State-dependent, non-smooth model of chatter vibrations in turning

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

This paper deals with the modeling and analysis of the cutting tool's global dynamics in the orthogonal cutting process of turning operations considering the effect of state dependency and fly-over in one model. In particular, the one-degree-of-freedom non-smooth model, presented by Wahi and Chatterjee in 2008, is extended by the consideration of vibrations in the direction perpendicular to the feed velocity. This results in the statedependency of the model and gives an additional direction in which fly-over can occur. The constructed mathematical model consists of a nonlinear PDE, which describes the evolution of the surface height of the workpiece and a two-degree-of-freedom ODE, which governs the motion of the tool. The PDE is connected to the solution of the ODE by a non-local, non-smooth boundary condition. For the case when the tool is within the cut, this model gives the conventional model of turning governed by delay-differential equations with state-dependent delays. In order to study the effect of vibrations in the tangential direction numerical simulations are carried out and their results are compared to the model presented by Wahi and Chatterjee (2008).

Original languageEnglish
Title of host publication11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791857168
DOIs
Publication statusPublished - Jan 1 2015
EventASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015 - Boston, United States
Duration: Aug 2 2015Aug 5 2015

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume6

Other

OtherASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015
CountryUnited States
CityBoston
Period8/2/158/5/15

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modelling and Simulation

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  • Cite this

    Lehotzky, D., Insperger, T., & Stépán, G. (2015). State-dependent, non-smooth model of chatter vibrations in turning. In 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Proceedings of the ASME Design Engineering Technical Conference; Vol. 6). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC2015-46748