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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Acknowledgements
The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NNSFC) through Grant Nos. 11290152, 11072008 and 10732020, the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB), and the Natural Science and Engineering Research Council for Discovery Accelerator Supplement of Canada (NSERC).
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Zhang, W., Zhou, R. & Zu, J.W. Nonlinear vibrations of a shell-shaped workpiece during high-speed milling process. Nonlinear Dyn 72, 767–787 (2013). https://doi.org/10.1007/s11071-013-0752-8
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DOI: https://doi.org/10.1007/s11071-013-0752-8