Choice of specific loadings in DC machine

The output coefficient $C_0 = \pi^2B_{av}\,ac\times10^{-3}$ shows that high specific loadings give a small machine. Their upper limits are set by the factors below.

Specific magnetic loading ($B_{av}$), usually 0.4–0.8 Wb/m²

1. Flux density in teeth: the teeth carry the gap flux through a smaller area. Tooth density should not exceed about 2.1–2.2 Wb/m² in dc machines; otherwise the teeth saturate and need a large field mmf.
2. Frequency of flux reversal: iron loss grows with frequency and $B^2$. High-speed or many-pole machines (high $f$) need a lower $B_{av}$.
3. Iron loss and efficiency: higher $B_{av}$ raises iron loss, lowers efficiency and raises temperature.
4. Size of machine: higher $B_{av}$ means smaller $D^2L$ and lower cost.
5. Field mmf: higher gap density needs more field ampere-turns, so more field copper and larger poles.
6. Armature reaction: a higher $B_{av}$ (stronger main field) keeps the armature mmf relatively smaller, which helps against distortion.

Specific electric loading ($ac$), usually 15000–50000 A/m

1. Temperature rise: more copper loss per unit surface; good ventilation allows a higher value.
2. Speed: fast machines cool better and can take a higher $ac$.
3. Voltage: thicker insulation at high voltage leaves less room for copper, so a lower $ac$.
4. Size of machine: large machines can take higher $ac$.
5. Armature reaction: armature AT per pole $= ac\,\pi D/2P$; high $ac$ means strong armature reaction.
6. Commutation: high $ac$ gives high reactance voltage and poor commutation.
7. Copper loss and efficiency: increase with $ac$.

Summary

The ratio $B_{av}/ac$ also fixes the ratio of iron to copper in the machine, so the two are chosen together.