Analytical and Machine Learning-based approaches to estimate the steady-state temperature limit on the surface of Cu powder beds when heated by a concentrated laser energy source

Abstract

Surface temperature induced by concentrated energy sources, such as a laser beam used during a selective laser sintering process, has been measured, modeled, and estimated before by several authors. Estimating surface temperature by models including radiation heat transfer has commonly been pursued using elaborated numerical schemes such as finite differences, finite volumes, or finite element schemes, which could be costly to implement. A systematic study of the evolution of the surface temperature at a given fixed point in Cu powder beds exposed to the focused laser beam of a selective laser sintering system is presented here. Incorporation of radiation heat transfer effect into the classical 1-D surface heating-cooling heat transfer model allowed the development of an implicit predictive model for the surface temperature evolution during the heating and cooling of the specimen, which in turn and at its time limit, arrived at a closed-form analytical expression for the plateau temperature of a given superficial point when heated up by a focused laser beam. On the other hand, this latter asymptotic expression, as expected, corresponds to the surface temperature, which can be isolated directly from Stefan-Boltzmann's radiation law—making it possible to predict plateau temperatures (i.e., Stefan-Boltzmann temperature limit) of the Cu powder bed surface at different laser powers with an error of less than 2% compared to surface temperature measurements done using an infrared pyrometer. Concerning the prediction capacity of this expression, the developed technique could be applied not only to different material systems but could also be adapted to handle a moving laser in a given scan pattern, thus obtaining an analytical tool to model better the heat transfer phenomena of, for example, laser powder bed - sintering/melting processes. In parallel, three Machine Learning techniques were implemented, an artificial neural network, specifically the Multi-layer Perceptron, a Support Vector Regression, and Random Forests Regressor, to study the feasibility of these approaches in predicting the steady-state temperature as well, depending on the laser power and the measurement time. From the achieved results, both methodologies are considered suitable to model the temperature behavior of the analyzed specimens.