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

Dávid Lehotzky, T. Insperger, G. Stépán

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)
Volume6
ISBN (Electronic)9780791857168
DOIs
Publication statusPublished - 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

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

Fingerprint

Chatter
Vibration
Dependent
Degree of freedom
Model
State-dependent Delay
Nonlinear PDE
Global Dynamics
Cutting tools
Delay Differential Equations
Perpendicular
Differential equations
Boundary conditions
Mathematical Model
Mathematical models
Numerical Simulation
Motion
Computer simulation
Modeling

ASJC Scopus subject areas

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

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 (Vol. 6). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC2015-46748

State-dependent, non-smooth model of chatter vibrations in turning. / Lehotzky, Dávid; Insperger, T.; Stépán, G.

11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2015.

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

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. vol. 6, American Society of Mechanical Engineers (ASME), ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015, Boston, United States, 8/2/15. https://doi.org/10.1115/DETC2015-46748
Lehotzky D, Insperger T, Stépán G. State-dependent, non-smooth model of chatter vibrations in turning. In 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6. American Society of Mechanical Engineers (ASME). 2015 https://doi.org/10.1115/DETC2015-46748
Lehotzky, Dávid ; Insperger, T. ; Stépán, G. / State-dependent, non-smooth model of chatter vibrations in turning. 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2015.
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