Evaluation of Cutting Forces and Roughness During Machining of Spherical Surfaces with Barrel Cutters

Barrel tools are increasingly used in high-precision machining of free-form surfaces. However, limited studies evaluate their performance specifically on spherical geometries, where tool–surface contact characteristics differ significantly. Understanding how tool geometry and process parameters influence surface quality and cutting forces in such cases remains underexplored. This study evaluates how barrel cutter radius and varying machining parameters affect cutting forces and surface roughness when milling internal and external spherical surfaces. Machining tests were conducted on structural steel 1.1191 using two barrel cutters with different curvature radii (85 mm and 250 mm) on a 5-axis CNC machine. Feed per tooth and radial depth of cut were systematically varied. Cutting forces were measured using a dynamometer, and surface roughness was assessed using the Rz parameter, which is more sensitive to peak deviations than Ra. Novelty lies in isolating spherical surface shapes (internal vs. external) under identical path trajectories and systematically correlating tool geometry to force and surface metrics. The larger curvature tool (250 mm) consistently generated up to twice the cutting force of the smaller radius tool under equivalent conditions. External surfaces showed higher Rz values than internal ones due to less favorable contact geometry. Radial depth of the cut had a linear influence on force magnitude, while feed rate had a limited effect except at higher depths. Smaller-radius barrel tools and internal geometries are preferable for minimizing cutting forces and achieving better surface quality when machining spherical components. The aim of this paper is to determine the actual force load and surface quality when using specific cutting conditions for internal and external spherical machined surfaces.