In this work, dimensional analysis is used to develop a general mathematical model to predict bulk density of SLMed components taking volumetric energy density, scanning speed, powder’s thermal conductivity, specific heat capacity, and average grain diameter as independent variables. Strong relation between dependent and independent dimensionless products is observed. Inconel 718 samples were additively manufactured and a particular expression, in the form of a power-law polynomial, for its bulk density, in the working domain of the independent dimensionless product, was obtained. It is found that with longer laser exposure time, and lower scanning speed, better densification is attained. Likewise, volumetric energy density has a positive influence on bulk density. The negative effect of laser power in bulk density is attributed to improper process conditions leading to powder particle sublimation and ejection. A maximum error percentage between experimental and predicted bulk density of 3.7119% is achieved, which corroborates the accuracy of our proposed model. A general expression for determining the scanning speed, with respect to laser power, needed to achieve highly dense components, was derived. The model’s applicability was further validated considering SLMed samples produced by AlSi10Mg and Ti6Al4V alloys. This article elucidates how to tune relevant manufacturing parameters to produce highly dense SLM parts using mathematical expressions derived from Buckingham’s π- theorem.

In this work, a previously developed mathematical model to predict bulk density of SLMed (produced via Selective Laser Melting) component is enhanced by taking laser power, scanning speed, hatch spacing, powder’s thermal conductivity and specific heat capacity as independent variables. Experimental data and manufacturing conditions for the selective laser melting (SLM) of metallic materials (which include aluminum, steel, titanium, copper, tungsten and nickel alloys) are adapted from the literature and used to evaluate the validity of the proposed enhanced model. A strong relation between dependent and independent dimensionless products is observed throughout the studied materials. The proposed enhanced mathematical model shows to be highly accurate since the computed root-mean-square-error values (RMSE) does not exceed 5 × 10−7. Furthermore, an analytical expression for the prediction of bulk density of SLMed components was developed. From this, an expression for determining the needed scanning speed, with respect to laser power, to achieve highly dense components produced via SLM, is derived.

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In this work, the fractal nature of Selective Laser Melting (SLM) additive manufacturing process (AM) is elucidated. Fractal dimension and lacunarity of metallic powders are calculated from Scanning Electron Microscopy (SEM) images adapted from literature. The complexity and homogeneity of the textures of the powder beds are also studied through the comparison of fractal dimension and lacunarity. It is found that better densification results are obtained when the powder bed’s fractal dimension is closer to the golden mean number of 1.618. Furthermore, this finding is extended to expressions for predicting the component’s bulk density produced via SLM by setting the [Formula: see text] exponent equal to the golden mean value and finding the proportionality constant, [Formula: see text], using a nonlinear least squares method. The proposed approach works well since theoretical prediction and experimental data compare well with root-mean-square-error (RMSE) values that do not exceed [Formula: see text]. This work sheds new light on enhancing additive manufacturing technologies considering the fractal nature of SLM since its process mathematical models are constructed around Euclidian space-time with continuous smooth assumptions that should be adapted to include the fractal nature of the manufacturing process aiming to improve their precision. The underlying interweaving of SLM, as a fractal process, and the golden mean number is revealed.