Numerical modeling of the effect of nozzle diameter and heat flux on the polymer flow in fused filament fabrication

Abstract

A numerical model that fully account for the velocity of the traveling filament (push velocity) in the liquefier is presented in the current work to predict the pressure, temperature, outlet melt viscosity, strain rate, and velocity in the hot-end of a FFF system for printing tough-poly(lactic acid) (TPLA). The numerical model was thoroughly validated by comparing the model predictions with experimentally measured feeding force data. The predicted numerical results closely approximated the experimentally measured feeding force. Then the model was also validated with extrudate temperature, measured with a thermal imaging camera, and the results obtained are in good agreement. Outlet capillary diameter, feeding rate, and heat flux (quantified in terms of Nusselt number) were varied to determine the response of pressure field, temperature, velocity, viscosity, and strain rate in the liquefier. The results show that an increase in the nozzle outlet diameter decreases the extrusion pressure in the hot-end. The maximum pressure predicted for TPLA is 3.34, 2.91, and 2.04 MPa for the 0.4, 0.6, and 0.8 mm outlet diameters nozzles, respectively. Also, an increase in the nozzle outlet diameter decreases the central velocity at the outlet and decreases the shear rate with an increase in the viscosity of TPLA at the exit during material extrusion. The area-weighted averaged outlet temperature for TPLA decreases as the feeding rate increases for all three nozzle diameters. Elucidated from the simulation results, significant variation of the normalized velocity at the center of the nozzle outlet suggests that different printing speeds for TPLA material extrusion should be set for different nozzle diameters. Otherwise, the accuracy and precision of the gantry motion during layer deposition on the print will be compromised. The simulation results indicate that based on the 90% core melting temperature requirement, at a liquefier set temperature of 503 K, the TPLA should be printed below 80mm/min for all outlet diameters considered. A Nusselt number of 49.61 was observed to be the upper limit where an increase in the heat flux in the liquefier has no significant effect on the area-weighted averaged outlet temperature of TPLA.