A dimensionless number for predicting universal processing parameter boundaries in metal powder bed additive manufacturing

One of the main challenges facing selective laser melting processes is finding suitable process parameters to achieve maximum density (pore-free) parts. In this letter, two newly discovered dimensionless numbers are presented that correlate process parameters to a part's density allowing for an initial estimation of suitable process parameters without the need for extensive modeling or experimentation. The prediction is achieved by utilizing the Buckingham-Π theorem and the implementation of Pawlowski's matrix transformation method. The universality of the new dimensionless numbers is verified by applying them to selective laser melting data for eight different metals and alloy systems, obtained both experimentally and gathered from the literature. The dimensionless numbers allow for identification of process parameters that will result in a maximum density regime in the as-built part. Finally, a universal scaling law is introduced that can aid in quantitative prediction of process parameters that result in the highest as-built density.