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Chatter costs money when you reduce the productivity of the machine by slowing it down to make the vibration go away.

Chatter.
Conventional wisdom states that there are two kinds of chatter: Forced and Self-Induced. Some shop guys like to think its caused by the
material.
Forced chatter is a result of alternating cutting forces that result from
1) Interrupted cuts (milling);
2) Machine vibrations such as out of balance motors, spindles, gear
or shaft irregularities, bad couplings or bearings, (Loose motor mounts
and weakened or stretched) couplings;
3) Load on tool / workpiece changing as a result of acceleration or decceleration;
4) Vibrations being transmitted through the machine and foundation from other equipment.
If forced vibration is what you have, confirming the integrity
of the machine tool and its power train is a critical first step.
Reducing the feed per revolution is one way to determine if it is the
variation in the cutting process that is forcing the vibration. Changing
the SFM or RPM's by at least 25% is also something to try (increase or
decrease!)
Self-excited chatter is induced by a change in the
cutting forces themselves, and is where I place the chatter that may be
caused by the material. Self-excited vibrations can be distinguished
from forced vibrations in the machining system because self-excited
vibrations stop when the cutting does. Forced vibrations are not
dependent on the cutting process, and so continue even when the tool is
not in the cut. Self-excited chatter can be caused by:
1) Change in forces needed to cut caused by differences in the
material - Material characteristics (such as workhardening or
microstructural differences) that result in variation in chip thickness.
2) Unstable built-up edge (BUE) forming then breaking off causing variation in the cutting forces.
3) Insufficient stiffness of the workpiece, spindle, tool and tool holding (think deflection and too much length).
To eliminate self-excited chatter, decrease the length of the tool
in the cut, shorten the tool holder, or substitute more rigid tooling
and support materials (a carbide boring bar deflects less and can make
three or more times heavier a cut than one made of steel for example).
Still think it's the material? Here's my Metallurgist's tip: Look and see if you have changing build up edge conditions on the tool that exhibits chatter.
If the self-excited chatter is due to material such as an unstable
built-up edge (BUE) forming, try increasing the RPMs / SFM. Spindle
speeds that are too slow allow workpiece material to weld to the tool
edge (pressure weld) and build up. This creates higher forces until it
sloughs off. Then forces go back to normal, and build up again until …
Higher RPMs help to keep BUE stable and under control. And they allow you to run faster cycle times, contributing to profits.
Bottom line: Chatter doesn't always mean you need to slow down.
Photo credit.
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