I think I have to eat my hat a little bit here. I just did some more modeling, trying to do a more quantitative analysis of the different scenarios. All of these look at a partial cycle (6 magnets) of the 30-degree configuration. I changed a few other things, so these results are not directly comparable to the previous models.
- Round magnets only (no steel)
- Round magnets with steel backing, but nothing in front
- Round magnets surrounded by steel level with the magnet faces
- Square magnets with no steel
These plots show flux density in the radial direction across the middle of the airgap (the useful flux). The important bit of data is basically the peak flux density (don't mind the negative sign). The magnets-only case actually shows the highest flux density of the round magnets, with the steel-surround case the lowest. It's worth pointing out that there's only about 10% difference here between best- and worst-case, but that's exactly opposite what I've been saying. Given the rough nature of these simulations, I'm going to call those all roughly equivalent.
But, note the plot for the square magnet array. Using square magnets gives you about a 27% increase in magnet volume over the round ones, but a 100% increase in the flux density.
So, a square-array is still more efficient, but it doesn't look like a round array is as bad as I thought it'd be without some steel. I'd say it's time for enoob to start making some metal shavings to see what happens in the real world.