## 3 Results
### Results of Experimental Studies
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Plan Level**} & \multicolumn{6}{c}{**Results of Measurements of the Ra [\(\mathrm{\SIUnitSymbolMicro m}\)] Parameter**} \\ \cline{2-5}  & **Ra1 [\(\mathrm{\SIUnitSymbolMicro m}\)]** & **Ra2 [\(\mathrm{\SIUnitSymbolMicro m}\)]** & **Ra [\(\mathrm{\SIUnitSymbolMicro m}\)]** & **Average Ra [\(\mathrm{\SIUnitSymbolMicro m}\)]** \\ \hline
1 & 0.295 & 0.350 & 0.335 & 0.326 \\
2 & 0.58 & 0.504 & 0.565 & 0.549 \\
3 & 0.39 & 0.364 & 0.398 & 0.384 \\
4 & 0.572 & 0.557 & 0.544 & 0.557 \\
5 & 0.535 & 0.556 & 0.577 & 0.556 \\
6 & 0.395 & 0.37 & 0.424 & 0.396 \\
7 & 0.477 & 0.481 & 0.479 & 0.479 \\
8 & 0.641 & 0.623 & 0.551 & 0.605 \\
9 & 0.528 & 0.527 & 0.534 & 0.529 \\
10 & 0.453 & 0.540 & 0.656 & 0.549 \\
11 & 0.458 & 0.473 & 0.49 & 0.473 \\
12 & 0.479 & 0.513 & 0.5 Exemplary results of the study of the stereometry of the surface machined, which had the lowest value of the Ra parameter, are presented in Figure 16. All the surfaces analyzed have a degressive-progressive material share curve. The traces of diamond sliding burnishing are clearly visible in the autocorrelation function. The distribution of ordinates is close to normal with slight positive skewness. The distribution of the tops of the local hills is close to normal, consisting of two overlapping independent processes, as evidenced by the presence of two peaks. Figure 16: Geometric Surface Structure for f = 0.048 [mm\(\cdot\)rev\({}^{-1}\)] and F = 8 [N]: **(a)** 3D surface topography, **(b)** Abbot load curve, **(c)** roughness profile (colours means: above zero – green, below zero – red). Figure 15: The view of the surface of the sample after grinding and after DSB. The results of the research, after statistical elaboration, allowed the Authors to obtain the required mathematical model of the process. For example, the model describing the dependence of the arithmetic mean deviation of the profile from the mean line Ra of the surface after the process on technological parameters describes the equation for the coded variables \(\widetilde{\textbf{x}}_{1}\) and \(\widetilde{\textbf{x}}_{2}\):  
\[\widehat{\textbf{Y}}=\widehat{\textbf{R}}_{a}=0.5134+0.055\cdot\widetilde{ \textbf{x}}_{1}-9.97\cdot 10^{-3}.\widetilde{\textbf{x}}_{2}-3.61\cdot 10^{-6}. \left(\widetilde{\textbf{x}}_{1}\right)^{2}+3.9\cdot 10^{-4}.\left(\widetilde{ \textbf{x}}_{2}\right)^{2}-6.17\cdot 10^{-3}.\widetilde{\textbf{x}}_{1}. \widetilde{\textbf{x}}_{2}, \tag{39}\]  
where \(\widetilde{\textbf{x}}_{i}\in[-1;+1];\;\mathrm{i}=1,\;2\). After decoding Equation (39) according to the code formulas:  
\[\widetilde{\textbf{x}}_{1}=\left(\widetilde{\textbf{t}}-0.07\right)/0.021, \tag{40}\]  
\[\widetilde{\textbf{x}}_{2}=\left(\widetilde{\textbf{F}}-15\right)/7.072, \tag{41}\]  
the equation for the real values of the technological parameters f and F is obtained, along with the 95% confidence area of the following form:  
\[ \begin{split}\widehat{\textbf{Y}}=&\widehat{\textbf {R}}_{a}=-0.1464+14.9\cdot\widetilde{\textbf{f}}+0.003296\cdot\overline{ \textbf{F}}-0.08227\cdot\widetilde{\textbf{f}}\cdot\overline{\textbf{F}}-71.3 8\cdot\overline{\textbf{f}}^{2}+1.56\cdot 10^{-5}.\overline{\textbf{F}}^{2}\\ \pm 0.0103\cdot&\sqrt{3.744\cdot\left[\left(\widetilde {\textbf{x}}_{1}\right)^{4}+\left(\widetilde{\textbf{x}}_{2}\right)^{4}\right] +7.488\cdot\left(\widetilde{\textbf{x}}_{1}\right)^{2}.\left(\widetilde{ \textbf{x}}_{2}\right)^{2}-0.989\cdot\left[\left(\widetilde{\textbf{x}}_{1} \right)^{2}+\left(\widetilde{\textbf{x}}_{2}\right)^{2}\right]+2.6},\end{split}  \tag{42}\]  
where \(\widetilde{\textbf{f}}\in[0.04;0.1]\)\(\left[\mathrm{mm}\cdot\mathrm{rev}^{-1}\right]\), \(\overline{\textbf{F}}\in[5;25]\)\(\left[\mathrm{N}\right]\), giving \(\widetilde{\textbf{x}}_{1}\) and \(\widetilde{\textbf{x}}_{2}\) according to formulas (40) and (41).