Analysis of Degenerate Bifurcation in Machining Using a Nonlinear Model

Abstract We present a two degrees of freedom model of machining dynamics that compactly captures the nonlinear effects of regeneration, tool wear and plowing under orthogonal machining. Extensive simulation experiments show that the solutions to the governing equations of the model bear distinct similarities to signals from our earlier experiments, as reflected by both visual state portraits as well as the values of the quantifiers of a steady state dynamic system. Governing equations of the model lead to nonlinear delay differential equations, which we reduce to ordinary differential equations using Hopf bifurcation theorem and centre manifold theorem. Despite the ongoing efforts by the authors of this paper to quantify the simulations results analytically and experimentally, we strongly believe that our proposed model will be found to be amenable for studying and analyzing bifurcations that can lead to chatter in machining.

Analysis of Degenerate Bifurcation in Machining Using a Nonlinear Model Conference Paper