DC Motor RPM

tachometer

More quietly.

See-for instance:

http://zone.ni.com/devzone/cda/ph/p/id/46

However Google is better!

Well first you should define the magnetic fields using Maxwell's equations. You then apply the Lorentz Force law equations to the perpendicular rotor current (a little derivation required here) or you could just look up the DC Motor operation. This will give you the force equation applied to the rotor wires. This force becomes torque at the motor shaft. This torque can then be applied to Newton's rotational kinematic laws to tell you the angular acceleration of the rotor. You will have to measure or calculate the moment of inertia at the motor shaft for rotor mass and anything attached to the motor shaft to generate a dragging torque against the motor generated torque. We're not done yet though, the motion of the wires through the magnetic field will also generate an opposing voltage in these wires that reduces the current in these wires. You must incorporate Faraday's law to make this opposing back EMF which will change the current equation.

Now I didn't include the important additional homework in the generation of the magnetic field in a core material that has hysteresis because you have more than enough homework to do now.

You should now notice our FAQ clearly states that we do not do homework here.

OK, lets assume this is not homework.

What is the application, motor NP data, running amps, volts, field amps, do you have the motor data sheets with performance curves?

Or lets say the motor NP is 1800 rpm at 500vdc, 5amp field (hot).

You are running with a 5 amp field and half armature volts, then the motor is running about 1/2 speed, about 900 rpm.

Also more rigorously:

Vt = Eg + IR

Eg = Kφω

measure I, measure armature circuit R, measure Vt, determine φ and K from field current and motor data sheets (field weakening curves), solve for Eg.

Of course if you really want to know the speed - use a tachometer.