Optimizing Magnets with Pole Pieces

[7ombie]

> A pole piece is a structure composed of material of high magnetic permeability that serves to direct the magnetic field produced by a magnet. A pole piece attaches to and in a sense extends a pole of the magnet, hence the name. -- Wikipedia | Pole Pieces

Pole pieces not only allow us to easily change the shape of a magnet, we can also redirect the flux through the pieces, so the poles no longer need to be at opposite ends.

The most obvious application of pole pieces (for magnetic cubes) would be to move each pole 90 degrees from the axis of the magnet, so both poles interact with the magnet in any adjacent piece, roughly doubling the effect. This could be achieved by simply attaching a pair of tombstone-shaped pole-pieces to each pole of a regular (axially-aligned, pill-shaped) magnet, as in this first image.

Note: The poles are on the very bottoms of the pole pieces (pointing downwards in the image). These poles also have a reduced surface area, so the flux would be denser at the poles.

Note: Here, I'll use iron to refer to any suitable material for the pole pieces. In practice, it would likely be a specialized alloy, like Permalloy.

In the images used here, the poles of the magnets are highlighted with bright red and blue, while the iron pole pieces are highlighted with dull red and blue to indicate their polarization (due to the influence of the magnet).

These magnetic assemblies would replace each magnet in a regular mod, one for one, and can be used with the Elite Mod, Xyzzy Mod et cetera. The assemblies are oriented to align with the corners of each piece, and the polarity is handled as in the regular mods, except that the polarity of each piece is determined by which of its magnet's poles is furthest from the core (and not the pole that is presented to adjacent pieces).

Below-left, is a 2D magnet map, showing how pole pieces would be applied to the 48 magnets in a conventional magnetized cube, with a 3D version of the same map below-right.

The shape of the pole pieces can be optimized in a bunch of different ways, and can be different for each pole. Below is an example where the pole nearest to the core has a long, rounded pole piece (that would allow the magnets to interact over greater distances, while the pole furthest from the core has a smaller (more concentrated), flat pole piece, designed to increase the precision of the overall effect.

Note: In practice, the pole-pieces would not need to be so bulky.

There are a bunch of ways pole pieces that can be applied, both to enhance and mute magnetic effects (even down to effectively being able to turn permanent magnets on and off by rotating them). Here, I just wanted to post an introduction, as I keep mentioning pole pieces in passing, but never really elaborate on what I mean.

To the right is an image showing a roughly optimal profile for the pole pieces, relative to the internal faces of a single layer. Again, the scale is not important. The image just illustrates the underlying idea.

For those that have followed my recent posts, note that the longer pole pieces would be similar in effect to the system GAN introduced for their 11th generation Pro and Duo cubes :]

 

[7ombie]

Quick clarification: While pole-pieces can be used with magnetic mods generally, the mods I specifically mentioned (Elite and Xyzzy) would be limited to using pole pieces that would fit in the upper 30-40% or so of the center- and edge-pieces (just due to their internal shapes).

For example, the blue, broken-circular shape in the last image of the previous post would need to be closer to the core, so it could cut across the edge pieces as well (making it almost a complete circle), and still leave room on the outside for the the red, precision poles (which would form a crosshair-shape in the image). In short, the poles in the corners would need to align with the poles in the edges mid-turn.

 

[SenorJuan]

One thing to bear in mind when using iron alloys to manipulate rare-earth magnet fields: the iron alloy will saturate magnetically. It cannot 'cope' with the strong field such as NIB's create. Even with special alloys of iron, like Permendur ( a largely cobalt-iron mix ) you are restricted, the result being less effective magnetic forces.
https://en.wikipedia.org/wiki/Permendur

( This is why pole pieces cannot be used to magnetise materials like NIB. They cannot reach field strengths high enough. Hence the ONLY suitable material for an electromagnet core of a magnetising tool is air. This then means that it's necessary to pass many thousands of amps through the magnetizing electromagnet. Thankfully, it's only needed for a few millisecs, so your magnetiser doesn't vapourise every time it's used.)

 

[7ombie]

@SenorJuan - I was aware of saturation, but don't understand it very well. It was why I designed the red pole pieces to form a rectangle, though a point would be more focussed.

Are you saying that NIB magnets will saturate alloys like Permendur to the extent that pole pieces are generally unviable, or just that we need to avoid concentrating things too much?

That Wikipedia article states that Permendur has a saturation flux density of around 2.4 tesla. If I understand correctly, n52s generate fields approximately half that strong (~1.4 tesla), so we could taper the pole piece down to have an area a little over half the area of the real pole of the magnet, before the alloy becomes saturated (assuming n52s). Is there any sense in that logic, or have I got it all wrong?

Concentrating the flux is not that important, as the magnets are already strong enough that we don't normally need n52s. Being able to optimize the shape (and move the poles, so they face the same direction) is far more useful (in this context).

 

[SenorJuan]

I don't have any real design experience with pole pieces, just second-hand exposure to designs of colleagues, and how they never seem to work as well as you think they should.
In theory, reducing the area of the iron (at the pole) to half that of the magnet face area should give double the flux density. In practice, you'll have to deal with various problems, that result in nearly all of that 'doubling' to vanish. The ferromagnetic material isn't perfect, and will partly saturate at flux-densities below maximum levels. The flux won't be just concentrated around a 'gap' , it will be across anywhere else it can possibly be across, for example the opposite side of your magnet/pole-piece assembly. The pole piece material needs to be kept 'thick and short' , until near the point where you're wanting to taper it down in area.
The best way nowadays to analyse these assemblies is to use computer simulation, based on finite-element analysis. I've no idea what 'free' types are available out there.. if you're a registered student, for example, you could have more options re. 'student' versions, maybe.
It's definitely worth investigating FEA tools, simple maths doesn't deliver the results.

 

[7ombie]

Thanks, @SenorJuan. I'll look into the points you raised, and see if I can learn more about it. I don't have the background to understand it properly, but will see what I can find out. Thanks.

 

[7ombie]

@SenorJuan - I think I understand what you mean now, and you're right, I did misunderstand how flux moves through pole pieces.

I was envisioning the field lines moving through the piece in parallel, as they do when they pass through the magnet itself, and was struggling to envision how the flux moves when the piece widens. This is all completely wrong though. The field lines always diverge as they move through a pole piece, so a lot of the flux escapes out the sides, so in short, you're right. They need to be short and stout.

There's a video on YouTube that illustrates the issue.

The other evening, I was thinking about magnetic wires, like electrical wires, and while I knew it wouldn't work, I couldn't understand why. I get it now.

Anyhow, I don't think this issue is insurmountable, but it definitely needs more attention than I've given it, and does place fairly strict limits on the geometry of the pole pieces.

Thanks again, @SenorJuan. It's an important aspect of magnetism that I had completely misunderstood.

 

[7ombie]

Another issue with having long poles is that they seem to repel each other sideways, not along their lengths (in the direction that the face rotates). I've been playing with some magnets at home, at don't think the force that they generate would push the face along (even if I dropped pole pieces entirely, and just used long, curved magnets).

The tombstone-shaped pole pieces I suggested at the beginning could still work, but having them formed into long, curved tracks is not going to work, even without considering a bunch of practical issues with the way the corner pieces conventionally fit together internally (which doesn't leave much room inside), and the fact that the corners have complex, curved, internal faces (to support better corner cutting).