Field form factor and choice of poles

Field form factor

The field form factor $\psi$ (or $K_f$) is the ratio of average gap flux density over a pole pitch to the maximum gap flux density:

$$\psi = \frac{B_{av}}{B_g} \approx \frac{\text{pole arc}}{\text{pole pitch}}$$

Its usual value is 0.64–0.72.

Factors in selecting the number of poles

1. Frequency: $f = Pn/2$ should usually be 25–50 Hz. More poles raise frequency and iron loss in the armature.
2. Weight of iron: flux per pole falls as $P$ increases, so the yoke and armature core become thinner; iron weight falls.
3. Weight of copper: armature end connections are shorter with smaller pole pitch, so armature copper falls; field copper changes little.
4. Armature reaction: armature AT per pole $= ac\,\pi D/2P$ falls with more poles, reducing distortion and the extra field mmf needed.
5. Current per brush arm: for a lap winding the current per path ($I_a/P$) should not exceed about 200 A; large-current machines need more poles.
6. Commutator length: more poles give more brush arms with less current each, so a shorter commutator.
7. Labour and cost: more poles mean more field coils and parts, so more labour.
8. Flashover: voltage between brush arms and the voltage between segments must stay within safe limits.

So the number of poles is chosen as a compromise. Usual choices: 2 poles up to about 5 kW, 4 poles for about 5–100 kW, and 6 or more for larger machines.