Analytical solution for nonlinear oscillation of workpiece in turning process

Abstract

Chatter phenomenon is one of the essential problems in metal machining processes. It causes cutting tool wear and increase of production costs. Chatter vibration is an unstable self-excited vibration that the regenerative chatter is its most common type. In this paper, regenerative chatter in turning process is investigated. A three-dimensional nonlinear dynamic model of the turning process including both structural and cutting force nonlinearities and gyroscopic effects is presented. The workpiece is modeled as a rotating clamped–free beam which is excited by cutting forces. Using the method of multiple-scales, analytical approximate response of the system is obtained. To validate the model its responses are compared with the experimental results. Using this model the influences of tool longitudinal position, workpiece diameter, depth of cut, and rotational speed of workpiece on the stability results are studied. Using these results, turning velocity intervals for stable and unstable cuts are determined.