back when i had a quality company cage, the wheel would rattle the cage so much that i couldn't sleep at night. rutherford doesn't exactly run on the wheel to exercise... he likes to sprint and sprint, and then run off as the wheel spins like crazy. ahhhh!
what i used to do to keep the rattling to a minimum was to put a shelf directly above the wheel, as close as possible without interfering with the movement of the wheel. then i'd put another shelf adjacent to it to firm up the long side of the cage. it doesn't completely eliminate the noise, but it does make it slightly less noisy.
also, have you checked the bearings? sometimes when the bearings need to be changed, the wheel will wobble and shake a lot more than usual.