Be good if you can to post a photo of the 'big old motor', especially the motor plate. It's almost certainly a single-phase motor, but these come in a few different configurations. One of the experts may recognise it. (Photo posting Instructions here.)
Single-phase motors all have 'start' and 'run' windings. The purpose of the start winding is to create a temporary magnetic field for the run winding to push against, and the field is usually angled electrically with a capacitor or two. Once the motor is turning, the 'start' winding might be disconnected by a centrifugal switch inside the motor (behind a removable cover on the back end) but not all motors have them. Myford motors usually do, so well worth a look.
Capacitors fail open-circuit. Not unusual and they are typically easy to replace.
So:
- If the centrifugal switch is stuck open or the contacts are filthy, the start winding gets no power and the motor buzzes
- If the capacitor fails the start winding gets no power and the motor buzzes.
As the start winding is only needed to get the motor turning when power is first applied, it should be possible to start the motor by spinning it manually. In the good old days when men were men and losing a few fingers was all in a day's work, early-design single-phase motors were started by pulling a rope wound around a drum on the shaft. Basically pull rope hard to spin the shaft and apply power. Yuk. You may be able to start the lathe by applying power and spinning the chuck by hand: if it runs, start problem as above confirmed.
If there's nothing obviously wrong with the centrifugal switch (does anyone have a photo?), I'd replace the capacitor. Nothing lost by replacing it as the first step because its fairly cheap and easy to do.
Also inspect connections & wiring carefully – not unknown for wires to come adrift from terminals or to chafe through. Make sure all is firm. Could be as easy as a loose connection.
Most serious possibility is a winding has failed, not easy or cheap to fix. If the motor has died I'd consider upgrading to a 3-phase motor and VFD. Speed control is lovely, and the motors are smooth…
Dave
Edited By SillyOldDuffer on 09/09/2020 09:15:18