Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations

Tamás Kalmár-Nagy, G. Stépán, Francis C. Moon

Research output: Contribution to journalArticle

191 Citations (Scopus)

Abstract

We show the existence of a subcritical Hopf bifurcation in the delay-differential equation model of the so-called regenerative machine tool vibration. The calculation is based on the reduction of the infinite-dimensional problem to a two-dimensional center manifold. Due to the special algebraic structure of the delayed terms in the nonlinear part of the equation, the computation results in simple analytical formulas. Numerical simulations gave excellent agreement with the results.

Original languageEnglish
Pages (from-to)121-142
Number of pages22
JournalNonlinear Dynamics
Volume26
Issue number2
DOIs
Publication statusPublished - Oct 2001

Fingerprint

Hopf bifurcation
Machine Tool
Delay Equations
Machine tools
Hopf Bifurcation
Vibration
Center Manifold
Algebraic Structure
Delay Differential Equations
Differential equations
Numerical Simulation
Computer simulation
Term
Model

Keywords

  • Center manifold
  • Chatter
  • Delay differential equation
  • Hopf bifurcation

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Computational Mechanics

Cite this

Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations. / Kalmár-Nagy, Tamás; Stépán, G.; Moon, Francis C.

In: Nonlinear Dynamics, Vol. 26, No. 2, 10.2001, p. 121-142.

Research output: Contribution to journalArticle

Kalmár-Nagy, Tamás ; Stépán, G. ; Moon, Francis C. / Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations. In: Nonlinear Dynamics. 2001 ; Vol. 26, No. 2. pp. 121-142.
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