期刊
NONLINEAR DYNAMICS
卷 26, 期 2, 页码 121-142出版社
SPRINGER
DOI: 10.1023/A:1012990608060
关键词
Hopf bifurcation; delay differential equation; center manifold; chatter
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 the infinite-dimensional problem to a two-dimensional center manifold. Due to the special algebraic structure of the delayed terms in the nonlinear part of the equation, the computation results in simple analytical formulas. Numerical simulations gave excellent agreement with the results.
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