State dependent regenerative delay in milling processes

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14 Citations (Scopus)

Abstract

Traditional models of regenerative machine tool chatter use constant time delays assuming that the period between two sub-sequent cuts is a constant determined definitely by the spindle speed. These models result in delay-differential equations with constant time delay. If the vibrations of the tool relative to the workpiece are also included in the surface regeneration model, then the resulted time delay is not constant, but it depends on the actual and a delayed position of the tool. In this case, the governing equation is a delay-differential equation with state dependent time delay. Equations with state dependent delays can not be linearized in the traditional sense, but there exists linear equations that can be associated to them. This way, the local behavior of the system with state dependent delays can be investigated. In this study, a two degree of freedom model is presented for milling process. A thorough modeling of the regeneration effect results in the governing delay-differential equation with state dependent time delay. It is shown through the linearization of the nonlinear equation that an additional term arises in the linearized equation of motion due to the state-dependency of the time delay.

Original languageEnglish
Title of host publicationProc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005
Subtitle of host publication5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
Pages955-964
Number of pages10
Publication statusPublished - Dec 1 2005
EventDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Long Beach, CA, United States
Duration: Sep 24 2005Sep 28 2005

Publication series

NameProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005
Volume6 B

Other

OtherDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
CountryUnited States
CityLong Beach, CA
Period9/24/059/28/05

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ASJC Scopus subject areas

  • Engineering(all)

Cite this

Insperger, T., Hartung, F., Stépán, G., & Turi, J. (2005). State dependent regenerative delay in milling processes. In Proc. of the ASME Int. Des. Eng. Tech. Conf. and Comput. and Information in Engineering Conferences - DETC2005: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (pp. 955-964). (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005; Vol. 6 B).