## 4 Summary and Conclusions from Numerical Analyses  
1. The workpiece in the process of moving the wedge is subjected to a complex deformation process, characterized by large displacements and large deformations. Rendering complex changes in the outline of an object requires a sufficiently fine mesh of finite elements. The use of a very fine mesh of finite elements for the entire workpiece and throughout the process leads to a numerical model with a very large number of unknowns, requiring long calculation times. The developed effective discrete models and numerical algorithms allow for automatic mesh refinement only in areas with high curvature and large deformation gradients. In the numerical examples presented in this article, discretization with 4-node PLANE 162 elements was used. The finite elements used to discretize the object well modeled the complex deformation state, and at the same time, they are characterized by high computational efficiency. 2. The shape factor of the finite element (SF) significantly affects both the accuracy of mapping the outline of the tool and the value of stresses and strains as well as the course of cracking. The most favorable results of the stresses and strains calculated are obtained for SF = 1. Further increase of SF (up to nine times) has no significant impact on the accuracy of the stresses and strains calculated, defined as the difference of their values in elements and nodes. 3. The results of the computer simulation of the wedge displacement process on the effective model and real material confirmed the results of the experimental research. This proves the correctness of the developed mathematical model and the method of integrating the discrete equation of motion. 4. The results of numerical calculations confirm the possibility of a correct analysis of the burnishing or micro-cutting processes and the determination of the states of displacements, strains and stresses, using the discrete effective models developed. 5. The application developed in the ANSYS system enables a time analysis of deformation and stress states at any point of the material. 6. For example, Figure 14b shows the displacement of selected nodes in the contact area in the direction of the Y axis. It is possible to determine the separation point of the material moving with the chip or remaining in the surface layer of the product. 7. The basic problem in the design of the wedge displacement process is the development of appropriate tool constructions and the selection of process conditions in order to ensure the technical requirements and properties of the product obtained, while increasing tool life and process efficiency. The results of computer simulations may form the basis for the selection of technological parameters in the machining or burnishing process, and they can be used to develop a new technology with the necessary technological equipment. 8. As a result of the analyses carried out, it was found that the angle of inclination of the shear plane is not the same for each rake angle \(\gamma\) and it varies in the range of \(\Phi=37\,[^{\circ}]-55\,[^{\circ}]\), which is consistent with the values given in the professional literature. The values of maximum stresses, for almost every simulation, prevailed in the contact area of the wedge tip with the base material, as well as in the contact areas of the wedge rake surface with the surface of the forming chip, and in the area of the shear plane. 9. For given machining conditions and tool depth \(\mathrm{a_{p}}>\mathrm{r_{d}}(1-\sin\gamma)\) there is a limited rake angle \(\gamma_{\mathrm{gr}}\) below which the burnishing process takes place (no chip) and above it, the micro-cutting process (chip formation) occurs.