Sounds / looks like the moving armature isn't cleanly mating with the fixed yoke, and there's an air-gap which allows a little vibration due to the AC supply. When you apply a little pressure it quietens down because you're damping out the vibration. I don't see it as a big problem - and it's by no means uncommon in contactors - but I can understand why it has been questioned. Not much you can do, unless you fancy stripping down the UVR to component level and using a surface grinder to very carefully true up the mating faces of the armature and yoke. Get this wrong and you could ruin the UVR, so think carefully before attempting this.

It's not resonance it's, as Scotty said, the armature not seated fully. Either the mating faces are deformed, there is some debris in between the faces (it can be very little), or (most likely) the secondary assembly mechanisms are out of spec and not allowing the armature to fully 'seal'. I would NOT put that into service. I have seen coils that make that amount of noise melt. This is because if the armature in not fully seated the coil is drawing more current than designed for as the maximum inductance is not being reached when the armature is not fully seated.

Keith Cress
kcress - http://www.flaminsystems.com