A centre-manifold analysis of variable speed machining

N Sri Namachchivaya, H. J. Van Roessel

Research output: Contribution to journalArticle

Abstract

The mathematical models representing 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 model 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 used to the centre-manifold reduction and the method of normal forms to determine the periodic solutions and analyse 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)
Pages (from-to)245-270
Number of pages26
JournalDynamical Systems
Volume18
Issue number3
DOIs
StatePublished - Sep 1 2003

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ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

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