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On the global dynamics of chatter in the orthogonal cutting model

On the global dynamics of chatter in the orthogonal cutting model
On the global dynamics of chatter in the orthogonal cutting model
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.

orthogonal cutting, delay differential equation, differential algebraic equation, non-smooth, chatter, fly-over
0020-7462
330-338
Dombovari, Zoltan
bd6aa703-6779-4259-b5ef-b6bbcb40d534
Barton, David A.W.
3003bb1f-d648-4d00-a309-8ab75f333df0
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd
Stepan, Gabor
5392004a-eed4-41eb-a137-b7586e8b54a9
Dombovari, Zoltan
bd6aa703-6779-4259-b5ef-b6bbcb40d534
Barton, David A.W.
3003bb1f-d648-4d00-a309-8ab75f333df0
Wilson, R. Eddie
01d7f1f2-f8ee-4661-b713-dcefcddb89bd
Stepan, Gabor
5392004a-eed4-41eb-a137-b7586e8b54a9

Dombovari, Zoltan, Barton, David A.W., Wilson, R. Eddie and Stepan, Gabor (2011) On the global dynamics of chatter in the orthogonal cutting model. International Journal of Non-Linear Mechanics, 46 (1), 330-338. (doi:10.1016/j.ijnonlinmec.2010.09.016).

Record type: Article

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.

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More information

Published date: January 2011
Keywords: orthogonal cutting, delay differential equation, differential algebraic equation, non-smooth, chatter, fly-over

Identifiers

Local EPrints ID: 184223
URI: http://eprints.soton.ac.uk/id/eprint/184223
ISSN: 0020-7462
PURE UUID: f7861264-3d13-4db2-8c14-43deed07d91b

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Date deposited: 05 May 2011 13:20
Last modified: 14 Mar 2024 03:07

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Contributors

Author: Zoltan Dombovari
Author: David A.W. Barton
Author: R. Eddie Wilson
Author: Gabor Stepan

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