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An Analytical Model to Predict Chatter in Multi-Dimensional Periodically Time-Varying Machining Processes

[+] Author Affiliations
William T. Corpus

Delphi Research Laboratories, Shelby Twp., MI

William J. Endres

Michigan Technological University, Houghton, MI

Paper No. IMECE2003-42488, pp. 129-135; 7 pages
  • ASME 2003 International Mechanical Engineering Congress and Exposition
  • Manufacturing
  • Washington, DC, USA, November 15–21, 2003
  • Conference Sponsors: Manufacturing Engineering Division
  • ISBN: 0-7918-3720-3 | eISBN: 0-7918-4663-6, 0-7918-4664-4, 0-7918-4665-2
  • Copyright © 2003 by ASME


An approach is presented to determine the stability limits for machining processes that exhibit periodic time variation and multi-dimensional structural dynamics. The approach leverages the solution for the single-dimensional case, which identified an added set of stability lobes in addition to those corresponding to the time-invariant case. The solution is developed for two-dimensional dynamics for both a damped system and an undamped system; it may be expanded to any order and extended to three-dimensional dynamics. The undamped solution provides a mathematical description of the stability lobe locations along the speed axis and asymptotes for the damped case. Numerical time-domain simulation is used to confirm the analytical solution. While the agreement is good even for a first-order analytical result, yet another extra stability lobe, not seen in the one-dimensional case, is now seen in the numerical simulation results. Some of its characteristics are noted; however, further study is needed to understand its source.

Copyright © 2003 by ASME
Topics: Machining , Chatter



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