Stability analysis in milling by taking into account the influence of forced vibrations on the actual tool-workpiece engagement conditions

In order to increase the material removal rate in milling, advanced cutting tools with complex geometry are typically applied under extreme cutting conditions which may trigger undesired chatter vibrations of the machining system. Recently some dynamic milling models were proposed in the literature which take into account the higher geometrical complexity of these tools. In these works, the tool-workpiece engagement conditions are computed from a purely geometric-kinematic analysis of the milling operation. Moreoever, they are kept constant throughout the stability analysis, independently from any possible increase of the axial depth of cut. In many cases the experimental validation of the proposed models is incomplete. In this work a novel methodology for assessing milling stability is presented, which is based on the correct linearization of the regenerative perturbations around the actual steady state forced vibrations. When the axial depth of cut is progressively increased, the resulting forced vibrations may cause a variation of each tooth-workpiece contact conditions, thus influencing the process dynamic behavior. This effect is more dominant when the degree of symmetry is poor as in the case of variable pitch cutters, when there is significant teeth runout, and when the average chip thickness is concurrently very small as in peripheral milling. The proposed approach for chatter prediction consists of an incremental linear stability analysis which does progressively adapt to the gradually increasing depth of cut up to the stability border. The concept was successfully verified with experimental cutting tests.