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<p>The stability and robustness of a nonlinear turning model subjected to acceleration feedback controller is studied. In the presence of machine tool stiffness and cutting force nonlinearities, the regenerative effect can induce subcritical bifurcations, which limit robustness in the vicinity of the critical parameter. By employing an averaging based nonlinear acceleration feedback controller, the local stability properties may be improved. The resulting equation of motion is a neutral delay differential equation with distributed delays. After asymptotic stability analysis, the center manifold reduction is derived for such systems to form a local approximant dynamical system. The analytical results are verified via numerical continuation, employing newly developed problem specific algorithms. While the analytical approach provides powerful closed form solutions near the vicinity of the bifurcations, the presented numerical methods also allow a global analysis of the system dynamics. This is showcased by identifying the boundaries of the present bi-stable parameter regimes, through following contact-loss grazing bifurcations of the emerging limit cycles.</p>

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Single degree of freedom orthogonal cutting model subjected to distributed acceleration feedback control

  • 期刊论文

  • 发表日期：

    2026年1月13日

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  • Andras Bartfai,
  • Zsolt Iklodi,
  • Zoltan Dombovari

摘要

The stability and robustness of a nonlinear turning model subjected to acceleration feedback controller is studied. In the presence of machine tool stiffness and cutting force nonlinearities, the regenerative effect can induce subcritical bifurcations, which limit robustness in the vicinity of the critical parameter. By employing an averaging based nonlinear acceleration feedback controller, the local stability properties may be improved. The resulting equation of motion is a neutral delay differential equation with distributed delays. After asymptotic stability analysis, the center manifold reduction is derived for such systems to form a local approximant dynamical system. The analytical results are verified via numerical continuation, employing newly developed problem specific algorithms. While the analytical approach provides powerful closed form solutions near the vicinity of the bifurcations, the presented numerical methods also allow a global analysis of the system dynamics. This is showcased by identifying the boundaries of the present bi-stable parameter regimes, through following contact-loss grazing bifurcations of the emerging limit cycles.