Sine wave to represent acceleration, triangle to represent translation, right?
I think you are getting into interesting territory. Would be cool to put a mic on the tool and vary speed based on filtering frequencies out of the range where harmonics exist.
I'm pretty sure I can get chatter/harmonics at any frequency on my lathe!
Rigidity should always be the first step in eliminating the shatter. There are situations though where the machine itself is rigid allright but the work piece is not. The work piece might have a tendency to resonate. This is where this small device should help.I usually just look for a way to increase rigidity in the set up or find the offending tool geometry. But hey I'm an old guy stuck in some old guy ways.