how are you messuring you "vibration" (I think you actually talking about radial runout) if its .001 thats probably what the chinees think is good for an export but .05" on a drill, I would think you drill chuck is wacked! (which unfortunatly isn't that uncommon in the cheaper stuff).
You probably need to isolate what the problem is. If you could get a ground piece of stock with a known "good" collet you might be able to get a good reading. After insertion into the spindle check the runout then mark the shaft and loosen and rotate 1/4 turn and check it again. Go all the way around and compare readings. this will tell you if your spindle is the problem or the collet/shafting.