## 3 Results
### Numerical Results  
With the help of the prepared geometric and finite element models, the process of burnishing of the AISI 52100 steel surface layers with an inclined cylindrical indenter was simulated at different values of burnishing force and indenter tilt angle, taking into account experimentally established values of the friction coefficient \(\upmu\). Besides, it was revealed how the values of the parameters of the selected constitutive relation (parameters of the Johnson-Cook model) and consideration of heat generation in the friction zone affect the results obtained. As an example of the solutions obtained, Figure 13 shows the distribution of hydrostatic (or contact) pressure, with an indenter tilt of 2.5 degrees, a burnishing force of 250 N, and a friction coefficient of \(\upmu\) = 0.26. To study the influence of the tilt angle of the cylindrical indenter on the characteristics of the stress-strain state in the deformation focus, as the latter, we consider the maximum values of pressure, cumulative inelastic deformation, and temperature. The dependence of the maximum pressure in the deformation focus on the burnishing force at different values of the indenter tilt angle is shown in Figure 14. As the burnishing force increases, the pressure increases. It can be seen that at small angles of inclination, the dependences have a maximum in the range of 200-230 N. The dependences of the maximum cumulative plastic deformation in the deformation focus on the burnishing force are shown in Figure 14. An increase in the burnishing force causes an almost linear increase in the cumulative deformation. Figure 12: Dependence of the relative (**a**) and true (**b**) shear strain on the indenter tilt angle. Figure 13: The distribution of hydrostatic pressure (Pa). The dependences of the contact pressure and the maximum cumulative plastic deformation in the deformation focus on the tilt angle of the cylindrical indenter at different values of the burnishing force are shown in Figure 15. All the graphs have a maximum in the range of about 2 degrees. The analysis of the results shows that with an increase in the tilt angle, the contact pressure increases, which is due to a decrease in the length of the contact zone. At the same time, the gradient of change in the characteristics of the stress state in the deformation focus increases with a decrease in the indenter tilt angle. The important characteristics, from the point of view of providing conditions for nanostructuring burnishing, are the change in the sign of shear stresses and the absence of tensile horizontal stresses. It should be noted that there is no pronounced influence of the tilt angle of the indenter on these parameters. A change in the sign of shear stresses is noted for a tilt angle of 0.5\({}^{\circ}\). With an increase in the burnishing force, the contact pressure increases slightly, which is explained by the fact that the length of the contact zone increases more noticeably. It should also be noted that there is no pronounced influence of the burnishing force on the level of shear stresses, and there is no change in the sign of shear stresses in the focus. The calculations also revealed that taking into account heat generation during contact friction leads to a significant (about 4 times) increase in temperature in the deformation zone, which indicates the importance of its consideration. The temperature distribution  
Figure 14: The dependences of (**a**) the contact pressure and (**b**) cumulative plastic strain on the burnishing force. Figure 15: The dependences of (**a**) the contact pressure and (**b**) cumulative plastic strain on the tilt angle. near the contact zone for such a calculation with a burnishing force of 250 N and an indenter tilt angle of 2\({}^{\circ}\) is shown in Figure 16.  
A significant increase in the values of contact pressure and cumulative deformation occurs in the case of exposure to a pre-hardened material.