On chatter stability in micro milling considering multiple delays from cutter runout and tool deflections

The existing body of research on multiple delays in micro milling has primarily focused on analyzing the effects induced by tool runout. However, under varying machining parameters, the variations in static tool deflections caused by different cutting forces from tool runout will further influence the distribution range of multiple delay periods, thereby introducing additional complexities to the stability analysis of the machining process. This article proposes a dynamic model to characterize the chatter stability of micro milling with the consideration of the coupled effects of cutter runout and tool deflections, emphasizing the advantage of taking account into multiple delays caused by both factors. Based on Timoshenko beam theory and the radial runout model, an iterative algorithm is constructed to calculate the tool's actual effective radii under deflections. Subsequently, instantaneous directional factors involved in the dynamic model are reconstructed with the aid of the obtained multiple delays and actual tool's radii. Finally, a numerical algorithm aiming at efficiently solving the stability lobe diagrams (SLDs) is constructed based on Newton–Raphson method, greatly reducing the computation time required by the traditional semi-discretization method. A series of micro milling experiments verify the proposed model.