Analysis of milling stability by the chebyshev collocation method: algorithm and optimal stable immersion levels

Eric A. Butcher, Oleg A. Bobrenkov, Ed Bueler, Praveen Nindujarla

Research output: Contribution to journalArticle

110 Scopus citations

Abstract

In this paper the dynamic stability of the milling process is investigated through a single degree-of-freedom model by determining the regions where chatter (unstable) vibrations occur in the two-parameter space of spindle speed and depth of cut. Dynamic systems such as milling are modeled by delay-differential equations with time-periodic coefficients. A new approximation technique for studying the stability properties of such systems is presented. The approach is based on the properties of Chebyshev polynomials and a collocation expansion of the solution. The collocation points are the extreme points of a Chebyshev polynomial of high degree. Specific cutting force profiles and stability charts are presented for the up-and down-milling cases of one or two cutting teeth and various immersion levels with linear and nonlinear regenerative cutting forces. The unstable regions due to both secondary Hopf and flip (period-doubling) bifurcations are found, and an in-depth investigation of the optimal stable immersion levels for down-milling in the vicinity of where the average cutting force changes sign is presented.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalJournal of Computational and Nonlinear Dynamics
Volume4
Issue number3
DOIs
StatePublished - Jul 1 2009
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics

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