## 4 Results and Discussion
### Determination of the Optimum Characteristics  
The next step in the study is to understand the optimum amplitude and wavelength of the induced vibrations to provide the most optimum infill of material in the printed parts. The printer is instructed to print one inner layer on a sheet of paper to achieve this. Instead of the filament, the pen attachment is also used in this process. Figure 8 shows the variation in the infill as the extruder head speed increases at the S16 vibration level for the  
Figure 7: [PERSON] plots for the errors observed in the two experimental conditions: x-direction (**above**) and y-direction (**below**). most commonly used raster angles. The frequency of vibration varies by changing the print head's speeds while keeping the vibration level constant. It is observed that the lines are filling more space within the boundary as the print speed slows down, except in the case of the 0\({}^{\circ}\) raster angle. Due to the design of the vibration attachment on the cartridge, the vibrations are predominant in the y-direction, while its effect is minimum in the x-direction. This is the reason for the lack of change of material distribution at the 0\({}^{\circ}\) raster angle. As a next step, the pen attachment is replaced with the material filament, and a line is printed in the y-direction at varying amplitudes. The y-direction is chosen as the vibration affects this direction the most. Figure 9 shows the lines printed with no vibration and then with three different speeds of the motor. It is observed that as the motor's speed increases, the printed lines' amplitude goes up, but this does not happen when the speed nears the maximum. The amplitude of vibrations reduces as the motor speed increases from level 2  
Figure 8: Variation in the infill of the printed parts with increasing print speeds for different standard raster angles. to level 3. This causes lower reach for the material dispensed by the nozzle and thus a non-uniform material distribution. To explore this further, the filament is again replaced with the pen attachment, and lines are printed on paper at varying speeds of the motor. The rates are varied from S16 to S26 at intervals of two. The resulting lines are put under the micro-metrology station to measure the amplitude and wavelength of each line (Figure 10). At each speed, five 100 mm lines were drawn in the middle of the print bed, spaced at 10 mm intervals. Each line is measured at five different locations. The results are shown in Figure 11. It is observed that as the motor speed increases, the wavelength decreases. The amplitude initially increases with the motor speed but begins to decrease at S24 and S26. This may result from the pen tip rubbing too much against the print bed. If the pen tip is too close to the bed, the vibration wave begins to collapse, as seen in Figure 12. In Figure 12, the vibrated line started to rip the paper due to being too close to the print bed. As the paper rips, the wave collapses into a straight line. This is consistent with higher motor speeds decreasing in amplitude because these amplitudes likely push the pen tip too close to the bed. These amplitudes are likely greater than the pen drawings may show. Proper pen height adjustment is important to ensure that proximity to the print bed does not affect the vibration profile. The pen tip was lowered until it was \(\sim\)1 mm above the print bed. It was then lowered in increments of 0.1 mm until solid lines could be drawn. This resulted in a pen tip that was roughly 0.1 mm depressed into the piece of paper. Two sheets of paper were used in this experiment, with one sitting directly on top of the other. This allowed for the pen tip to depress the second piece of paper slightly, reducing the chance of the paper ripping. Figure 13 shows magnified images of the same lines in Figure 9. Different vibration levels cause the nozzle to smear material along the width of the print bead.