Title: On the robustness of stable turning processes

Authors: Zoltan Dombovari, R. Eddie Wilson, Gabor Stepan

Addresses: Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary. ' Department of Engineering Mathematics, University of Bristol, England, UK. ' Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

Abstract: Self-excited non-linear vibrations occurring in the machining processes are investigated in this paper. Our treatment applies analytical techniques to a one Degree of Freedom (DOF) but strongly non-linear mechanical model of the turning process. This tool enables us to describe and analyse the highly non-linear dynamics of the appearing periodic motions. Using normal form calculations for the Delay-Differential Equation (DDE) model, we prove that the low-amplitude vibrations are unstable all along the stability lobes due to the subcriticality of Hopf bifurcations. This means that self-excited vibrations of the machine tool may occur below the stability boundaries predicted by the linear theory. Consequently, stable stationary cutting may not be robust enough for external perturbations close to the linear stability limits determined during the parameter optimisation of turning processes. Robustness is characterised by the amplitude of unstable oscillations along the stability lobes for non-linear cutting force characteristics having essential inflection points against chip thickness.

Keywords: orthogonal cutting; Hopf bifurcations; subcriticality bi-stable; turning processes; self-excited vibrations; nonlinear vibrations; modelling; stability; machine tool vibrations; parameter optimisation; cutting force; chip thickness.

DOI: 10.1504/IJMMM.2008.023716

International Journal of Machining and Machinability of Materials, 2008 Vol.4 No.4, pp.320 - 334

Published online: 08 Mar 2009 *

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