## 1 Introduction
Thus, the literature review in the field of experimental studies of the burnishing process indicates that most of the works are devoted to using a traditional spherical shape of a diamond processing tool (85% according to the review [8]). In the case of a cylindrical tool shape, it is usually a long cylinder, the axis of which is parallel to the surface to be processed. Steels are the most commonly used material (64% according to the survey [8]), which is subjected to sliding burnishing. Friction conditions are not reported in more than 1/3 articles, and only 9% of studies are devoted to dry friction conditions [8]. Therefore, the use of a disc-shaped tool made of cubic boron nitride with an axis tilt to the treated surface is innovative and little studied. The numerical simulation of this mechanical finishing process has aroused growing interest in research and industry. Recently, a comprehensive and critical review of literature focusing on the modern advances in ball burnishing simulation using the Finite Element Method (FEM) numerical technique has been performed in [9]. This review involves up-to-date 2D and 3D numerical simulations of the ball burnishing treatment to study surface roughness, residual stresses, microhardness, plastic strain, phase transformation, elastic recovery effect, ball indentation mark, and thermal behavior. In the work of [PERSON] et al. [10], finite element simulation of 37 Cr4 steel diamond burnishing in the Abaqus package was used to predict the effect of process parameters(speed, force, feed, and friction coefficient) on the change of residual stresses and temperature in the treated surface layer depending on the burnishing speed. In the article [11], using the FEM method, [PERSON] et al. investigated the influence of the process parameters and the number of tool passes on the distribution of residual stresses and of equivalent plastic deformation. Based on the results, the fatigue endurance dependence on stresses and the number of cycles of 2024-T3 aluminum alloy loading were constructed. The study of compression stresses and axial residual stresses during the diamond burnishing of EN 1.4301 steel with a spherical indenter \(R\) = 3.5 mm by the 2D FEM method was carried out in the work of [PERSON] and [PERSON] [12]. The simulation takes into account the friction coefficient and the initial surface roughness after preliminary turning. The effect of the friction force in the process of nanostructuring burnishing with a spherical indenter on the change of deformations and stresses in the contact zone by the dynamic FEM method was studied in [13]. The relationship between the burnishing force and the friction coefficient in the contact zone of the indenter and 20 Cr4 steel with the height of the plastically displaced metal pile-up, the depth of the tool insertion, and the intensity of cumulative shear deformations is established. The regularities of changes in shear stresses along the surface layer depth in the contact and non-contact zones of the deformation focus are revealed. Summing up the review in the field of numerical modeling of the burnishing process and related phenomena, it should be concluded that such studies are much less common than experimental ones (12% and 75%, respectively, according to [8]), the studies with a combined approach (numerical-experimental) are also rare. The main object of modeling is residual stresses and roughness. The processed object is more often modeled with an elastic-plastic material, and thermomechanical problem formulations are much less common (about 4% [9]). ABAQUS software is the most common means of modeling processes such as burnishing (38% according to the review [9]). Both 3D and 2D calculations are widely represented in the research works. Therefore, a combined study including experimental and numerical methods is in demand.