Schuyler,
The other posts are correct but there are a couple of other factors that I found make a difference as well.
The relief ground on the cutter can cause a rubbing action and so set up flexing. One of the other posts suggests varying the infeed and sometimes finding the correct combination of relief and infeed works.
Somewhat related to this is the height of the tool relative to centerline. In my experience, we ran the tool slightly above the centerline when ID cutting to maintain a good relief. If run too high, you will end up trying to wipe material with an extremely negative rake relative to the material; if run too low, you lose the benefit of the relief angles on the sides and nose.
When working on ODs, you will want to be slightly below centerline. By running here, you may be able to decrease some of the relief and thereby use a little stronger tool.
It sounds from your post as though you are taking some relatively wide cuts relative to the cutting edge. I found that as width of cut increases, sometimes the rake needed to increase to lessen the shear pressure on the edge.
Chatter generally seemed to be a matter of pressure building up to the point that the tool or work had flexed as far as it could and snapped back into position. Then the next cycle started. Consequently, uniform loading through either depth of cut, rate of feed, or tool geometry would reduce the problem.
Hope this helps.
Griffy