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, R t , R a , and R q , 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.