**5. Summary and Future Trends**

This section summarizes the current knowledge and presents future tends regarding multi-scale surface textures applied to tribological problems. Even though several experimental and numerical works have tried to address the effects of multi-scale textures on friction and wear, the mechanisms responsible for the observed friction and wear reduction has not been fully identified yet. Therefore, we intend to derive some hypotheses regarding the underlying mechanisms for the improved tribological performance.

As already described in the introduction and depicted in Figure 19, surface textures may contribute to (i) increase the hydrodynamic pressure thus improving the load-carrying capacity (micro-hydrodynamic bearing effect) and reduce the shear-strain rate in the oil over the texture, (ii) draw additional lubricant into the contact area (inlet-suction effect), (iii) store lubricant and supply it to the interface (oil reservoir effect), (iv) trap wear particles (debris trapping effect), and (v) reduce the real contact area thus reducing friction. Furthermore, under boundary and severe mixed lubrication conditions, surface textures may also affect sealing performance and percolation effects.

**Figure 19.** Schematic illustration of the possible mechanisms responsible for improved tribological performance of multi-scale surface textures. In this example, larger dimples with superimposed smaller cross-like textures are shown.

All the above-mentioned contributions are well known and accepted for single-scale textures. However, when taking multi-scale surface textures into consideration, it can be expected that a combination of different contributions may be responsible for superior friction and wear behavior. In this context, it is particularly important to simultaneously consider the type of contact (conformal or non-conformal), the operating conditions and the associated lubrication regime for the design of effective surface textures, since different mechanisms and design strategies need to be taken into consideration depending on the respective contact characteristics. Thereby, it must be emphasized that surface textures, which improve the tribological performance for specific conditions such as a certain range of film thicknesses or a specific lubrication regime, are not necessarily beneficial for all operating conditions [55]. It has been shown that beneficial surface textures optimized for a specific lubrication regime may even induce detrimental effects when used in another regime thus increasing friction and/or wear. In this sense, multi-scale surface textures pursue the goal to extend the range of operations conditions, in which a specific set of surface textures leads to superior tribological performance. This improves the general applicability of surface textures for industrial applications, since many machine elements operate under different lubrication regimes, sometimes even over a single operating cycle, as in piston and piston-ring cylinder liner contacts, connecting-rod bearings, gear meshing, cam-tapped systems among other.

For high-load and low-speed conditions inducing rather small film thicknesses (boundary lubrication), all texture types irrespective of the scale contribute to an improved frictional performance by reducing the real area of contact, supplying additional lubricant to the contact and trapping wear particles (reservoir effect). In this sense, multi-scale surfaces offer the advantage of having a greater surface area covered with textures in which a potentially higher volume of lubricant and wear particles can be stored. However, the combination of low film thickness and small features can also weaken surface integrity due to induced edge effects and stress raisers thus accelerating wear processes. [238,239]. At intermediate load and speed conditions (mixed lubrication), the lubricant film starts to partially carry the applied load. For these conditions, especially shallow textures with

rather low depths tend to increase the hydrodynamic pressure and therefore improve the overall frictional behavior. It has been numerically and experimentally shown that when the structural depth is in the same range as the resulting lubricant film thickness, the greatest effects in terms of an additional pressure build-up can be expected [21,34,36,240]. In this regard, under mixed lubrication conditions, multi-scale surfaces can increase the hydrodynamic pressure due to small texture features and, additionally, offer the advantage to provide a great reservoir volume for lubricant and wear debris. Finally, at high lubricant film thicknesses for which the load is mostly carried by the oil, mainly larger texture features improve the frictional performance by increasing the hydrodynamic pressure (inlet suction mechanism and reducing of oil shear-strain rate) thus reducing the transition speed from mixed to hydrodynamic lubrication [93]. Furthermore, it can be assumed that smaller textures have a negligible effect in this lubrication regime. Hence, while not improving the tribological properties compared to single-scale textures, in this case, multi-scale surfaces can still perform well in this lubrication regime.

Summarizing, it can be stated that multi-scale surfaces can have a synergetic effect when suitably combined thus reducing friction and wear over a broader range of operating conditions. To fully use the advantages of multi-scale surface textures, they must be carefully and properly designed. Under hydrodynamic lubrication, this comprises maximizing the hydrodynamic pressure and/or reduce leakage flow without inducing negative effects due to pronounced cavitation or flow circulation problems inside bigger texture features. For mixed lubrication with a significant solid-solid contact (small film thicknesses), textures should be designed in a way that the advantages of an additional hydrodynamic pressure induced by the shallow features overcompensate potential negative effects induced by pronounced cavitation, flow circulation or edge effects (stress raisers) [21, 241,242]. Additionally, smaller and more densely distributed textures may also lead to improved wetting behavior and a better lubricant's distribution in the contact zone, which can help to reduce cavitation and flow circulation thus ultimately improving the load-carrying capacity. Nevertheless, it must be stressed that more fundamental studies will be needed to properly evaluate important parameters in multi-scale textures. In this context, it has already been demonstrated that certain geometrical parameters, such as the aspect ratio, the area density, and their ratio to the texture size, determine the tribological behavior of single-scale surface textures. A comprehensive overview of beneficial single-scale texture geometries under different speed and load conditions can be found in the review presented by Gachot et al. [22]. Moreover, the relation between the acting oil thickness and the involved scales (depths) in multi-scale textures needs to be investigated systematically.

Numerical modeling of the tribological behavior of multi-scale textures is considered to be a powerful tool to optimize the design of multi-scale textures since this approach is more time-efficient and less costly thus reducing the well-practiced trial-and-error methodology. However, it should be emphasized that it is always desirable to cross-correlate the obtained numerical results with experimental data to validate and further improve the mathematical models and optimize the overall design process of multi-scale textures. Since cavitation and the lubricant's flow and distribution in the contact zone play an important role, one interesting approach would be to design tribological experiments with multi-scale textured samples allowing the imaging of the contact zone (in- or ex-situ) and/or the measurement of the lubricant film thickness, the fluid flow velocity, and temperature distributions.

Moreover, modeling and simulation should be further integrated into the design process. In this context, the future trends regarding modeling and simulation of surface textures reside on the continuous development and consolidation of virtual simulation tools, which smartly combine:


The development of this computational surface engineering framework can be structured according to the following aspects:


Summarizing, numerical methods and experiments should be suitably combined to further push the development and design of multi-scale surfaces to enable lower friction and wear over a broader range of tribological conditions. By doing so, optimized designs such as new texture geometries and multi-scale textures being comprised of features on more than two scales can be tested. Additionally, texturing techniques, which enable the fabrication of multi-scale surfaces should be subject to further investigation. In this context, techniques with many degrees of freedom to create new interesting shapes and efficient techniques, thus paving the way to mass production, are interesting. Gaining more knowledge about the potential tribological effects of multi-scale surface texture combined with the possibility to fabricate more sophisticated texture arrangement can also boost the application side in the future. Having the beneficial effects of multi-scale textures in journal bearings in mind, as outlined in Section 3, it can be imagined that this can be just the beginning of the journey. Multi-scale textures seem to be very promising to improve the friction and wear characteristics in the piston ring cylinder liner contacts. In this regard, textures on different scales could be designed appropriately to enable beneficial frictional properties along the entire stroke irrespective of the sliding velocity. Other machine components, which could significantly benefit from the usage of multi-scale surface textures, are cam followers, rolling element bearings, thrust and sliding bearings among others.

**Author Contributions:** P.G.G., F.J.P. and A.R. contributed equally regarding the manuscript's conception, the literature review, the manuscript's writing as well as its proof-reading.

**Funding:** A. Rosenkranz gratefully acknowledges the financial support given by CONICYT in the framework of the project (Fondecyt Iniciacion 11180121). In addition, A. Rosenkranz would like to acknowledge the VID for the financial support given in the project UI 013/2018.

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