# Why are motor constants (Kt, Ke) not same, given the motor spec?

I have been struggling to find correct values for Kt (Torque constant ), Ke (Back EMF constant ) of the motor with 20.4:1 Metal Gearmotor 25Dx50L mm HP 12V (https://www.pololu.com/product/3203/specs).
But they are not close each other.

# As far as I know, Kt and Ke should be same or close each other.

Given the spec, I calculated as below.

Kt = Stall torque / Stall current = 85 oz·in / 5600 mA = (85 x 0.007 Nm/oz-in )/ 5.6 A = 0.1062 Nm/ A

Ke = Rated Voltage / No load speed =12 V/ 500 rpm = 12 / (500 rpm /60 * 2pi ) = 12 / 52.5 = 0.2292 Vsec/rad

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Although they are supposed to be same or roughly close each other, Kt and Ke are totally different each other !!

Taking small approximation error ( 10~20 %) in this calculation into account, the calculated value from given spec doesn’t still make sense to me.

Am I doing something wrong ?
Solving this issue is urgent, so it would be very thankful if you could figure out.

Hello.

We have recently started to better characterize our gearmotors by measuring the speed and current at different known loads between free run and stall, which makes it possible to compute some of these motor constants more accurately than just looking at our approximation of the stall endpoint. We have some very preliminary data for item #3203, and the slope of the torque-vs-current curve in the region where it is still linear (i.e. where the current is less than 50% of the stall current, so the effect of motor heat on performance is reduced) is approximately 0.16 Nm/A. It’s still not quite equal to Ke (0.23 V*s/rad), but it’s closer.

By the way, there is a similar thread here about a different gearmotor that you might also find relevant.

Grant

Hello, thank you for kind reply.

If you could share any graph or measurement for the motor constants of the item to my email, I wish to compare with mine. It would be very thankful for helping me.

Also, could you provide the link again as it seems not working ?

Oops, sorry; the link is fixed now! Here are the preliminary performance curves for that gearmotor:

3203-12v-preliminary.pdf (15.8 KB)

Grant

Thank you very much for valuable information.
This data looks better than before and Kt, Ke got closer each other.

Thank you.