Investigating multiscale phenomena in machining: The effect of cutting-force distribution along the tool's rake face on process stability

Tamás G. Molnár, T. Insperger, S. John Hogan, G. Stépán

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

2 Citations (Scopus)

Abstract

Regenerative machine tool chatter is investigated in a nonlinear single-degree-of-freedom model of turning processes. The nonlinearity arises from the dependence of the cutting-force magnitude on the chip thickness. The cutting-force is modeled as the resultant of a force system distributed along the rake face of the tool. It introduces a distributed delay in the governing equations of the system in addition to the well-known regenerative delay, which is often referred to as the short regenerative effect. The corresponding stability lobe diagrams are depicted, and it is shown that a subcritical Hopf bifurcation occurs along the stability limits in the case of realistic cutting-force distributions. Due to the subcriticality a so-called unsafe zone exists near the stability limits, where the linearly stable cutting process becomes unstable to large perturbations. Based on center-manifold reduction and normal form calculations analytic formulas are obtained to estimate the size of the unsafe zone.

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

Cutting Force
Machining
Face
Center Manifold Reduction
Chatter
Distributed Delay
Machine Tool
Hopf Bifurcation
Normal Form
Hopf bifurcation
Distributed Systems
Governing equation
Chip
Diagram
Linearly
Unstable
Degree of freedom
Machine tools
Nonlinearity
Perturbation

Keywords

  • Bistable Zones
  • Delay-Differential Equation
  • Distributed Delay
  • Hopf Bifurcation
  • Limit Cycle
  • Metal Cutting
  • Subcritical
  • Turning

ASJC Scopus subject areas

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

Cite this

Molnár, T. G., Insperger, T., Hogan, S. J., & Stépán, G. (2015). Investigating multiscale phenomena in machining: The effect of cutting-force distribution along the tool's rake face on process stability. In 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Vol. 6). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC2015-47165

Investigating multiscale phenomena in machining : The effect of cutting-force distribution along the tool's rake face on process stability. / Molnár, Tamás G.; Insperger, T.; Hogan, S. John; 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

Molnár, TG, Insperger, T, Hogan, SJ & Stépán, G 2015, Investigating multiscale phenomena in machining: The effect of cutting-force distribution along the tool's rake face on process stability. 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/DETC2015-47165
Molnár TG, Insperger T, Hogan SJ, Stépán G. Investigating multiscale phenomena in machining: The effect of cutting-force distribution along the tool's rake face on process stability. 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/DETC2015-47165
Molnár, Tamás G. ; Insperger, T. ; Hogan, S. John ; Stépán, G. / Investigating multiscale phenomena in machining : The effect of cutting-force distribution along the tool's rake face on process stability. 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2015.
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abstract = "Regenerative machine tool chatter is investigated in a nonlinear single-degree-of-freedom model of turning processes. The nonlinearity arises from the dependence of the cutting-force magnitude on the chip thickness. The cutting-force is modeled as the resultant of a force system distributed along the rake face of the tool. It introduces a distributed delay in the governing equations of the system in addition to the well-known regenerative delay, which is often referred to as the short regenerative effect. The corresponding stability lobe diagrams are depicted, and it is shown that a subcritical Hopf bifurcation occurs along the stability limits in the case of realistic cutting-force distributions. Due to the subcriticality a so-called unsafe zone exists near the stability limits, where the linearly stable cutting process becomes unstable to large perturbations. Based on center-manifold reduction and normal form calculations analytic formulas are obtained to estimate the size of the unsafe zone.",
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