I have a 1.5HP 3ph variable speed motor drive from a varaible frequency drive to give about 10:1 speed range. What is the speed / torque characteristic common to this setup.
Suggestion: Since there are different principles of Variable Speed Drives, it may be a good idea to check with its manufacturer for correct application settings.
My application experience has shown me that with a standard volts/hertz drive, the torque produced by the motor will drop off exponentially at about 17 HZ. If you need to run slower, you may need to get a drive capable of open loop vector or a vector drive which with encoder feedback will allow you to run to zero speed with full torque.
Lathes are constant HP applications; not constant torque.
Check motor manufacturer for minimum operating speed on inverter power for a lathe application.
I.E. Marathon Electric makes a BlackMax motor that is capable of 1000:1 constant torque..... They also make Blue max motors rated for 20:1 and 10:1 constant torque speed ranges w/o requiring auxiliary cooling. Their inverter motors, such as those stated above, are often closer to a NEMA design A than a design B motor speed-torque curve. They have a stiffer speed-torque characteristic, and because of less copper in the slots, are able to produce the torque with less heat (copper losses) ...
Back to application, ... lathe mfgr can give you either curves of data points or curves that show HP vs speed requirements.
That will be the determinent when discussing the application with the motor manufacturer.