Nonlinear delay equations with fluctuating delay: Application to regenerative chatter

Ali Demir, N. Sri Namachchivaya, W. F. Langford

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which models the machine tool chatter with continuously modulated spindle speed. 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 eigenvalues without resonance. We make use of Lyapunov-Schmidt Reduction method 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.

Original languageEnglish (US)
Title of host publicationDesign Engineering
PublisherAmerican Society of Mechanical Engineers (ASME)
Number of pages11
ISBN (Print)0791836282, 9780791836286
StatePublished - 2002
Externally publishedYes

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings

ASJC Scopus subject areas

  • Mechanical Engineering


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