I am building a machine that will use a 10 hp motor. I only have single phase.
Would it make any sense to convert my single phase to 3 phase and use a 3 phase motor over a 220v single phase?

Do you mean convert your entire home service from single phase to 3 phase to accommodate one motor?

First question, is this motor for use in a residence? Next question, will your utility be able to supply 3 phase to your home?

Next question, are you willing to pay the costs associated with changing out you main service panelboard and rewiring all of the branch circuits going to the new panelboard, plus upgrading most of the circuit breakers to AFCI breakers which are roughly $50 ea. for a 15 or 20 amp AFCI breaker?

Personally, I would not do that. What is the size of your service now, 200 amp? The motor would have a 50 amp "FLC" so you would need to use # 6/2 with ground AWG conductors. The branch circuit short circuit/fault protection breaker would be a 125 amp. The O/L protection depends on the "FLA" and "SF" or "Temp rise" data off the motor's label and I don't have that info.

The cost of installing the proper electrical circuit for the motor should not anywhere close to the cost of converting to 3 phase.

Just curious, but what are you going to use a motor that size for in a residence?