Delay equations with fluctuating delay related to the regenerative chatter II: analysis of reduced bifurcation equation

Authors: Demir, Ali¹; Hasanov, Alemdar¹; Sri Namachchivaya, N.²

Source: Applicable Analysis, Volume 84, Number 6, June 2005 , pp. 631-647(17)

Publisher: Taylor and Francis Ltd

Abstract:

In this article, we study the reduced bifurcation equations of the nonlinear delay differential equations with periodic delays, which models the machine tool chatter with continuously modulated spindle speed to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.

Keywords: Bifurcation equation; Periodic solutions; Stability boundaries; AMS Subject Classifications: 34C35; 34K15; 34K20

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00036810500047345

Affiliations: 1: Applied Mathematical Sciences Research Center, Kocaeli University, Ataturk Bulvari, 41300, Izmit-Kocaeli, Turkey 2: Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana–Champaign, 104 South Wright Street, Urbana, IL 61801, USA

Publication date: 2005-06-01

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