**5. Machine learning approach**

This preliminary model aims at predicting COF based on topographical characteristics of interfaces (surface pores and texture) rather than investigating the physical mechanisms associated to the tribological behavior.

The average coefficient of friction from 6228 experiments was organized in a training dataset of 1704 different combinations of geometric and operational parameters and, subsequently, used as inputs to a Hardy Multiquadric Radial Basis Function (RBF), as illustrated schematically in **Figure 6**. The mathematical development and detailed results are reported in [33]. Similar to several Artificial Neural Networks (ANN) methods, the RBF approach can produce a correct input–output mapping even for noisy and dispersed data. The RBF and experimental COF output were compared using the coefficient of determination (*R*<sup>2</sup> ) evaluation to avoid that the variation among the tribological experiments could be wrongly assessed as a surface feature or test parameter (*i.e.* overfitting). The results were considered satisfactory under this perspective because the error percentage was not significantly different from the maximum relative standard deviation of the dataset.

A summary of the model fitting capacity is shown in **Figure 7**, where the RBF and experimental COF results were plotted together. Overall, results from all the

#### **Figure 6.**

*Schematic of the machine learning model proposed to predict the frictional behavior of porous and textured interfaces from the experimental dataset.*

**Figure 7.**

*Comparative plots for some surface features. Each number in the horizontal axis represents a single experimental test (single combination of surface and test parameters) sorted in ascending order according to friction results rather than in chronological order for improving readability.*

different samples presented a high fitting capacity (*R*<sup>2</sup> ≈ 0.94), being the worst Ball-Sint (≈0.64) and the best fitting Disc-Si4 (≈0.97). The *R*<sup>2</sup> values from the other surface configurations are distributed between these two extremity values.

The proposed model is more sensitive to high values of *W*, *D* and *Ca*. Low values of *W* and *D* for shallow configurations could be difficult to be interpreted by the model since the overall topography is not mathematically significantly different from the smooth samples NP. Furthermore, shallow features in Ball-Sint and Disc-Di also occupied a very small area (low *Ca* values), making it even more challenging to discern between NP and shallow features.

Together with the continuous improvement of the mathematical model and expansion of the dataset to shallow and less dense surfaces, these results indicate that the RBF methodology can be an effective tool for designing novel surface features for tribological applications.

#### **6. Conclusions**

The frictional performance of textured discs and balls containing surface pores or laser textures was assessed carrying out a wide range of experiments under lubricated non-conformal contact and varying kinematic conditions (speed and slide-to-roll-ratio).

Between the different texture geometries studied, dimples generally performed best, demonstrating the lowest COFs and lowest lift-off speed, which can be traced

#### *Tribological Performance of Random Sinter Pores vs. Deterministic Laser Surface Textures… DOI: http://dx.doi.org/10.5772/intechopen.100245*

back to the increment of the hydrodynamic load-carrying capacity at lower speeds, further separating the rubbing surfaces and consequently reducing asperity contact. This was proven by film thickness and electric contact resistance measurements. Perpendicular grooves demonstrated beneficial performance compared with polished reference samples, depending on depth and transversal dimension. Potential beneficial effects of perpendicular grooves were partially mitigated by textures' excessive transversal dimension or depth. Longitudinal grooves led to unbeneficial tribological behavior, as equal entrainment and groove direction probably promoted lubricant migration out of the contact.

Sintering parameter tuning permitted to obtain different porosities and pore characteristics. The pore configuration achieved by machining the sintered ball samples reduced friction compared to the unstructured reference at the same specific film thickness.

Deterministic laser textures seem to outperform surface pores with random distribution and size despite the difficulties of comparing sintered with laser textured samples. This is particularly evident when considering the entrainment speed, showing that laser textures can significantly decrease the lift-off speed, after which full-film lubrication prevails by generating additional hydrodynamic pressure. Both textures have in common that textures of small dimensions being smaller than the contact area yielded the best results. However, it should be noted that laser texturing requires an additional manufacturing step, thus making the production process more complex.

Finally, considering that using advanced machine learning methods to describe tribological problems is still in its infancy, the proposed radial bias function approach showcased promising results that open new perspectives for its extension to support the optimum design of surface texturing for tribological applications in the future.

## **Acknowledgements**

The State of São Paulo Research Foundation, Brazil (FAPESP grant N. 2016/25067-9), the Brazilian National Council for Scientific and Technological Development (CNPq) and the"Austrian COMET Program" (project InTribology, no. 872176) via the Austrian Research Promotion Agency (FFG) and the federal states of Niederösterreich and Vorarlberg are acknowledged for funding this work. Part of this work was carried out within the "Excellence Centre of Tribology" (AC2T research GmbH). C. Gachot acknowledges the government of Lower Austria for financially supporting the endowed professorship tribology at the TU Wien (Grant No. WST3-F-5031370/001–2017) in collaboration with AC2T research GmbH. D. Dini also acknowledges the support received from the Engineering and Physical Sciences Research Council (EPSRC) via his Established Career Fellowship EP/N025954/1. M. Roudrigues da Silva thanks the Centro Educacional da Fundação Salvador Arena and Termomecanica São Paulo S.A. for the financial support.
