3-D PRINTING EXTRUSION RATES THROUGH A TAPERED NOZZLE
Date
2020-05
Authors
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Journal ISSN
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Publisher
University of Delaware
Abstract
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.
Description
Keywords
applied mathematice, 3-D printing, extrusion rates