2.3.1. Description of the Experimental Method and Setup

A reversal bending fatigue test similar to that in [36] was performed on a vibration exciter (see Figure 2). The test specimen was mounted as a cantilever beam on the exciter's vibration table. Two accelerometers were mounted: one at the free end of the specimen and the other at the exciter table. The vibration exciter was harmonically excited with a frequency close to the fundamental resonance mode shape of the specimen.

**Figure 2.** Components of the fatigue failure experimental setup.

As the difference between the tip and base acceleration is proportional to the applied stress, the load was controlled by adjusting the amplitude and the frequency of the shaker signal during testing. An algorithm similar to those realized in [38] was developed and installed in the MyRio 1900 (National Instruments, Austin, TX, USA) for automatic adjustment of the excitation signal frequency in order to keep the applied stress constant during the test. The test was stopped automatically when the algorithm was unable to maintain the preset stress amplitude by adjusting the frequency of the exciting signal. In order to ensure the stable working of the self-adjustment algorithm, the frequency of the exciting signal must be a little greater than that at the resonance. This way, the possibility of the exciting signal frequency starting the amendment in the wrong direction is eliminated. Using a personal computer and the LabView (National Instruments, Austin, TX, USA) visual programing environment, software was developed to monitor the experimental parameters and to count the cycles until fatigue failure of the specimens. The software saved incoming data from MyRio 1900 as logs, which were used for further analyses of the results.

All the specimens in the current experimental investigation were tested at equal loading, in order to investigate the impact of the BB regime parameters on fatigue failure.

2.3.2. Determining Experimental Conditions of the Fatigue Failure Test Using FE Analysis

The purpose of the conducted finite element (FE) analysis (see Figure 3a–d) was to determine the vibration fatigue test setup parameters, in order to assure invariable conditions of the fatigue failure experimental investigation. A linear dynamic study was carried out for the investigated materials. It was based on natural frequencies and mode

shapes to evaluate the response of the test specimens to dynamic loading, caused by shaker's table.

**Figure 3.** (**a**) Meshed 3D model with fixed geometry and excitation applied with (**b**,**c**) results from finite element analysis (FEA) for maximal obtained stress and acceleration at the free end of the specimen and (**d**) response graphs of "frequencyacceleration" (amplitude) obtained after FEA and experimental study conducted.

To conduct the FE analysis study, a SOLIDWORKS Simulation module (Education edition 2020–2021, SolidWorks Corporation, Waltham, MA, USA) was used. The input parameters in the FE model included the test specimens' material properties (see Table 1) and applied uniform excitation (acceleration) of 10 m/s<sup>2</sup> which was restrained only in the vertical direction (see Figure 3a). The masses of the test specimens and the used acceleration sensor at the cantilever's free end were set in the FE model, based on weight measurements of the real items, using a precise scale. The global damping ratio for each mode was set to be 0.01.

As the 3D components participating in the assembly had relatively simple geometric shapes, a standard high-quality mesh was used with the global size of the elements being 2.0 mm, and tolerance 0.1 mm. As a result, the total number of the obtained mesh elements was 66,382, and they had 99,510 nodes.

The obtained FE model results for maximum (Von Misses) stress (218.1 MPa) at the concentrator of the fatigue specimen, along with displacement (2.36 mm), and acceleration (569.1 m/s2) at its free end (shown in Figure 3b–d), were calculated for the resonant frequency (77.326 Hz). The last two parameters were determined in the mesh model with the number 45,628, which was located as near as possible to the center of gravity of the accelerometer (see Figure 3c) in order to bring the simulation analysis as close as possible to the actual experimental conditions.

Using real test specimens (without RR formed by ball burnishing) and adjusting the electromagnetic shaker to sweep the frequency diapason around the obtained resonance frequency, a "frequency-acceleration" (amplitude) response graph was obtained. A similar response graph also was obtained from the FE model. Both graphs are shown together in Figure 3d for illustration. The comparison between them shows that the FE model gave results close to those obtained after the physical test. The resonant frequencies of the measured (77.75 Hz) and the calculated (77.33 Hz) response graphs differ by only 0.5%. The difference in respect to the maximum acceleration values at resonance between the measured (531 m/s2) and the calculated (557.7 m/s2) response graphs did not exceed 5%. Therefore, the results derived from the FE model can be considered as adequate.

Due to the algorithm implemented to automatically adjust the frequency of the excitation load of the exciter, which was used to control the acceleration at the free end of specimen and thus to keep the stresses obtained in the concentrator constant during the fatigue test, it was not advisable for the exact resonant frequency (i.e., the peak of the response graphs) to be chosen as a work point. In order to guarantee stable working of the auto-adjusting algorithm, the work frequency of the shaker had to exceed the resonant one. Using the FE model, and the obtained response graph, it was possible to specify previously the suitable initial working frequency and the corresponding acceleration at the free end, which defined the resulting stress at the concentrator of the fatigue specimens. This way the FE model facilitated the preparation of the fatigue failure experimental investigation, and allowed us to reach optimal experimental conditions without the need of carrying out many preliminary physical tests.
