Experimental and analytical study of the polymer melt flow through the hot-end in material extrusion additive manufacturing

Material extrusion additive manufacturing utilizes a thermoplastic polymer in the form of a solid filament as a built material. The polymer melts inside the hot-end channel and flows under the pressure generated by the filament feeding force. The flow of polymer through the hot-end is not fully understood yet, as it involves many complex phenomena, such as phase transition, shear rate and temperature dependent viscosity, as well as viscoelastic effects. In this paper, we investigate experimentally the filament feeding force, as a function of the feeding rate, for different materials (PLA and ABS), liquefier temperatures, nozzle diameters, and lengths of the liquefier. Two extrusion regimes are identified: a linear regime with a stable flow, and a non-linear regime with fluctuations in the feeding force, which are concomitant to unstable extrusion. Increasing the liquefier length and liquefier temperature are found to extend the linear extrusion regime. It is shown that the filament feeding force predicted by the analytical models available in the literature deviates from the measurements, especially at high feeding rates. A model solely based on heat transfer considerations is proposed to estimate the maximum feeding rate before the extrusion becomes unstable. The modelling results agree well with the measurements. The model can be used to select the hot-end design as well as appropriate printing parameters.