On extreme value theory-based estimation of surface quality for metal additive manufacturing

Abstract Surface roughness of additively manufactured metal parts has significant impacts on the part’s performance (e.g., fatigue resistance) and poses a significant roadblock to the wider adoption of metal additive manufacturing. This work aims to show that, in some cases, it is possible to estimate the depth of the deepest valley of an additively manufactured part with a relatively high accuracy using either only line measurements from a contact profilometer (and limited areal scans used for calibration) or areal scans from optical areal scanners of a considerably smaller area of the same specimen or even another specimen produced in the same batch under the same conditions. Both problems are approached by employing the block-maxima method from extreme value theory, whereby the underlying distribution of the depth of individual valleys is modeled with a Gumbel distribution. The experimental results from additively manufactured Ti-6Al-4V specimens demonstrate that the proposed methods can produce estimates that significantly outperform more straightforward benchmarks (e.g., simply using linear parameters for areal ones), and the proposed methods achieve a relatively accurate estimation with mean errors of 5–15%. The proposed methodology can contribute to enabling a cheaper and more efficient way to quantify and estimate surface roughness, consequently facilitating a more efficient investigation of its impacts on mechanical performance (especially fatigue) and the quality control of additively manufactured parts.