## 4 Evaluation of Experimental Results
### Investigation of Surface Roughness by Experimental Design for Different Process Parameters  
Based on the previous considerations, a full factorial experimental design was carried out, comparing the results of diamond burnishing at 80 N and 100 N burnishing force. This was performed to gain a more accurate understanding of the outcomes when machining with a force lower than the theoretical optimum in order to improve the energy efficiency of the process. Using the factorial design [77], empirical formulas were developed with PTC Mathcad Prime 10 software. Performing the design of experiments requires the definition of factors and levels, which in this case correspond to the previously introduced technological pa  
\begin{table}
\begin{tabular}{c c c  
rameters: feed rate, burnishing speed, and burnishing force. For each parameter--with burnishing force values informed by the findings in earlier subsections--two levels are assigned, referred to hereafter as minimum and maximum values. By combining these parameters, we obtain a total of eight independent parameter combinations, which can be calculated using the number of factors (\(\
ot{f}=3\)) and the number of levels (\(p=2\)), according to the following formula:  
\[n=p^{f}=2^{3}=8, \tag{11}\]  
The data from these experiments are summarized in Table 6.  
In all cases, solutions are sought in the form of Equation (12), where \(k_{0}\); \(k_{1}\); \(k_{2}\); \(k_{3}\); \(k_{12}\); \(k_{13}\); \(k_{23}\); \(k_{123}\) are arbitrary real numbers derived from the calculations. The variable \"X\" substitutes the letter \"R\" for 2D roughness values and \"S\" for 3D roughness values, while the subscript \"y\" generalizes the different types of roughness indicators, written as follows:  
\[(I)X_{y}=k_{0}+k_{1}\cdot f+k_{2}\cdot F_{v}+k_{3}\cdot v_{v}+k_{12}\cdot f \cdot F_{v}+k_{13}\cdot f\cdot v_{v}+k_{23}\cdot F_{v}\cdot v_{v}+k_{123}\cdot f \cdot F_{v}\cdot v_{v} \tag{12}\]  
Figure 11 shows the experimental results for the two- and three-dimensional surface roughness indicators, while Equations (13)-(16) present the corresponding empirical formulas. All four graphs exhibit essentially the same characteristics, suggesting that no significant differences exist among the various roughness indicators in this case. \[Ra=3.2548- 35.7575\cdot f-4.1532\cdot v_{v}-0.0343\cdot F_{v}+49.2671\cdot f \cdot v_{v}+0.3954\cdot f\cdot F_{v}+0.0448\cdot v \tag{13}\] \[\cdot F_{v}-0.5221\cdot f\cdot v_{v}\cdot F_{v}\] \[Rq=4.5951- 50.7559\cdot f-6.0219\cdot v_{v}-0.0493\cdot F_{v}+72.2195\cdot f \cdot v_{v}+0.5717\cdot f\cdot F_{v}+0.0659\cdot v\] (14) \[\cdot F_{v}-0.7774\cdot f\cdot v_{v}\cdot F_{v}\] \[Sa=2.2685- 18.8935\cdot f-2.8288\cdot v_{v}-0.0221\cdot F_{v}+27.3011\cdot f \cdot v_{v}+0.1863\cdot f\cdot F_{v}+0.0282\cdot v\] (15) \[\cdot F_{v}-0.2459\cdot f\cdot v_{v}\cdot F_{v}\] \[Sq=3.7459- 34.0105\cdot f-4.8333\cdot v_{v}-0.038\cdot F_{v}+50.462\cdot f \cdot v_{v}+0.355\cdot f\cdot F_{v}+0.0501\cdot v\cdot F_{v}\] (16) Table 6.0  
In the graphs, the green color represents the results of diamond burnishing with 80 N, while blue indicates those with 100 N. In most cases, the higher burnishing force results in better surface roughness, within the current intervals of the other two parameters--feed rate and burnishing speed. However, this trend reverses when higher burnishing speed and lower feed rate are applied. \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & \(\
ot{f}\)\(\frac{mm}{rev}\) & \(\mathbf{v}_{v}\)\(\left[\frac{m}{s}\right]\) & \(\mathbf{F}_{v}\)**[N]** \\ \hline
1-3 & 0.05 & 0.6938 & 80 \\
2-3 & 0.1 & 0.6938 & 80 \\
3-3 & 0.05 & 0.9817 & 80 \\
4-3 & 0.1 & 0.9817 & 80 \\
1-2 & 0.05 & 0.6938 & 100 \\
2-2 & 0.1 & 0.6938 & 100 \\
3-2 & 0.05 & 0.9817 & 100 \\
4-2 & 0.1 & 0.9817 & 100 \\ \hline \end{tabular}
\end{table} 
Table 6: The technological data used for the factorial experimental design. Increasing feed rate worsened surface roughness, while increasing burnishing speed improved surface roughness.