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Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations. (English) Zbl 1005.70019

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.

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
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