Stability analysis of machine-tool vibrations in the frequency domain

The identification of the stability lobes for machine-tool vibrations via frequency domain methods is presented using the example of interrupted turning process with round inserts. An analytic cutting force model for round inserts is derived, where the directional factors depend nonlinear and non-homogeneous on the depth of cut. Vibrations in tangential, normal and axial direction are taken into account. In particular, tangential vibrations in cutting speed direction lead to a state-dependent delay. Thus, the model is characterized by periodic excitation due to interrupted cutting and state-dependent delays due to tangential vibrations. The application of the multifrequency solution for the stability analysis of such non-autonomous systems with state-dependent delays is presented.