Choice of magnetic loading in induction machine

Specific magnetic loading ($B_{av}$) is the average flux density over the air-gap surface:

$$B_{av} = \frac{P\Phi}{\pi DL}$$

For induction motors it usually lies between 0.3 and 0.6 Wb/m². The following factors decide its value.

1. Power factor

The magnetising current depends mostly on the gap flux density. A higher $B_{av}$ needs more magnetising mmf, so the magnetising current rises and the power factor falls. Since an induction motor takes all its magnetising current from the supply, this is the main limit on $B_{av}$.

2. Iron loss and efficiency

Iron loss rises roughly as $B^2$ (and with frequency). A high $B_{av}$ raises core loss, lowers efficiency and raises temperature rise. High-frequency machines use lower $B_{av}$.

3. Overload capacity

A higher $B_{av}$ means fewer turns for the same voltage ($T \propto 1/\Phi$), so leakage reactance is lower and maximum torque is higher. A high value therefore improves overload capacity.

4. Flux density in teeth

The teeth carry the gap flux. Tooth flux density must not exceed about 1.7 Wb/m² (to avoid saturation and high magnetising current). With narrow teeth, $B_{av}$ must be lower.

5. Size and cost

From $Q = C_0D^2Ln_s$ with $C_0 \propto B_{av}$, a higher $B_{av}$ gives a smaller machine with less material and lower cost.

6. Quality of core material

Better (low-loss, cold-rolled) steel allows a higher $B_{av}$ without excessive loss.

Summary

So the designer chooses a value (about 0.4–0.5 Wb/m² for 50 Hz motors) that balances power factor and efficiency against size, cost and overload capacity.