Highspeed with gearbox or low speed for brushless motor?

Question

I'm attempting to control a small vehicle at relatively slow (.5 m/s - 1 m/s) speeds, but with extreme accuracy (1mm). For the drive system, I'm considering using brushless motors as they have a much greater power / volume ratio than I am able to find with brushed motors, especially at this small size.

I will be using wheels between 1" and 2" diameter, so the RPM I will be looking for is between 150 - 500 RPM at max. This would suggest either driving the motors at a low speed directly, or driving them at a high speed and gearing them down. As I understand it, both setups will give high torques, as brushless motors decrease torque with speed. With brushed motors, it's quite obvious that a gearbox is necessary as otherwise there is no torque in the system, but here the choice isn't as clear, which is why I am asking.

tl;dr Use brushless motors at high speed with gearbox or low speed (ungeared) for high torque / low speed / high precision application?

Answer 1

Page 7 of this PDF states that, "A permanent magnet DC brushless motor behaves like any permanent magnet DC brush motor."

You can read more about DC motor operation at this MIT site. I'm not sure if you've got a typo or what you're trying to say, but your question states, "brushless motors decrease torque with speed," after you state that using a gearbox and directly controlling the motor at low speed both, "will give high torques."

If you're looking to do speed control at a very low percentage of the motor's speed, I would suggest using a gearbox simply because you won't have much headroom to modulate the motor's speed. For example, assume the motor's top speed is 50,000RPM. You want to control the motor to 150RPM +/- 10RPM, which means that, if you're going to directly operate those motors at low speed with no gearbox, you need to be able to control the motor speed to within +/- 0.02% of the top speed. This will be hard, and you would probably actually want control within +/-1RPM, or 0.002% of top speed.

If you were to use a 100:1 gearbox, then top output speed becomes 500RPM, which means now you have to control motor speed to +/- 2%, or 0.2% for the +/-1RPM case, which suddenly becomes far more manageable.

The downside to using a gearbox is that they are physical, mechanical devices, meaning that they will have friction, backlash, and other drawbacks. Essentially you wind up paying a percentage of your motor's power for the advantage that speed becomes easier to control.

tl;dr - use gearboxes.