# Computer-Aided Analysis of the Formation of the Deformation Zone in the Burnishing Process
## 2 Analysis of the Stereometry of the Deformation Zone

Table 1: Chemical characteristics of C55/1.0535 steel. To describe the three-dimensional shape (Figure 2) of the deformation zone obtained after the burnishing process, it was proposed to use parameters describing its shape both in the axial section (in the feed plane)--the letters with parameter \(\mathrm{f}\)--and in the circumferential section (in the plane of the main movement)--the letters with parameter \(\mathrm{v}\):  
* \(\mathrm{h_{f}/h_{v}}\): deformation wave height,
* \(\mathrm{h_{f0}/h_{vo}}\): tool cavity height relative to the surface of the raw material,
* \(\mathrm{L_{1}/L_{2}}\): initial deformation wavelength,
* \(\mathrm{a=a_{1}+a_{2}/b=b_{1}+b_{2}}\): length and width of the deformation centre,
* \(\mathrm{L_{f}/L_{v}}\): length and width of the deformation wave. Additionally, the parameters describing forces, geometry and roughness were used:  
* F--burnishing force [kN],
* R--radius of the ball-shaped tools [mm],
* R\({}_{\mathrm{k}}\)--radius of the disc-shaped tools [mm],
* f\({}_{\mathrm{fum}}\)--feed used in turning [mm/rev],
* f\({}_{\mathrm{bum}}\)--feed used in burnishing process [mm/rev],
* S\({}_{\mathrm{a}}\)--parameter, similar to Ra, characterizing the stereometric profile [um]. The arithmetic averages of roughness from the average plane within the sampling area--the elementary square,
* S\({}_{\mathrm{z}}\)--parameter, similar to Rz, characterizing the stereometric profile [um]. The ten-point height of the surface irregularities--the average value of the absolute heights of the five highest peaks and the five lowest depressions within the sampling area--the elementary square. It can be concluded that, during the burnishing process using tools with larger radii (Figure 4c,d), the moment of transition from parameters leading to the formation of a deformation centre of type I, typical for small unit pressures, to parameters leading to the formation of a centre of deformation of type II and III can occur using greater burnishing forces [1; 3; 4; 32]. However, the significance of the increase in the burnishing feed is not so clear. At small feed rates (0.05-0.2 mm/rev) (Figure 5), the course of deformation formation is to some extent similar to the phenomena characteristic of the process of forming a circumferential groove. For this reason, the mere increase in the feed rate without a simultaneous increase in the burnishing force does not result in an increase in the dimensions of the deformation area and the penetration of the burnishing ball into the material (Figure 5). The obtained results made it possible to present the dependence of selected parameters of the deformation zone on the feed and force used during ball pressure burnishing (Figure 6). Figure 3: Description of the geometric parameters of the deformation centre. Ball burnishing. R = 5 mm, F = 2.75 kN, f\({}_{\mathrm{fum}}\) = 0.410 mm/rev, f\({}_{\mathrm{bum}}\) = 0.102 mm/rev (area after turning: S\({}_{\mathrm{z}}\) = 91.7 μm, S\({}_{\mathrm{a}}\) = 18.9 μm; area after burnishing S\({}_{\mathrm{z}}\) = 21.2 μm, S\({}_{\mathrm{a}}\) = 2.4 μm): (a) main motion plane, (b) feed plane. Figure 4: Ball burnishing—the impact of force on some parameters of the deformation centre (f\({}_{\rm burn}\) = 0.102 mm/rev) determined in (**a,c**) axial cross-section (h\({}_{\rm fr}\), h\({}_{\rm fo}\), L\({}_{\rm 1}\), a, L\({}_{\rm f}\)), (**b,d**) cross-section peripheral (h\({}_{\rm v}\), h\({}_{\rm vo}\), L\({}_{\rm 2}\), b, L\({}_{\rm v}\)), (**a,b**) ball radius R = 5 mm, (**c,d**) ball radius R = 13.5 mm. Figure 5: Ball burnishing (R = 5 mm, F = 2.75 kN)—the impact of feed on some parameters of the deformation centre determined in: (**a**) axial section (h\({}_{\rm fr}\), h\({}_{\rm fo}\), L\({}_{\rm 1}\), a, L\({}_{\rm f}\)), (**b**) circumferential section (h\({}_{\rm v}\), h\({}_{\rm vo}\), L\({}_{\rm 2}\), b, L\({}_{\rm v}\)).