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Investigating Multiscale Phenomena in Machining: The Effect of Cutting-Force Distribution Along the Tool’s Rake Face on Process Stability

[+] Author Affiliations
Tamás G. Molnár, Tamás Insperger, Gábor Stépán

Budapest University of Technology and Economics, Budapest, Hungary

S. John Hogan

University of Bristol, Bristol, UK

Paper No. DETC2015-47165, pp. V006T10A063; 14 pages
doi:10.1115/DETC2015-47165
From:
  • 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

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.

Copyright © 2015 by ASME

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