# Effect of Filament Material and Printing Temperature on 3D Printing Extrusion Force
## 3 Results and Discussion  
A typical measurement is shown in Figure 2. The force data were recorded during the entire printing process. The first peak in the force graph corresponds to the nozzle cleaning phase, in which the printer extruded two short lines on the left side of the printer bed to clean the nozzle, remove material residue, and establish a constant flow; in this step, the extrusion speed and layer thickness were controlled by the printer firmware. The print head then moved to the center of the bed and began printing using configured settings. In this stage, the force increased as the molten polymer was forced through the nozzle onto the bed surface. When printing in air (blue curve), the recorded forces were lower as the material was able to flow freely through the nozzle without any backpressure from previously deposited material. The force values during the first layer of printing were lower than those of the subsequent layers. This difference is probably due to the material flow: The first layer had a thickness of 0.3 mm, while the subsequent layers were 0.5 mm thick. As a result, about 50% more material had to be pushed through the nozzle in the second and subsequent layers (with a volumetric flow rate from 5.96 mm\({}^{3}\)/s to 8.93 mm\({}^{3}\)/s). The last part of the extrusion on each printing line always showed a short increase (Figure 3) because a little material is extruded into the wall overlap of the printing lines to ensure a better connection of the current printing line with the existing lines and a better strength of the printed parts. This parameter was set in the Cura Slicer and was 0.3 mm--the nozzle prints 0.3 mm into the walls. After finishing one layer, the nozzle moves upwards to print the next layer. To prevent the material from oozing during the Z-movement to the next layer height, the filament is retracted--this is indicated by a sudden drop in force. The filament is pulled back 5 mm by the feeding roller, followed by an increase in force as the feeding roller begins to push the filament into the nozzle and extrude the next layer. During each layer, the forces are relatively constant with small fluctuations due to material inhomogeneity, deceleration and acceleration in printer movement as the printer changes direction (e.g., across the nine longitudinal infill lines--Figure 4), and likely some contribution from vibrations of the printer head during movement. Lastly, with printing on the last layer, the increase in force is greater again as the extruded material overlaps the outer surface more to ensure closed solid surface. Figure 2: Typical measurement of extrusion forces for PLA filament (T = 200 \({}^{\circ}\)C, printing speed 20 mm/s). One of the conditions for steady extrusion is constant temperature in hotend. The power required to maintain a constant temperature can be calculated from  
\[P=\frac{q\times Cp\times(Tm-Tamb)}{efficiency} \tag{1}\]  
where the following apply:  
P = Power (in watts). q = Flow rate (in mm\({}^{3}\)/s). C\({}_{\rm P}\) = Specific heat capacity (in J/g\({}^{\circ}\)C). T\({}_{\rm m}\) = Melting temperature of PLA (in \({}^{\circ}\)C). T\({}_{\rm amb}\) = Ambient temperature (in \({}^{\circ}\)C). efficiency = efficiency (as a fraction, 1 for 100% efficiency). The specific heat capacity of PLA is about 1.9 J/g \({}^{\circ}\)C, and the extruding temperature of PLA is 220 \({}^{\circ}\)C. Max flow rate (q) is 8.93 mm\({}^{3}\)/s. PLA filament typically has a density of around 1.24 g/cm\({}^{3}\). Assuming 100% efficiency, meaning all electrical energy is used to heat the filament, the required power for heating the hot end is  
P = 8.93 \(\times\) 1.24 \(\times\) 1.9 \(\times\) 0.001 \(\times\) (220-25) = 4.1 W  
The actual cartridge heater (rated 40 W) should be capable of heating the material to the desired T even at the highest used material volumetric flow. In addition, the heater cartridge is mounted in an aluminum block, which ensures thermal inertia to minimize temperature fluctuations.