In this paper, the nonlinear vibration of a thin-plate workpiece during milling process is investigated. The thin-plate workpiece is modeling as a cantilevered thin plate. The equations of motion for the thin-plate workpiece are derived based on the Kirchhoff-plate theory and the von Karman strain-displacement relations by using the Hamilton’s principle. By applying the Galerkin’s approach, the resulting equations are reduced to a two-degree-of-freedom nonlinear system with external excitations. Considering the case of 1:1 internal resonance, the method of Asymptotic Perturbation method is utilized to obtain the averaged equations of the cantilevered thin-plate workpiece. Numerical method is used to study nonlinear dynamics of the cantilevered thin plate and get the two-dimensional phase portraits, waveforms phase, three-dimensional phase and frequency spectrum phase. The result shows that the cantilevered thin-plate workpiece exhibits the complex dynamic behavior with the increase of the amplitude of the forcing excitation.
Nonlinear Vibration of a Thin-Plate Workpiece During High Speed Milling Under 1:1 Internal Resonance Condition
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Zhang, W, Zhou, R, Zu, JW, & Wang, Q. "Nonlinear Vibration of a Thin-Plate Workpiece During High Speed Milling Under 1:1 Internal Resonance Condition." Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition. Volume 3: Design, Materials and Manufacturing, Parts A, B, and C. Houston, Texas, USA. November 9–15, 2012. pp. 1891-1903. ASME. https://doi.org/10.1115/IMECE2012-86159
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