Development of an analytical model to investigate temperature distribution and melt geometry in the laser powder bed fusion process under different operating parameters

Laser powder bed fusion (L-PBF) fabricates components by melting layers of metal powder. Consequently, it has the potential to induce interparticle air gaps or generate unpredictable stresses. As such, understanding temperature distribution and predicting the melt pool based on process parameters are essential. While numerous numerical studies in the literature aim to determine these parameters, these numerical estimation methods often demand extensive computational time and powerful processors. This study introduces a new analytical model and a solution method, offering a significantly faster and more precise solution compared to numerical approaches. Furthermore, the developed model allows the identification of liquid and solid phase regions within the part during production, along with insights into the phase region changes over time. Eigenfunction expansion, separation of variables, and variable transformation methods were employed in the analytical solution of the model equations. Results obtained from this method have been validated by experimental studies available in the literature. By utilizing the derived solution function, the L-PBF process was parametrically investigated, revealing temperature distributions and melt pool geometries. The parametric study focused on the laser power, spot size, and powder layer thicknesses as variable parameters. The study determined that a 50 W increase in laser power raises the maximum melt pool temperature by an average of 800 K, and laser power has been identified as the most influential parameter affecting temperature distribution and melt pool geometry.