Originally Posted by
Bear5k
Now you are getting into a more complicated question (system-level vs. motor). Assuming the same payload for each and decent quality servo drives, the motor attached to the ball screw with the 5mm lead will be producing (and consuming) more power than the one with the 25mm lead -- most likely -- but this will be almost entirely due to the increased friction in the 5mm lead and the accumulated electrical inefficiency in the motor spinning at higher RPM. This last bit is a guess based upon the motors I've researched. Since it would be a result of practical implementation, it's a testable hypothesis rather than a derivable fact.
In pure theoretical physics, they would be doing the same amount of work (force times distance) and consuming the same amount of power (work over time; force times distance divided by time). Think about it this way:
To get to the same linear speed, the 5mm lead screw has to turn 5x as much, but with only 1/5th the load per revolution. The 25mm lead screw would need to turn 1/5th as much, but it will need 5x the torque per revolution. This may be the source of the gearing question?
The good thing about servos is that they will only consume as much power as needed, up to their limits (they are more efficient than steppers, which pump out a lot of waste heat). Thus, if you sized the motors for the torque requirement of the 25mm lead and the angular velocity requirement of the 5mm lead, you would see both screws operating well within their limits. The 5mm lead being able to take on more payload (5x more) at that same speed, while the 25mm screw could take on more speed (5x as much) at the same payload.
Make sense?