Delay equations with fluctuating delay related to the regenerative chatter

Demir A. , Hasanov A., Namachchivaya N.

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, vol.41, pp.464-474, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 3
  • Publication Date: 2006
  • Doi Number: 10.1016/j.ijnonlinmec.2005.06.012
  • Page Numbers: pp.464-474


The mathematical models representing machine too] chatter dynamics have been cast as differential equations with delay. In this paper, nonlinear delay differential equations with periodic delays which model the machine tool chatter with continuously modulated spindle speed are studied. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state-dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigervalues without resonance. The reduced bifurcation equation is obtained by making use of Lyapunov-Schmidt Reduction method. By using the reduced bifurcation equations, the periodic solutions are determined to analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions near the new stability boundary. (c) 2005 Elsevier Ltd. All rights reserved.