文档介绍：We also assume that the rotor and stator have current distributions that are axially (z) directed
and sinusoidal:
S
Kz = KS cos pθ
R
K = K cos p (θφ)
z R −
Here, the angle φ is the physical angle of the rotor. The current distribution on the rotor is
fixed with respect to the rotor. Now: assume that the air-gap dimension g is much less than the
radius: g << R. It is not difficult to show that with this assumption the radial flux density Br is
nearly uniform across the gap (. not a function of radius) and obeys:
S R
∂Br Kz + Kz
= µ0
∂Rθ− g
Then the radial ic flux density for this case is simply:
µ0R
B = (K sin pθ+ K sin p (θφ))
r − pg S R −
Now it is possible pute the traction on rotor and stator surfaces by recognizing that
the surface current distributions are the azimuthal ic fields: at the surface of the stator,
S R
H = K , and at the surface of the rotor, H = K . So at the surface of the rotor, traction is:
θ− z θ z
µ0R
τ= T = (K sin pθ+ K sin p (θφ)) K cos p (θφ)
θ rθ− pg S R − R −
The average of that is simply:
µ0R
< τ>= K K sin pφ
θ− 2pg S R
The same exercise done at the surface of the stator yields the same results (with opposite sign).
To find torque, use:
3
µ0πR
T = 2πR2 < τ>= K K sin pφ
θ pg S R
We pause here to make a few observations:
1. For a given value of surface currents Ks and Kr, torque goes as the fourth power of linear
dimension. The volume of the machine goes as the third power, so this implies that torque
capability goes as the 4/3 power of machine volume. Actually, this understates the situation
since the assumed surface current densities are the products of volume current densities and
winding depth, which one would expect to increase with machine size. Thus machine torque
(and power) densities tend to increase somewhat faster with size.
2. The current distributions want to align with each other. In actual practice what is done is to