Chatter Stability Characterization of a Plastic End-Milling CNC Machine

The desire to carry out this work arose from an observation during a practical work on a typical plastic end milling CNC machine. It was noticed that under certain conditions of cutting, operation of the machine became noisy with increasing depth of cut and eventual perforation of workpiece therefore the basic aim 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 . In modelling this machine, a slot creating mode of operation is used since the machine is mainly used for creating logos which are basically collection of slots. The significance of the resulting stability chart lies in the result that the cause of the aforementioned noisy operation is due to unstable parameter combination. For example a laboratory operation at spindle speed of 1500rpm and depth of cut of 1.5mm was noisy while that at spindle speed of 1500rpm and depth of cut of 1mm was serene. The stability chart generated for the system thus shows close agreement with both practice and theory. A unique impact this work will have on the reading community will be in the area of validity of the resulting stability chart on the basis of MATLAB dde23 numerical simulation. The parameters of the end milling process are; tool mass tool natural frequency  damping factor  and workpiece cutting coefficient . Keywords: chatter, time history, Fargue approximation, Floquet theory, bifurcatio

Third-order least squares modelling of milling state term for improved computation of stability boundaries

The general least squares model for milling process state term is presented. A discrete map for milling stability analysis that is based on the third-order case of the presented general least squares milling state term model is first studied and compared with its third-order counterpart that is based on the interpolation theory. Both numerical rate of convergence and chatter stability results of the two maps are compared using the single degree of freedom (1DOF) milling model. The numerical rate of convergence of the presented third-order model is also studied using the two degree of freedom (2DOF) milling process model. Comparison gave that stability results from the two maps agree closely but the presented map demonstrated reduction in number of needed calculations leading to about 30% savings in computational time (CT). It is seen in earlier works that accuracy of milling stability analysis using the full-discretization method rises from first-order theory to second-order theory and continues to rise to the third-order theory. The present work confirms this trend. In conclusion, the method presented in this work will enable fast and accurate computation of stability diagrams for use by machinists