Optimization of Process Parameters for Powder Bed Fusion Additive Manufacturing Using a Linear Programming Method: A Conceptual Framework

Abstract

At present, the selection of optimal technological parameters for laser powder bed fusion (LPBF) is determined by the requirements of the fusion process. The main parameters that are commonly varied include laser power (P), scanning speed (v), hatch spacing (h), and layer thickness (t). The productivity of the LPBF process (the increment in the fused volume of the material) is equal to the product of the last three parameters, and the mechanical properties are largely determined by the volumetric fusion energy density, which is equal to the ratio of laser power to productivity. While ensuring maximum process productivity, it is possible to obtain acceptable quality characteristics—mechanical properties, surface roughness, etc.—for a certain range of LPBF technological parameters. In these cases, several quality characteristics act as constraints on the optimization process, and productivity and the key quality characteristics become components of the objective function. Therefore, this article proposes a formalized representation of the optimization problem for the LPBF process, including the derivation of the objective function with the constraint matrix, and provides a solution to the problem using the linear programming (LP) method. The advantages of the proposed method include the guaranteed convergence of the solution with an unlimited number of constraints; the disadvantage concerns the adequacy of the solution, which is limited by a relatively narrow range of parameter changes. The proposed method was tested in determining the optimal LPBF parameters for an HN58MBYu powder LP model that included 13 constraints and an objective function with two target parameters. The obtained results made it possible to increase the productivity by 15% relative to the basic technological parameters.