Analysis on nonlinear dynamics of a thin-plate workpiece in milling process with cutting force nonlinearities

This paper aims to investigate the nonlinear dynamics of a thin-plate workpiece during milling process with cutting force nonlinearities. By modeling the thin-plate workpiece as a cantilevered thin plate and applying the Hamilton's principle, the equations of motion of the thin-plate workpiece are derived based on the Kirchhoff-plate theory and the von Karman strain-displacement relations. Using the Galerkin's approach, the equations of motion are reduced to a two-degree-freedom nonlinear system. The method of Asymptotic Perturbation is utilized to obtain the averaged equations in the case of 1:1 internal resonance and foundational resonance. Numerical methods are used to find the periodic and chaotic oscillations of the cantilevered thin-plate workpiece. The results show that the cantilevered thin-plate workpiece demonstrate complex dynamic behaviors under time-delay effects, the external and parametric excitations.