# The Predictive Model of Surface Texture Generated by Abrasive Water Jet for Austenitic Steels
## 3 Results and Discussion
### Evaluation of Measurement Results from the Mathematical-Statistical Point of View  
When analyzing the individual cutting speeds used and their effect on the change in the surface roughness value \(Ra\) using the non-parametric Kruskal-Wallis analysis of variance (Table 11), it can be said that (H3, N = 68) = 15.05391) the cutting head feed rate is a significant factor affecting the change in surface roughness (\(p\) = 0.0018). The value \(p\) = 0.0018 represents the result of the Kruskal-Wallis analysis of variance for the compared groups of feed rate: 50 [mm\(\cdot\)min\({}^{-1}\)], 75 [mm\(\cdot\)min\({}^{-1}\)], 100 [mm\(\cdot\)min\({}^{-1}\)], 125 [mm\(\cdot\)min\({}^{-1}\)] of the investigated parameter \(Ra\) in the probability scale. Given the chosen value of the significance level \(\alpha\) = 0.05, we reject the null statistical hypothesis, which follows from the nature of the Kruskal-Wallis test, and we can say that there is at least one sample (feed rate) that is statistically different from the others. Figure 4: Effect of cutting head feed rate on the surface roughness value \(Ra\). Further analysis by multiple comparisons of \(p\) values shows that the statistically significant difference in surface roughness value \(Ra\) is 50 mm\(\cdot\)min\({}^{-1}\) and 100 mm\(\cdot\)min\({}^{-1}\). Thus, an increase in the speed of 50 mm\(\cdot\)min\({}^{-1}\) causes an increase in the surface roughness value of \(Ra\) by 31.5%. The second statistically significant difference in surface roughness value \(Ra\) is 50 mm\(\cdot\)min\({}^{-1}\) and 125 mm\(\cdot\)min\({}^{-1}\), respectively. Increasing the speed by 70 mm\(\cdot\)min\({}^{-1}\) will increase the surface roughness \(Ra\) by 37.1%. The difference between the surface roughness value \(Ra\) at the cutting head feed rate of 100 mm\(\cdot\)min\({}^{-1}\) and 125 mm\(\cdot\)min\({}^{-1}\) is 8.21%, but this difference is not significant at a significance level of 5%. With AWJ cutting technology, increasing the flow rate increases the erosion efficiency, assuming a higher number of abrasive particles involved in the cutting process itself. Increasing abrasive mass flow means a relative increase in the depth of cut and on the other hand, a decrease in the surface roughness value (Figure 5b). Increasing the abrasive mass flow from 100 g\(\cdot\)min\({}^{-1}\) to 150 g\(\cdot\)min\({}^{-1}\) will result in a 14.6% reduction in surface roughness. A further increase in abrasive mass flow to 200 g\(\cdot\)min\({}^{-1}\) results in an 11.8% reduction in surface roughness. Within the range of experimentally used abrasive mass flow values, the surface roughness value decreased by almost 40.5% compared to the lower and upper limits. In the case of water flow and water pressure, increasing the pressure increases the kinetic energy of the individual particles within the stream, thereby improving the ability of the abrasive particles to remove the material. On the other hand, increasing water flow and pressure can lead to random collisions between particles inside the stream, to accelerating them and also to an increase in energy, which ultimately leads to surfaces with a higher roughness value (Figure 5a). Increasing the current effective diameter in relation to the nozzle diameter can cause a loss of kinetic energy, resulting in surfaces with a higher roughness value (Figure 6). The table of model parameters estimation (Table 11) shows that the change in the values of the investigated parameter in the range of experimentally used input variables has a significant effect on the significance level of 5% nozzle distance from the material, the effect of this input study variable on the overall variability of \(Ra\) being 8.67%. Furthermore, it can be concluded that increasing the distance of the nozzle from the material increases the conditional value of surface roughness \(Ra\). Another significant input parameter that affects the surface roughness value is the cutting head feed rate with an overall effect on \(Ra\) variability of 26.81%.