Optimum Conditions for Variable Pitch Milling

Abstract

From the perspective of regenerative chatter, variable-pitch milling process offers a mathematically very challenging task. It can be reduced to the problem of stability assessment on a linear time-invariant dynamics (LTI) which has more than one independent delays. This mathematically notorious problem is uniquely solved by a recent paradigm. It is called Cluster Treatment of Characteristic Roots (CTCR). This paper presents a process optimization procedure using CTCR over a special milling operation with variable pitch cutters. The optimization is based on maximizing the metal removal rate while avoiding the onset of chatter, which, in turn, enables production of the parts with a desirable surface quality. The end result is a powerful tool to determine some important geometrical and operational features of the process: (i) the pitch angle selection on the tool (i.e., variable pitch cutter vs. uniform pitch cutter), (ii) the optimum cutting conditions (i.e., depth of cut and the spindle speeds).