Stability analysis of milling process by combining the gyroscopic effect with the symmetry and runout of the cutter

Abstract Existing studies on gyroscopic effect, which is the mode changing phenomenon of the cutter in high speed rotating status, did not consider the influences of the tool’s actual crosse section and the cutter runout, which unavoidably exist in actual machining process, and thus, they cannot be used to well reveal the underlying mechanism of the gyroscopic effect in practical milling process. This article systematically studies the gyroscopic effect in milling process, and theoretically, the actual tool’s cross section and the cutter runout are integrated together to derive the expression of the sectional inertia moment of the cutter, which is then utilized to formulate the gyroscopic effect-induced motion equations of the cutter. Derivations show that for the cutter with symmetrical cross section, the motion equation expressed in the global Cartesian coordinate system can capture the dynamic response of the process, while for the asymmetrical section tool, its motion should be modelled in the rotation coordinate system. The obtained motion equation, whether it is formulated in the global Cartesian coordinate system or the rotation coordinate system, is then used to solve the speed-dependent frequency response functions (FRFs) of the tool, and subsequently, it is combined with the semi-discretization method to estimate the stability lobe diagrams (SLDs) by introducing the multiple delays induced either by the cutter runout or by the tool’s uniform pitches. A series of milling tests shows that the predicted SLDs involving the comprehensive influences of the cutter runout and the tool’s cross section on the gyroscopic effect reasonably agree with the experimentally observed results, and especially, they are much closer to the experimental observations than the SLDs without this consideration. It turns out that the combination of the cutter runout and the tools’ cross section has an unavoidable effect on the gyroscopic effect together with the process stability.