# Brushless gear and force calculation thoughts

Hi all, I hope this is the right section.
I’m trying to use SimpleFoc to automate the rotation of a shaft and i would like to share my calculation about it, and see if I need a different motor.

Specs.
I need to rotate a shaft by approximately 17 degree in about 10 - 20 ms.
the amount of force I’ve measured to move the shaft, is about 17 kg with a lever 50 mm long.
With that data I have calculated a force of 0.85Nm to complete the work.

the actual simpleFoc setup is a geared brushless 20 teeth connected to another gear to the shaft 40 teeth giving me a mechanical advantage of 2.

So the question is, how I have to calculate the force I need from the motor?

Another question is: how to choose the motor?
what i’ve found is that there is an easy formula where we can estimate the motor torque.

based on that using a 12 V source, with a 0.1 ohm resistance and 800KV motor.
(8.3 * 120) / 800 = 1.2Nm
That is a lot of current for roughly 1Nm force.
moving to a lower kv motor seems to be a solution.

Hi,

The explanation in the linked blog is a little misleading. The motor torque constant (Kt) and the motor’s Kv rating are reciprocals of each other (when both in SI units):

Kv = 1 / Kt (in SI units).

See here: http://learningrc.com/motor-kv/
or just the the wiki page for motor constants: https://en.wikipedia.org/wiki/Motor_constants

More accurately, for 0.85 Nm torque with a Kv = 800 (RPM/V) motor you’d need:

Kt = 1 / Kv (rad/sec) = 1 / 84 = 1.2e-2 (Nm/A)
I = 0.85 / 1.2e-2 ~ 70 Amps.

This is still a lot of current - and so yes, you’d need to get a lower rated Kv motor.

I would go about finding specs for your motor a different way:

• you need to rotate a shaft 17 deg in ~15 ms, i.e. ~20 rad/sec (189 RPM), [aside note, with your 800Kv motor, you’d need to apply just 189/800 = 0.24 V to get the motor to spin at your desired velocity]
• you need to develop a torque of 0.85 Nm, hence the power your system develops is:
P = T * w,
= 0.85 * 20 = 17 [W]
where T - torque in Nm, w is rotational velocity in rad/sec.
• now, if your available voltage is 12 V, that means: 17/12 = 1.4 A
• and we can calculate the desired motor constants:
Kt = 0.85 Nm / 1.4 A = 0.61,
Kv = 1 / Kt = 1.65 [(rad/sec)/V] or
= ~ 16 [RPM/V]

Of course these are just back of the envelope calculations, and are not accounting for losses and inefficiencies in the system - but they should give you a rough idea of what kind of motor you are looking for and/or if you need to adjust your gearing or other system parameters to accommodate motors that you do have on hand.

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Is your torque of 0.85 correct? Should it not be 8.5Nm? 17kg = 170N, 170N * 0.05m = 8.5Nm? Just double check, it‘s late already.