Cogging takes place when the iron circuit has a variable reluctance that aligns with the magnet.
The worst cog occurs with teeth the size and shape of the magnet and the number of magnets and teeth are the same.
One trick is to use a non integer for the number of teeth so that only one tooth is at maximum cog at any instant. With a bit of luck you can make the average cog torque round the circle zero.
With tooth numbers equal to magnet number or an integer you can avoid cog by spacing the magnets such that you get the same effect as the non integer tooth situation. The magnet spacing ends up with a gap equal to a tooth width or thereabouts.
Skewing works by making the leading edge of a tooth come to one end of the magnet while the trailing edge comes to the other so that the tooth is pulled one way at one end and the other way at the other, the net pull is zero.
Anything that makes the attraction ill defined will reduce the effect and that includes rounding poles or magnets but the thing probably can't be analysed and comes to trial and error and you may not get a perfect result.
The skewing and asymmetric magnet spacing can in theory be calculated such that the angle gives you the condition where the magnet ends line up to opposite sides of the tooth. The angle depends on magnet and tooth geometry but you can consider it as the equivalent of designing a helical gear that transfers torque from one tooth to the next smoothly.
I think Peter " Dinges" has done the calculations for the ideal case for induction conversions. For things like the F & P there are more problems as the angle needs to be large to deal with short magnets and wide tooth spacing. These angles need to be for the circular arc not actual skew of the pole or magnet face angle as that will depend on core and magnet length.
Probably if you use the theoretical angle it will be fairly good and a bit of rounding here and there would make it less critical.
Flux
