Well the cutter carriage needs to travel at 2mm min and it needs to travel smoothly i.e moving all the time, so surely you need a very fine pitch lead screw to acheive this?
No, you just need to turn the screw slowly ;)

For your application all you need is to ensure any noise (vibration) produced by the screw is not transmitted to the cutter head (making a silent slide way for the cutter is the greatest problem you will have)

The lead screw itself need not be too special - I'd use a polished stainless steel rolled threaded rod with a PTFE nut for a home-brewed machine

I would use a servo motor and a simple speed controller with tacho feedback (a positional servo controller is unnecessary and would add noise to you machine)

I would use one or perhaps two stages of plain rubber belt speed reduction between the motor and lead-screw (stepper motors, gears and notch belts are noisy)

Are you going to use vari-pitch groove cutting? (i.e. making the groove spacing wider as (before!) the signal level increases)


Bill