Regenerative Tool Chatter Near a Codimension 2 Hopf Point Using Multiple Scales

Wahi, Pankaj and Chatterjee, Anindya (2005) Regenerative Tool Chatter Near a Codimension 2 Hopf Point Using Multiple Scales. In: Nonlinear Dynamics, 40 (4). pp. 323-338.

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Abstract

We study a well-known regenerative machine tool vibration model (a delay differential equation) near a codimension 2 Hopf bifurcation point. The method of multiple scales is used directly, bypassing a center manifold reduction. We use a nonstandard choice of expansion parameter that helps understand practically relevant aspects of the dynamics for not-too-small amplitudes. Analytical expressions are then obtained for the double Hopf points. Both sub- and supercritical bifurcations are predicted to occur near the reference point; and analytical conditions on the parameter variations for each type of bifurcation to occur are obtained as well. Analytical approximations are supported by numerics.

Item Type:	Journal Article
Publication:	Nonlinear Dynamics
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Keywords:	Codimension 2 Hopf bifurcation;Delay differential equation; Method of multiple scales;Regenerative tool chatter
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	30 Apr 2007
Last Modified:	19 Sep 2010 04:37
URI:	http://eprints.iisc.ac.in/id/eprint/10777

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