I have a gas furnace. I recently replaced a bad blower motor. At that time I also cleaned out the blower housing and squirrel cage. The AC runs fine with no vibrations or any symptoms of an off balance squirrel cage.
However, when I turn on the heat, the furnace vibrates. I think it is coming from the blower, but it seems to be turning freely and again, it runs fine with the AC.
Does the blower fan spin at different speeds for hot vs cold air, and could it still be an out of balance squirrel cage? Could something else be causing the vibration? It sounds like an slightly out of balance washer on a spin cycle.