well, I can give you my thoughts on this since I ran a motor, generator, alternator shop and built several Phase converters.
If you use a phase converter, you have to wire in 3 phase power, that means additional wiring and all that expense. If the whole shop will be wired and all stuff is 3 phase, great. If not, add money for the wiring and box and breakers for 3 phase and they ain't the cheapest things you can buy.
3 phase motors are cheap, single phase are not cheap. If the windings in 3 phase are bad, new motor. Bearings are cheap. Single phase motors have capacitors and centrifugal switches and as a rule, the caps go bad first, then the cent. switch which then burns the motor up. I have repaired a few centrifugal switches but it was lucky that the motor used a switch I had. Usually single phase motors are made somewhere on earth and nothing is standard.
And remember, with a VFD and 3 phase motor, you get variable speed, simple switch reversing, and, If you order now, motor deceleration which means an electrical brake to slow the motor quickly instead of waiting for it to run down.
3 phase motors are easy to reverse while each time you start and stop a single phase motor, the caps. and the centrifugal switch cycle, and they only have so many cycles in their life. Wiring a single phase, reversable motor with a switch or relays is a pain. VFD reverses for you. I don't like lathes with single phase motors that cycle a lot because of the failure of both the caps. and the centrifugal switch causes motor changes more often than I like. All the lathes I worked on were either 3 phase or converted to 3 phase with a VFD. My current lathe is single phase and the 3 phase motor and VFD are on the shelve ready to change out but then, I'm only a hobby machinist and don't use it like we did in the shop. When I got my lathe, I spent 9 hours fixing the control circuits and wiring so it worked right.
On the negative side, you don't fix VFD's unless you got the skills and equipment. I tried several times and found it easier to just get a new one. If you pay someone, do a cost benefit for sure. Also, wiring one up for your application takes a bit of electrical skill which you may or may not have. Your decision.
Boils down to what you have. If you have a spare 3 phase motor around, use it to make a phase converter. They are not complicated in their primitive state and the wiring diagrams are out there on the net. I have done most conversions using 220 single phase to a VFD. Rarely does it pay, if you already are wired for single phase, to run a rotary phase converter for 1 or 2 machines unless the wiring between them is close. I used rotary phase converters where I had really big motors or lots of them and then the phase converter usually is cheaper than a VFD, especially to run a 30-50 horse motor or to power a whole machine shop.
