Modeling and analysis of paste freezing in freeze-form extrusion fabrication of thin-wall parts via a lumped method

Abstract During the Freeze-form Extrusion Fabrication (FEF) process using aqueous-based pastes, the freezing environment solidifies the water content in the paste and thus aids the part in maintaining its shape. Because of the small temperature variation in the paste and the paste’s large latent heat introduced by the water contained in the paste, the paste typically freezes slowly during the FEF process. In this study, a lumped method was used to model the solidification process of thin-wall parts fabricated in a layer-by-layer manner. A non-dimensional analytical solution for the freezing time of parts with large numbers of layers was obtained using the lumped method, and its corresponding dimensional solution was compared with numerical simulation results. Based on the analytical solution, the effects of two non-dimensional factors (i.e., non-dimensional latent heat and effective Biot number) and six dimensional factors (i.e., convection coefficient, paste material, paste solids loading, ambient temperature, filament height, and filament width) on the freezing time were investigated. Experiments using different solids loadings pastes and extrusion parameters were conducted to validate the freezing time predictions generated by the lumped method. Possible error sources during the experiments were discussed and their effects were estimated. The results show that the lumped method can be used to accurately predict the freezing time of thin-wall parts within 17.9% differences from the measured results.