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I have a hobby motor that claims to be a 2200KV motor. This particular one is a 4-pole motor.

Using a drill, I spun the motor at 1312 RPM. On an oscilloscope I see 1.3V peak-to-peak waveform between two of the phases (a pretty distorted sine-ish wave) having a frequency of 43.73 Hz.

Converting this frequency into radians per second, I get 274.649 radians per second. Calculating KT from this I get 0.65 volts peak / 274.649 rads/sec = 0.002367 N*M/Amp, which just seems really low.

Since the motor is a 4-pole motor, whose electrical frequency is twice the mechanical frequency, should I have used half the frequency seen on the oscilloscope? That would make the calculation 0.65 volts peak / 137.325 rads/sec = 0.0047333 NM*Amp, which might seem more reasonable.

I guess the main question is -- when calculating torque constant by dividing the back-EMF voltage by radians per second, is it the radians per second of the shaft speed itself, or radians per second of the back-EMF frequency (which increases for each pole-pair)?

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You are correct - motor constants asre calculated from shaft speed and you must take into account the number of pole pairs if you use the output frequency of a driven motor to determine speed. Shaft speed (mechanical rotation) is the basis for calculating torque and velocity constants for motors. Therefore, for a four-pole motor (or any number of poles) driven by at 1312 rpm, the shaft speed should be used (1312 rpm = 137 rad/sec).

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