I have been doing a bunch of research to add ball screws to my CoreXY X and Y. So I could still be wrong.
Steppers motors die off in power after @500RPM. Some math at end..
If screw is fixed on both ends you may get some warp from heat expansion when using aluminum frames. Less is steel is used.
Regardless the size of Screw relates to how fast it can spin before deforming.
12xx are good for Z.
2020/2025, 2520,2525 screws for X and Y. Requiring NEMA 24/34 minimum. Motors need to stop and move a lot of mass.
I was going to use 1616 for X and Y, but after doing math the screws themselves would only be good for @100mms before deforming.
So then we get to the motors that you would need to move 20xx/25xx ball screws.
Steppers just do not do it. Need Servos, and they are the costly.
All ya, 1616 ball screws should have 15mm rails min. 20xx screws should have 20mm rails. Dual blocks per rail.
So, I am now at a point that smaller rails with liner motors may be best.
Also, you need to have you ball screws perfect with your rails. Even 0.01mm will mess things up.
Hope that helps,
Stepper max rpm 500 = 8.3333333 Rotations per second
5 =41.666666665 mms
40 =333.333332 mms
SERVO max rpm 3000
=50 rps /25 rps /10 rps
5 =250 mms
10 =500mms /250mms /100mms
20 =1000mms at 50rps /500mms at 25rps / *Goal 200mms at 10rps