*3.5. Factors and Levels Selected*

The values selected for the levels of factors analyzed in this study are shown in Table 4. The depth of cut, *d*, was recorded at 25 mm and was equal in all tests. This value was selected to simulate repair and maintenance operations in which it is necessary to adhere to the tolerance dimensions established during the design of the parts.


#### **4. Results, Analysis, and Discussion**

#### *4.1. Results*

The surface roughness in terms of the roughness average, *Ra*, was measured after performing all the drilling trials inside all the holes and in the different locations established in Table 4, following the direction and locations shown in Figure 5b,c for each hole. The results obtained for the 48 *Ra* experimental values are outlined in the last two columns of Table 5.

We firstly assessed the initial obtained results to determine any trend and to compare the findings with those obtained in previous works in which the materials were studied separately or along with other materials. The *Ra* mean values in the three measured zones are provided in Table 6.

The values obtained in this work aligned with those in other previous works about titanium using a similar feed rate, cutting speed, or point angle [81,89–91], as well as with those obtained when drilling magnesium matrix composites [83]. For optimizing magnesium alloys during drilling operations, other point angles are suitable; however, similar surface roughness values were obtained in this work [92].


**Table 5.** Roughness average *Ra* (μm) obtained during the experiments.

**Table 6.** *Ra* (μm) mean values in the three measured zones versus the feed rate, *f*, and the cutting speed, *V*.


#### *4.2. Analysis and Discussion*

In order to statistically analyze the experimental *Ra* data collected (Table 5), a fixed effects ANOVA was performed to examine the interactions up to second order and excluding an effect each time. The selection criteria of the significant effects in the ANOVA after each iteration were as follows [93]: in each new ANOVA, the effect with a higher *p*-value (which was therefore less statistically significant) was excluded; the backward algorithm finishes when all the effects that remain in the ANOVA have a *p*-value lower than 0.05.

The final outcome of this iterative ANOVA algorithm over the experimental *Ra* data did not lead to any conclusive result. For that reason, a logarithmic transformation of the experimental *Ra* data was performed. Such a transformation allows maintaining the order of the original *Ra* data while smoothing the impact of the outliers. The outcome of the first iteration of the ANOVA over the transformed *Ra* data—over the *Ra* Naperian logarithm ln*Ra*—is provided in Table 7. A second iteration for the ANOVA was then completed for the effects contained in the table, excluding the *LRI\*V* effect which had a maximum *p*-value of 0.828.


**Table 7.** Outcome of the first iteration for the ANOVA over *Ra* Naperian logarithm.

DF: Degrees of Freedom.

The final result of the backward algorithm for the last iteration is displayed in Table 8. In this table, all the *p*-values are lower than 0.05, so the three effects in the first column of this table can be considered statistically significant. Therefore, as a consequence of the ANOVA, we concluded that the interaction between type of tool and the location with respect to the insert *T\*LRI*, the location with respect to the insert *LRI*, and the interaction between type of tool and feed rate *T\*f* are the three effects among the 15 analyzed with a significant statistical influence on the surface finish of the machining on the dry drilling stack, composed of magnesium alloy UNS M11917 and titanium alloy UNS R56400. For example, the *LRS* effect, which measures the roughness differences between the beginning and end of the specimen along the feeding direction, did not have a statistically significant influence on the surface finish because this effect was not included in the outcome of the last iteration for the ANOVA summarized in Table 8.


**Table 8.** Outcome of the last iteration for the ANOVA over *Ra* Naperian logarithm.

DF: Degrees of Freedom.

Considering the variability in the surface roughness of the magnesium–titanium–magnesium drilling stacks explained by the statistically significant effects obtained from the ANOVA, the percentage of variability attributed to each effect is shown in the pictogram in Figure 6. The contribution of each effect was obtained as the ratio of the sum of squares of the effect to the sum of squares due to the model. For example, the percentage of variability attributed to the *T\*f* effect is the ratio of 2.206 to 7.673 (%). That is, 39.63% of the variability is due to the *T\*LRI* effect, 31.63% of the variability is due to the *LRI* effect, and the remaining 28.73% of the variability is due to the *T\*f* effect.

**Figure 6.** Distribution of the percentage of variability attributed to each effect over the variability explained by the ANOVA model.

The distribution of the Naperian logarithm of the surface roughness of the drilling process (ln*Ra*) with respect to the three levels of the measurement location on the insert (*LRI)* is depicted in Figure 7. As shown in the figure, small differences existed between ln*Ra* before and after the insert. The dispersion is observably greater for small values before the insert.

**Figure 7.** Distribution of the Naperian logarithm of the surface roughness (ln*Ra*) for each of the three levels of measurement location on the insert (*LRI*).

On the other hand, when assessing statistically significant interactions, considering the behavior of the interaction between type of tool and the location with respect to the insert *T\*LRI*, the A1 1253 tool produced better results in terms of roughness before the insert and worse after the insert. This did not occur with the A1 1240 tool, which had a few differences. This behavior is illustrated in Figure 8.

**Figure 8.** ln*Ra* interaction between type of tool and the location with respect to the insert *T\*LRI*.

With respect to the interaction between type of tool and feed rate *T\*f* (Figure 9), an increase in the advance of *f* generated a reduction in the roughness for the A1 1240 tool, whereas for the A1 1253 tool, the opposite occurred. The figure clearly demonstrates the *T\*f* interaction.

**Figure 9.** ln*Ra* interaction between type of tool and feed rate *T\*f*.

The variability in the logarithm of the surface roughness ln*Ra* of dry drilling magnesium–titanium– magnesium stacks was modelled from the ANOVA using Equation (1). In this equation, *μ* is a constant term to adjust the mean; *αi, βαji*, and *βγjk* represent the effects of the levels of the location with respect to the insert, the interaction of the type of tool with the measurement location with respect to the insert, and the interaction of the type of tool with the feed rate, respectively; and *εijk* is the error term.

$$
\ln R a\_{i\bar{j}k} = \mu + \alpha\_i + \beta \alpha\_{\bar{j}i} + \beta \gamma\_{\bar{j}k} + \varepsilon\_{i\bar{j}k} \tag{1}
$$

The estimations of the parameters of the model in Equation (1) are listed in the third column of Table 9. The table also includes an indicator of the parameter estimation errors (the standard deviation) in the fourth column. The fifth column collects the *t*-statistic values, and the sixth column provides the statistical significances of the parameter estimations.


**Table 9.** Parameter estimations of the model in Equation (1).

The parameter estimations included in Table 9 allowed us to obtain the residuals of the model in Equation (2), which provides the differences between the observed values and the estimated values of ln*Ra*. Analyzing these residuals, the model hypotheses were checked. Figure 10 shows that the residuals follow a normal law, so the hypothesis is supported. This hypothesis can be contrasted by different tests, such as normality on residuals, as shown in Table 10.

**Figure 10.** Checking the hypothesis of normality for the residuals: (**a**) histogram of residuals and (**b**) Probability–Probability plot for residuals.

**Table 10.** Tests for normality on residuals.


Figure 11a shows that the residuals satisfy the homoscedasticity hypothesis and Figure 11b shows that the existence of nonrandomized patterns in the residuals was not observed.

**Figure 11.** (**a**) Checking the homoscedasticity hypothesis for residuals; (**b**) Checking the nonexistence of special patterns on residuals.

Once the hypotheses of the model in Equation (1) were checked, we confirmed that the variability in the surface roughness *Ra* of dry drilling stacks composed of magnesium alloy UNS M11917 and titanium alloy UNS R56400 could be statistically modelled by Equation (2).

$$Ra\_{i\bar{i}k} = \exp\left(\mu + \alpha\_{\bar{i}} + \beta\alpha\_{\bar{j}\bar{i}} + \beta\gamma\_{\bar{j}k} + \varepsilon\_{i\bar{j}k}\right) \tag{2}$$

From modelling the surface roughness *Ra* described in Equation (2), and considering the parameter estimations in Table 9, the predicted values for surface roughness of the drilling machining were computed for the various combinations of the levels of the statistically significant effects in the surface finish of the dry drilling stacks. The values of the predicted roughness of these combinations are listed in increasing order in Table 11. The second predicted roughness, denoted with an asterisk (\*) and included in the last column of the table, contains the predicted *Ra* values using only the parameters with a statistical significance at the *p* < 0.05 level. Considering this second roughness prediction (\*), the combinations of the levels of statistically significant effects were classified into four roughness classes, as shown in the last column of Table 11.


**Table 11.** Predicted roughness of the level combinations of significant effects on dry drilling.

Focusing on this classification, the best combinations of the levels of parameters that achieved a lower predicted roughness value (a better surface finish) during the dry drilling process on a stack composed of magnesium alloy UNS M11917 and titanium alloy UNS R56400 included the A1 1240 cutting tool with a feed rate of 100 mm/min. Appropriate levels of surface finish should be

achieved by these drilling conditions: a predicted roughness of 0.92 μm on the insert and after the insert (in the second class), and a predicted roughness of 0.95 μm before the insert (in the third class). A mean roughness *Ra* under 1 μm could be achieved in all the stack superficial areas.

These types of light alloys are usually employed in the aeronautical industry and in this industrial sector, the values for the surface roughness specifications of *Ra* usually lie between 0.8 μm and 1.6 μm [91]. As such, roughness values *Ra* under 1 μm clearly satisfy the surface finish requirements. Notably, the quality improvement in the surface finish was achieved with higher feed rates, which promoted a decrease in machining time and, consequently, a decrease in costs, enabling the efficient optimization of the surface quality.

#### *4.3. Technological Point of View*

To apply the results obtained in this study, analyzing them from a technological point of view was necessary. Thus, as most components in the aeronautical and aerospace sectors are complex and have strict dimensional and surface quality requirements (within the range of 0.8 μ < *Ra* < 1.6 μm [94]), their manufacturing is usually expensive and pieces are not stocked for repair or maintenance purposes. Therefore, parts have to be repaired or maintained as soon as possible to restore the plane or the aircraft to its functional conditions.

In this study, the best results were obtained for the following combinations of cutting parameters: *f* = 100 mm/min, *V* = 25, and *T* = A1 1240 m/min; and *f* = 50 mm/min, *V* = 25, and *T* = A1 1253 m/min. The surface roughness achieved in the holes of the different materials and locations in the stack were all within the range usually required in the aeronautical industry [94]. Between the two combinations, the first was better due to the feed rate value being higher so the repair operation can be finished in a shorter time, thereby reducing costs associated with the operation. Additionally, these real results are in accordance with the results of the ranking of the cutting condition combinations based on the estimated values of *Ra*.

Performing all tests under dry conditions is important not only from an economic point of view but an environmental viewpoint as well. Not using any additional lubricant or coolant provides cost savings and allows for more sustainable repair and maintenance operations.

#### **5. Conclusions**

In this paper, we examined a drilling process on a stack formed by two UNS M11917 magnesium alloy bases and one UNS R56400 titanium alloy insert in an experimental study. The interaction between the type of tool and the measurement location on the insert influences the inner surface of the holes. The best type of tool for the drilling repair operations was determined to be the A1 1240, which was especially efficient for higher values of feed rate (100 mm/min) and cutting speed (25 m/min). The surface roughness obtained in the inner of the holes was independent of material and location considered, and the values fell within the usual acceptable range in the aeronautical sector. The surface roughness increased as the tool advanced through the stack, especially after the insert. However, the differences observed along each component in the stack, at both the beginning and the end of the component, were not statistically significant. The repair operations performed with drilling can be sustainably completed, as was proven in this study, which was completed under dry conditions.

**Author Contributions:** Conceptualization, E.M.R., M.V., J.L.V. and J.M.S.d.P.; Data curation, E.M.R. and J.M.S.d.P.; Formal analysis, E.M.R., M.V., J.L.V. and J.M.S.d.P.; Funding acquisition, E.M.R., M.V. and J.L.V.; Investigation, E.M.R., M.V., J.L.V. and J.M.S.d.P.; Methodology, E.M.R., M.V. and J.L.V.; Project administration, E.M.R.; Resources, E.M.R.; Software, M.V. and J.L.V.; Supervision, E.M.R., M.V. and J.L.V.; Validation, E.M.R., M.V., J.L.V. and J.M.S.d.P.; Visualization, E.M.R., M.V., J.L.V. and J.M.S.d.P.; Writing—original draft, E.M.R., M.V., J.L.V. and J.M.S.d.P.; Writing—review & editing, E.M.R., M.V., J.L.V. and J.M.S.d.P.

**Funding:** This work has been funding, in part, by five grants from Ministerio de Ciencia e Innovación, Ministerio de Economía y Competitividad, AgenciaEstatal de Investigación (AEI), Fondo Europeo de Desarrollo Regional (FEDER), and Industrial Engineering School-UNED (DPI2014-58007-R, CGL2014-58322-R MTM2016-78227-C2-1-P, MTM2017-90584-REDT and REF2018-ICF05), Spain.

**Acknowledgments:** The authors thank the Research Group of the UNED "Industrial Production and Manufacturing Engineering (IPME)" for the support given during the development of this work and they also thank the Antolín Group for the material provided.

**Conflicts of Interest:** The authors declare no conflict of interest.
