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Originally Posted by Max Lobovsky
But isn't speed proportional to voltage for a given load? (ie speed=V*someConstant). In that case, we have
power = ((V-V*k*kv)^2)/armature resistance
and hence
power = ((V*(1-k*kv))^2)/armature resistance
Anyway, I think there is some very obvious and simple evidence that your data is wrong. I would guess that most of the community gathered data for RPM/torque/current curves were gathered using Victors to control voltage, and all these curves report the expected linear curve, and therefore, the Victor must be outputting a linear voltage.
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Let's get a better look at this. The equation that Rick quoted is input electrical power derived from Ohm's Law for power, P=V^2/R. In the case of the motor, the available voltage for determining armature current (for DC permanent magnet motors) is the power source voltage-the counter EMF produced by the motor. CEMF varies with speed, hence the introduction of the speed constant and CEMF spec as a reduction in the available voltage. V-(speed*kv)=voltage available to motor winding. Then the reults are simply plugged into Ohm's Law for power as above. Unfortunately, armature resistance is not the only loss that affects total series resistance. Brushes, wiring, armature connections, etc. are all losses that will affect current through the armature and heat will change all of these. All of the losses summed together (electrical and mechanical) determine the output power vs. input power, or efficiency. That is why efficiency is never 100%!
Max, the data sheets are provided by manufacturers and cannot use controllers. All of the variables must be tightly controlled in order for porduction specs to be guaranteed. Imagine what would happen if only half of the motors in the four million CD players you just made, could not meet RPM as specified.