## 2 Experimental Approach  
### Experimental Data  
Increasing the strength of steel materials, which are widely used in the production of various machine parts, including axles, crankshafts, gears, shafts, and engine parts, operating under wear and fatigue conditions, is crucial for the manufacturing industry. For this purpose, AISI 8620, AISI 5140, AISI 4140, and AISI 1020 steel materials were used in the study. A low-carbon steel AISI 1020 is used in machine parts, structural components, fasteners, shafts, and applications. AISI 5140 is chromium steel often used in gears, connecting rods, spindles, and other mechanical parts that require moderate strength. AISI 4140 is a chromium-molybdenum alloy steel used in axles, shafts, bolts, crankshafts, and high-performance automotive and industrial components. AISI 8620 is a low-alloy, nickel-chromium-molybdenum steel commonly used for gears, camshafts, crankshafts, and fasteners, where a tough core and a wear-resistant surface are required. We aimed to see how the properties of these steels, which have a widespread use, will change with mechanical surface treatment as well as heat treatment. Table 1 provides their chemical makeup and Table 2 displays the mechanical properties of these materials [25]. In the study, SP (SP) and vibrating SP processes (VSP) were applied to the samples. Figure 1 schematically illustrates how the samples were shot pened. The samples were shot-peened by Sigma SP Company (Istanbul, T\(\ddot{\text{u}}\)rkiye). The peening process was carried out in a device where the process time and air pressure could be controlled. In the SP process applied to the samples in the study, S230 standard steel balls with 90\({}^{\circ}\) impact angle, 6.35 mm nozzle diameter, and a 48-51 HRC hardness range were used [26]. A frequency of 50 Hz was selected for the VSP process [27]. One of the factors that significantly affects the SP process is the Almen intensity [28]. Therefore, the aim of \begin{table}
\begin{tabular}{l l l l l l l l} \hline \multicolumn{2}{c}{**Material**} & \multicolumn{6}{c}{**Chemical Composition/wt \%**} \\ \hline AISI 8620 & C & Si & Mn & Cr & Mo & Ni & Fe \\  & 0.23 & 0.30 & 0.90 & 0.60 & 0.25 & 0.70 & Balance \\ \hline AISI 4140 & C & Si & Mn & Cr & Mo & Smax & Fe \\  & 0.40 & 0.28 & 0.80 & 0.9 & 0.20 & 0.040 & Balance \\ \hline AISI 5140 & C & Si & Mn & Cr & Mo & Smax & Fe \\  & 0.40 & 0.20 & 0.8 & 0.8 & - & 0.040 & Balance \\ \hline AISI 1020 & C & Si & Mn & Cr & Pmax & Smax & Fe \\  & 0.22 & - & 0.50 & - & 0.04 & 0.05 & Balance \\ \hline \end{tabular}
\end{table} 
Table 1: Chemical composition of test sample materials. Figure 1: A schematization of the SP processes used in the study: (**a**) SP process; (**b**) VSP process [24]. \begin{table}
\begin{tabular}{l l l l l l} \hline \multicolumn{2}{c}{**Material**} & \multicolumn{6}{c}{**Mechanical Properties**} \\ \hline AISI 8620 & Tensile strength & Yield strength & Elongation\% & Elasticity module & Hardness (HB) \\  & 563.4 MPa & 385.4 MPa & 31.3 & 200 GPa & 149 \\ \hline AISI 4140 & Tensile strength & Yield strength & Elongation\% & Elasticity module & Hardness (HB) \\  & 655 MPa & 417.1 MPa & 25.7 & 205 GPa & 197 \\ \hline AISI 5140 & Tensile strength & Yield strength & Elongation\% & Elasticity module & Hardness (HB) \\  & 572 MPa & 293 MPa & 28.6 & 200 GPa & 167 \\ \hline AISI 1020 & Tensile strength & Yield strength & Elongation\% & Elasticity module & Hardness (HB) \\  & 394 MPa & 294 MPa & 36.5 & 205 GPa & 111 \\ \hline \end{tabular}
\end{table} 
Table 2: Mechanical properties of materials used in experimental studies. this research is to determine the most appropriate Almen intensity. The process parameters selected for the study are shown in Table 3.  
Hardness measurements were taken on a TTS Matsuzawa HWMMT-X3 micro hardness tester (Tokyo, Japan) using a Vickers indenter at a load of 2000 kgf and a duration of 10 s. Measurements of hardness were carried out along the depth profile.