For a quick fix, take two "C" clamps, and clamp down each side of the steel plates that make up the 'iron' of the transformer. See if that quiets it down. If yes, you could have a clamp made (or make one yourself) to do the same thing in a more discrete manner.
Usually it is the laminate plates (the iron) that get loose and buzz. They use a shellac to glue them together, and age and deterioration breaks the bonds. No problem for the transformer, just for your ears.
Clamping the plates should make it quiet.
Usually it is the laminate plates (the iron) that get loose and buzz. They use a shellac to glue them together, and age and deterioration breaks the bonds. No problem for the transformer, just for your ears.
Clamping the plates should make it quiet.

