@Broli,
Your images will not mean much to those not familiar with FEMM. I have never come across your outer boundary consisting of shells of varying permeability, why have you done this? I note that your outer boundary is not symmetrical with the inner working part, it is shifted in the x direction by about 7mm. I think that accounts for the x force you get when your toroid is not carrying current, the x force should be zero but threre will still be a y force even if you correct that displacement because I think those forces are between your horseshoe and the boundary. When the toroid is carrying current the small coupling between the coil and the horseshoe alters those force values but you can't claim the force is between the coil and the horseshoe because you have this magnetic type of boundary. Why have you not used the open boundary conditions offered by the FEMM manual?
Smudge
Hey Smudge you may be right about not everyone getting this, but I was also kind of hoping you would be replying to this as well as I respect your knowledgeablee insights and experience. As for the other people you could say that this has similarities to Thane Heins Bi-Toroid transformer. However unlike Thane's design this is only using an AIR core and the shape is toroidal to prevent any debates about edge and corner effects. As for the Boundary thing. This is in fact using the Open Boundary tool of FEMM. It automatically creates those concentric circles around the problem area with materials going from u1-ux. See here for the explanation of this feature: https://www.femm.info/wiki/OpenBoundaryExampleAnd yeah honestly I dont trust the force calculations myself knowing FEMM and how fiddley it is with small forces and mesh densities. I just included them for the heck of it. But logically speaking you dont expect there even would be force coupling between the outside magnet and toroid. The toroid is an air core so has the same permeability as the air around the magnet. Since the toroid is a closed loop system magnetic field wise there should be no coupling or else you would violate the Lorentz force that requires the toroid to generate a field outside of itself as well for it to affect the external magnet and we all know a toroidal coil has no field on its outside. This is why I found it surprising that a toroidal coil could have a non zero flux due to an outside magnetic field, it first started out small and I thought it was a mesh refinement anomaly, But then using different designs I managed to increase the flux by a factor of 20 where you would see a flux equivalence of 1A+ and 100 turns on the in the toroid. I was expecting this value to be negligible small and be an artifact due to simulation accuracy. However no matter much I increased the mesh refinement the value did not deviate much.
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