In-process density measurement for model-based process optimization of functionally graded foam microcellular structures in material extrusion additive manufacturing

Abstract

Additive manufacturing with in-process foaming enables the creation of complex, porous structures with graded density and porosity. However, the current process planning method, based on volume conservation principles, fails to accurately capture the nonlinear process-density relationship, thereby limiting the precision of density control. Herein, this study proposes a model-based process optimization approach that utilizes a non-contact in-process density measurement method, enabling optimization of both density and track width. First, this approach accelerates data collection and constructs a reliable process-density and process-width regression model, facilitating rapid process optimization of functionally graded foam. Then, the model captures the nonlinear effects of temperature and printing speed on thermally expandable microspheres, where high temperatures and low speeds promote foaming, and vice versa. Finally, foam samples with gradient densities, produced using optimized parameters, validate the regression model's accuracy and feasibility for customizing intralayer and interlayer density, investigating continuous density gradients, and pressure distribution-driven insoles. Generally, the results highlight the critical role of temperature and printing speed in determining foam density and microstructure, significantly advancing high-quality, controlled-density foam production via material extrusion additive manufacturing. Moreover, the study presents a framework for in-situ, in-process density measurement, aiding the rapid development of process parameter windows for density-variable novel materials based on mass conservation.