Greeny thank for your answer

Jazzcnc also thank for your calculations. I want to say that the plan that i upload are not the final plans. I just upload the images in order to give a general idea about what am i going to build
You told me

" Buy 20mm Dia 10mm Pitch ballscrews and Gear the Motor 2:1 "

My motors have 3000 RPM ( according Yaskawa ).

According this calculator

Metric Critical Speed Calculator | Nook Industries

for 1400 mm distance between bearings and 20mm ballscrew, i will have 1234 RPM max speed for my ballscrews. Even if i gear them with 2:1 ratio i will reach 2468 rpm to the motor when the ballscrew turns with 1234 rpm. What will happen if the motor turns with 3000( or even more) ? that means that the ballscrew will turn with 1500rpm >1234 limit ( according the calculator )
You think i will have problem at this speed for my ballscrews?
Is the rotative nut a solution ? ( at this case i cannot move two ballscrew with one motor )
Is 3:1 gear a choice ( and the same time increase the mm per revolution at the ballscrew )
I think that the key factor is to know what cutting speed and rapids is possible to achieve with the 3 Yaskawa 400 watt motors for a machine that will be made for cutting wood plastic and aluminium if possible. I have no sense about my motors abilities. If i knew cutting speed and rapids, i think will be more simple to make calculations and combinations between ballscrews and pulleys

Anyway, so far thanks everybody for the time that spend to read, calculate and answer to my post.
Any other advice will be welcome.

Vagelis