A refined and accurate method for stability analysis of milling process

Abstract

Chatter is a prevalent defect in milling operations, which can cause poor surface finish and machine tool damage. To enhance the accuracy and efficiency of regenerative chatter prediction, we propose an advanced full-discretization approach for milling stability analysis. The motion equations are approximated with fourth- and second-order Lagrange polynomials, leading to a discrete dynamical map correlating current and preceding tooth periods. Stability is determined through the eigenvalues of the transition matrix, derived from the map based on Floquet theory. The proposed method’s effectiveness is validated through benchmark examples and experiments. The algorithm exhibits optimal convergence efficiency when the number of discrete intervals exceeds 50. Compared to the semi-discretization method, it shows improvements of 24.8 % for the one-degree-of-freedom (1-DOF) model and 22.6 % for the two-degree-of-freedom (2-DOF) model in computational speed. Distinct chatter frequencies and elevated force root-mean-square (RMS) values indicate chatter occurrence at measurement point A, contrasting the stable milling observed at point B. This stability is reflected in the distribution of synchronized sampling markers and the superior surface quality of finished parts, further affirming the efficacy of the proposed method for enhancing milling operation outcomes.

Keywords

• Milling stability
• Chatter detection
• Floquet theory
• Stability lobe diagram