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Infinite Dimensional Slow Modulations In A Delayed Model For Orthogonal Cutting Vibrations

Nandakumar, K and Wahi, Pankaj and Chatterjee, Anindya (2009) Infinite Dimensional Slow Modulations In A Delayed Model For Orthogonal Cutting Vibrations. In: 9th Biennial Conference on Engineering Systems Design and Analysis, JUL 07-09, 2008, Haifa, Israel, pp. 665-672.

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Abstract

We apply the method of multiple scales (MMS) to a well known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the time scale of typical cutting tool oscillations. The MMS upto second order for such systems has been developed recently, and is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy. The main advantage of the present analysis is that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space. Lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS. Finally, the strong sensitivity of the dynamics to small changes in parameter values is seen clearly.

Item Type: Conference Paper
Additional Information: Copyright of this article belongs to American Soc Mechanical Engineers.
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Depositing User: Rajalaxmi Ashok Govanakoppa
Date Deposited: 21 Aug 2009 10:21
Last Modified: 21 Aug 2009 10:21
URI: http://eprints.iisc.ac.in/id/eprint/19576

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