Does a queen sized bed need a bed frame?

I have queen sized bed and box spring set that sits on a metal frame. The frame was the cheapest one the mattress store sold, and the bed shakes from any movement. Does this bed need the frame? It's a large, heavy bed, and I don't want to ruin it. Also, if you have any remedies for stopping the frame from shaking, that would be good as well. all of the screws are tightened as much as they can be.