Dynamics of Cutting Near Double Hopf Bifurcation

Tamás G. Molnár, Zoltán Dombóvári, T. Insperger, G. Stépán

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

Bifurcation analysis of the orthogonal cutting model with cutting force nonlinearity is presented with special attention to double Hopf bifurcations. The normal form of the system in the vicinity of the double Hopf point is derived analytically by means of center manifold reduction. The dynamics is restricted to a four-dimensional center manifold, and the long-term behavior is illustrated on simplified phase portraits in two dimensions. The topology of the phase portraits reveal the coexistence of periodic and quasi-periodic solutions, which are computed by approximate analytical formulas.

Original languageEnglish
Pages (from-to)123-130
Number of pages8
JournalProcedia IUTAM
Volume22
DOIs
Publication statusPublished - Jan 1 2017
EventIUTAM Symposium on Nonlinear and Delayed Dynamics of Mechatronic Systems, IUTAM Symposia 2016 - Nanjing, China
Duration: Oct 17 2016Oct 21 2016

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Hopf bifurcation
Bifurcation (mathematics)
Topology

Keywords

  • center manifold reduction
  • double Hopf bifurcation
  • Hopf bifurcation
  • machine tool vibrations
  • nonlinearity

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Dynamics of Cutting Near Double Hopf Bifurcation. / Molnár, Tamás G.; Dombóvári, Zoltán; Insperger, T.; Stépán, G.

In: Procedia IUTAM, Vol. 22, 01.01.2017, p. 123-130.

Research output: Contribution to journalConference article

Molnár, Tamás G. ; Dombóvári, Zoltán ; Insperger, T. ; Stépán, G. / Dynamics of Cutting Near Double Hopf Bifurcation. In: Procedia IUTAM. 2017 ; Vol. 22. pp. 123-130.
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AB - Bifurcation analysis of the orthogonal cutting model with cutting force nonlinearity is presented with special attention to double Hopf bifurcations. The normal form of the system in the vicinity of the double Hopf point is derived analytically by means of center manifold reduction. The dynamics is restricted to a four-dimensional center manifold, and the long-term behavior is illustrated on simplified phase portraits in two dimensions. The topology of the phase portraits reveal the coexistence of periodic and quasi-periodic solutions, which are computed by approximate analytical formulas.

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