I have disassembled contactors that have cores like I-E transformer cores, with the coil on the stationary E section and the contacts operated by the moving I section.
The moving section usually has a pivot to permit alignment. I have been able to quiet down loud contactor hum by lubricating and excercising the pivot of the armature.
The tighter the moveable part meets the face of the stationary part, the less the hum. If you've ever tried to pry apart an energized contactor or solenoid, you know how loud the buzz can get.