## 2 Materials and Methods
Therefore, the selected curves and arcs profile, i.e., 10-40 mm, provided evidence of high kerf taper and geometrical inaccuracies from previous investigations [28; 29; 30; 31], demonstrating the need for further analyses using hard-to-cut materials. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Profile No.** & **Profile Description** & **Measurement (mm)** & **Cutting Path** \\ \hline
1 & External Arc & R5 & R15 \\
2 & External Arc & R10 & \\
3 & External Arc & R15 & \\
4 & External Arc & R20 & \\
5 & Internal Arc & R5 & \\
6 & Internal Arc & R10 & \\
7 & Internal Arc & R15 & \\
8 & Internal Arc & R20 & \\
9 & Straight line & 10 & \\
10 & Straight line & 20 & \\
11 & Straight line & 30 & \\
12 & Straight line & 40 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: AW cutting profiles and path. Figure 2: Experimental set-up (**a**) Schematic diagram of the nozzle system and (**b**) AWJ cutting head and material positioning. The input parameters selected in this study were traverse speed and material thickness, while waterjet pressure, abrasive mass flow rate, standoff distance, abrasive type, and mesh number were held constant. Three levels of material thickness and traverse speed were applied, as shown in Table 4. The selection of variable parameters, and the assignment of levels, was made following an intensive review of current research data. Input parameter settings were constantly redefined, due to limitations with the machine and/or constraints in effectiveness shown in previous AWIJM experiments [8; 15; 18; 19; 20; 21; 22]. The input parameters that were kept constant during the tests are shown in Table 5.  
The performance of AWIJM is determined by the amount of material removed from the target workpiece and by the accuracy of the geometry of the cut relying on the kerf width and taper angle [32]. Therefore, the kerf taper angle and material removal rate have been selected for consideration as output parameters in this study. Kerf taper angle resulting from abrasive waterjet contour cutting is measured according to the proportion of the sum of kerf top width and kerf bottom and thickness of the workpiece [10]. Kerf width refers to the ratio of entry and exit cut width. Kerf width dimensions are measured on the top as well as bottom by using an optical microscope, model LEICA M80, with a precision scale of 100 \(\upmu\)m. Equation (1) was utilised to calculate the kerf taper angle following abrasive waterjet cutting of AISI 304L [33]. A scheme of the applied kerf geometries is illustrated in Figure 3[14]. \[\begin{split} Kerf\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\  
The material removal rate, which is the volume of material removed from the material per unit of time, is measured by kerf width, traverse speed, and depth of cut. The material removal rate was calculated using Equation (2) [32]:  
\[MRR=h_{t}\cdot W\cdot V_{f} \tag{2}\]  
wherein: \(W=\frac{Wt+Wb}{2}\)  
Finally, analysis of variance (ANOVA) was applied to quantify the influence of the selected variable parameters. The ANOVA was employed to identify the significant effect of input parameters and their corresponding levels [34]. ANOVA was performed with a confidence interval of 95%, which has typically been applied in several related studies. The confidence interval determines how precise the estimated statistics are, whereby a 95% confidence interval denotes a 5% chance of having an incorrect estimation [35; 36]. The percentage contribution assesses the effect of each input parameter on the output, where \(p\)-values estimated at more than 0.05 or 5%, are considered insignificant [37].