Delayed dynamical sytem strongly coupled to a nonlinear energy sink : application to machining chatter

Abstract

This paper investigate the different response regimes of a cutting tool on a lathe strongly coupled to a nonlinear energy sink. The equations of motion are analysed via the method of multiple scales. Condition of elimination of secular terms permit to derive equation of the slow invariant manifold (SIM) and the behavior of the system has been explained by studying the location of the fixed points of the slow flow on the SIM. Different types of responses are revealed such as periodic response and also strongly modulated response (SMR) wich are not related to the fixed points of the slow flow. Analytic results are then compared to numerical simulations.