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Regenerative Machine Tool Vibrations

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Controlling Delayed Dynamics

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 604))

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Abstract

Two basic models of machine tool vibrations are presented. First, a simple model of orthogonal turning process is discussed where material is removed from the rotating workpiece by a tool. Vibrations of the tool are copied on the workpiece’s surface and, after one revolution, the tool cuts this wavy surface. This phenomenon is called surface regeneration and the equations governing the vibrations are delay differential equations where the time delay is equal to the rotation period of the workpiece. Then, the mechanical model of milling operation is presented. Here the surface regeneration effect is combined by the parametric forcing of the entering and exiting cutting teeth. The governing equation is hence a time-periodic delay differential equation where the time delay and the principal period are both equal to the tooth passing period. Stability diagrams in the plane of the technological parameters are constructed for both turning and milling operations.

The research reported in this paper and carried out at BME has been supported by the Hungarian National Research, Development and Innovation Office (NKFI-K-132477 and NKFI-KKP-133846), by the NRDI Fund (TKP2020 IES,Grant No. BME-IE-MIFM and TKP2020 NC, Grant No. BME-NC) based on the charter of bolster issued by the NRDI Office under the auspices of the Ministry for Innovation and Technology.

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Authors and Affiliations

  1. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Tamás Insperger & Gabor Stépán

Authors
  1. Tamás Insperger
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  2. Gabor Stépán
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Correspondence to Tamás Insperger .

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Editors and Affiliations

  1. CDLab - Computational Dynamics Laboratory, University of Udine, Udine, Italy

    Dimitri Breda

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Insperger, T., Stépán, G. (2023). Regenerative Machine Tool Vibrations. In: Breda, D. (eds) Controlling Delayed Dynamics. CISM International Centre for Mechanical Sciences, vol 604. Springer, Cham. https://doi.org/10.1007/978-3-031-01129-0_10

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  • DOI: https://doi.org/10.1007/978-3-031-01129-0_10

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  • Online ISBN: 978-3-031-01129-0

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