Improved Methods for the Prediction of Chatter in Turning, Part 3: A Generalized Linear Theory

Abstract

The linear theory of chatter has been generalized to any machining configuration without a priori assumptions on either the direction of the cutting force or the modal directions of the machine tool structure. Furthermore, the effects of the tool’s orientation on the stability of the machining system are directly expressed by its closed loop characteristic equation. Using experimental measurements for the dynamics of both the machine tool structure and the cutting process obtained previously under actual cutting conditions, the proposed theory is applied to two cases of orthogonal turning. The resulting predictions of the critical depth of cut are in excellent agreement with the measurements of actual chatter for a wide range of cutting conditions.