# Speed/torque curves for brushless DC motor

## Main Question or Discussion Point

Hi everyone. I came across this site yesterday during some targeted Googling and thought I'd give it a shot. I have a basic question about speed/torque curves for brushless DC motors.

I would like to compute a speed/torque curve for a small three-phase brushless DC motor that I have. It doesn't need to be exact but I'd like it to be theoretically close.

I've read plenty online about how this can be done by constructing a plot with speed on one axis and torque on the other, then drawing a line between speed at zero torque and torque at zero speed at the intercept of each respective axis. Here is an example: http://lancet.mit.edu/motors/motors3.html. This level of simplicity is fine for my purposes.

My motor's data sheet gives me everything I need to create this plot: winding resistance (0.54 Ohms), back EMF constant (0.021 V/rad/sec), and torque sensitivity (2.97 oz-in/A). The data sheet also lists stall torque (13 oz-in), peak torque (15 oz-in), and no-load speed (130 rad/sec) at 2.73 V operation. Great. Using this I can run the equations, confirm the results, and plot the speed-torque curve for 2.73 V operation.

What I want is to produce the same curve for 15 V operation. When I compute the stall torque for 15 V (Kt * V / R = 83 oz-in), the result is much, much higher than the motor's stated peak torque (15 oz-in). As I understand it, peak torque does not increase as voltage increases, and so I'm left with a computed stall torque that doesn't make sense to me.

Here (finally) is my question: Is the torque-speed curve for this motor at 15 V simply the line intersecting the torque axis at the motor's peak torque (15 oz-in) and the speed axis at the no-load speed for 15 V (Vt / Kb = 714 rad/sec)? If not, what the heck does the speed-torque curve look like at this voltage? Am I trying to do something naughty by running this motor at a voltage that is so much higher than the peak torque voltage (2.73 V) on the data sheet?

Thanks in advance for any insight you might be able to provide.

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