By Request,
some speed and acceleration figures:
This formula:
Force = (Td x 2 x 3.14 x Efficiency) / (Ph (in mm/Rev) x 0.001)
Td = Driving Torque (Nm), Force is in Newtons, Ph is the lead in mm/Rev
Found here:
Nook Industries
Yes, the same equation works for Rack and pinion. If you aren't certain, do a few calculations based on the pitch circle radius and compare the numbers. They are the same. If I've made any mistakes, let me know.
This motor:
https://www.teknic.com/model-info/CPM-SDSK-3421P-RLN/
Also, a generic 1kW Servo from EBay is used as a comparison.
A few things I know this graph and charts do not include that would make the results less favorable:
The inertia of the spinning motor and reduction gear. This gets worse the faster you spin, so worse for a servo than a stepper. I don't know how much, I don't know the angular momentum values to use for the motor and reducer and I haven't done the math.
Friction. Compared to everything else, I doubt this amounts to much. Nice linear bearings and you can slide it back and forth with one finger.
Backlash compensation. This requires extra acceleration according to the software manual.
Cutting Forces.
I would prefer a servo that has a flatter curve to it, especially when using 10:1 reduction. I hope this helps.