Approximate analytical solutions for primary chatter in nonlinear metal cutting model

J. Warminski, G. Litak, M. P. Cartmell, R. Khanin, Marian Wiercigroch

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

This paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non-linear differential equations of motion. The process model is based upon the established mechanics of orthogonal cutting and results in a pair of non-linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution. The chosen solution technique is the perturbation method of multiple time scales and approximate closed-form solutions are generated for the most important non-resonant case. Numerical data are then substituted into the analytical solutions and key results are obtained and presented. Some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given. It is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used, these being chosen to represent a real orthogonal cutting process. In an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter, this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co-ordinates. (C) 2002 Elsevier Science Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)917-933
Number of pages17
JournalJournal of Sound and Vibration
Volume259
Issue number4
DOIs
Publication statusPublished - 23 Feb 2003

Keywords

  • NONLINEAR DYNAMICS
  • VIBRATIONS

Cite this

Approximate analytical solutions for primary chatter in nonlinear metal cutting model. / Warminski, J.; Litak, G.; Cartmell, M. P.; Khanin, R.; Wiercigroch, Marian.

In: Journal of Sound and Vibration, Vol. 259, No. 4, 23.02.2003, p. 917-933.

Research output: Contribution to journalArticle

Warminski, J. ; Litak, G. ; Cartmell, M. P. ; Khanin, R. ; Wiercigroch, Marian. / Approximate analytical solutions for primary chatter in nonlinear metal cutting model. In: Journal of Sound and Vibration. 2003 ; Vol. 259, No. 4. pp. 917-933.
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N2 - This paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non-linear differential equations of motion. The process model is based upon the established mechanics of orthogonal cutting and results in a pair of non-linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution. The chosen solution technique is the perturbation method of multiple time scales and approximate closed-form solutions are generated for the most important non-resonant case. Numerical data are then substituted into the analytical solutions and key results are obtained and presented. Some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given. It is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used, these being chosen to represent a real orthogonal cutting process. In an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter, this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co-ordinates. (C) 2002 Elsevier Science Ltd. All rights reserved.

AB - This paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non-linear differential equations of motion. The process model is based upon the established mechanics of orthogonal cutting and results in a pair of non-linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution. The chosen solution technique is the perturbation method of multiple time scales and approximate closed-form solutions are generated for the most important non-resonant case. Numerical data are then substituted into the analytical solutions and key results are obtained and presented. Some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given. It is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used, these being chosen to represent a real orthogonal cutting process. In an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter, this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co-ordinates. (C) 2002 Elsevier Science Ltd. All rights reserved.

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