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This thread lacks photos. Please post photos of the lathe. Everyone likes photos of lathe.
This is too much focus on rated power in the selection of the motors. That tends to be a pretty unimport secondary parameter, in that once you have sized the motor for the inertial loads, and necessary torque, the resulting motor will have some rated power (typically way way more powerful than you would expect).
I did a course on this at the TU, and summarised the process they teach here:
The expectation of a manufacturer would be for a very rigid, highly dynamic drive system. For your purpose, you are prepared to compromise in the machine dynamic performance, and also the cutting power, but when you run through the inertial calculations, you may find you need a pretty beefy AC motor, to get it to work at all, especially if it has a long, large diameter Z ball screw, direct driven. On a lathe, the inertial load of the Z ball screw and motion of the saddle can be significant, with the sort of light cuts you are willing to accept maybe buried in uncertainty of those loads.
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