Maximal 3D printing extrusion rates

Many applications of 3D printing are enhanced by increased printing speed. In the hot end of a 3D printer, the polymer feed stock flows in a heated cylinder at a set temperature. Since the polymer must be hot enough to reach a pliant state before extrusion, this establishes a maximum velocity beyond which the polymer is too rigid to be extruded. A mathematical model is presented for this system, and both amorphous and crystalline polymer systems are examined. The former is a heat transfer problem; the latter is a Stefan problem. Several different conditions for establishing the maximum velocity are considered; using the average polymer temperature in the hot end matches well with experimental data.