Motor winding constants

Motor winding constants are changed by how the available copper space is wound.  For example if you already have a motor datasheet and the motor has a back EMF constant of 10 V per kRPM then you could modify the back EMF constant to 20 V per kRPM by doubling the number of turns in the winding.

The relationship between the new motor winding constants and the previous constants is really quite simple: the new back EMF constant, Ke prime, is equal to the old back EMF constant, Ke, times the ratio of the new turns divided by the old turns. The same equation holds true for the torque constant. Both the resistance and the inductance vary as the squared of the ratio of the new turns divided by the old turns.

To most people the fact that the inductance varies with the square of the turns ratio makes a great deal of sense while resistance varying with the turns ratio squared seems a bit puzzling. However think of it this way, by doubling the number of turns the length of the wire has doubled, doublilng the length and therefore the resistance. Also, to fit twice the turns into the same cross-sectional area you now need to half the cross-section of each wire, again doubling the reistance. The result of this is that the resistance varies by the square of the turns ratio. This holds true for resistance in any device where the cross-sectional of area available for winding is fixed such as in inductors, solenoids or solenoid brakes.

One of the things that becomes obvious is that the electrical time constant of the motor is a size constant since both the inductance and resistance vary by the same ratio.

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