Development of the heat transfer model in the selective laser melting process

In this study, a 3-D time-dependent mathematical model has been developed to determine the process parameters used in the production process of powder materials by the selective laser melting method. Within the scope of the study, the temperature distribution, and the change of the melt pool geometry during the manufacturing process with the Selective Laser Melting (SLM) method were investigated under the influence of operating parameters. The problem geometry has been chosen to be semi-cylindrical, including the powder layer region, the melt pool, and the solid region formed because of the machining. Considering that laser-induced heat generation was in geometry, the 3D time-dependent non-homogeneous heat equation was defined for three consecutive processes - 2D steady-state heat transfer in the x-y plane, 2D time-dependent heat transfer in the x-y plane, and 1D time-dependent heat transfer in the z-direction in the y-z plane and analytically solved on the Cartesian coordinate system. The analytical solution was obtained by using "Eigenfunction expansion", "separation of variables" and "change of variables" methods. The verification of the developed analytical model was carried out using the experimental data available in the literature to produce parts by the SLM method using Ti6V4 material. The parametric study was carried out for laser power applications in the range of 20-80 W to 100-250 W, and comparative analyzes were performed by determining temperature distributions and phase transition geometries for different laser power, laser diameter, and metal powder layer thickness. The results of the study show that the designed model has high prediction accuracy, low solution time and is suitable for multiple scanning compared to existing analytical models.