I have done this successfully. Can’t provide details – never kept any notes but I can give a few pointers.
The need arose when I acquired, very cheaply, a Pollard high speed drilling machine that had a 415v 3 phase motor. Changing the motor would not be easy and a transformer + inverter would have cost far more than the machine but I did, potentially have the bits to make a rotary converter – to whit, a spare 3 phase motor with all connections available and a assortment of capacitors.
Most (all?) published designs based on ‘idler motors’ are 240Vin/240Vout or 415Vin/415Vout. I needed 240Vin/415Vout so:-
Question 1: Will a 415V star connected 3phase motor continue to run with just 240V applied to a single winding (phase to star point)?
Answer: Yes and the rotary transformer action gives a reasonably balanced 415V between phases.
Question 2: Is the current in the single winding reasonable – again yes.
Question 3: Can we get it to self start?
Answer: Not with the components that were to hand. It would start but not at the right speed.
This problem was solved by using a small single phase motor (again from the ‘come in handy one day’ pile) as a pony motor to spin up the idler motor before applying power to it.
So modus operandi:
Press and hold start button while pony motor spins up.
Release start button. This removes power from the pony motor and applies power to the idler motor (you need a few relays to do this sensibly).
Points to note:
All the output power is provided by a single winding in the idler motor so be mindful of the current rating.
The output voltages will not be perfectly balanced but this can be improved by adding capacitors between phases (bit of a select on test exercise).

As a final assessment the converter is actually bigger than the drilling machine but it does work and didn’t cost me anything. Hope this helps.

Mike

That's an interesting and cost-effective solution. I'd hate to work out what the magnetics were up to, mind! It's not actually boosting the voltage so much as presumably generating the additional phases.

If I understand correctly, the machine motor has no neutral so the single phase power is only driving one phase of the idler motor. I'd love to see what the phase voltages and currents in the machine motor look like.