i was trying to say / but as i was busy at workshop/ people typically use for woodworking machines xx10 screws on all axis and xx05 on Z, as this more or less gives compromise between speed, precision and step count/pulse train needed to generate movement


So say you have a servo motor that will spin to 3000rpm. From look of the servo it says 2500PPR/ pulses per revolution/ if i am not wrong. And ball screw moves 10mm per revolution.
Then ball screw needs 1/10 rev to move 1mm. If no geared then 3000/max rpm/x10=30 000mm/min max speed , like Gerry says thats your max velocity in Mach3. So from above it seems then you will need 250pulses per mm , so 1mm/250pulses=0.004mm resolution.

There is something important that Gerry told you but you missed his point. The servos should not be greatly OTT as you may think, they must be closed mutch to what effort they will do, otherwise youwill run in other problems. read literature about servo sizing. Its not a good thing to be much bigger than job they are meant to do.

Then read carefully page 14 from my build thread where Johnatan explained me very well how to calculate details and especially about snappiness.

And by the way i was suggesting 20t at the motor and 30t at the rotating ball nut, not vice versa. So you finish with slightly geared up machine, 0.7-1kw servos, and very fast acceleration. But just do your self the calc. My gantry is moved by 2x 400w servos, not 2x1.5kw ha ha