*2.1. Deformation Behaviour*

To understand the deformation behavior of the hammering integrated with the ISF process, the deformation of the workpiece needs to be studied based on the linear tool movement due to the hammering operation. Figure 2 shows the schematics of deformation of the workpiece with respect to the hammering induced linear tool movement. The tool moves from one position to another position in certain steps. Initially, the tool aligns itself to the first hammering position where it deforms the workpiece with predefined amplitude. In the next step, the tool retracts to its original position and then moves to the next hammering position and similarly deforms the workpiece.

**Figure 2.** Schematics of deformation of the workpiece based on linear tool movement with hammering.

When the tool deforms two successive hammering positions, it forms an overlapping region, as shown in Figure 3a. The overlapping region affects the surface quality of the formed component, i.e., if the overlapping region is bigger, the surface quality of the deformed product is poor. Further, the overlapping region dimension adversely affects the production time. Thus, the overlapping region should be chosen such that the surface quality of the product is maintained, and the production time is minimized [18].

**Figure 3.** (**a**) Schematics of the overlapping region caused due to linear tool movement with hammering (**b**) Schematics of the basic hammering mechanics.

Figure 3b shows the basic hammering mechanics in which a hemispherical tool with radius (*r*, mm) impacts the workpiece with predetermined amplitude (*<sup>a</sup>*, mm). '*d*' is the maximum length of the deformed area of the workpiece (mm), which further helps in deducing the frequency of the impact (*f*, Hz), when the tool moves with certain feed rate (*V*, mm/s). The frequency of the impact is calculated using Equations (1) and (2).

$$f = \frac{V}{d} \tag{1}$$

$$d = 2\sqrt{2ra - a^2} \tag{2}$$

Equations (1) and (2) help to investigate the frequency of the impact during the spiral movement of the tool deforming the workpiece as shown in Figure 3b. Further, the indentation marks and the overlapping region can be controlled with the help of controlling the input process parameters such as predetermined amplitude and feed rate of the tool.
