Mathematical Modeling of Multi-Performance Metrics and Process Parameter Optimization in Laser Powder Bed Fusion

This study aims to develop mathematical models to improve multi-performance metrics, such as relative density and operating costs, in laser powder bed fusion (LPBF), also known as selective laser melting, a metallic additive manufacturing technique, by optimizing the printing process parameters. The work develops a data-driven model for relative density based on measurements and an analytical model for operating costs related to the process parameters. Optimization models are formulated to maximize relative density or minimize operating costs by determining the optimal set of process parameters, while meeting a target level of the other performance metrics (i.e., relative density or operating costs). Furthermore, new metrics are devised to test the sensitivity of the optimization solutions, which are used in a novel robust optimization model to acquire less sensitive process parameters. The sensitivity analysis examines the effect of varying some parameters on the relative density of the fabricated specimens. Samples with a relative density greater than 99% and a machine operating cost of USD 1.00 per sample can be produced, utilizing a combination of low laser power (100 W), high scan speed (444 mm/s), moderate layer thickness (0.11 mm), and large hatch distance (0.4 mm). This is the first work to investigate the relationship between the quality of the fabricated samples and operating cost in the LPBF process. The formulated robust optimization model achieved less sensitive parameter values that may be more suitable for real operations. The equations used in the models are verified via 10-fold cross-validation, and the predicted results are further verified by comparing them with the experimental data in the literature. The multi-performance optimization models and framework presented in this study can pave the way for other additive manufacturing techniques and material grades for successful industrial-level implementation.