I had a single phase induction motor of unknown origin that I used to
drive a circular saw. It functioned fine for 25 years until the smoke
got out ! But during that 25 years it would regularly do exactly what
yours is doing because sawdust got into the centrifugal switch. It was
not a sealed motor and on occasions a bit of sawdust would end up
between the contacts when the motor was running down and consequently
it would go into the 'buzz' mode the next time I started it. Immediate
switch off the power. I was fortunate in that I could just push a
spring plate through the slots on the motor end with a screwdriver and
the problem was solved and away it would go when the power was next
applied.

In time however the damage to the insulation accumulated such that the
smoke got out as I said. The cf switch operated a capacitor fed
starter winding.

I've now got a 3hp motor out of an old pressure washer which is sealed
and has an electronic timer for the starter; interestingly the saw is
quite a different load from a pressure pump and the machine ate fuses
until I got the timing right.

I may be wrong but I think starter caps for cf switched starter
windings are smaller than those for constant run ones. Having looked
at your pictures, I'm wondering if there is a cf switch under the end
plate with 3 screws - I don't think there would be any problems taking
off that cover plate and having a look. What I would discourage you
from doing is putting poer on to it until you've found the problem as
each time you do so you're weakening the insulation in the widings.

Replacement may not be so easy as this is a four pole motor to give
1500 revs - most inexpensive motors of this type are 2 pole and hence
3000 revs. At one point Screwfix had motors and I think Machine Mart
did too.

Rob