The failure (maximum) feed velocity in a LulzBot Taz 4 3D printer at various temperatures is determined for three polymers: Acrylonitrile butadiene styrene, poly(lactic acid) (PLA), and a PLA polyhydroxybutyrate copolymer. Through an approximate solution of the energy balance, we develop a model to correlate the dimensionless fiber feed velocity (represented by a Peclet number) with a dimensionless temperature. Using these dimensionless parameters, all polymers fall onto the same curve. However, when molten polymer is forced through a small nozzle to enable 3D printing, this curve also depends on another parameter: Nozzle diameter. Our model does not account for this parameter because it does not consider hydrodynamics due to the complexity of the coupled energy and momentum balances. Thus, we modify the Peclet number to account for hydrodynamics and produce a satisfactory master curve for all diameters and polymers. Our dimensionless numbers require determining the polymer thermal and rheological properties as well as the minimum possible temperature that can be used for 3D printing of any given polymer. We discuss a way to predict this temperature based on the entry pressure drop into the nozzle. Our results will enable designers and engineers to modify the extrusion die and polymer in order to obtain better 3D printed items, and these findings can be generalized to other 3D printers. (C) 2017 The Society of Rheology.