## 2 Materials and Methods
### Experimental Station and Measurements
This approach represents a limitation of the present study; however, it is justified by the high cost and time-consuming nature of producing test specimens from Inconel 939 using LPBF, followed by standardized post-processing procedures including heat treatment and vibratory finishing. These constraints are well-recognized within the field of additive manufacturing research and are frequently reported as a challenge in experimental studies involving superalloys. Furthermore, the standard deviations presented in the results refer to the repeatability of roughness measurements performed at different locations of a single specimen rather than reflecting the variability of the process itself. As such, they provide an estimate of local surface uniformity rather than batch-level reproducibility. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**Star Arm**} \\ \cline{2-5}  & \(-\)**1** & **0** & **1** \\ \hline Eccentricity a [mm] & 5.5 & 8.5 & 11.5 \\ Rotational speed n [rpm] & 560 & 710 & 900 \\ Time t [min] & 8 & 14 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values of input parameters of the design of the experiment. Figure 4: Solid ferromagnetic abrasive grains: Fe-Si 160/80 \(\upmu\)m. Magnification (**a**) 10\(\times\), (**b**) 20\(\times\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample No. **} & \multicolumn{6}{c}{**Parameters Value**} & \multicolumn{6}{c}{**Roughness [\(\upmu\)m]**} \\ \cline{2-13}  & **a [mm]** & **n [rpm]** & **t [min]** & **Ra** & **SD** & **Rq** & **SD** & **Ry** & **SD** & **Rz** & **SD** & **Sm** & **SD** \\ \hline
1 & 5.5 & 710 & 8 & 0.97 & 0.17 & 1.25 & 0.19 & 3.30 & 1.20 & 5.79 & 0.69 & 216.57  
The box plot (Figure 5) illustrates the statistical distribution of four surface roughness parameters--Ra, Rq, Ry, and Rz--measured across all samples. While Ra and Rq exhibit relatively narrow ranges and consistent values, Ry and Rz display greater variability and higher absolute magnitudes, reflecting their sensitivity to isolated surface peaks. The presence of individual outliers in Ry and Rz further indicates localized irregularities likely influenced by residual surface defects. Overall, the plot provides a comparative insight into the behavior and dispersion of each parameter, offering a more nuanced interpretation of surface texture after the finishing process. The surface roughness improvement mechanism is based on the action of ferromagnetic abrasive particles suspended in a magnetic field, which form a flexible brush that conforms to the sample's surface. As the sample rotates with controlled eccentricity, these particles exert a combination of normal and tangential forces that gradually remove surface peaks through micro-cutting. The planetary kinematics enhance the uniformity of contact and promote a multidirectional abrasive motion, which improves surface leveling, particularly in regions with high initial roughness. This process is especially effective in reducing asperities typical of LPBF-manufactured Inconel 939, leading to significant improvements in the surface finish.