Gene,
I think you are dealing with ringing as opposed to chatter. Chatter is usually a low frequency vibration caused by the tool biting in and releasing repeatedly. The frequency and intensity will change as you change spindle speed, cutting depth and feed rate.

Ringing on the other hand is just like the ringing in an LC circuit. It is a function of the stiffness of the material, its diameter, its length and how it is restrained at each end. Given an appropriate text book and a calculator you can actually calculate what the frequency should be. The only way to stop the ringing is to add damping, a lossy element (resistor)to dissipate the energy.

Think about a bell or a guitar string. As long as the work piece is significantly longer than its diameter it will ring like a bell. The only way to stop the ringing is to absorb the vibrations, think putting your hand on the guitar string. I have solve "ringing" problems by working only on one half or less of the stock and sticking gobs of modeling clay on the other half and wrapping all that up with duct tape. That kills the vibration. when I finish the first half I move the "damper" to the other end.

The simplest way is to use a follower rest. That stops the vibration immediately. Didn't you get a follow rest with the lathe? This might call for a few manual passes with the follow rest before you get fancy with the CNC. That's why I insist that my CNC conversions retain handwheel operation.

Cecil

At 06:12 PM 6/29/2017, you wrote:

yes, momentarily Andy, but it right back as soon as the speed steadies,
at rpms from 50 to 600.  And the oscillation frequency is quite constant
over that range.  Feeling the spinning workpiece, its much stronger
there, than anyplace else.
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