Doesn't help, because I agree with John's answer. 'Plumes of smoke' mean the motor's insulation is done for – even if it still runs, its untrustworthy and a potential fire hazard. Cause maybe:
- the motor was accidentally wired so it was running on the Start winding, and Starting with the run winding, or,
- the centrifugal switch was bypassed by a wiring error or stuck after being disturbed.
On this design the Start winding is only connected for as long as it takes to get the motor moving from stopped. As the winding is only used for starting, it isn't particularly robust and overheats If left connected for too long.
I see single-phase motors as a clever compromise rather than good performers. They work from single-phase AC, which is highly convenient. But their performance is inferior and moderately unreliable. Fitting a three-phase motor and VFD will improve the lathe. You can buy VFD/motor/cabling kits that come with full instructions. The only disadvantage is the cost…
Dave