Parameters of the cross-section of the cut during finishing turning with cutters operating with an oblique cutting pattern

This article presents a comprehensive study of the geometric parameters of chip cross-section during finishing turning using cutting tools with straight, concave, and convex cutting edges under oblique cutting conditions. A mathematical model is developed to calculate the chip cross-section shape, taking into account the intersection of the cutting edge with the previously machined surface (modeled as a single-sheet hyperboloid) and the unmachined cylindrical surface of the workpiece. The influence of cutting edge inclination angle (λ = 0–60°), feed rate, cutting depth, and workpiece radius on the chip geometry is investigated.Results show that the ratio of active cutting edge length to average chip thickness decreases with increasing λ. For straight and concave edges, this reduction is most significant at λ < 20°, while for convex edges it is most pronounced at λ > 20°. The convex edge generates the highest surface roughness, whereas replacing the straight edge with a concave one reduces surface micro-roughness more than tenfold. It is shown that increased values of the L/asr ratio, which characterizes the deformation distribution in the cutting zone, may lead to vibrations; however, their stabilization is achieved at specific combinations of tool geometry and cutting parameters.The research outcomes are supported by analytical calculations and experimental validation. The findings are valuable for improving tool design and optimizing cutting conditions in high-precision machining. They contribute to enhancing surface quality, increasing process stability, and reducing tool wear in oblique cutting operations involving complex cutting tool geometries and challenging material removal conditions.