Limit cycles, bifurcations, and accuracy of the milling process

By Brian P. Mann, P. Bayly, M. Davies, J. Halley. 2004

142 citations recorded by the source corpus.

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Stability of Delay Equations Written as State Space Models (2010, methodology): “Following a similar methodology, the approach was adapted to examine second-order delay equations with timeperiodic coefficients and piecewise continuity by Mann et al. (Mann et al., 2004, 2005 Mann and Young, 2006).”
A New Metric for Automated Stability Identification in Time Domain Milling Simulation (2016, unknown): “stability charts that demonstrate both instabilities [32–36].”
Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels (2009, methodology): “Next, the exact solution during the period in which the coefficients of the time-delay vanish is utilized in a similar way to [15-17].”
Milling Bifurcations from Structural Asymmetry and Nonlinear Regeneration (2005, methodology): “Unstable period-doubling behavior, commonly referred to as a flip bifurcation [ 5 , 12, 19, 20, 22, 23], is predicted when the dominant characteristic multiplier of the discrete map model is negative and real with a magnitude greater than one.”