Halbach demystified

Posted on January 30, 2008

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Now I try to understand the correct way of using the Halbach magnetic layout.

Brett White, the creator of a couple of hybrid electric trikes, has reverse engineered an explanation on how the CSIRO motor functions (half-way down that page). As far as I can tell, there is nothing extremely novel in that motor. True, the stator is kind of original, but it could be replaced with multi-winding coils, could it not?

He points to this Ph.D. thesis by Stanley Robert Holm (Randse Afrikaanse Universiteit, South Africa), that deeply and thoroughly describes a permanent magnet motorized flywheel. On page 165, fig. 8.1, he shows how the Halbach array can be used in substitution of a normal radial array for a 4 pole machine.

halbach_equivalents_by_holm.png

Fig. 1 – Equivalent Halbach and Radial magnetic layouts for a 4 pole machine.

(Copyright Stanley Robert Holm)

As we can see, the number of poles should not change between radial and Halbach layouts. From this I can see an error in my Halbach simulations: I’ve been comparing oranges to apples. It’s not fair to compare 5 radial magnets against 5 halbach magnets, since only 1 in 5 of the halbach magnets will be outputting flux into the useful direction. What must be kept equal is the number of effective poles (duh!).

So I drew up a new simulation, this time doing a fair comparison.

nohalbach.png
Fig 2 – Normal (radial) magnet layout with 4 poles.

halbach.png
Fig. 3 – Halbach magnet layout with 4 poles.

Now we’re cookin’!!!! :D Not bad at all; for the same exact setup, the Halbach layout exactly doubled the tangential force while halving the radial force! Great.

Just in case, I ran another comparison again with the magnets in radial position, but with twice the density (2 magnets up, 2 magnets down, 2 magnets up…):

doubleradial.png
Fig. 4 – Normal (radial) magnet layout with double density for same 4 poles.

Results of this experiment:

  • Normal (radial with intervals) layout produced 264 N tangential force;
  • Normal (radial) double-density layout produced 383 N tangential force;
  • Halbach layout produced 541 N tangential force.

Conclusion:

Halbach layout is the clear winner, if you know how to arrange the magnets in relative position to the stator coils. Therefore, it is a great technique, as long as you have a good time-control of the stator currents.

I deliberately chose those relative positions for the “stator” magnet thinking that they would be the highest tangential force generating positions; but just in case I am wrong, I decided to run a full scan of all positions in small steps, taking the X and Y forces.

Here are the movies (yes, I like making these things ;) ):

Fig. 5 – movie of relative magnet position scan with a single radial layout.

Fig. 6 – same thing, but with a double radial layout.

Fig. 7 – same thing, but with a halbach layout.

Now, the interesting part: the results!

halbach-scan-x-force.png

Fig. 8 – Tangential force (X axis) graph for all magnet layouts, relative to position (please don’t consider the position as exactly equivalent for all layouts, I ignored that during model construction)

halbach-scan-y-force.png

Fig. 9 – Radial force (Y axis) graph for all magnet layouts, relative to position.

  • Single radial layout: maximum X force (tangential) = 547 N
  • Double radial layout: maximum X force (tangential) = 882 N
  • Halbach layout: maximum X force (tangential) = 1166 N

Halbach confirmation achieved beyond any doubt. That closes the subject of rotor design.

Now in the subject of stator design, can anyone tell me why “Wolfgang’s Aircrafts and Engines” designed such a strange stator for a radial flux Halbach motor?…

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