Analytical model to predict the extrusion force as a function of the layer height, in extrusion based 3D printing

Fused Filament Fabrication is the most widespread 3D printing process, and issues such as improving accuracy and speed are significant areas of research. To better understand and foresee the process, accurate models would be very useful. Several analytical models have been proposed in the literature; however, while the behavior inside the print core has been investigated, to the best of the authors’ knowledge, no studies are reported on the behavior of the melt filament downstream of the nozzle. This lack of research is very important, since the behavior downstream of the nozzle is influenced by the counterpressure generated by the deposited material. Qualitatively, the lower the layer height, the higher the counterpressure should be, while the higher the printing speed, the lower the counterpressure. No such models are available in the literature that take these phenomena into account, and such a model would help in managing the printing process when low layer height is required for improving the accuracy and roughness of the part. In the present study, a new analytical model was developed to compute the minimum force necessary to push the filament into the extruder according to given values of printing process parameters. The model considers both the contribution of the extrusion force and of the deposition force, allowing the prediction of the variation of the required pushing force when variations of the layer height occur and can be a useful tool in the design of process parameters when very accurate components are needed in the process of additive manufacturing (AM).