Every so often, a natural texture is discovered and presented as a great texture for tribology purposes! Shark skin, leaf surface, or even snake skin are the most renowned examples. And it is true that the textures found on these organisms are amazing. But these textures are only ideal for a very specific operating condition: the one that helps the most this organism to survive and reproduce itself within its environment. This is natural selection applied to tribology! It is an optimisation algorithm that takes betweens weeks and millenaries (or more!) to obtain a new and better design.
This hints us that a human made optimisation algorithm could also improve the tribological performances of a human made mechanism for specific operating conditions. Optimisation approaches have been employed by many research teams in tribology for many devices, many operating conditions and many goals, but most of them were based on trial and error parametric optimisation strategies. The paper I would like to introduce to you today takes a rigorous mathematical approach. Codrignani et al.  have developed a modeling of the sliding bearing through Reynolds equation which is solved together with its adjoint equation. The adjoint equation allows for computing the impact of a variable on the goal set by the modeler. The variable impact can be obtained on every single mesh node! If you want to increase the hydrodynamic load carrying capacity of the bearing by changing the surface shape, you can: the adjoint equation will guide the optimisation algorithm and define where the gap should be increased and where it should be decreased… and by how much! Such an approach neither requires to impose a given texture pattern nor to guess which areas should be textured and which should not.
Codrignani et al. first validated their algorithm on the 1D sliding bearing. The maximum load carrying capacity is obtained for a specific optimised geometry, which is well known from tribologists . As this bearing is optimised, the algorithm should provide the same solution independently*. And it is indeed what Codrignani et al. obtained with this adjoint method.
After validating the model, the method is similarly applied to a real world pin 2D bearing (see Figure 2, left). The initial profile is parabolic, and the algorithm is only authorised to remove material to increase the load carrying capacity. The team applied the method with different driving constraints:
- No additional constraint. With this configuration, the algorithm solution is to increase the gap at the inlet (see Figure 2, right). According to the authors, this geometry is the one offering the largest load carrying capacity. However, during start and stop, the contact only occurs along an edge which would easily wear out.
- Central line constraint. To solve the start and stop problem, the authors imposed that the material next to the central line could not be adjusted by the algorithm, resulting in another design (see Figure 3, left). This configuration produces less load carrying capacity, but it is more applicable to real life industrial needs.
- Patterned texture with limited shape constraint. In this configuration, the authors imposed almost the whole area to be left unchanged. The only surface that could be optimised by the algorithm was the area within discs arranged in a pattern. This means that the shape of the texture within this pattern is not fully imposed: it only has to be located within the discs. The design generated is represented in Figure 3, on the right side. Whereas the depth is different depending on the location the shape of the dimples is different as well. In the central area, the whole disc area was carved by the algorithm. On the sides, an elongated shape oriented toward the contact center was generated. However, the load carrying capacity of this optimised texture bearing was only increased by a few percent compared to the original bearing.
The different results obtained offer different optimum solutions to increase the load carrying capacity. Production method and operating conditions will define which would be the best for a given contact. Other designs may also be obtained if the optimisation goal was friction reduction.
After this short overview of the article, optimisation methods may seem like a magic wand that allows for finding the best configuration in no time at all. It is not the case! While it can help further improve the performances of a device, it is not an easy task. Feel free to read the full article to get more details about Codrignani et al. approach, and please write in the comment section if you think this kind of method could be useful for your job.
 A.Codrignani, D.Savio, L.Pastewka, B.Frohnapfel, R.van Ostayend, Optimization of surface textures in hydrodynamic lubrication through the adjoint method, Trib Int (2020), 148, 106352
 Hamrock BJ, Schmid SR, Jacobson BO. Fundamentals of fluid film lubrication. CRC press; 2004.
* Although it is not often specified, optimisation algorithms almost never guarantee to obtain the overall optimum, but a local optimum instead. As a result, the optimum solution obtained by two different methods may differ, and one of them is likely to be better than the other.