Computation of conductive thermal distribution using non-homogenous graph theory for real-time applications in metal PBF process

Abstract

The Powder Bed Fusion (PBF) process is inherently a thermal process with complex thermal interactions between different printed zones as well as different layers. There exist only a few methods such as finite element analysis (FEA), finite element differences (FDM), graph theory (GT), Goldak’s FEA, and Rosenthal equation, which are able to predict thermal temperature distribution throughout a printed layer (2D) or part (3D). All these approaches suffer from inherent limitations including the applied boundary conditions and computational time. A rapid and reliable method to compute thermal distribution throughout a printed part is pivotal to supporting real-time closed-loop monitoring and control, enabling thermal simulation software with rapid and precise prediction, and advancing current research on thermal-related abnormalities such as residual stress and distortion. The literature shows that the conventional graph theory is the fastest approach that generates relatively precise results in a fraction of the computational time of other techniques; however, the lack of a solution to the non-homogeneous governing thermal equation through GT has hampered this method in terms of thermal load resolution, accuracy in highly rapid process such as PBF, and scope of application. In this paper, we describe the characteristics that make GT a superior approach for real-time computation of thermal field compared to other similar approaches such as FDM. Also, we develop a solution to the non-homogeneous term of the thermal conduction equation by using GT. This solution represents a breakthrough for the development of precise real-time closed-loop monitoring and control systems by providing a precise numerical solution to the thermal conduction equation in a fraction of time compared with previous traditional methods such as FEA and FDM. Ongoing work includes the development of an intelligent monitoring and control system that leverages this solution in order to optimize scan strategy real-time in metal PBF.