**1. Introduction**

Nature shows examples of how periodic and self-organized surface structures decrease the coefficient of friction (CoF), for example, the skin of a snake, pangolin, and other animals. Such examples inspired surface engineering to generate surfaces with low CoF. Bearing in mind the processing time, which is requested by the different kinds of lithography, LIPSS-based process can be a potentially strong candidate for improving tribological performances. The mutual configurations of micro-andnanostructures can improve tribological properties by guiding wear particles along the direction of the grooves or by inducing the particles rolling between them [1].

Material processing by lasers with a pulse duration in the femtosecond range (10−<sup>15</sup> s) has recently drawn a lot of attention due to nonthermal ablation mechanisms [2]. This characteristic makes this class of laser particularly appealing in material treatments, related to the absence of heat-induced material damage on dielectric, semiconductors, and metallic material [3]. Femtosecond pulses have also been exploited to induce periodic surface structures known as laser-induced periodic surface structures (LIPSS), firstly observed in 1965 [4]. As it is commonly accepted, LIPSS are divided into 2 groups: Low Frequency LIPSS, where period of structures is around laser wavelength, and High Frequency LIPSS, where period of structures by order of magnitude less than laser wavelength. Further, in paper Low Frequency LIPSS will be noted like LIPSS, while High Frequence LIPSS will be indicated as it is. LIPSS are already used and have a potential to be applied in numerous fields, including improving

adhesion [5], wettability [6], surface colorization [7], better proliferation and adhesion of tissue cells [8], and others.

The shortcomings to apply LIPSS for tribology were recognized by Yu and Lu in 1999 [9]. They obtained microstructures with a nanosecond excimer laser and demonstrated the improvement of tribological characteristics in comparison to a non-treated surface. Furthermore, Honda at al. [10] used femtosecond laser-generated LIPSS on diamond-like carbon (DLC) and tested friction properties with an atomic-force microscope. This test showed a reduction of friction on the film with LIPSS compared with the untreated ones. Yasumaru et al. [11] also tested DLC, additionally coated with a thin layer of MoS2, showing how to decrease and increase CoF. Using different beam scanning strategies, they generated LIPSS and demonstrated a CoF reduction compared to a flat surface. The study in [12] showed a CoF decrease even without lubricant in a pin-on-disc configuration on TiC-coated steel surface. The first tribological tests on LIPSS-textured semiconductors were made by Eichstadt et al. in [13], where an increase of the CoF was observed in both lubricated and non-lubricated conditions.

The tribological performances were investigated on large LIPSS-treated area of 100Cr6 stainless steel, high toughness bearing steel X30CrMoN15, pure titanium and titanium alloy (Ti6Al4V) by using a ball-on-disc configuration under paraffin and engine oil as lubricants in [14] and [15]. No effect was measured on CoF for LIPSS-treated samples tested with both the mentioned lubricants. While a significant reduction of CoF and wear for Ti and Ti6Al4V was shown with engine oil in the case of ripples oriented perpendicularly to the sliding motion, no beneficial influence appeared with paraffin oil. It should be outlined that these were the first experiments demonstrating the dependence of the CoF by LIPSS orientation, while the mechanisms relating to the influence of nanometric structures on the CoF have not been correctly explained.

The first research on wear and tribological performances for High Spatial LIPSS (HSFL) was made by Bonse et al. [16], where the large Titanium samples were covered by LIPSS and tested with paraffin and engine oil as lubricants. The related tribological analysis did not demonstrate the effects of HSFL on CoF, concluding that the depth of LIPSS played a crucial role in friction behavior.

In [17], the authors investigated the effects of LIPSS on AISI 316, obtaining a sensible CoF reduction on both dry and lubricated conditions. Another important tribological quantity is the Stribeck curve. In fact, in a lubricated contact, the CoF is not a univocal quantity independent on the load and velocity, as in the case of dry contacts. In fact, in the presence of lubricants, the CoF is a function of the Stribeck number, given by the relation:

#### **Stribeck number** = η **v**/**L**

where η is the viscosity of the oil, v is the sliding velocity, and L is the applied load.

The typical Stribeck curve is divided into three regimes, the boundary lubrication (BL), the mixed lubrication (ML), and the elastohydrodynamic (EH) regimes. At low Stribeck number, the two counterparts are completely in contact, and a small amount of lubricant is present between them; this situation represents the BL regime. This regime is characterized by high CoF and high wear. Increasing the Stribeck number increases the oil thickness, leading to a decrease in the CoF down to its minimum; this situation represents the ML regime. Increasing the Stribeck number further leads to the transition into the EH regime, where the lubricant thickness is continuous, and the friction is ruled by the viscosity characteristics of the oil. In this last regime, the CoF slightly increases with the Stribeck parameter due to viscous effects. The building of the Stribeck curve enables to define the three different Stribeck regimes as a function of the load and the sliding velocity.

One of the main drawbacks of the cited works is that, in case of linear textures, only reciprocating friction can be investigated, with the known issues about control of speed and, in the case of lubricant, the fluid dynamic conditions. In the present paper, the tribological properties of LIPSS-textured stainless steel samples were investigated, using advanced techniques to generate highly regular LIPSS (HR-LIPSS) [18]. The textures were obtained with radial symmetry, permitting to investigate the Stribeck curve in a pin-on-disc configuration, with a fixed orientation of the LIPSS texture with respect to the sliding direction. In particular, we were interested in surface texturing as a tool to improve the

tribological performance of tribo-pairs in BL and ML regimes, the most critical regimes in a mechanical device. To the author's knowledge, this approach was never applied in the aforementioned literature.
