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State-Dependent, Non-Smooth Model of Chatter Vibrations in Turning

[+] Author Affiliations
Dávid Lehotzky, Tamás Insperger, Gábor Stépán

Budapest University of Technology and Economics, Budapest, Hungary

Paper No. DETC2015-46748, pp. V006T10A061; 8 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5716-8
  • Copyright © 2015 by ASME


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 state-dependency 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).

Copyright © 2015 by ASME
Topics: Turning , Vibration , Chatter



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