With your help I made the first design.
I see that's a three-phase design. The geometry can be substantially improved, as follows:
- Change from rectangular coils to trapezoidal coils.
- Butt them up tightly to each other so they touch. The lines where they touch will be radial.
- D ~= 1/2 E, so a magnet would just cover the TWO coil-sides that are touching.
- The hole is ~E at the center of the magnet, so a magnet over the hole just (pretty much) covers the hole.
- Space the magnets ~ 1/2 E, so that the layout is like this, working clockwise:
a) The first magnet (N) is exactly over the combination of the right side of coil 1 with the left side of coil 2
b) The second magnet (S) has its right edge over the boundary between the right side of coil two with the left side of coil 3
c) The third magnet (N) is over the hole in coil 3
d) The fourth magnet (S) has its left edge is over the boundary between the right side of coil 3 with the left side of coil 4
e) (like a) The fifth magnet (N) is over the combination of the right side of coil 4 with the left side of coil 5
and so on around the device.
This makes the waveform of each phase work in six equal steps:
1 Ramp up from zero to max +.
2 Hold at max +
3 Ramp down to zero.
4 Continue ramping down to max -
5 Hold at max -
6 ramp up to zero.
At the position drawn (assuming clockwise magnet motion and the handedness of the coils causes N over left side to generate +):
- Coils 1, 4, 7 are at the boundary between steps 5 and 6
- Coils 2, 5, 8 are at the boundary between steps 1 and 2
- Coils 3, 6, 9 are at the boundary between steps 3 and 4