Analytical investigation of machining chatter by considering the nonlinearity of process damping

In this paper, the well-established problem of self-excited vibrations in machining is revisited to include the nonlinearity of process damping at the tool and workpiece interface. Machining dynamics is modeled using a time-delayed system with nonlinear damping, and the method of averaging is used to obtain the amplitude of the resulting limit cycles. As a result, an analytical relationship is presented to establish the stability charts corresponding with arbitrary limit cycles in machining systems. The presented analytical solutions are verified using experiments and numerical solutions. Crown Copyright (C) 2017 Published by Elsevier Ltd. All rights reserved.