## 4 Evaluation of Experimental Results
### Optimum Force Calculation for Surface Roughness Optimisation
\begin{table}
\begin{tabular}{c c c c c c} \hline R/S & \(f(\frac{mm}{\kappa\kappa})\) & \(v_{r}\left[\frac{m}{s}\right]\) & \(\text{Equation}\) & \(P_{opt}[W]\) & \(F_{opt}[N]\) \\ \hline \(R_{a}\) & & & & y = 0.0107x\({}^{2}-0.1519\)x + 0.6844 & 7.10 & 102 \\ \(R_{q}\) & 0.05 & 0.6938 & & y = 0.0126x\({}^{2}-0.1821\)x + 0.8436 & 7.23 & 104 \\ \(S_{a}\) & & & & y = 0.0177x\({}^{2}-0.2382\)x + 0.946 & 6.73 & 97 \\ \(S_{q}\) & & & & y = 0.0225x\({}^{2}-0.3057\)x + 1.2277 & 6.79 & 98 \\ \(R_{a}\) & & & & y = 0.006x\({}^{2}-0.0982\)x + 0.5512 & 8.18 & 83 \\ \(R_{q}\) & 0.05 & 0.9817 & & y = 0.0057x\({}^{2}-0.0924\)x + 0.5819 & 8.11 & 83 \\ \(S_{a}\) & & & & y = 0.0089x\({}^{2}-0.1554\)x + 0.818 & 8.73 & 89 \\ \(S_{q}\) & & & & y = 0.0125x\({}^{2}-0.2172\)x + 1.1365 & 8.69 & 88 \\ \(R_{a}\) & & & & y = 0.0103x\({}^{2}-0.1538\)x + 0.7815 & 7.47 & 108 \\ \(R_{q}\) & 0.1 & 0.6938 & & y = 0.0081x\({}^{2}-0.1356\)x + 0.846 & 8.37 & 121 \\ \(S_{a}\) & & & & y = 0.0177x\({}^{2}-0.2417\)x + 1.0418 & 6.83 & 98 \\ \(S_{q}\) & & & & y = 0.02x\({}^{2}-0.2843\)x + 1.306 & 7.11 & 102 \\ \(R_{a}\) & & & & y = 0.0123x\({}^{2}-0.2346\)x + 1.3576 & 9.54 & 97 \\ \(R_{q}\) & 0.1 & & 0.9817 & & y = 0.0138x\({}^{2}-0.2724\)x + 1.6716 & 9.87 & 101 \\ \(S_{a}\) & & & & y = 0.0168x\({}^{2}-0.3107\)x + 1.7141 & 9.25 & 94 \\ \(S_{a}\) & & & & y = 0.0203x\({}^{2}-0.3785\)x + 2.1508 & 9.32 & 95 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of force optimization calculation for surface roughness indicators. Figures 5 and 6 trendline's equations are included in Table 4. We concluded that the most favorable combination in terms of both surface quality and required performance was the one with a lower feed rate and lower burnishing speed (red trendline). Therefore, based on the Kraljic matrices and the calculated force optimum values, the optimal parameter combination in terms of surface roughness is as follows:  
\[f_{1}=0.05\ \frac{mm}{rev};\ v_{v1}=0.6938\ \frac{m}{s};\ F_{opt}=97\ldots 104\ N\]  
By contrast, applying a larger feed rate (gray-coded) resulted in worse surface quality and higher force optimum, written as follows:  
\[f_{2}=0.1\ \frac{mm}{rev};\ v_{v1}=0.6938\ \frac{m}{s};\ F_{opt}=98\ldots 121\ N\]  
The use of higher burnishing speed (according to Equation (2)) increased the power, as shown by the blue and yellow trendlines in the figures. Machining with a higher feed rate again led to significantly worse surface quality (yellow) compared to a lower feed rate (blue), which produced nearly identical roughness values to those measured at the lower burnishing speed (red). Due to the higher burnishing speed, the optimum force came out lower for these combinations, but the required power made these processes less favorable from an energy perspective, written as follows:  
\[f_{1}=0.05\ \frac{mm}{rev};\ v_{v2}=0.9817\ \frac{m}{s};\ F_{opt}=83\ldots 89\ N\]  
\[f_{2}=0.1\ \frac{mm}{rev};\ v_{v2}=0.9817\ \frac{m}{s};\ F_{opt}=94\ldots 101\ N\]  
Table 5 contains the calculations made for the improvement factors. In every case, the \(x^{2}\) components of the equations are negative, meaning the calculated extremum points represent maximum points of the parabolas. However, the concept of force optimum still applies. This table contains the same data as Table 4, with the difference that calculations were made for the improvement factors instead of the surface roughness indicators. The meaning of force optimum is again aligned with the concept illustrated in Figure 10. Based on a study of the Kraljic matrices in Section 4.1, the improvement factors presented in Figures 7 and 8 showed that the combination of higher feed rate and lower burnishing speed (gray-coded) produced the most favorable trendline in terms of both improvement percentage and power demand. Based on the Kraljic matrices and the calculated force  
Figure 10: Defining the meaning of force optimum.