Abstract
The ability of additive manufacturing (AM) to produce components with virtually any ge-ometry presents a unique challenge in terms of quantifying the quality of the part. In this paper, a novel spectral graph theory (SGT) approach is proposed for resolving two critical quality assurance concerns in AM: (1) how to quantify the dimensional integrity of complex AM components; and (2) how to isolate specific spatial locations on a component that deviate significantly from their normal condition. Here, the SGT approach is demonstrated for classifying the dimensional integrity of standardized test components produced from three different AM processes. The SGT-based topological invariant Fiedler number (λ2) was calculated from 3D point cloud coordinate measurements and used to quantify the dimensional integrity of test components. The Fiedler number was found to differ significantly for parts originating from different AM processes (statistical significance p-val. < 1%). By comparison, traditional statistical quantifiers (such as mean and standard deviation) and examination of specific facets/landmarks failed to capture these variations and proved incapable of quantifying the quality of the component in a consistent manner. The SGT approach was verified to consistently rank the quality of the AM components with a high degree of statistical confidence independent of sampling technique used (pooled standard deviation ~ 3% – 10% of mean). From a practical standpoint, the SGT approach can be a powerful tool for quantifying and monitoring the dimensional integrity and overall quality of AM components, and thus encourage wider adoption of AM capabilities.
