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Harmonically Excited Delay Equation for Machine Tool Vibrations

[+] Author Affiliations
János Lelkes, Tamás Kalmár-Nagy

Budapest University of Technology and Economics, Budapest, Hungary

Paper No. DETC2018-86145, pp. V006T09A049; 7 pages
doi:10.1115/DETC2018-86145
From:
  • ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Quebec City, Quebec, Canada, August 26–29, 2018
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5183-8
  • Copyright © 2018 by ASME

abstract

A machining tool can be subject to different kinds of excitations. The forcing may have external sources (such as rotating imbalance or misalignment of the workpiece) or it can arise from the cutting process itself (e.g. chip formation). We investigate the classical tool vibration model which is a delay-differential equation with a quadratic and cubic nonlinearity and periodic forcing. The method of multiple scales was used to derive the slow-flow equations. The resonance curves of the system are similar to those for the Duffing-equation, having a hardening characteristic. Stability analysis for the fixed points of the slow-flow equations was performed. Local and global bifurcations were studied and illustrated with phase portraits and direct numerical integration of the original equation. Subcritical Hopf, saddle-node and heteroclinic bifurcations were found.

Copyright © 2018 by ASME

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