Analytical Surface Roughness Parameters of a Theoretical Profile Consisting of Elliptical Arcs

The closed-form solutions of surface roughness parameters for a theoretical profile consisting of elliptical arcs are presented. Parabolic and simplified approximation methods are commonly used to estimate the surface roughness parameters for such machined surface profiles. The closed-form solution presented in this study reveals the range of errors of approximation methods for any elliptical arc size. Using both implicit and parametric methods, the closed-form solutions of three surface roughness parameters, Rt, Ra, and Rq, were derived. Their dimensionless expressions were also studied and a single chart was developed to present the surface roughness parameters. This research provides a guideline on the use of approximate methods. The error is smaller than 1.6% when the ratio of the feed and major semi-axis of the elliptical arc is smaller than 0.5. The closed-form expressions developed in this study can be used for the surface roughness modeling in CAD/CAM simulations.