Stability of shaping trajectories in milling: Synergetic concepts

Abstract

The use of synergetic concepts in studying the steady shaping trajectories of the tool relative to the workpiece in end milling is discussed, with allowance for elastic displacements and their stability. A two-level hierarchy of dynamic equations is employed. At the first level, steady trajectories are considered. At the second, their stability is analyzed on the basis of variational equations for these trajectories. The case in which the pulsed reaction of the system is an order of magnitude less than one period of the displacement cycle is considered.