A 3 phase motor will operate (meaning spin) with single phase, but will not START spinning, because there is no relative rotation direction, so it just shakes back and forth, or if it does start turning, the direction is unpredictable.
So a Static Phase Converter (SPC) at it's basic form just uses capacitors to create a phase shift in the beginning that tells the motor to start spinning in your desired direction. Once it IS spinning, then the power capacity is effectively reduced, because all of the work will be done by only 2 sets of windings. So if the motor were to be fully loaded, the current on those windings would increase by the square root of 3, or 173% and the motor would be overloaded. So if you want to use it, you must de-rate the motor by the inverse, to 58% at least, and even then the unbalanced current will cause added heating in the windings by virtue of what's called "negative sequence currents", so further de-rating is necessary. The generally accepted rule is 50% de-rate for things like tools that are not used continuously, but I always tell people if it is going to run for 3 hours or more at a time, de-rate to 33%.
A Rotary Phase Converter (RPC) takes a larger 3 phase motor that is driven by a single phase motor (Pony Motor RPC), or in some cases people use an SPC to start the 3 phase motor of the RPC so it is self contained, and uses the 3 phase motor to "generate" a voltage on the unused leg by induction, thus making it useful to other motors connected down stream. But from an energy standpoint, that second (or 3rd) motor represents energy consumed to create the 3 phase power for the tool motor, so the overall energy efficiency is quite low, in the neighborhood of 60-70%. Again, for a tool running occasionally, that might not be a big deal but for something that needs to run a lot, it adds up fast in terms of cost of ownership. It also means having to start the RPC first, THEN start the tool, every time, or leave the RPC running continuously, which is a total waste of energy.
A VFD works by converting AC to DC, then back into what the motor thinks is AC. So the incoming AC can be single phase or 3 phase, it doesn't matter because it's just rectified to DC anyway. But to feed the VFD with single phase, again that current increases by 1.732, so the front end components need to be larger, plus there is more undesirable bus ripple from rectifying single phase, so you need more capacitance on the bus and the caps will run hotter. So the rule there is at least a 50% de-rate of the VFD, IF you also de-rate the operating temperature by 50%, or if you want rated operating temperature, de-rate the VFD to 35%. So for a 10HP 230V motor, you would buy at least a 20HP VFD if you can keep it at about 20C (68F), or a 30-40HP VFD is you want to use is at up to 40C (104F). If the VFD has DC Bus Chokes you can usually get away with just the 50% de-rate without the temperature de-rate, but of course that means the VFD costs more.
Another alternative is an Electronic Phase Added system that uses the equivalent o a VFD only to create the 3rd leg. They are made by a company called Phase Perfect. That might be a viable option for you here.
I would just replace the motor if it were me...
