Nonlinear milling of a flexible plate-workpiece with tool wear & process damping: Bifurcation, stability analysis, and chatter suppression via tunable vibration absorbers

This paper investigates regenerative chatter and its suppression during the peripheral milling of a flexible, thin plate-workpiece with substantial dimensions and low natural frequencies, a configuration that has not been previously analyzed. A realistic nonlinear cutting force model is proposed, and dynamic equations for a nonlinear cantilever plate are derived using von Kármán plate theory and Hamilton's principle. The coupled nonlinear delayed differential equations (NDDEs) governing the process are obtained using the Galerkin and mode summation method, incorporating tool wear and process damping. Three tunable vibration absorbers (TVAs) are designed in two planes, and stability lobes are obtained, considering the significant modes of the plate. The effects of tool location, tool wear, and process damping on the stability lobes are illustrated. Through bifurcation analyses, stable $\tau -$periodic orbits, secondary Hopf bifurcation, and transitions from stable orbits to quasi-periodic and chaotic behaviors, as well as quasi-periodic windows, are demonstrated by adjusting the axial depth of cut. Additionally, the impacts of both the cutting force's nonlinearity and the plate's nonlinearity are examined. Power spectrum responses are employed to analyze chatter frequency behavior, and the significance of higher modes at high spindle speeds is shown. Finally, TVAs are designed to suppress chatter, and optimal locations and parameter values for one and two absorbers are determined. A single absorber improves the stable axial depth of cut at low spindle speeds, while two absorbers enhance it across both low and high spindle speeds. Therefore, TVAs effectively mitigate the adverse effects of nonlinear phenomena, increasing the stable material removal rate.