Am NOT an electrician, but it may be, as already suggested, a failed capacitor.
The one on my small air compressor failed quite suddenly; a loud bang followed by fluid leaking out. Replacement cost £6.00, a few years ago, from the local motor rewinders.
If, the centrifugal switch contacts have welded, then the Start windings will have been in circuit continuously, which they are not supposed to be. Another possible source of heat and smoke.
The motor on my Myford once gave a good show of flashes and smoke. Fortunately, the local rewinders diagnosed it as swarf across the centrifugal switch and managed to clean it up enough to continue working until after I had sold it
If in any doubt, have your local motor repairers check it out. Hopefully it will be capable of further service, after a bit of rectification.
Howard