Model simulation results, part 1

At the request of many families, here are some results.

The following results where compiled like this:

1. The FEMM scripts simulated the “Halbach Rotor” (HR) and the “Sparse Rotor” (SR) motor models while exploring several variable variations (like I explained before), dumping the results to file; Used constants where 50 turns per stator tooth and 100 Amps per phase.
2. The results were parsed into a spreadsheet table (you can download it here in ODS format – change the extension to “.ods” before opening);
3. Then I filtered out the candidates that generated less than 500Nm torque;
4. Then I applied a “score” to each candidate according to my personal criteria: Score = 3 * (Nm/Euro) + 2 * (Nm/kW) + 1 * (Nm/kg). The ratios are weighed by their average before used. This means that, for me, a design’s cost-effectiveness is 3 times more important than it’s magnet weight, and the energy efficiency is 2 times more important than it’s magnet weight. If I were rich, this would be different. If you have alternative criteria to propose, I’d like to hear it.
5. Then I sorted the survivors by their score, and put them on the graph below. They are sorted decreasingly left-to-right according to their score (which does not show in the graph). The graph presents the most interesting data: variant name, max torque, Nm/Euro, Nm/kW, Nm/kg.

I reduced the size of the graph here to a thumbnail because it is huge. Click on it to get to the full-size thing (3686*1145 px).

Here are the Top15 candidates descending by order of their score.

Model Magnet Poles Occ	Mags	Kg	Nm	Nm/Kg	Nm/kW	Nm/€	€
SR 11(20*10*5) 60 85%	560	4,2	1650,04	392,87	93,97	5,89	280
SR 7(15*15*3) 36 85%	420	2,14	843,81	393,94	85,41	4,1	205,8
SR 11(20*10*5) 36 85%	336	2,52	706,17	280,23	67	4,2	168
SR 2(7*7*7) 60 85%	1540	4	1244,63	310,85	73,65	3,37	369,6
SR 10(20*4*2) 60 85%	1120	1,34	1207,74	898,62	68,78	2,4	504
SR 9(19.1*12.7*6.4) 48 85%	448	5,38	1343,48	249,9	100,11	2,88	465,92
SR 6(15*4*4) 60 85%	1400	2,52	1352,62	536,75	82,18	2,42	560
SR 3(10*10*5) 60 85%	1120	4,2	1650,04	392,87	93,97	2,42	683,2
SR 10(20*4*2) 48 77%	896	1,08	828,12	770,2	58,94	2,05	403,2
SR 10(20*4*2) 48 85%	1344	1,61	1147,53	711,51	81,67	1,9	604,8
SR 2(7*7*7) 48 85%	1232	3,2	813,07	253,83	60,14	2,75	295,68
SR 10(20*4*2) 60 64%	560	0,67	514,35	765,4	29,29	2,04	252
SR 6(15*4*4) 48 85%	1680	3,02	1280,88	423,57	97,26	1,91	672
SR 6(15*4*4) 48 77%	1120	2,02	935,03	463,8	71	2,09	448
SR 3(10*10*5) 48 85%	896	3,36	1170,99	348,51	83,34	2,14	546,56

The first column includes the input variables of the simulation: model, dimensions of the magnet, number of magnetic poles, and the percentage of stator occupied by the stator teeth. The remaining columns are all calculated outputs.

The “Mags” column holds the number of magnets used; the “Kg” column holds the total weight of magnets; the “Nm” holds the maximum stall torque of the motor; the next 3 you already know; and the “€” column holds the total price of the magnets in Euro.

Important note: the electric power (kW) was calculated in pure DC; this is a very basic approximation of the real motor power, since it does not take into account the losses or the back-EMF that occur during rotation. That is something that won’t be easy to do with FEMM… but anyway, its still valid for stall (zero speed).

Various things are evident here (and after you examine the full data set):

1. The higher the number of magnetic poles, the higher the torque.
2. The closer the stator teeth are to each other, the higher the torque.
3. The magnet dimensions are not directly responsible for torque, we must take into account the strength (grade) of the magnet type as well (which is not shown here); And even then, there is an interplay between the effective “curveness” of the magnetic pole (as achieved by joining several flat magnets together in a round configuration) and the stator tooth.
4. I’m glad I set up this automated system, otherwise I would never be able to pick a good combination of magnets and geometry by manual trial-and-error.

So, judging from these results, the best candidate would be “SR 11(20*10*5) 60 85%” (Sparse Rotor, magnet = 20mm*10mm*5mm, 60 poles, 85% stator occupation), capable of 1650 Nm, for a modest price of 280 Euros in 4,2 kg of magnets.

However, there are still 2 problems:

1. I haven’t explored all magnet options, because of a nasty script bug that causes error accumulation and geometric failure of the simulation models in FEMM, when larger magnets are used in the “Sparse Rotor” model;
2. The comparison between the Sparse and Halbach models is not fair, because of the thickness of flux-carrying iron core in the rotors. The Sparse Rotor is much easier to place right in the middle of the available space, no matter which magnets are used. The Halbach Rotor, however, can only be placed at certain specific radii because the magnets have to sit side-by-side all around the rotors. So, depending on the number and size of magnets used, the Halbach Rotor will have a different radius, whereas the Sparse Rotor always has the same radius. This difference has an important consequence not only in the torque’s “arm” length, but also in the space available for the rotor iron core that sits outside the magnets. The Halbach variants often have less iron to carry the flux than their Sparse counterparts.

These two problems have to be solved before a total candidate list is produced. I intend to tweak the Halbach model in order to give it enough iron thickness to compete with the Sparse model. As to the bug… oh well, I’ll get it some day.

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