Kalmár-Nagy, Tamás; Stépán, Gábor; Moon, Francis C. Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations. (English) Zbl 1005.70019 Nonlinear Dyn. 26, No. 2, 121-142 (2001). Summary: We show the existence of a subcritical Hopf bifurcation in the delay-differential equation model of the so-called regenerative machine tool vibration. The calculation is based on the reduction of infinite-dimensional problem to a two-dimensional center manifold. Due to a special algebraic structure of delayed terms in the nonlinear part of the equation, the computation results in simple analytical formulas. Numerical simulations give an excellent agreement with analytical results. Cited in 61 Documents MSC: 70K50 Bifurcations and instability for nonlinear problems in mechanics 70K20 Stability for nonlinear problems in mechanics 74H55 Stability of dynamical problems in solid mechanics 74H45 Vibrations in dynamical problems in solid mechanics Keywords:chatter; existence; subcritical Hopf bifurcation; delay-differential equation model; regenerative machine tool vibration; reduction; infinite-dimensional problem; two-dimensional center manifold PDFBibTeX XMLCite \textit{T. Kalmár-Nagy} et al., Nonlinear Dyn. 26, No. 2, 121--142 (2001; Zbl 1005.70019) Full Text: DOI