Hi Bill,
You should be able to find a text book which teaches you all this. But in the mean time:
Eg = Kt * w * Flux
Tem = Kt * Flux * Ia
Where:
Eg is the generated voltage in the armature
Kt is the torque constant of the motor, depending on the turns, poles, etc.
w is rotational velocity
Flux is the flux per pole (I can't make those Greek symbols, Phi, I think)
Ia is the armature current
Tem is electromagnetic torque (shaft torque before rotational losses)
Pretty simple. The rest is just Ohm's law and Kirchhoff's equations for circuits.
The flux is determined mainly by the field excitation. Or MMF, magnetomotive force.
Flux = function (N * If)
Where N is the numbers of turns in the field coil
If is the field current.
The function is linear up to a point called saturation. This saturation is dependent on the magnetic circuit design for that particular motor. Once sufficient MMF (or ampere turns) is provided by the field coil, little or essentially no further increase in flux will be realized.
So, if you manipulate the first equation, you will see that for a fixed voltage (Eg taking in consideration voltage drops due to resistance and brushes), the speed (w) is inversely proportional to flux. So, field weakening is simply the reduction of flux to increase speed.
The opposite works only so far. An increase in flux will slow the armature. But one soon reaches a point called full field, where no further increase in flux is possible. The speed at that point is called base speed for that voltage.
All the while, (while you're messing about with flux to change the speed), realize that you are also changing the torque because the same flux is used in that equation. So you decrease flux to increase speed, it decreases torque. So power is about the same. You don't get something for nothing.
This is a pretty basic explanation. For rough approximations, those simple equations will work pretty well. But this is hardly enough for motor, or control, or system design. There are some things to bite you in the a$$, like commutation.
Hope that showed you something.
major