Ballscrew Thickness!

Please don't resurrect ancient threads, start a new one.

Anyway, to answer your question, there is no easy 'optimal' as it all depends. However the easy option is to go near like for like and use 30mm dia 5mm pitch.

However that screw is rarely going to be turning at more than a few rpm (<1 for metric fine threading, <100 for a finishing pass and maybe 1000 for a rapid traverse) and despite it's 11kg weight only needs <1Nm to accelerate it to cutting speed in under 1mm of traverse. So a servo is massive overkill and gearing it down while avoiding backlash is going to be tricky.

Thank you for your answer.
My lathe has prismatic ways not linear ways with bearings.
So you suggest me to go with 3205 ballscrew and direct driving with coupler ?
1000rpm*5mm = 5m/min rapids is 5m/min good linear rapid speed for a lathe ?
Because my servo is 3000rpm with this setup i will get max 15m/min rapids but the question is if the ballscrew can rotate at 3000rpm without problems.

Because of ballscrew inertia higher pitch ballscrew (10mm) at lower rpm and gearing down would be better ?
If i gear down what pulleys-timing belts will eliminate backlash ?