Foam-assisted fused filament fabrication enables the production of lightweight, architected thermoplastic components with tailored internal porosity; however, a quantitative understanding of process–structure relationships in foamed thermoplastic polyurethane (TPU) remains limited. In this study, the influence of nozzle temperature, printing speed, and layer height on porosity evolution in foamed TPU is systematically investigated using a \(2^3\) full factorial design of experiments with center points. High-resolution synchrotron X-ray micro-computed tomography performed at the BEATS beamline (SESAME, Jordan) enables three-dimensional reconstruction and quantitative pore characterization with a resolution up to 0.9 \(\mu \) m. Using a dedicated protocol developed for this purpose, it was possible to classify porosity within scanned samples which allowed in-depth analysis of the foaming process. Two porosity metrics are distinguished: Total Porosity (TP), representing all voids within the specimen, and Foam Induced porosity (FIP), isolating spherical pores generated by the foaming agent. First, a qualitative analysis of the porosity within the printed samples is presented. Afterwards, the results of a quantitative analysis show that TP ranges from 5.44% to 41.59%, while FIP varies from 0.01% to 32.97%, exhibiting a strongly non-proportional dependence on temperature. Analysis of variance identifies temperature as the dominant factor, contributing 88.2% and 85.4% of the variance in TP and FIP, respectively (p < 0.001). Additionally, speed showed a significant but limited effect both on TP and FIP. In terms of interaction effects, the interaction between temperature and speed and temperature and layer height was significant in TP, while only the interaction effect of temperature and speed was significant in FIP. Regression models incorporating interaction and curvature terms achieve high predictive capability ( \(R^{2}_{pred}>\) 0.99), confirming robustness within the investigated parameter space. By combining synchrotron-based three-dimensional characterization with statistical modeling, this work establishes a quantitative process–porosity framework for foamed TPU extrusion, providing mechanistic insight into thermally activated foam formation and enabling predictive control of internal architecture in extrusion-based additive manufacturing.
