Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations

Authors
Kalmar-Nagy, T Stepan, G Moon, FC
Citation
T. Kalmar-nagy et al., Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations, NONLIN DYN, 26(2), 2001, pp. 121-142
Citations number
20
Categorie Soggetti
Mechanical Engineering
Journal title
NONLINEAR DYNAMICS
ISSN journal
0924090X → ACNP
Volume
26
Issue
2
Year of publication
2001
Pages
121 - 142
Database
ISI
SICI code
0924-090X(200110)26:2<121:SHBITD>2.0.ZU;2-1
Abstract
We show the existence of a subcritical Hopf bifurcation in the delay-differ ential equation model of the so-called regenerative machine tool vibration. The calculation is based on the reduction of the infinite-dimensional prob lem to a two-dimensional center manifold. Due to the special algebraic stru cture of the delayed terms in the nonlinear part of the equation, the compu tation results in simple analytical formulas. Numerical simulations gave ex cellent agreement with the results.