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

Abstract

It was noticed in laboratory practice that certain conditions of slotting operation of a plastic end milling computer Nu merical control (CNC) machine became noisy with increasing depth of cut and eventual perforation of workp iece 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 fro m the unstable operation. Chatter stability analysis is carried out here using a recently developed method called Fu ll-discretization. The resulting chart is partit ioned into portions of secondary Hopf and flip bifurcations through MATLAB eigen-value analysis of resulting monodro my operator. These two types of bifurcation are d iscovered to be visible for high speed range while only secondary Hopf bifurcat ion is visible for the lo w spindle speed range. It is also discovered for the studied slotting operation, that critical characteristic mu ltipliers 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 min imu m points. Equation describing the infinitely many but discrete secondary Hopf bifurcation chatter frequencies at min imu m points is postulated. The parameters of the end milling process are; tool mass m = 0.0431kg, tool natural frequency ���� n = 5700 rad s −1 , damping factor ξ = 0.02 and workpiece cutting coefficient C = 3.5 × 10 7 Nm −7 4 ⁄ . The stability chart generated for the system shows close agreement with both practice and theory.