As said, i made some assumptions.
1) the root diameter.
2) fixing method.
The root diameter is the smallest diameter on the actual screw and 10mm lead ballscrews of this size normally have large balls so i would have guessed the root to be about 38mm.
Any motor will turn this screw with the correct amount of gearing, but you need to look at what speeds you need and also take the cutting forces and inertia into account.
A machine of this size is on the limit of stepper technology and would perform so much better with a servo motor.
With this 8.5Nm motor you will only get about 5-6Nm running and to get any good speeds you will need very high voltage driver.
The 5-6Nm is the maximum you will get before it stalls, but even a 400W AC servo motor with 4:1 gearing will give you about this with the peak being three times this.
The peak also depends on the driver, so you need to check what the peak current of the drive is.

Originally Posted by
motionindo
Zapp, I use the web link and I enter Root diameter 40mm, length between bearing 3000mm, fixed on both ends and it comes out to 632rpm, but yours is 400rpm. Did I make a mistake here?
Btw is 1250 Oz stepper would be enough to handle 40mm diameter ballscrew?
Thanks in advance!
Zapp Automation Ltd
www.slidesandballscrews.com