Calculation of Torque Constant For DC-Brush Motors

[djberry555]

I am currently trying to design an armature for an electric motor. In trying to work out what my expected torque characteristics would be, I ran across an equation which calculates this value using flux, # of conductors, current, armature paths, and # of poles. I know the equation is correct because I used it to verify the parameters of a known motor. However, nowhere in the equation does it mention the diameter of the armature. Since packaging is an issue, I would like that parameter as part of my analysis. Does anyone know where to find some literature that shows how the armature diameter influences motor torque?

 

[waross]

For starters, torque is proportional to rotor diameter.
As the armature gets smaller, (less surface area) the total flux drops for the same flux density. This will also reduce torque. If you try a couple of simple designs of different diameter rotors your software should show the difference.
respectfully

 

[Clyde38]

Basic sizing guidelines are provided in “Design of Brushless Permanent-Magnet Motors” by J.R. Hendershot and T.J.E. Miller. This discusses a “classical output equation which applies to all electrical machines”;
T=KDr2Lstk, where K is the output coefficient, Dr is the rotor diameter and Lstk is the rotor stack length.

 

[aolalde]

How this expression compares to yours?

T = 0.1175*Z*phi*Ia*P/m*R/100,000,000

T = Torque (Lb.-Ft)
Z = Total number of armature conductors
Phi = Total flux per pole (Lines)
Ia = Armature current (Amperes)
P = Poles
‘m = parallel paths
R = Conductors average radius (Ft)

 

[djberry555]

My expression is similar to the one you posted aolalde, however my expression does not contain the conductor average radius. Another thing I was considering is that I know that if I decrease the wire diameter, I will also decrease the torque. This really isn't taken into account in the above equation (current is a factor, but if I am designing an armature from scratch I really don't know what I can expect the current to be). I am really looking to try to understand the physics behind it and not so much just finding a quick formula. I should say my background is in mechanical engineering so I really don't have a lot of experience with electronics and magnetisim, but that is why I am trying to learn.

 

[aolalde]

The wire cross sectional area will define the Armature Resistance. Except for the locked rotor condition, the current will be mainly regulated by the counter electromotive force "emf" induced by the magnetic flux in the armature winding and proportional to the speed.

Va = emf + Ia*Ra
emf = Z*phi*rpm/60*P/m/10,000,000
Va = Applied Armature voltage.