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.
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