I need a point in the right direction with the following question:

Q: The rotor of a d.c. motor had an original diameter of 30 cm and an air gap under the poles of 2mm. During refurbishment the rotor diameter was accidentally reground and was then undersized by 0.5mm. Estime by how much the field MMF would have to be increased to restore normal performance. How might the extra MMF be provided?

All I can think of to solve the question is ohms law (magnetic). The reluctance of the air gap I can solve but not the flux?

 

http://www.national.com/onlineseminar/2004/magnetics/Magnetics_033104.pdf

Start at page 33

 

The air gap flux is notionally

\(\Phi=\mu_0 \frac{MMF}{g}A \ \ [Wb]\)

Where
g = the total air gap
A = the rotor surface area
μ0 = free space permeability

Presumably we want to keep the pole tip flux the same.

For the original condition

A1=k*D1=k*30 where k is an arbitrary (dimensional) constant for the motor.
g1=2mm

For the final ground condition

A2=k*D2=k*29.5
g2=2.5mm

Plugging in those values will give two values of flux for a given MMF

The ratio of the two fluxes (post grinding/original condition) will reduce to a ratio related only to g1,g2,A1 & A2. The ratio [let's call it 'r'] will be less than unity.

The MMF must then be increased (by 1/r) so as to restore the flux ratio to unity.