**6. Conclusions**

The results from the conducted experiment show that the performed BB process on the test specimens leads in general to increase of the number of cycles until fatigue failure for both steels investigated. The gain in the fatigue life is more than 10 dB (about three times) for 75% of the AISI 304 and AISI 316L specimens, in comparison with those which had only preliminary plastic deformation, obtained after the steel sheets were rolled by the manufacturer (i.e., those without formed RR after applying BB). Thus, the formatted RR, after presenting a modification of the BB process, do not affect negatively the fatigue life results for these two steels. This is because the ridges of the RR cells' boundaries do not play the role of stress concentrators which cause the formation of microcracks. This can be reported as an important operational characteristic for those parts which have RR, formed by using BB on their contact surface, in order to ensure a low slip resistance and a low wear, due to increased abilities to retain lubricants, dust, and/or debris which causes wear, in comparison with the smooth surface topographies, obtained after other traditional finishing processes, such as grinding, polishing, traditional ball burnishing, etc. Surfaces with RR could be part of equipment which works in highly dusty, abrasive or saltwater environments in marine, mining, petroleum, or chemistry industries, etc., and for which there are also requirements for high fatigue strength. The experimentally obtained results give us grounds to recommend this variant of the BB process, in which a specific RR of the IV-th type could be formed as a suitable finishing operation for such parts, subjected to both cyclic loads, for work in high-wear operating conditions. Using the advances of the contemporary CNC production equipment, and the presented approach for mathematical modeling of the toolpath of the ball tool, allows BB to be carried out as a finishing operation on the same machine, along with the previous cutting operations. This makes the BB operation easy to add to standard (generic) sequences of manufacturing operations for the production of such machine parts.

As can be seen from Table 9 and Figure 14, the optimal combination of the BB regime's parameter values, in order to maximize the probability (up to 97%) of obtaining the maximum fatigue life of the parts made of AISI 304 or 316L, is A = 1, B = 1, C = 1 D = −1. In other words, the deforming force *F*, *N*, the amplitude of the sinewaves *e*, *mm*, and their number *i* must be set at their high values. However, the parameter feed rate *f*, mm/min must be set at its low values.

The presented approach for using the factorial experiment designs and Bayesian rule for data analysis reveals some tendencies about the impact of the main regime parameters of the BB process and their iterations on the fatigue life of the investigated steels. It provides good enough results in case of experimental investigations, in which it is not appropriate to perform a large number of trials, and the obtained results for the investigated parameter (i.e., fatigue failure cycles in our case) can have comparatively high variance. This can significantly shorten the time and facilitate the efforts for obtaining the needed results, in order to determine the optimal combination of BB regime parameters values in manufacturing conditions.

The methodological sequence for fatigue failure testing presented in the current work can also be applied to other materials, processing methods, and experimental plans, involving a different number of influencing factors. Our future work will be focused on its development and improvement in future research, similar to that presented in this paper.

**Author Contributions:** Conceptualization, S.S. and D.D.; methodology, S.S., D.D., and M.K.-B.; software, D.D. and M.K.-B.; validation, S.S. and D.D.; formal analysis, D.D.; investigation, S.S., D.D., and D.V.; resources, D.V.; data curation, D.D.; writing—original draft preparation, S.S. and D.D.; writing—review and editing, S.S., D.D., M.K.-B., and D.V.; visualization, S.S. and D.D.; supervision, S.S.; project administration, S.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The raw fatigue data and solved Bayesian models can be found and downloaded for free from the GitHub repository: https://github.com/DMDimitrovJ/BurnishingFat igue (accessed on 2 April 2021)

**Conflicts of Interest:** The authors declare no conflict of interest.
