*2.6. Residual Stress*

In order to evaluate the residual stresses onto the treated surfaces, it is used an X-ray diffraction method based on applying Bragg's law while quantifying the change in the inter-planar spacings. The experimental application was performed with a V-α anode, 600 s of exposition time, and 20 measures. The post-processing method was curve fitting vs. sin2(ψ).

The application of the test was delivered in terms of the residual stress tensor. In which *σ<sup>i</sup>* corresponds to the tangential direction and *σii* corresponds to the axial direction of the specimen's generatrix (see Figure 3), *τ*<sup>12</sup> and *τ*<sup>21</sup> are the shear stresses.

$$
\sigma = \begin{bmatrix} \sigma\_i & \sigma\_{12} \\ \sigma\_{21} & \sigma\_{ii} \end{bmatrix} \tag{1}
$$

**Figure 3.** Residual stresses measurement unit and setup for cylindrical samples.

However, another indicator may be included to analyze the general residual stress state of the surface, the von Mises stress which is described in Equation (2).

$$
\sigma\_{vm} = \sqrt{\sigma\_i^2 + \sigma\_{ii}^2 - \sigma\_i \sigma\_{ii} + 3\tau\_{12}\tau\_{21}} \tag{2}
$$

### **3. Results**

### *3.1. Topography*

The Sa and height parameters were measured according to the ISO 25178 Standard [28]. The results are presented in Figure 4.

**Figure 4.** Three-dimensional Roughness results for 316L specimens.

Results show a reduction of the Sa and Sq when the number of passes is increased, and the vibration assistance is activated. It is clear that there is a decreasing tendency of the average and maximum roughness from lower levels of the number of passes plus the nonaddition of vibration assistance to high levels of the number of passes and the vibration assistance activated [29]. It seems that the number of passes has the more significant importance in order to enhance the surface in terms of roughness, having a great association with the vibration assistance. When looking more carefully, it can also be appreciated that when those medium–high levels of the number of passes are applied, the input force seems to enhance the topology when this one is increased. For example, comparing the specimens 80-5-40 vs. 120-5-40 or 120-3-40 vs. 160-3-40, it is noticed a roughness improvement by only increasing the input force. The best combinations obtained are 120-5-40, 160-3-40, and 160-5-0 (obtaining 63%, 61%, and 58% of Sa enhancement, respectively, as it is shown in Table 3), in that order, which may indicate that the number of passes is the most significant parameter and, combined with the vibration assistance and a high force, boosts the final surface roughness improvement.


**Table 3.** Sa improvement for each specimen compared to the initial surface after machining.

As can be seen, roughness is reduced by increasing the degree of plastic deformation by means of the augmentation of the three burnishing inputs analyzed. In particular, the increase in the burnishing force seems to not exceed the material limit at high forces, meaning that there could still be scope for force increase to obtain optimized roughness. The roughness trend is descending if an equal number of passes and VA value pairs are compared, as is seen by analyzing 120-3-0 with 80-3-0 or 160-3-40 with 120-3-40, so it is confirmed the positive effect of increasing the burnishing force to enhance the resultant roughness. In similar studies, Attabi et al. [21] obtained average roughness improvement with 240 N of force with a 10 mm ball but also experienced texture deterioration (compared to this optimal value) if the ball diameter was reduced, thus increasing the equivalent contact pressure. The descending trend of roughness when the number of passes and the VA is applied is evident and agrees with the bibliography [30,31]. In terms of force and number of passes increase, improvement can be explained by the fact that the ball is rolling and smoothing out the bulged edges of the initial machining or the previous pass, so the probability of deforming the asperities is increased by augmenting the force and performing successive burnishing passes; thus, the surface is being smoothed at each pass. Concerning the VA, the kinematic energy added to the process enhances the work-hardening but to a lower degree than the burnishing force [32], explaining why VABB roughness values are better than BB when the same level of plastic deformation (burnishing force and several passes) is applied.

The mean effects and the interaction plots of the model, taking the Sa as the output, are presented in Figure 5. First of all, the *p*-value analysis determines that the number of passes, the burnishing force, and the vibration assistance, in that order, are the most important and significant parameters due to having a *p*-value lower than 5%. However, none of the interactions analyzed are significant enough to be considered, so they are rejected as a hypothesis. The 0.000 *p*-value registered for the number of passes means the huge impact that this variable has on the final value of the average roughness.

**Figure 5.** ANOVA results taking the Sa as the output value.

As it was alleged in the experimental results section, the increase in the force and the number of passes, plus the addition of the vibration assistance, improve the final topology of the specimen after the ball burnishing process within the parameter interval chosen in this study.
