Halbach-Array Simulation FEMM

[StudentonaOdyssey]

TL;DR Summary

Simulation of Halbach array does not match reality. Is the FEMM simulation correct?

Hello everone,
I have recently come across the need of a strong constant magnetic field while being limited in space. The field needs to be unidirectional and up until now was generated by two magnets (12x12x12mm N48). Then I came across Halbach arrays and their potentially stronger magnetic field. I created a simulation in FEMM4.2 which suggests that the Halbach array with (5x5x5mm N42) is indeed stronger. When I built the setup and did some measurements, it seemed to be weaker than the afore mentioned setup with 12x12x12mm magnets. My problem now is that I do not know whether simulations are wrong or the problem lies with the magnets.
Here is a picture of the simulations:

I am not sure if I am able to upload a file as well.
For anyone wondering the simulations suggest about 0.85T in the center, while I was only able to measure about 0.35T max.
The simulation for a two 12x12x12mm Magnet seem to fit to reality very well.
If any specific information is needed I will provide that as required.
If someone has experience with simulating magnets or even Halbach arrays, your advice would be very much appreciated. Any other help is welcome as well. Thanks a lot in advance.

 

[Baluncore]

Welcome to PF.

You appear to have separate 2 arrays, each of 2 x 3 = 6 cubes.
I cannot identify the orientation of the magnets.
Are they simple bipolar cubes with N and S on opposite faces?
Please give a link to the magnets you use (or similar) on the web.

A sketch of the polar orientation would help.
You can drag and drop a file onto your post.

Halbach beginners start here. https://en.wikipedia.org/wiki/Halbach_array

 

[StudentonaOdyssey]

Hello and thank you.
Yes there are two Halbach-Arrays with 6 magnets each, in the picture i attached you can see an arrow in each square that gives the direction of the magnetic field. The order of the Magnets should, from my understanding create a strong north pole on the bottom array and a strong south pole on the upper array, therefore a very Strong magnetic field, inbetween those two poles.
The magnets are cubic neodymium magnets and they are polarized in the direction of the arrows so they would look something like this, while red would be the north pole:

Here is the link to the magnets:
https://www.supermagnete.de/eng/cube-magnets-neodymium/cube-magnet-5mm_W-05-N

When i built the setup i had all the magnets aligned in one line, sticking to each other and marked one of their sides, similar to the picture above. Then I put them in a 3D-printed holder and glued them in place. Therefore I am fairly sure the alignment of the magnets is the same as in the simulation.

Here is a link to download the simulation file for further info.
https://file.io/L5n4j1Elp1OH
I used the 4.2 version of Femm, available here
http://www.femm.info/wiki/Download

I hope I could explain my problem a little better now, if there is anything else that is missing, I will of course further specify. Again I appreciate any further input and thank you in advance for the effort.

 

[Baluncore]

Magnets should, from my understanding create a strong north pole on the bottom array and a strong south pole on the upper array, therefore a very Strong magnetic field, inbetween those two poles.

It is difficult to build two small isolated monopoles with a wide gap between them. The fields tend to remain local to the individual patches. There needs to be some magnetic circuit to connect the back of the separated N and S patches.
Also, it is difficult to build an efficient Halbach array with only 6 cubes.

 

[StudentonaOdyssey]

Could you please specify what you mean by that?

There needs to be some magnetic circuit to connect the back of the separated N and S patches.

Do you think the power of the 5x5x5mm cubes is simply to little to be used with a 7mm gap in between the arrays?
I measured the resulting magnetic field of two 5x5x5mm cubes with a distance of 7mm and got around 220mT while the simulation gives me around 280mT.
Do you think there would need to be more magnets in the horizontal direction or overall? For example a 5x2 Array?
The area where the magnetic field is required is just 1mm wide in the center of the setup.

 

[Baluncore]

The difference between 220mT and the simulated 280mT is not the problem.

A Halbach array is designed to produce a strong field of alternating -N-S-N-S- poles along one face, with a weaker field on other faces, in other directions. That is quite different to the problem here in that you want a N-pole and a S-pole some distance apart, but are not prepared to connect them magnetically. Think of a horseshoe magnet, where the strongest field is between the poles, while the curve of the shoe provides the magnetic path between the back of the poles.

The distance from the N-pole to the S-pole of a 5x5x5 mm cube is less than 5 mm, so the field will be strongest along the sides of the cube. Why would that field flow out and across an open area if there was no easy path back to close the magnetic path.

 

[StudentonaOdyssey]

I am not sure if I understand you correctly, but do you mean that the problem is the missing connection of the weaker sides of each Array?
Because for other applications it does not seem to be required to connect two magnets at all in order two create a magnetic field in the gap between them.
Or do you mean that the distance between the arrays is bigger than the distance to the next opposing pole on the same array?

So because the distance 'b' is longer than distance 'a'?

Do you have experience with simulating magnets? Because I still don't understand why the simulation itself shows different results, even if there is a problem with the array-setup.

The difference between 220mT and the simulated 280mT is not the problem.

I also don't think that this is a problem if anything I think it shows that the simulation is fairly close and therefore should also work for the full array.

 

[Baluncore]

I am not sure if I understand you correctly, but do you mean that the problem is the missing connection of the weaker sides of each Array?
Because for other applications it does not seem to be required to connect two magnets at all in order two create a magnetic field in the gap between them.

That is true, but the presence of a field does not mean it is as strong a field as might be obtained with a different magnetic circuit. The Halbach array does not produce monopoles, it produces tight fields close to the array surface.

Or do you mean that the distance between the arrays is bigger than the distance to the next opposing pole on the same array?
So because the distance 'b' is longer than distance 'a'?

Correct, the field lines will remain local to the patch and do not need to cross the dividing gap.

Do you have experience with simulating magnets? Because I still don't understand why the simulation itself shows different results, even if there is a problem with the array-setup.

I simulate AC fields, not PMs.
I don't know what you mean by “different results”. Have you simulated and plotted the field of your proposed arrays and tried different ways to optimise the field in the central region?

I find it hard to suggest alternatives without some idea of what you are trying to do, or how the 3D space about the poles is obstructed, or otherwise utilised.

Can you place magnets above and/or below the mapped plane?

A Helmholtz coil provides a flat field in an enclosed area. It can use DC current.
https://en.wikipedia.org/wiki/Helmholtz_coil

 

[StudentonaOdyssey]

Thank you for explaining that again.

I don't know what you mean by “different results”. Have you simulated and plotted the field of your proposed arrays and tried different ways to optimise the field in the central region?

I was referring to the difference between my simulation and the measurement in reality. Yes I simulated different arrangements and tried to get the strongest field possible in the center ob the whole setup. The model is only 2D though and I am going to try a 3D simulation with a different software soon, to make sure the problem does not stem from that.

From these results it would suggest to have about 0.8T in the center between the arrays. Even though the arrangement is not 100% correct because the magnets are not real squares and have small gaps between them, this does not seem to make a big difference when I tried to account for that as well.

The magnetic field is used for detecting an out of plane motion of a MEMS resonator that is placed in the center on a PCB. The only real requirement is to have a strong magnetic field, but the limitation is that the PCB has to fit in between. Since the whole setup has to be inside a vacuum-chamber there is not much space left. So the 35mm ring is already the end of available space.

There is more space above and below the magnets and i was thinking of adding another layer of Halbach-Arrays but I first wanted to look at a 3D-Simulation of that.