*2.2. Experimental Plan*

In additive manufacturing, there are several factors that could influence surface roughness, such as [25–28]:


Due to the high number of factors, a selection of factors to carry out a more economical and practical study was made. The experimental investigation was divided into two stages. The first stage was designed as a screening stage [29] to identify the most critical printing factors for surface roughness. The second stage was performed in order to increase the knowledge of the printing factors based on the results of the first stage.

All printed samples had dimensions of 30 mm in diameter and 40 mm in height. The first analysis was done to study the influence of layer height, wall thickness, printing speed, and temperature (material). These factors were varied using two levels: minimum and maximum. So, eight tests were performed by means of a fractional factorial design of four factors with two levels. Fractional factorial designs allow carrying out experimental studies with limited number of experiments and, thus, reducing cost and time.

For layer height, values of 0.15 and 0.25 mm were chosen. The first one is the minimum recommended by the predefined options of the Cura software. The second one is a higher value, which was selected expecting an increase in surface roughness as it was identified in the literature. For printing speed, a value of 40 mm/s was selected; a speed lower than that recommended by the printer manufacturer, and a value of 80 mm/s, the maximum recommended. For temperature, a maximum value lower than the one recommended by the PLA filament manufacturer (240 ◦C) was selected, i.e., 225 ◦C and, as minimum value, 195 ◦C was selected that lies slightly below the minimum recommended (200 ◦C). Finally, values of 1 and 3 mm were selected for wall thickness, considering that wall thickness should be higher than two times the size of the nozzle extruder (0.4 mm), according to Noorani [30]. The experimental factors, along their symbols, units, and levels are listed in Table 2.

Factors and levels for experiment 1 allow generating an experimental plan to carry out experiment 1, as shown in Table 3. The experimental plan was made in a random order to guarantee that the observations or errors are independently distributed random variables [29].


**Table 2.** Experimental factors for experiment 1.

**Table 3.** Experimental plan for experiment 1.


The second analysis was done to specifically study the influence of wall thickness and its relation to the printing path: zig-zag, concentric, and grid. These tests were performed using the parameters used in the first stage to obtain one of the best surface roughness, so the lowest layer height was chosen (0.15 mm), but it was decided to also have a reduced printing time (estimated printing time of 47 min), so the printing speed of 80 mm/s was selected. Moreover, temperature of 225 ◦C was chosen. So, two factors were analyzed in this stage, using three levels for printing strategy and five for wall thickness. For printing path, concentric, zig-zag, and grid were selected. The experimental factors, along with their symbols, units, and levels are listed in Table 4.

**Table 4.** Experimental factors for experiment 2.


The experiment was done using a full factorial design and the experimental tests were performed in a random order as shown in Table 5.

**Table 5.** Experimental plan for experiment 2.


#### *2.3. Surface Roughness Evaluation*

Surface roughness was evaluated in terms of the arithmetic average of the roughness profile (*Ra*). Six surface roughness measurements were taken in each sample. The samples were divided into two sections: bottom (printing start) and top (printing end) sections. In addition, three generatrices were drawn on the surface. No measurement was done in the section where the zipper effect generated by the layer change can be seen. The measurements of *Ra*1, *Ra*2, and *Ra*<sup>3</sup> were taken at the top in the generatrices in a clockwise direction. The measurements of *Ra*4, *Ra*5, and *Ra*<sup>6</sup> were taken at the bottom in the generatrices in a counter clockwise direction (Figure 3). Therefore, 48 and 90 measurements were obtained for experiment 1 and 2, respectively. Finally, with the six surface roughness measurements, the average roughness was calculated for each sample.

**Figure 3.** Details of the measurement procedure.

#### **3. Results and Discussion**

#### *3.1. Surface Roughness Results*

The surface roughness results obtained, their mean values and standard deviation (SD), in terms of *Ra*, are listed in Tables 6 and 7 for experiment 1 and 2, respectively.


**Table 6.** Experimental surface roughness results for experiment 1.

**Table 7.** Experimental surface roughness results for experiment 2.


From the tables, it is possible to see how the values of surface roughness are high compared to other conventional manufacturing processes, such as machining. In all cases, the values are higher than 12 μm. Moreover, the results present high variability depending on the measuring point for all the tests. This variability makes it difficult to obtain conclusions on surface roughness depending on the measuring location (bottom and top). No clear trends can be found depending on the location. The standard deviation calculated for all tests show clearly this performance. It is important to see how the ranges obtained for the mean values are also high. So, for experiment 1, the values varied between 15.377 μm and 22.844 μm and, for experiment 2, they varied between 12.746 μm and 20.715 μm. Mean values for experiment 1 and experiment 2 were 19.813 and 16.460 μm, respectively. These results are used for selecting a layer height of 0.15 mm for experiment 2, expecting that the surface roughness in experiment 2 would be similar to that obtained in experiment 1.

#### *3.2. Identification of Critical Factors*

Statistical methods are adequate tools for identifying influential factors in datasets such as those obtained for surface roughness. Thus, Analysis of Variance (ANOVA) is performed for both experiment 1 and 2. The results are listed in Tables 8 and 9 for experiment 1 and 2, respectively.


**Table 8.** Analysis of variance for experiment 1.



The normality of the residuals is checked using the Shapiro–Wilk test. Normality is verified by the calculated statistics and *p*-values: 0.86373 (W statistic) and 0.1308 (*p*-value), and 0.95369 (W statistic), and 0.5844 (*p*-value) for experiment 1 and 2, respectively. In both cases, the *p*-values are lower than the statistic, so no departure from normality was identified.

Considering that *p*-values lower than 0.05 are related to influential sources of variation, from Table 8, it is possible to recognize that layer height and wall thickness are influential factors on surface roughness. In particular, layer height has the lowest value. In addition, printing speed and temperature can be considered as nonsignificant factors for surface roughness. When analyzing the results listed in Table 9, only wall thickness is a significant source of variation, with printing path being nonsignificant.
