force On Conductor Calc. Average B ~0.5T over that portion of conductors adjacent to the 2” magnet. N*I=0.5*1000A~500A (only 2” out of 4” = half of the turns see that flux density). L = 1”=0.025m. F=(NI) L B = 500*0.025*0.5 =6.25N. Reasonably close to FE results.

10. 10 Fx = 0.05 N

11. 11 Fx = -0.93 N

12. 12 Fx = -5.4

13. 13 Fx = 7.5

14. 14 Fx = -2.3

15. 15 Fx = -7.1

16. 16 Fx = 6.7

17. 17 Fx = 1.4

18. 18 Fx = -0.02