Chatter Stability Characterization of a Three-Flute End-Miller Using the Method of Full-Discretization

It was noticed in laboratory practice that certain conditions of slotting operation of a plastic end milling computer Numerical control (CNC) machine became noisy with increasing depth of cut and eventual perforation of workpiece thus objective is to generate stability characterization of the machine in the form of a chart on the plane of cutting parameters on which stable operation is demarcated from the unstable operation. Chatter stability analysis is carried out here using a recently developed method called Full-discretization. The resulting chart is partitioned into portions of secondary Hopf and flip bifurcations through MATLAB eigen-value analysis of resulting monodromy operator. These two types of bifurcation are discovered to be visible for high speed range while only secondary Hopf bifurcation is visible for the low spindle speed range. It is also discovered for the studied slotting operation, that critical characteristic multipliers are almost pure imaginary at the turning points of secondary Hopf bifurcation lobes and get closer to the negative real axis when critical points move away from minimum points. Equation describing the infinitely many but discrete secondary Hopf bifurcation chatter frequencies at minimum points is postulated. The parameters of the end milling process are; tool mass m=0.0431kg tool natural frequency damping factor and workpiece cutting coefficient. The stability chart generated for the system shows close agreement with both practice and theory.