Global dynamics of low immersion high-speed milling

R Szalai; G Stépán; SJ Hogan

Global dynamics of low immersion high-speed milling

R Szalai, G Stépán, SJ Hogan

Department of Engineering Mathematics

Research output: Working paper

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Abstract

In the case of low immersion high-speed milling, the ratio of time spent cutting to not cutting can be considered as a small parameter. In this case the classical regenerative vibration model of machine tool vibrations reduces to a simplified discrete mathematical model. The corresponding stability charts contain stability boundaries related to period doubling and Neimark-Sacker bifurcations. The subcriticality of both types of bifurcations is proved in this paper. Further, global period-2 orbits are found and analyzed. In connection with these orbits, the existence of chaotic motion is demonstrated for realistic high-speed milling parameters.

Original language	English
Publication status	Published - 2002

Bibliographical note

Additional information: Preprint of a paper later published by American Institute of Physics (2004), Chaos, 14(4), pp.1069-1077, ISSN 1054-1500

Research Groups and Themes

Engineering Mathematics Research Group

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Bcanm 2004r22Submitted manuscript, 1.18 MB

http://hdl.handle.net/1983/437

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1 Article (Academic Journal)

Global dynamics of low immersion high-speed milling
Szalai, R., Stépán, G. & Hogan, S., Dec 2004, In: Chaos. 14 (4), p. 1069 - 1077 9 p.
Research output: Contribution to journal › Article (Academic Journal) › peer-review
63 Citations (Scopus)

Cite this

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title = "Global dynamics of low immersion high-speed milling",

abstract = "In the case of low immersion high-speed milling, the ratio of time spent cutting to not cutting can be considered as a small parameter. In this case the classical regenerative vibration model of machine tool vibrations reduces to a simplified discrete mathematical model. The corresponding stability charts contain stability boundaries related to period doubling and Neimark-Sacker bifurcations. The subcriticality of both types of bifurcations is proved in this paper. Further, global period-2 orbits are found and analyzed. In connection with these orbits, the existence of chaotic motion is demonstrated for realistic high-speed milling parameters.",

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AU - Stépán, G

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PY - 2002

Y1 - 2002

N2 - In the case of low immersion high-speed milling, the ratio of time spent cutting to not cutting can be considered as a small parameter. In this case the classical regenerative vibration model of machine tool vibrations reduces to a simplified discrete mathematical model. The corresponding stability charts contain stability boundaries related to period doubling and Neimark-Sacker bifurcations. The subcriticality of both types of bifurcations is proved in this paper. Further, global period-2 orbits are found and analyzed. In connection with these orbits, the existence of chaotic motion is demonstrated for realistic high-speed milling parameters.

AB - In the case of low immersion high-speed milling, the ratio of time spent cutting to not cutting can be considered as a small parameter. In this case the classical regenerative vibration model of machine tool vibrations reduces to a simplified discrete mathematical model. The corresponding stability charts contain stability boundaries related to period doubling and Neimark-Sacker bifurcations. The subcriticality of both types of bifurcations is proved in this paper. Further, global period-2 orbits are found and analyzed. In connection with these orbits, the existence of chaotic motion is demonstrated for realistic high-speed milling parameters.

M3 - Working paper

BT - Global dynamics of low immersion high-speed milling

ER -

Global dynamics of low immersion high-speed milling

Abstract

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Research output

Global dynamics of low immersion high-speed milling

Cite this