3-D PRINTING EXTRUSION RATES THROUGH A TAPERED NOZZLE
University of Delaware
In applications of 3-D printing, production rates and product quality are enhanced by increased printing speeds. A polymer feedstock is fed through the hot end of the 3-D printer, which operates at a set temperature. Since some amount of heating time is necessary for the polymer to become pliant, there is an upper bound on the ow velocity before it remains too rigid to be extruded. The hot end is comprised of a cylinder that feeds directly into a tapered nozzle immediately prior to extrusion. In this study, we model the e ects of this geometry in both amorphous and crystalline polymers. We consider the former case, a heat transfer problem, in an idealized tapered hot end (without cylindrical portion) using separation of variables to provide an analytical temperature pro le. We consider the latter case, a Stefan (moving boundary) problem, in three geometries (a cylinder, a taper, and a combined system) using the heat balance integral method to provide an analytical approximation for the temperature pro le. We develop several di erent conditions based on these temperature pro les to predict maximum velocity. In amorphous polymers, the model fails to predict the experimental data due to limitations from the considered geometry. In crystalline polymers, using the exit temperature of the hot end yields a model that adheres well to the experimental data regardless of the geometry considered.
applied mathematice, 3-D printing, extrusion rates