Torque in a DC motor (equations?)

[infamous_Q]

hey, I've been looking EVERYwhere for equations for torque in a DC motor. I've come accorss plenty too:

T = µBsinθ
and T = k(magnetic flux per pole)I <- where k is a "mechanical and conversion constant" and I is the current in the armature, and i couldnt' find the magnetic flux symbol key thing.


now here's where I am troubled...which is right? if ne of these are. and if it's the second one...wut the hell is k supposed to be?

thanx for any help guys...itd be real awesome if someone had this knowledge tucked away in the back of their heads.

 

[anorlunda]

@jim hardy , can you help with this question?

 

[jim hardy]

I'm mighty out of date and still use Imperial untsbut Torque = 7.04 K X Φ(which is flux) X Ia(which is armature current)
so T = KΦIa

to find K you establish flux, spin the motor and measure open circuit voltage it makes (so Ia = zero and there's no voltage drop)
Voltage = (same K) X RPM

Now that pesky 7.04 - where does it fit in?
It accounts for Imperial units of ft-lb and RPM.
If instead you use SI units NM and Radians/Sec you'll find the 7.04 disappears and a single constant, which i call "Metric K", works for both torque and voltage.
You should prove that for yourself. See this thread, especially post 23.
https://www.physicsforums.com/threa...-motor-the-same-regardless-of-voltage.911438/

Any help?

old jim