**3. Experimental Research**

In order to investigate the impact of the main regime parameters of the BB process on fatigue failure effects, an experimental investigation was conducted according to the first goal. Its purpose was to reveal the main effects and interactions between the BB regime parameters: deforming force—*F*, N and feed rate—*f*, mm/min, which were expected to a have major influence on the degree of the plastic deformation in the surface layer of the material, and the toolpath trajectory parameters: *e*, mm and *i*, which are known to determine the shape and the size of the RR cells. The experimental research was based on the approach of the full factorial designs [39]. The selected four factors (i.e., the BB regime parameters *F*, *f*, *i*, and *e*) varied on two levels—"low" and "high". The experimental design executed is shown in Table 2.

**Table 2.** Levels of factors (i.e., regime parameters of the BB operation).


As a response criterion, the number of cycles until fatigue failure was used. For every trial, included in the experimental design, two replicates were performed. The obtained results were subjected to several different analysis techniques, including the Pareto, *t*-test, and Bayesian rule.

The natural values of *i*, and *e* were selected on the basis of the previous research of the authors [40]. Their low and high levels were set to obtain RR with different size cells. In Table 3, the four toolpath types which had different unfolded lengths, derived by using Equation (1), are illustrated. The unfolded toolpath length gives the relief degree of imbrication, which is proportional to the number of passes in conventional burnishing technology.

**Table 3.** Unfolded length of the toolpaths at chosen factor level combinations.


The values for *F* and *f* were selected from the operational capabilities of the ball burnishing tool [41], and those of the CNC milling machine (3-axes HAAS TM-1, USA [42]) used.

The rest of the BB parameters, which were not varied during the experiments, were fixed as follows: diameter of the deforming element was *dc* = 14, mm; number of points of the toolpath *p* = 10,000; the distance between toolpath segments *dfn* was set to be equal of half of the sinewave amplitude *e*. In order to avoid jamming of the ball tool, Mobil DTE 25 was used as a lubricant for all ball burnished experimental specimens.

The test specimens were made of austenitic stainless steels AISI 304 and AISI 316L, described in Section 2.1. They had a specific shape and dimensions, shown in Figure 4a,b. The specimens had two stress concentrators whose purpose was to guarantee the fatigue cracks developed in the narrowest section of the material (see Figure 4b), i.e., where the RR were formed after applying the BB operation. According to the experimental design shown in Table 2, 16 × 2 = 32 specimens were processed by BB for AISI 304 steel and another 32 specimens with the same characteristics for AISI 316L steel, respectively. Fourteen additional specimens (without RR) were also made of both of the steels (see Figure 4c,d). Their purpose was to adjust the fatigue test setup, as well as to compare the results obtained for the number of cycles to fatigue failure with and without the application of the BB operation.

**Figure 4.** (**a**) Fatigue test specimens' shape and dimensions; (**b**) BB area with RR of the IV-th type; (**c**) arrangement of the specimens within the plates of AISI 304 and AISI 316L. (**d**) Physical BB-operation for obtaining the real RR from the IV-th type.

The BB operation was applied on both sides of the plates, with one and the same combinations of the regime parameter values, according to experimental design, shown in Table 2. Thus, each specimen processed by BB had two-sided RR. After all RR were formed onto both sides of the plate, the different specimens were cut off the plate using a CO2 laser cutting machine MAZAK SUPER X48-Champion. In order to avoid the impact of the sharp edges after the laser cutting operation at the stress concentrator on fatigue life of the specimens, they were subjected to electropolishing.
