Easy, if its a machine with one motor and bugger all control gear, purchase a single phase motor:D
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There is 2 types of 2 phase power:D
1. 2 phases from a 3 phase transformer, sign wave 120* out of phase to each other
2. centre tap transformer, grabbing both legs, its actually commonly known (atlease in Vic) as 480V or farm supply, sign wave 180* out of phase to each other....These are sommonly from a SWER (single wire earth return transformer, from a single phase
Lots of Rural areas use this, lots of old dairy's had 2 phase 480V motors, which know single phase stuff is alot better are never seen new
As an industrial breakdown sparky, I get to replace motors regularly which didn't have good 3 phase supply (once the smoke gets out you can't put it back, won't run without the smoke in). Never seen a "phase converter", industrial customers always have 3 phase supply available, sounds pretty fishy to be honest.
Single phase to 3 phase VFds are common and cheap but only up to around 1.1 kw. Price goes up from there. They only output 220v 3phase so you need to connect a 415v motor in delta (often chinese motors are internally connected in star and the motor needs to come apart to do this). Big single phase motor might be the easiest.
Either way, remember you're playing with power.
Edit, if you change the motor you might still find the lathe has a control transformer that's 415 to something lower and will not work on 240v supply.
One of those phase converters might be a proposition if your machine has an integral motor which can not readily be replaced with something else. If, however, your motor is freestanding or separate and drives the machine via belts or other transmission devices then buying an appropriate 240 volt motor is likely cheaper.
My experiences at auctions are that 240 volt machines fetch quite a bit more than three phase machines. This made me think that if buying new machines and a 240 volt version is available at little or lower cost, then buy the 240 volt jobbie for the better resale value.
Three phase motors have little resale value. I have seen pallets of them go at auction for $200 - $400.
Well, I hope I have not appeared to representing myself as an expert on this subject, everything I know about this has come from either the internet or conversations with others, and my own very limited experience with one machine. I posted what info I have simply to raise awareness of the possibilities, as a lot of very good, cheap, heavy-duty second hand machinery is overlooked by people like me with a home workshop, on the assumption that they cannot run it.
There wouldn't be much discussion on these forums if everyone had to pass an exam before entering a conversation.