Stability Analysis of Milling Process With Time-Varying Delays Via Lyapunov-Krasovskii Functional

Abstract

The regenerative chatter during milling seriously affects the stability of the system. This paper proposes a method based on Lyapunov-Krasovski functional analysis for the stability of the milling process. First, the mechanism analysis of the milling process is performed, then the state-space equation of the time-varying delay system caused by the regeneration effect is established. Secondly, based on the model of a time-delay system, a stability criterion is developed by constructing an augmented Lyapunov-Krasovski functional (LKF) and using auxiliary function inequality with reciprocally convex combination technology. Finally, the validity of the method is verified through an example, and the milling stability domain lobe diagram with a parameter combination of spindle speed-cutting depth is obtained which provides operational guidelines to guarantee a stable vibration-free process.