Analytical modeling of in-process temperature in powder feed metal additive manufacturing considering heat transfer boundary condition

This paper presents a physics-based predictive model to estimate the in-process temperature in powder feed metal additive manufacturing (PFAM) based on the absolute coordinate with a stationary origin. Quasi-analytical solutions are developed without resorting to FEM or any iteration-based simulations. Heat transfer boundary condition, laser power absorption, scanning strategy, and latent heat are considered in the prediction of time-dependent thermal profiles. The temperature rise due to a moving laser heat source is predicted using a moving point heat source solution. The temperature drop due to convection and radiation at the part boundary is predicted by a heat sink solution, which is derived by modifying the heat source solution with an equivalent power for heat loss and zero velocity. The final temperature solution is constructed from the superposition of the heat source solution and the heat sink solution. Temperature profiles are predicted in multiple layers using the presented model in PFAM of Ti-6Al-4 V for a thin wall structure. Molten pool evolution is investigated with respect to laser travel distance from its starting point. The stabilized molten pool dimensions in multiple layers are obtained from predicted temperatures and agreed well with experimental measurements in the literature. In addition, the increasing molten pool dimensions were observed from predictions with increasing wall thickness, which confirms the finding reported in the literature. With benefits of high computational efficiency of the developed solution, consideration of heat transfer boundary conditions, and absolute coordinate, the presented model can be used for temperature analysis for a dimensional part in real applications.