Nonlinear vibrations of a shell-shaped workpiece during high-speed milling process

W. Zhang, R. Zhou, Jean W. Zu

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10 Scopus citations

Abstract

This paper is focused on nonlinear dynamics of a shell-shaped workpiece during high speed milling. The shell-shaped workpiece is modeled as a double-curved cantilevered shell subjected to a cutting force with time delay effects. Equations of motion are derived by using the Hamilton principle based on the classical shell theory and von Karman strain-displacement relation. The resulting nonlinear partial differential equations are reduced to a two-degree-of-freedom nonlinear system by applying the Galerkin approach. The averaging method is used to obtain four-dimensional averaged equations for the case of foundational parametric resonance and 1:2 internal resonance. Using a numerical method, the dynamics of the cantilevered shell-shaped workpiece is studied under time-delay effects, parametric excitation, and forcing excitation. It is found that time-delay parameters have great impact on chaotic motion. With increasing amplitude of forcing and parametric excitations, the shell-shaped workpiece exhibits different dynamic behavior.

Original languageEnglish
Pages (from-to)767-787
Number of pages21
JournalNonlinear Dynamics
Volume72
Issue number4
DOIs
StatePublished - Jun 2013

Keywords

  • Cantilevered shell
  • Chaotic dynamics
  • Milling process
  • Nonlinear vibrations
  • Time-delay effect

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