Analytical modeling of temperature evolution in laser powder bed fusion considering the size and shape of the build part

Abstract

This paper develops an analytical model of temperature in Laser Powder Bed Fusion (LPBF) considering the geometrical effect of the build part, which is reflected by the part size and shape. The model is established based on the moving point heat source under a semi-infinite medium. A modified coefficient is utilized to calibrate the temperature along the build direction. The heat sink is adopted to consider the heat loss at the edge of the build part, and the superposition method is applied to calculate the multi-tracks effect of the laser beam. The material thermal properties are dependent on the temperature, and an iteration method is utilized to obtain the dynamic stable melt pool during the process. To validate the proposed model, the experimental data in the published paper are compared with the model predictions. Good agreement is found about the melt pool size. Based on the verified model, a sensitivity analysis of temperature with respect to the laser process parameters, the material properties, and the geometry of the build part is discussed. Both the depth and width of the melt pool have a negative relationship with the size of the part within the explored range. It is also shown that the size of the melt pool has a negative correlation with the length of the previous track, which is determined by the shape of the build part.