Lyapunov–Krasovskii approach to the stability analysis of the milling process

Abstract

Self-excited milling vibrations represent an important problem in the manufacturing industry. This study presents an out-of-process analysis based on the Lyapunov–Krasovskii approach which provides operational guidelines for the proper selection of the cutting parameters to guarantee a stable vibration-free process. The proposed approach considers a time-delay two degree of freedom model and takes advantage of some useful tools of the control theory developed for time-delay systems such as the descriptor method and the Bessel–Legendre inequalities.