car painting tool problem

As mentioned, you can buy or make phase converters. However, it would NEVER be worth the cost. "The rule" in using a 3 phase motor off single phase is when you have a special motor such as special flange bolted to a gearbox, for which you cannot easily get a single phase replacement.

Make sure you get a GOOD motor one that is for certain rated for replacement. Compressor starting and running conditions are severe. There is a lot of "BS" in modern ratings. In other words some HP ratings are simply imagined by the chineseoated builder.
We got used Amusement rides from overseas. Voltage was wrong as well as Hz being wrong. It was a mess. I did not buy these rides but I had to "make it work" fail. Phase converters are expensive to run. Look out for "Fake 5" HP motors. Usually found on those inexpensive 5HP compressors. Not real 5 HP motors. you need Comressor duty motor.