RCSA-Based Analysis of Stability Lobes in Milling Incorporating Tool Clamping Errors

This study proposes a methodology for selecting robust stable cutting conditions from a Receptance Coupling Substructure Analysis (RCSA)-based Stability Lobe Diagram (SLD) by considering tool clamping errors that may occur during operator tool setup. However, most existing RCSA studies have been conducted under the assumption of a constant tool clamping length and thus do not sufficiently reflect the clamping length variation observed in practical machining environments. Since the tool tip dynamic characteristics can be sensitive even to small variations in clamping length, operator-induced tool clamping errors in actual processes can introduce such variations and consequently degrade the prediction accuracy of the SLD. Moreover, uncertainty studies in milling stability have largely focused on variations in model parameters, such as cutting coefficients, damping, and modal parameters, whereas experimental quantification of operator-induced clamping length variability and its direct integration into RCSA-based tool tip Frequency Response Function (FRF) and SLD prediction has been relatively limited. Therefore, this study quantifies the distribution of tool clamping errors through clamping experiments and incorporates it into RCSA to derive an SLD band that accounts for tool clamping errors. The width of the SLD band is defined as a physical variation induced by clamping uncertainty, and the corresponding uncertainty range is set as an avoidance region. Robust cutting conditions are then selected from the remaining stable region while considering the physical variation width. The physical variation width was quantified as 60 rpm (minor axis) and 1.62 mm (major axis), representing the dispersion of the stability limit in the spindle speed and axial depth directions caused by clamping errors. As a result, stable cutting conditions that do not cross the stability limit can be determined even in the presence of process variations and disturbances.