## 5 Summary  
The aim of our research was to analyze and optimize the surface roughness of diamond-burnished surfaces using Kraljic matrices and design of experiments.  
From the analysis of the Kraljic matrices generated for the surface roughness parameters, we concluded that the parameter combination involving lower feed rate and lower burnishing speed best fulfilled the principles of energy efficiency: good surface quality was associated with low power demand. In contrast, machining processes with higher feed rates and higher burnishing speeds were deemed undesirable due to their high power requirements and poor surface quality.  
By examining the improvement factors of the surface roughness parameters using Kraljic matrices, we found that the greatest improvement was achieved with the parameter combination of high feed rate and low burnishing speed, which also proved optimal in terms of power demand. At constant burnishing speed, increasing the feed rate resulted in a higher improvement factor, while increasing the burnishing speed led to a reduction in improvement values.  
The data points of the Kraljic matrices were approximated with second-order polynomials. These curves exhibited a minimum point for the surface roughness values and a maximum point for their improvement factors. During the calculations, we determined the optimal burnishing force required to achieve the best surface quality, thus optimizing the process from a surface roughness perspective. These values indicate the threshold beyond which increasing the burnishing force becomes detrimental in terms of both surface quality and energy efficiency, while decreasing the force can improve energy efficiency but at the cost of surface quality.  
Based on the Kraljic matrices and the calculated force optima, the parameter combination that proved optimal for surface roughness across the examined roughness metrics was the following:  
\[f_{1}=0.05\ \frac{mm}{rev};\ v_{v1}=0.6938\ \frac{m}{s};\ F_{opt}=97\ldots 104\ N\]  
We also applied a full factorial design of experiments to derive empirical equations for surface roughness and its improvement factors as a function of the changes in technological parameters. We found that increasing feed rate worsened surface roughness, while increasing burnishing speed improved surface roughness. Within the investigated parameter ranges, the following combination was found to be the most effective for minimizing surface roughness:  
\[f=0.05\frac{mm}{rev}\ \ \ v_{v}=0.9817\frac{m}{s}\ \ \ \ \ \ F=80\ N\]  
**Author Contributions**: Conceptualization, S.S. and G.V.; methodology, S.S. and G.V.; software, S.S. and G.V.; validation, S.S.; formal analysis, S.S.; investigation, S.S. and G.V.; resources, S.S. and G.V.; data curation, S.S. and G.V.; writing--original draft preparation, S.S. and G.V.; writing--review and editing, S.S. and G.V.; supervision, G.V.; project administration, S.S. and G.V.; funding acquisition G.V. All authors have read and agreed to the published version of the manuscript.  
**Funding**: This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.