Nonlinear Oscillation of Shell Workpiece in High Speed Milling Under 1:2 Internal Resonance Condition
We aim to study nonlinear dynamics of a shell-shaped workpiece during milling processes in this paper. The shell-shaped workpiece is modelled as a cantilever thin shell subjected to a cutting force with time-delay effects. The formulas of the cantilever shell were derived by the classical shell theory and the von Karman strain-displacement relations. The resulting differential equations are reduced to a two-degree-of-freedom nonlinear system ordinary differential equations by applying the Galerkin’s approach. The method of Asymptotic Perturbation method is used to obtain the averaged equations, which were dealt with the resonance cases of 1:2 internal resonance and principal parametric resonance. Dynamic behaviors are presented based on the numerical solutions. The results show that different time-delay parameters result in periodic motion, multiple periodic motion, and chaotic motion.