Hey

I was wondering (not wondering actually, this is for a project) what determines the maximum speed for a motor under a load. (I'm not sure about the terminology, but

what I mean is the following,) if a wheel of a given radius attached to a motor and gearbox (with a certain gear ratio) was used to climb up a rope, it's maximum velocity is slower than if the wheel were spinning by itself, without any external forces/torques applied. (I've tried this out). I know that normally, the maximum speed is determined by the voltage of the electricity supply (and torque by the current), but what happens when the motor has to do work? (does the voltage drop change or something?)

Thanks

## Maximum speed of a motor under load

**Moderator:** msmod

### Re: Maximum speed of a motor under load

Also, I'm referring to a simple DC motor with brushes..

### Re: Maximum speed of a motor under load

In an ideal motor with no losses and a simple geometry, it's easy enough to use the expressions for force on a current carrying wire to calculate the torque produced by the motor in terms of the current. If it's turning quickly, one can average these over a cycle to get an average torque.

Next, if the motor is turning at constant angular speed, then the torques add up to zero, so one can then calculate

motor torque = load torque (+ torques due to various losses if not ideal)

A complication is that this gives you load torque in terms of current. If you supply a constant voltage, the current

http://www.animations.physics.unsw.edu. ... .html#back

Joe

Next, if the motor is turning at constant angular speed, then the torques add up to zero, so one can then calculate

motor torque = load torque (+ torques due to various losses if not ideal)

A complication is that this gives you load torque in terms of current. If you supply a constant voltage, the current

*decreases*with angular speed, because of the back emf.http://www.animations.physics.unsw.edu. ... .html#back

Joe

### Re: Maximum speed of a motor under load

Thanks for the reply

When is the angular speed at a maximum? Given that the motor/gearbox/wheel 'system' requires a certain amount of torque to climb vertically up a rope (including inefficiencies), if one supplied a constant voltage to a certain motor, with a given wheel (which does not slip on the rope), how would changing the gear ratio affect the eventual climbing speed up the rope? If one had a gear ratio so that the torque output was just large enough for the system to climb, would the eventual maximum climbing speed be faster than if a slightly larger gear ratio (and thus larger torque output) were used? I have tested this in practice and it seems that if the gear ratio and torque are only just large enough for the device to climb, the eventual maximum climbing speed will be very small. If a slightly larger gear ratio is used, then the maximum speed is significantly higher. Finally if a very large gear ratio is used, then as you would expect, the maximum speed is also very small.

When is the angular speed at a maximum? Given that the motor/gearbox/wheel 'system' requires a certain amount of torque to climb vertically up a rope (including inefficiencies), if one supplied a constant voltage to a certain motor, with a given wheel (which does not slip on the rope), how would changing the gear ratio affect the eventual climbing speed up the rope? If one had a gear ratio so that the torque output was just large enough for the system to climb, would the eventual maximum climbing speed be faster than if a slightly larger gear ratio (and thus larger torque output) were used? I have tested this in practice and it seems that if the gear ratio and torque are only just large enough for the device to climb, the eventual maximum climbing speed will be very small. If a slightly larger gear ratio is used, then the maximum speed is significantly higher. Finally if a very large gear ratio is used, then as you would expect, the maximum speed is also very small.

### Re: Maximum speed of a motor under load

Making the approximation that the motor is ideal, you can either calculate or measure the torque as a function of current under a given condition. Then you need to consider the back emf at different rotation rates and calculate how much this reduces the currents.

An ideal gear system increases the torque by the same factor that it reduces the angular velocity (omega).

Of course the motor and gears won't be ideal, so a calculation like this will overestimate the possible omega under any load. If you want a more accurate answer you'll need to look up the specifications or make measurements yourself.

Joe

An ideal gear system increases the torque by the same factor that it reduces the angular velocity (omega).

Of course the motor and gears won't be ideal, so a calculation like this will overestimate the possible omega under any load. If you want a more accurate answer you'll need to look up the specifications or make measurements yourself.

Joe