# Determining Optimal Parameters of Regular Microrelief Formed on the End Surfaces of Rotary Bodies
## 1 Introduction
Such relative areas of burnishing are determined by the optimal value of the relative reference length of the profile top [22]. This value is defined as the ratio of the reference length of the profile to its base length. The Abbott-Firestone curve can describe the relationship between surface performance and roughness parameters. This relationship was described in [23]. The performance characteristics of the surface were evaluated not by the surface roughness, but the parameters of the Abbott-Firestone curve. According to the authors, the above three parameters determined from the Abbott-Firestone curve (\(R_{\text{pk}}\), \(R_{k}\) and \(R_{\text{pk}}\)) illustrate the surface texture's ability to resist friction. Peculiarities of evaluating the surface condition by the Abbott-Firestone curve parameters are described in [24]. The authors have found that surface integrity illustrates the relationship between the surface's required functional properties and changes in the new surface properties. The surface can be evaluated using two fundamental properties: The spatial arrangement of the surface (surface roughness) and the surface layer's physico-chemical properties. To determine the burnishing area of a partially regular microrelief of the 3 rd type formed on the rotary body end surface with V-shaped grooves, which were shifted by an angular pitch of \(0.5^{\circ}\), it was necessary to determine the overlap area of PRMR grooves [25]. PRMR grooves of the 3 rd type with a large degree of overlap significantly reduce the microrelief's total area and, accordingly, the relative area of vibration. Studies in this area focus mainly on determining the relative area of burnishing and the influence of the grooves' geometric parameters and arrangement. In [26; 27], the formation of a regular microrelief on profile surfaces with different geometric parameters depending on the formation conditions was considered. The authors conducted a full-factor experiment with four variables: The diameter of the deforming element, the deformation force, the amplitude of the deforming element, and the number of oscillations. According to the research findings, Pareto histograms were constructed, which show that the number of oscillations and the deforming element amplitude significantly influence changes in the shape of the regular microrelief cells. The authors of [28] presented the results obtained with the experimental tool L8 Taguchi, which was used to form a regular microrelief on planar surfaces. The parameters that significantly affect the process of forming a regular microrelief using a CNC milling machine on flat surfaces were determined. By changing the processing modes, regular microreliefs of different sizes were formed, on which the orientation of grooves was different. Such an element of the forming mode as the feed was also used. A comparative analysis of different types of regular microrelief was conducted subject to the condition of forming the largest area of contact with the liquid [29]. RMR types, such as concave cones, spherical holes, and longitudinal lines, were compared. It was found that with other identical parameters, the microrelief represented by conical holes was the most optimal. The smallest area of contact with the liquid was provided by a microrelief represented by a plurality of holes of concave spherical shape. The area of triangular grooves, depending on the groove's geometric parameters and their location on the rotary body end surfaces, was calculated in [30]. The authors of [31], [PERSON] and [PERSON], developed an algorithm for the technological process of forming geometric parameters of a partially regular microrelief by burnishing on the outer cylindrical surface of printing equipment. The influence of technological factors on changes in the surface area with partially regular microrelief was established. The limits and conditions of possible variation of the relative surface area were determined to enhance the performance of the printing equipment parts.