*2.2. Methodology*

The formability was studied for both the ISF and ISH processes with the aluminum alloy (AA1050) in terms of the wall angle, forming depth, and forming limits of the formed geometries. Hussain et al. [19] had proposed that the number of experiments would increase to study the formability of the component. Thus, to minimize the number of experiments to determine the formability of a material, it was advised to form a varying wall angle truncated cone (VWATC). The VWATC was used as the initial test geometry, with wall angle, varying from 0 degrees on the top to 90◦ at the bottom of the cone, as shown in Figure 4. In the incremental forming process, the tool motion was controlled with the help of numerical control (NC) codes of the desired component. Generally, the NC codes were obtained by generating a spiral toolpath of the required geometry in CAD/CAM software [16]. The toolpath for the VWATC was prepared with the help of an in-house developed generalized python code (kindly refer to Appendix A), which is independent of any commercial CAD/CAM software. The input of the generalized python code for VWATC was the major and minor diameters of the geometry, the height of the VWATC, number of layers or step depth and number of points in one spiral contour. Figure 5 shows the toolpath trajectory for the ISF and ISH processes. The enlarged section in Figure 5 shows the tool motion during both processes.

**Figure 4.** Varying wall angle truncated cone (VWATC) test geometry.

**Figure 5.** Toolpath for the VWATC for (**a**) ISF process and (**b**) ISH process.

During forming of the VWATC, the sheet thickness decreases continuously with increasing wall angle, which ultimately leads to rupture of the component at the point of minimum thickness. The angle at which the VWATC fractures was considered as the maximum achievable wall angle for the sheet material. The present work initiated with the forming of VWATC using the toolpath strategies for ISF and ISH processes as shown in Figure 5. Further, the wall angle achieved through both processes was investigated through experimentation. The VWATC was formed till the point of fracture to determine the forming height achieved through both processes. The formed height of the VWATC was used to determine the wall angle achieved for the respective components formed through ISF and ISH processes. The tangent at the point of fracture revealed the wall angle achieved in the components formed through ISF and ISH processes. To ensure correctness in the results, three sets of VWATC components were formed through ISF and ISH processes individually. Further, the mean values of the wall angle achieved through ISF and ISH processes were compared to find the minimum value of the achieved wall angle. The minimum wall angle observed after comparison was taken as an input wall angle for the constant wall angle truncated cone (CWATC) geometry. The minimum wall angle found through comparison was 78◦ and it was considered as the wall angle for CWATC. The schematic of the CWATC is shown with the help of Figure 6. To form the CWATC through ISF and ISH processes, the toolpaths were developed using the similar generalized python code which was discussed earlier. The results obtained in terms of sheet thickness, depth achieved, surface roughness, wall angle, and forming limits were compared for the two processes.

**Figure 6.** Constant wall angle truncated cone (CWATC) test geometry.

#### **3. Numerical Simulation and Experimental Work**
