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Hopf Bifurcation in the Drilling Process under Regenerative Cutting Conditions

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Bifurcation: Analysis, Algorithms, Applications

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Abstract

Regenerative effects are observed in many naturally occurring nonconservative systems. The purpose of this paper is to describe the regenerative effects; namely, those related to what is called Hopf bifurcation in the drilling process. Here, the bifurcation refers to changes in the qualitative behaviour of the radial drilling machine tool and the solutions of its delay differential equation with a varying parameter. Regenerative effect is a dynamic problem in metal cutting machine tools because of its adverse effects especially on machining accuracy, surface finish and tool life. Vibration may occur as a result of this instability effect.

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References

  1. Baráti A: Vibration test of the radial drilling machine tool Rfh-75, research report No. 19917, SZIMFI, 1981. (in Hungarian)

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  2. Bakondi and Kardos: Machine tool production. Tankönyvkiadó, Budapest, 1979. (in Hungarian).

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  3. Stépán G: Stability investigation of retarded differential equations, Acta Technica, 90 (109–132), 1980.

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  4. Tobias S. A.: Machine tool vibration, Blackie and son LTD, Glasgow, 1965.

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Author information

Authors and Affiliations

  1. Department of Production Engineering, Budapest University of Technology, H-1521, Budapest, Hungary

    Mustapha S. Fofana M.Sc.(mechanical engineering)

  2. No.48 Pillar street, Freetown, Sierra Leone

    Mustapha S. Fofana M.Sc.(mechanical engineering)

Authors
  1. Mustapha S. Fofana M.Sc.(mechanical engineering)
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Editor information

Editors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, D-3000, Hannover 1, Germany

    T. Küpper

  2. Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, D-8700, Würzburg, Germany

    R. Seydel

  3. Institut für Mechanik, Technische Universität Wien, Karlsplatz 13, A-1040, Wien, Austria

    H. Troger

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© 1987 Birkhäuser Verlag Basel

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Fofana, M.S. (1987). Hopf Bifurcation in the Drilling Process under Regenerative Cutting Conditions. In: Küpper, T., Seydel, R., Troger, H. (eds) Bifurcation: Analysis, Algorithms, Applications. ISNM 79: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 79. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7241-6_9

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  • DOI: https://doi.org/10.1007/978-3-0348-7241-6_9

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7243-0

  • Online ISBN: 978-3-0348-7241-6

  • eBook Packages: Springer Book Archive

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