On the global dynamics of chatter in the orthogonal cuttingmodel

Zoltan Dombovari, David A W Barton, R. Eddie Wilson, G. Stépán

Research output: Contribution to journalArticle

62 Citations (Scopus)

Abstract

The large-amplitude motions of a one degree-of-freedom model of orthogonal cutting are analysed. The model takes the form of a delay differential equation which is non-smooth at the instant at which the tool loses contact with the workpiece, and which is coupled to an algebraic equation that stores the profile of the cut surface whilst the tool is not in contact. This system is approximated by a smooth delay differential equation without algebraic effects which is analysed with numerical continuation software. The grazing bifurcation that defines the onset of chattering motion is thus analysed as are secondary (period-doubling, etc.) bifurcations of chattering orbits, and convergence of the bifurcation diagrams is established in the vanishing limit of the smoothing parameters. The bifurcation diagrams of the smoothed system are then compared with initial value simulations of the full non-smooth delay differential algebraic equation. These simulations mostly validate the smoothing technique and show in detail how chaotic chattering dynamics emerge from the non-smooth bifurcations of periodic orbits.

Original languageEnglish
Pages (from-to)330-338
Number of pages9
JournalInternational Journal of Non-Linear Mechanics
Volume46
Issue number1
DOIs
Publication statusPublished - Jan 2011

Fingerprint

Chatter
Chattering
Global Dynamics
Differential equations
Bifurcation Diagram
Delay Differential Equations
Orbits
Bifurcation
Grazing Bifurcation
Contact
Numerical Continuation
Smoothing Techniques
Motion
Period Doubling
Smoothing Parameter
Algebraic Differential Equations
Algebraic Equation
Instant
Periodic Orbits
Simulation

Keywords

  • Chatter
  • Delay differential equation
  • Differential algebraic equation
  • Fly-over
  • Non-smooth
  • Orthogonal cutting

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Applied Mathematics

Cite this

On the global dynamics of chatter in the orthogonal cuttingmodel. / Dombovari, Zoltan; Barton, David A W; Eddie Wilson, R.; Stépán, G.

In: International Journal of Non-Linear Mechanics, Vol. 46, No. 1, 01.2011, p. 330-338.

Research output: Contribution to journalArticle

Dombovari, Zoltan ; Barton, David A W ; Eddie Wilson, R. ; Stépán, G. / On the global dynamics of chatter in the orthogonal cuttingmodel. In: International Journal of Non-Linear Mechanics. 2011 ; Vol. 46, No. 1. pp. 330-338.
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