Best way to achieve x travel...

[JAZZCNC]

am I correct in my assumptions that reduction gearing is a good idea on the stepper drives? I was working on 3:1 for each axis but I'm not 100% convinced yet. My motors are 3Nm 4.2A Nema 23's.

Well that depends what you attach them to.? . . . . You mention timing belts so if this means your using them has the linear drive rather than say Ballscrews or R&P then you'll definatley need some gearing.! . . . . .Not because of lack of power but to increase resolution.?
Problem with timing belts is the pulley diameter determines the Pitch, now I've built several machines that use timing belts for linear drive and 18-20T is about has low has you want to go. If you go lower then the amount of teeth engaged is lower and you get premature wear etc.

Now the diameter for HTD 5mm pitch 20T pulley is approx 30mm so the amount traveld (pitch) for 1 revolution is 30*pi so 30*3.141=94mm.!!!
This is massive pitch and not practicle so you'll need at least 3:1 for plasma and more if router. I used 5:1 on last machine I made.
The other problem with timing belts with no gearing is the speed is so high that to go slow means the motors have to turn very slow and this can make them run very rough.
Typical steppers will give approx 1000rpm of usable speed so with 94mm pitch you'd get 94mtrs/min rapid speeds which is stupidly fast.
Now say you just want to cut at say 5mtrs/min which is still quite fast feed rate for cutting even with plasma the motors will only be spinning at 53 RPM so say you want cut at more realistic cutting speed of 2.5mtr/min for thicker material then your down at 26rpm which is slow and so going any lower really makes the motors unhappy.

The principle is very similair for R&P and often 3:1 is enough.

Ballscrews mostly don't need any gearing if correct pitch is choosen.

One other thing I've found it's often not much cheaper if any using belts than buying ballscrews from china.!!

[Jonathan]

Now the diameter for HTD 5mm pitch 20T pulley is approx 30mm so the amount traveld (pitch) for 1 revolution is 30*pi so 30*3.141=94mm.!!!

It doesn't change the point you're making, but that's a rather roundabout way to get the circumference! To find the distance traveled per revolution just multiply the pitch by the number of teeth - i.e. 5*20=100mm. Save the pi for other occasions.