## 4 Evaluation of Experimental Results
### Analysis of the Kraljic Matrices  
We begin the evaluation of the experimental results using the Kraljic matrices introduced in the previous section. In our earlier research ([8]), we established that diamond burnishing with a burnishing force less than 60 N did not yield significant improvements in surface roughness. Therefore, these data points were excluded from the dataset to obtain more accurate results, as they were significant outliers that considerably distorted the optimization. Figure 5 shows the Kraljic matrices for the 2D surface roughness parameters--on the left side, the average roughness (\(R_{a}\) and on the right side, the root mean square roughness (\(R_{q}\)). Different colors indicate the four feed rate and burnishing speed combinations, with the following values:  
\[f_{1}=0.05\frac{mm}{rev};\;f_{2}=0.1\frac{mm}{rev}\]  
\[v_{v1}=0.6938\frac{m}{s};\;v_{v2}=0.9817\frac{m}{s}\]  
These combinations and their color codes are explained in the figure legends. Vertical and horizontal lines mark the matrix cell boundaries, with Roman numerals identifying the cells. To improve data interpretation, four quadratic polynomials were fitted per matrix using the trendline function in Microsoft Excel (Microsoft(r) Excel(r) for Microsoft 365 MSO (Build 2506 Version 16.0.18925.20076) 64-bit). The R-squared values for these trendlines are shown at the top of the figures in color-coded rectangles, indicating the accuracy of fit--i.e., how reliably conclusions can be drawn from the shape of the trendlines. The R-squared value ranges from 0 to 1, where values near 1 indicate a reliable model, while values near 0 imply unreliability, meaning no suitable function (in our case, a quadratic polynomial) fits the dataset well. Expressed as a percentage, for example, the red trendline corresponding to \(f=0.05\frac{mm}{rev}\) and \(v_{v}=0.6938\frac{m}{s}\) in the average roughness matrix reproduces the actual measured values with 99.75% reliability. Figure 5 shows that the data points for average roughness and root mean square roughness are quite similar, so it is worth combining the conclusions from both matrices. Considering the R-squared values of the trendlines, it can be stated that all but the blue trendline offer a high level of reliability. The red trendline falls into cell I of the Kraljic matrix, indicating that the parameter combination with lower feed rate and lower burnishing speed  
Figure 5: Kraljic matrices of 2D surface roughness parameters during diamond burnishing. best satisfies energy efficiency principles--that is, good surface quality coupled with low power demand. In contrast, the yellow trendline--representing data points with higher feed and higher burnishing speed--is mainly found in cell IV, which should therefore be avoided due to high power demand and poor surface roughness. The other two trendlines lie in the \"compromise\" cells of the matrices: the gray trendline is favorable in terms of power demand, while the blue trendline favors surface quality but shows less optimal values in terms of the other parameter. Nevertheless, based solely on these data and matrices, it is advisable to use the parameter combination of the red trendline in all respects. Since quadratic polynomials were used for approximation, each trendline represents a parabola, which has a minimum point due to the positive x\({}^{2}\) coefficient in their equations. In Section 4.2, these minimum points will be used to determine the minimum power and the minimum burnishing force. Figures 4a and 5 and Figure 6 correspond to each other. For example, Quadrant **1. ** marked with Arabic numerals in Figure 4a corresponds to Quadrant **1. ** marked with Roman numerals in Figures 5 and 6. Similarly, Quadrant **1. ** marked with Arabic numerals in Figure 4b corresponds to Quadrant **1. ** marked with Roman numerals in Figures 7 and 8. In Figure 6, similarly to the previous figure, the Kraljic matrices of 3D surface roughness parameters are shown: the arithmetic mean on the left and the root mean square equivalent on the right.