Period doubling bifurcation and center manifold reduction in a time-periodic and time-delayed model of machining

Róbert Szalai, G. Stépán

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

A closed-form calculation is presented for the analysis of the period-doubling bifurcation in the time-periodic delay-differential equation model of interrupted machining processes such as milling where the nonlinearity is essentially nonsymmetric. We prove the subcritical sense of this period-doubling bifurcation and approximate the emerging period-two oscillations by the Lyapunovg-Perron method for computing the center manifold and by calculating the Poincarég-Lyapunov constant of the bifurcation analytically at certain characteristic parameter values. The existence of the unstable period-two oscillations around the stable stationary cutting is confirmed using a numerical continuation algorithm developed for time-periodic delay-differential equations.

Original languageEnglish
Pages (from-to)1169-1187
Number of pages19
JournalJVC/Journal of Vibration and Control
Volume16
Issue number7-8
DOIs
Publication statusPublished - Jun 2010

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Bifurcation (mathematics)
Machining
Differential equations
Milling (machining)

Keywords

  • Bifurcation
  • center manifold
  • high-speed milling
  • normal form
  • period doubling

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)
  • Aerospace Engineering
  • Automotive Engineering

Cite this

Period doubling bifurcation and center manifold reduction in a time-periodic and time-delayed model of machining. / Szalai, Róbert; Stépán, G.

In: JVC/Journal of Vibration and Control, Vol. 16, No. 7-8, 06.2010, p. 1169-1187.

Research output: Contribution to journalArticle

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