Attractive manifolds in end milling

The attractive manifolds formed in end milling are analyzed. Such states are formed if the trajectories of steady periodic deformational tool displacements are unstable overall or in individual sections. In the dynamic milling system, attractive manifolds in the form of limit cycles, invariant tori, and strange (chaotic) attractors may appear. Bifurcations of attractive manifolds in parameter space are analyzed at length, with examples. Interest centers on how attractive manifolds affect manufacturing quality.