Robust evaluation of chatter stability for milling process with uncertainties based on optimal configuration of machining position and spindle speed

Chatter vibration in milling process is a major obstacle that limits the machining quality and productivity, which may be avoided by using stability lobe diagrams (SLDs). Many traditional models developed to predict chatter stability assume that dynamic parameters of the machine tool remain constant under operational conditions. However, these parameters such as natural frequencies, damping ratios, stiffness, and cutting force coefficients vary depending upon different aspects including spindle speed, tool wear, and machining position, reducing the accuracy of chatter prediction. In this study, a robust chatter prediction method based on conventional analytical milling stability models is presented by employing the Edge theorem and Zero Exclusion condition. In this method, optimal combinations of spindle speeds and machining positions are firstly researched to obtain higher critical depths of cut, based on the conventional stability model, modal fitting technique, Kriging model, and improved particle swarm optimization. At each combination, related nominal modal parameters and cutting force coefficients are identified, and their left and right worst-case deviations are also determined. Critical stable condition for each combination is detected by a graphic approach within the minimum and maximum bounds of uncertainties. Accordingly, a robust stability lobe diagram is obtained with related spindle speeds and critical cutting depths. The proposed method was verified by chatter tests on a real vertical machining center, demonstrating its reliability in chatter prediction compared to the conventional stability lobe diagram.