Stack dimension relationship to power

[HomeMadeSin]

I've heard that for AC motors, P=(d^2)*L, where P is power, d is diameter of laminate stack and L is the stack length. True? If so, d is ID of stator, right? And P is watts?

 

[Aranrhod]

For a material of given permeability and a design of given air gap and constant supply frequency then yes I guess that Power = constant x d^2 x l (in other words the magnetic volume). But the formula is largely useless because the 'constant' depends on almost everything associated with the motor including winding type, speed of rotor, air resistance, magnetic circuit shape, bearing losses, lamination design and so on.

 

[HomeMadeSin]

Thanks Aranrhod. Is there any way to get an understanding of what variables affect the "constant" you mention? I just need a convenient way to determine the power (or specifically torque) of various motors by varying the diameter or length.For instance, if I need 0.76 lb ft of torque at 3450, and a motor with say 4.25" stack length and 0.9" diameter can produce only 0.11 lb ft, what diameter/length ratios would I need to get there?

 

[jbartos]

Suggestion: The relationships that are sought are more on an empirical side. For example:
Output HP = Co x N x L x D**2
where
HP is horsepower
Co is factor
N is r.p.m.
D is diameter or aigap or rotor in centimeters or inches
L is length in centimeters or inches
Also,

Co=Bav x q x eta x cos(fi)/(4 x 10**11)

Bav = Total pole flux FI / total area of the gap per pole
as if the pole faces were of smooth iron
q is the specific ampere-conductors per cm of periphery
eta is efficiency
cos(fi) is power factor