Dependence of computed trajectory on step-size in a nonlinear dynamic system: An investigation into cutting tool dynamics

Satishmohan T. Bukkapatnam; Soundar R.T. Kumara; Akhlesh Lakhtakia

doi:10.1080/07408179508936768

Dependence of computed trajectory on step-size in a nonlinear dynamic system: An investigation into cutting tool dynamics

Satishmohan T. Bukkapatnam
, Soundar R.T. Kumara
, Akhlesh Lakhtakia

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The nonlinear model of an orthogonal cutting process devised by Grabec is studied to demonstrate the importance of choosing an appropriate step-size and evolutionary algorithm for numerically integrating a system of nonlinear differential equations. Two different algorithms are used for computing the system trajectory, and the dependence of the phase portrait on the step-size is shown. A qualitative understanding to connect the proper step-size and the system nonlinearity is established.

Original language	English (US)
Pages (from-to)	519-529
Number of pages	11
Journal	IIE Transactions (Institute of Industrial Engineers)
Volume	27
Issue number	4
DOIs	https://doi.org/10.1080/07408179508936768
State	Published - Aug 1995

All Science Journal Classification (ASJC) codes

Industrial and Manufacturing Engineering

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10.1080/07408179508936768

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title = "Dependence of computed trajectory on step-size in a nonlinear dynamic system: An investigation into cutting tool dynamics",

abstract = "The nonlinear model of an orthogonal cutting process devised by Grabec is studied to demonstrate the importance of choosing an appropriate step-size and evolutionary algorithm for numerically integrating a system of nonlinear differential equations. Two different algorithms are used for computing the system trajectory, and the dependence of the phase portrait on the step-size is shown. A qualitative understanding to connect the proper step-size and the system nonlinearity is established.",

author = "Bukkapatnam, \{Satishmohan T.\} and Kumara, \{Soundar R.T.\} and Akhlesh Lakhtakia",

note = "Funding Information: The authors acknowledge the National Science Foundation for the support of this work under NSF Grant No. DDM-9223181.",

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AU - Kumara, Soundar R.T.

AU - Lakhtakia, Akhlesh

N1 - Funding Information: The authors acknowledge the National Science Foundation for the support of this work under NSF Grant No. DDM-9223181.

PY - 1995/8

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N2 - The nonlinear model of an orthogonal cutting process devised by Grabec is studied to demonstrate the importance of choosing an appropriate step-size and evolutionary algorithm for numerically integrating a system of nonlinear differential equations. Two different algorithms are used for computing the system trajectory, and the dependence of the phase portrait on the step-size is shown. A qualitative understanding to connect the proper step-size and the system nonlinearity is established.

AB - The nonlinear model of an orthogonal cutting process devised by Grabec is studied to demonstrate the importance of choosing an appropriate step-size and evolutionary algorithm for numerically integrating a system of nonlinear differential equations. Two different algorithms are used for computing the system trajectory, and the dependence of the phase portrait on the step-size is shown. A qualitative understanding to connect the proper step-size and the system nonlinearity is established.

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Dependence of computed trajectory on step-size in a nonlinear dynamic system: An investigation into cutting tool dynamics

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