I have a very old bandsaw and motor. Right now, the motor still works - kind of. When I turn on the band saw, it take about 5 sec to get up to speed, which it did not do a few days ago. Next, I can saw for about 15 sec until the motor starts to smoke. I don't know if I should go for a different motor(I can't find an identical one anywhere) or see if I can fix it.
I do not know what is wrong with the motor and did not know if anyone could guess.
Here is the manual for it: http://vintagemachinery.org/pubs/detail.aspx?id=2920
With that type of motor there should be a definite click when it comes up to speed.
1/3 Hp motors are very common, and can be picked up used for very little so if it is a matter of getting back to work that is probably your best option unless it is important to have a motor from the same period as the saw.
You likely have a bad coil. If you are wanting to keep the saw original, you can take the saw in and have it rebuilt by a rewinding shop, otherwise, you can order a new motor with the same frame size and bolt pattern.