**4. Conclusions**

The presented research was aimed at the dependence of selected technological parameters of the AWJ system on selected parameters of the quality of the cut surface. The multiple linear regression function describing the cut wall roughness as a function of the mentioned selected cutting variables has been determined for both *Ra* and *Rz*.

The main results can be summarized as follows:

With increasing material thickness from 6 to 10 and 15 mm, the roughness in its central part increases by more than 18% at *Ra* and 5.5% at *Rz* for 6 and 10 mm thicknesses and by one third for *Ra* and 21% for *Rz* for 10 and 15 mm thicknesses.

The values of technological parameters *ma* = 170 g/min, *p* = 300 MPa, *v* = 80 mm/min represent the combination with which the highest roughness values while the values of technological parameters *ma* = 270 g/min, *p* = 380 MPa, *v* = 40 mm/min represent the combination with which the smallest roughness values were achieved. By increasing *ma* from 170 to 270 g/min at *p* = 340 MPa, it is possible to twice the speed *v* with an unchanged roughness value *Ra* of the cut surface.

The largest influence of the monitored technological parameters on the roughness (*Ra*, *Rz*) was found for the abrasive mass flow, a smaller influence was revealed for the cutting speed *v*.

Derived regression models (Equations (1) and (2)) show linear relationships have been determined between studied independent variables of the cutting process (traverse speed, liquid pressure, and abrasive mass flow rate) and roughness characteristics. Simultaneously, the linear relationships (Equations (3) and (4)) have also been found between declination angle values and roughness parameters *Ra* and *Rz*.

The models can be used both for a prediction of cutting variables and for a calculation of the cutting characteristics, such as traverse speeds, abrasive flow rates, and other influencing cutting walls quality. The achieved results are utilizable for improvement of the control software of the CNC machines used for water jet and abrasive water jet cutting and complement the existing solutions in the scientific field and can be used to reduce operating costs and increase the economic e fficiency of production systems with AWJ technology.

The authors plan to include non-contact measurements on the samples cut using the AWJ systems, more complex roughness and waviness parameter analysis, and texture modeling of measured surfaces using their merging for future work.

**Author Contributions:** Conceptualization, M.S. and T.K.; methodology, M.S.; validation, T.K. and M.S.; formal analysis, M.S.; data curation, T.K.; writing—original draft preparation, M.S.; writing—review and editing, T.K.; visualization, J.M.; supervision, T.K.; project administration, J.M.; funding acquisition, S.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Slovak Ministry of Education within project VEGA No. 1/0116/20 and by the Slovak Research and Development Agency under contract No. APVV-18-0316.

**Acknowledgments:** Authors would like to acknowledge Stanislav Fabian for valuable comments.

**Conflicts of Interest:** The authors declare no conflict of interest and the funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
