## 3 Modeling of Circular Quality Responses
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Circular Kerf Width**} & \multicolumn{6}{c}{**Circular Bevel Angle**} \\ \hline
**Source** & **DF** & **SS** & **MS** & **F-Value** & **\(p\)-Value** & **DF** & **SS** & **MS** & **F-Value** & **\(p\)-Value** \\ \hline \(v\) & 2 & 0.77796 & 0.388978 & 49.27 & 0.000 & 2 & 92.394 & 46.1968 & 75.91 & 0.000 \\ \(I\) & 2 & 0.44207 & 0.221033 & 28.00 & 0.000 & 2 & 87.425 & 43.7123 & 71.83 & 0.000 \\ \(H\) & 2 & 0.07340 & 0.036700 & 4.65 & 0.046 & 2 & 4.948 & 2.4739 & 4.06 & 0.061 \\ _v-I_ & 4 & 0.01298 & 0.003244 & 0.41 & 0.796 & 4 & 30.646 & 7.6614 & 12.59 & 0.002 \\ _v-H_ & 4 & 0.01538 & 0.003844 & 0.49 & 0.746 & 4 & 0.705 & 0.1763 & 0.29 & 0.877 \\ _I-H_ & 4 & 0.05967 & 0.014917 & 1.89 & 0.206 & 4 & 2.418 & 0.6045 & 0.99 & 0.464 \\ Error & 8 & 0.06316 & 0.007894 & - & - & 8 & 4.869 & 0.6086 & - & - \\ \hline Total & 26 & 1.44460 & - & - & - & 26 & 223.404 & - & - & - \\ \hline \multicolumn{6}{c}{**Circularity Error—Top**} & \multicolumn{6}{c}{**Circularity Error—Bottom**} \\ \hline
**Source** & **DF** & **SS** & **MS** & **F-Value** & **\(p\)-Value** & **DF** & **SS** & **MS** & **F-Value** & **\(p\)-Value** \\ \hline \(v\) & 2 & 0.025874 & 0.012937 & 11.78 & 0.004 & 2 & 0.113252 & 0.056626 & 11.88 & 0.004 \\ _I  
From Figure 8 and according to the ANOVA results regarding the further discussion of the most significant parameters, it is evident that a higher arc current, lower cutting speed, and greater cutting height lead to an increase in the kerf width. In [27], it was concluded that the plasma jet cutting heat input is proportional to the product of the arc current and arc voltage and inversely proportional to the cutting speed. That means that a higher arc current and lower cutting speed result in the increased removal of the cutting workpiece material and, accordingly, of the larger kerf width. Here is the same situation. Also, regarding the influence of the cutting height parameter on the circular kerf width, as in [27], it was determined that an increase in the cutting height causes a loss of arc coherence, resulting in arc deflection and the formation of a wider kerf; here, the same phenomenon can be also noticed. Regarding the analysis of the level angle response, it is obvious from Figure 9 that higher cutting speeds and lower arc currents lead to the larger level angle. A lower arc current combined with a higher cutting speed results in a reduced amount of plasma jet cutting energy. Consequently, these parameter settings lead to a narrower circular kerf width. Due to the conical shape and characteristics of the plasma jet, the kerf width on the bottom side of the workpiece decreases more rapidly than on the top side, ultimately producing a larger level angle [28]. A greater level angle requires more demanding post-processing in order to achieve the optimal cut quality of the workpiece. In addition to the analysis of the circular kerf width and level angle, two more responses significantly affect the circular cut quality and need for post-processing treatments. These responses are focused on the circularity error on the top and bottom side of the workpiece sheet. When circularity error--top is considered, taking into account the ANOVA  
Figure 11: Three-dimensional surface plots of circularity error—bottom quality response under the influence of parameters interactions: (**a**) cutting speed–arc current, (**b**) cutting speed–cutting height, and (**c**) arc current–cutting height. Figure 10: Three-dimensional surface plots of circularity error—top quality response under the influence of parameters interactions: (**a**) cutting speed–arc current, (**b**) cutting speed–cutting height, and (**c**) arc current–cutting height. results and parameters/interactions significance as well as surface plots from Figure 10, it can be seen that higher cutting speeds result in larger values of the circularity error. The arc current has a dual effect.