## 1 Introduction  
The surface layers (SL) of structural and machine elements are their outermost layers, and, therefore, they are the physical boundary interacting with other elements and/or the environment. The technological process of manufacturing the blanks and components implies various impacts: mechanical, thermal, physical, and chemical, as well as others. As a result, the properties of the base material and SL before commissioning are different in engineering terms. In the process of operation, the SL are the most loaded. Working stresses are maximised, as a result, fatigue micro-cracks appear and develop in them and are, often aggressively, subjected to intense wear and the direct impact of the environment. Consequently, the complex state of SL changes during the process of operation. Over time, failures, most commonly caused by wear, corrosion, and material fatigue occur in SL. Damage to the SL during component operation is inevitable. On the one hand, the wear and corrosion disrupt the normal interaction between the components, and, on the other hand, reduce their load-bearing capacity [1]. As a result, additional loads, strokes and vibrations, ploughing and wedging, and, sometimes, accidents occur. Whereas replacing the respective components with new ones due to wear and corrosion manifests mainly in material losses, the process of formation and propagation of fatigue cracks is a potential threat to the human factor. The nucleation of fatigue micro-cracks in the material of the real metal components is determined by their non-uniform crystal structure, characterised by numerous micro-defects, such as dislocations, vacancies, non-metallic inclusions, etc. [2]. These defects are introduced in the process of making the blanks and cannot be avoided. [PERSON] [2] formulated the thesis of repeatedly increasing the strength resource of solid bodies by optimising an 'ideal microstructure'. The methods based on the phenomenon of severe plastic deformation (equal channel angular extrusion [3; 4; 5; 6] and high-pressure torsion [7]) realise this idea in laboratory conditions but with a very high ratio of the necessary energy to the obtained modified volume of material. Therefore, at this stage, these methods are not widely applied in engineering practice. In the context of determining the role of SL for the operational behaviour of the components, the practice of modifying only the SL is many times more effective, since it can be applied at the stage of producing the components from the respective workpieces. Alternative technological production cycles, containing a different sequence of operations and techniques, may be used to manufacture a given component. The different technological cycles correspond to different states of SL. For a specific material and operating conditions, the life cycle of the components is determined by the state of their SL immediately prior to their commissioning, i.e., the finishing process is of the utmost importance. Surface integrity (SI) describes the complex condition and attributes of the SL of the engineering components. SI is the totality of topographic, mechanical, physical, chemical, and metallurgical properties of the SL of engineering components, which are in mutual correlation with their operational characteristics: fatigue strength, corrosion resistance, and tribological behaviour (friction, wear, and lubrication) [8; 9; 10]. According to [PERSON] and [PERSON] [11], the height roughness parameters R\({}_{\text{t}}\) and R\({}_{\text{z}}\) significantly affect the fatigue strength and tribological behaviour. The shape parameters skewness and kurtosis also have a significant influence on the tribological behaviour. The combination of negative skewness and kurtosis greater than three significantly reduces the sliding wear of the contact surfaces of the friction pair in boundary lubrication friction condition [12; 13].