Influence of Plane-parallel Finishing Trajectories to the Roughness Obtained by Milling of Spherical Surfaces

The purpose of the present paper is to determine a mathematical model in order to evaluate theoretically the roughness of a spherical surface finished with a torodial end mill. The parameters that influence the theoretical value of the roughness are: (i) technological parameters (cutting speed, feed per tooth, radial feed) or (ii) geometrical (the geometry of the semi-product, the geometry of the cutting tool). The calculus to determine the roughness value is a difficult task taking into consideration the complexity of the mathematical relations; the paper presents a graphic method using a CAD application (AutoCAD) and a programming environment (AutoLISP).