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Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations |
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| Authors: | Kalmár-Nagy Tamás Stépán Gábor Moon Francis C. |
| Affiliation: | (1) Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY, 14853, U.S.A;(2) Department of Applied Mechanics, Technical University of Budapest, H-1521 Budapest, Hungary;(3) Sibley School of Aerospace & Mechanical Engineering, Cornell University, Ithaca, NY, 14853, U.S.A |
| Abstract: | We show the existence of a subcritical Hopf bifurcation in thedelay-differential equation model of the so-called regenerative machine toolvibration. The calculation is based on the reduction of the infinite-dimensional problem to a two-dimensional center manifold. Due to the specialalgebraic structure of the delayed terms in the nonlinear part of the equation,the computation results in simple analytical formulas. Numerical simulationsgave excellent agreement with the results. |
| Keywords: | Hopf bifurcation delay differential equation center manifold chatter |
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