Self-interrupted regenerative metal cutting in turning

Wahi, Pankaj and Chatterjee, Anindya (2008) Self-interrupted regenerative metal cutting in turning. In: International Journal of Non-Linear Mechanics, 43 (2). pp. 111-123.

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Abstract

A new approach is used to study the global dynamics of regenerative metal cutting in turning. The cut surface is modeled using a partial differential equation (PDE) coupled, via boundary conditions, to an ordinary differential equation (ODE) modeling the dynamics of the cutting tool. This approach automatically incorporates the multiple-regenerative effects accompanying self-interrupted cutting. Taylor's 3/4 power law model for the cutting force is adopted. Lower dimensional ODE approximations are obtained for the combined tool–workpiece model using Galerkin projections, and a bifurcation diagram computed. The unstable solution branch off the subcritical Hopf bifurcation meets the stable branch involving self-interrupted dynamics in a turning point bifurcation. The tool displacement at that turning point is estimated, which helps identify cutting parameter ranges where loss of stability leads to much larger self-interrupted motions than in some other ranges. Numerical bounds are also obtained on the parameter values which guarantee global stability of steady-state cutting, i.e., parameter values for which there exist neither unstable periodic motions nor self-interrupted motions about the stable equilibrium.

Item Type:	Journal Article
Publication:	International Journal of Non-Linear Mechanics
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Self-interruption;Regenerative chatter;Turning;Global dynamics;Bifurcation diagram.
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	30 Mar 2010 11:47
Last Modified:	19 Sep 2010 05:58
URI:	http://eprints.iisc.ac.in/id/eprint/26701

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