The Super Transformer: A Transformer that has no effect on the source.

[broli]

Playing around with FEMM I was curious about if it was possible to induce flux in a toroidal AIR (this is key) coil without having anything wrapped around it. To my surprise it WAS! However it was not much but there was actually a none zero amount of flux going through it. Now why would this be significant?

Well a toroid has no field on outside of it, it means it cannot affect an external coil or magnet when it is powered on. 

The initial designs started with a low flux linkage how ever below you see several iterations where you also see the flux linkage growing. I managed to make the flux linkage equivalent to a toroid that is about 100mm in diameter and has 100 turns and 2,3A goings through it. This is quite a significant amount.

The simulated design is focused on permanent magnets meaning it would be a mechanical model, imagine the outside PM structures moving across the toroid out of or into the screen. The Toroid would generate an EMF which would be decoupled from the moving magnets as the toroid should not affect it. In fact the simulation shows a more interesting effect force wise, the force seems to become slightly less no matter how fine I make the mesh.

I also attached the FEMM file, you may find that the mesh size might be too much for your pc.

[Smudge]

@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

[broli]

@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/OpenBoundaryExample

And 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.

[Smudge]

My experience with FEMM goes back over 20 years and I could have an old manual that doesn't mention that method.  I downloaded your FEMM file and changed the boundary to the periodic version where you have a second circular region that has infinity at the centre.  I also changed the soft iron to the linear version so as to speed up calculation time.  With zero coil current I was surprised that this gave force readings of Fx = -0.07235 and Fy = -0.20568.  Can't explain that.  Then with 0.6A coil current the readings were -0.07264 and -0.20507, so really no change there.  I then looked at the force on the coil and got positive values there of 0.06679 and 0.19215 for the 0.6A case with 0.066499 and 0.192762 for the zero amps case.  I suspect that the stress tensor method of calculating force has limitations, my reading of the Maxwell Stress Tensor tells me the mask should be very close to the surface of material and FEMM does not draw masks that close.  So I find all those readings suspect.

Smudge

[broli]

Yes I never trust small forces in FEMM especially when they are very mesh refinement dependent. However already due to the fact a toroid has no field outside of it, it should not be able to affect an outside magnetic source.

In the meanwhile I kept distilling the problem further down. And I came to what I believe is the essence of this idea. Its quite interesting in fact, but you can get rid of the horseshoe magnet and employ a magnetic array. Now at first I first tried the obvious one; a Halbach array but if you were sharper than me you would already know that that would give a null result. However when the arrangement was slightly altered with some 45 angle magnetization then the result becomes the largest value of flux linkage I have seen so far. The array is so simple and elegant and even looks sinusoidal.

Basically I made a long solenoid to test some array setups on it. And below you can see the sim result of this. The Halbach is essentially zero while the other is quite significant. Generally speaking it might be small but its also still and air core.

The coming days I would like to extend this to a circular shape but this looks like exciting stuff. Going from a Halbach array to something 4 orders of magnitude stronger is cool.

FEMM files of this are attached too.

[stivep]

The toroid is an air core so has the same permeability as the air around the magnet.

<sub>"Air permeability is a measure of how well a fabric allows the passage of air through it"
https://textilelearner.net/air-permeability-and-porosity-of-fabric/


I assume you were talking about  relative permeability.</sub>

The relative permeability of air is always 1. Relative permeability is the ratio of the permeability of any medium
to the permeability of air or vacuum1. The permeability of free space is approximately equal to the permeability of air^.
The relative permeability of a material is the ratio of the permeability of that material to the permeability of free space.

https://www.vedantu.com/question-answer/relative-permeability-of-air-a-1-b-2-c-class-12-physics-cbse-5f92a504a946521147ca3153
https://www.tutorialspoint.com/permittivity-and-permeability

The relative magnetic permeability of a magnetic material is the measure of relative ease with which that magnetic material conducts magnetic flux as compared with the conduction of magnetic flux in air.
Air or vacuum is the poorest conductor of the magnetic flux
by that if we start to talk now about   absolute  permeability
The relative permeability will be the ratio of absolute permeability (μ) of magnetic material to the absolute permeability (μ0) of air or vacuum and is denoted by μr,
The absolute (or actual) magnetic permeability of a material is its conductivity for the magnetic flux.

conclusion:
The higher the permeability of a magnetic material, the greater its conductivity for magnetic flux and vice-versa.
https://www.tutorialspoint.com/absolute-and-relative-magnetic-permeability#:~:text=Air%20or%20vacuum%20is%20the%20poorest%20conductor%20of,%CE%BC%200%20%3D%204%CF%80%20%C3%97%2010%20%E2%88%927%20H%2Fm.

additional material:
https://en.wikipedia.org/wiki/Toroidal_inductors_and_transformers
Wesley

[broli]

Hey @Wesley, indeed I meant magnetic permeability.

I have done some more follow up on this and finally came to the below array configuration. In essence I got rid of the 45 degree magnetization direction as such magnets would be hard to source.

The conclusion is that this ironically is a unidirectional halbach array like array. What that means is that the horizontally orientated magnets all point in the same direction unlike in a regular Halbach array. This means that the "strong" field side oscillates between inside the toroid and outside of it where the inside part always points in the same direction and thus would be a non zero flux if you summed all parts.

The flux linkage shows this as well. In the regular Halbach array you can see it is 2 orders of magnitude smaller, which makes sense as in a Halbach array the field points back and forth and thus cancels.