OK... (opens and stirs can of worms) - I've done a few conversions on belt-drive lathes and mills (mostly Chinese 8250 clones!) as well as my own gear/belt drive lathe, so my opinion:
The VFD/3-phase setup will give you a constant-torque characteristic, rather than constant-power (which you get by shifting the belts). You'll probably end up shifting belts for a couple of good reasons:
When you need more torque (e.g. large cutters, slitting saws, hard / tough materials, pushing a 2" drill through an inch of gauge plate...) you'll want the "mechanical advantage" gained by gearing down the motor;
When you need more RPM (e.g. small cutters, soft aluminium or plastics etc.) you'll end up needing more than the VFD can give you on a medium gear so want to "gear up" using the pulley ratios!
Although a VFD may run from (e.g.) 5Hz through to 100 or 120Hz, at the low end you lose HP (constant torque, power = torque x RPM), and the motor can start to "cog", moving in a succession of jerks rather than smoothly; at the high end power again drops off due to the inductance and iron losses of the motor...
Best approach is to pick a somewhat oversized motor and VFD (e.g. 1.5 HP, 1725 RPM) in the interests of higher torque overall, choose a frequency range that gives you flexibility *in each belt position* - I'll use my own lathe as an example, I run 25-75Hz most of the time from a range of 10Hz up (with 5Hz "jog" for setup and meshing gears) which gives me 11 to 33RPM in lowest back-gear through to 750 - 2250 RPM in highest direct, without too much loss of power at the extremes, and I have an external fan set to cut in whenever the VFD output drops below 30Hz to ensure adequate cooling - it seems to work OK for me
Just my ha'pennorth,
Dave H. (the other one)
