## 2 Basis of Increased Tool Life by Selective Exchange of Worn Cutting Edge--SEWCE Effect  
Tools are increasingly used with edges in the form of round inserts [1; 3; 28]. For this insert, it is possible to apply the method of restoration of worn cutting edges by the SEWCE effect [28]. This insert is used especially in and near orthogonal cutting for turning or milling. The main advantage provided by this special tool is to develop an effective cutting ability, producing good surface roughness owing to the large tool tip radius [1; 3; 28]. Figure 1 shows the edge circle view, which is appropriate to make an analysis of the contact conditions between the cutting edge and the surface area during orthogonal cutting. The arc between points A and B' limits the contact conditions between the cutting edge and the machined surface. This addresses an angular part of the cutting-edge corners with a radius \(\tau_{\beta}\) and an angle \(\alpha+\beta\). The cutting-edge part--arc BB' with an angle-2\(\alpha\)--is critical to the state of the surface texture formation and in this respect it is the development of surface roughness \(Rzt\), which can be achieved based on geometric and kinematic mapping of the edge GKME from Equation (1) [3; 31; 32]:  
\[Rzt=\frac{f^{2}}{r_{\epsilon}} \tag{1}\]  
The values for angles \(\alpha\) and \(\beta\) can be found according to Equations (2) and (3) [28]:  
\[\alpha=\arcsin\left(\frac{\mathrm{f}}{2\tau_{\epsilon}}\right) \tag{2}\]  
\[\beta=\arcsin\left(\frac{\sqrt{2a_{\mathrm{P}}\tau_{\epsilon}-a_{\mathrm{P}}^ {2}}}{\tau_{\epsilon}}\right) \tag{3}\]  
where \(\tau_{\epsilon}\) represents the cutting-edge radius of the cutting tool, f is the feed rate, and a\({}_{\mathrm{P}}\) addresses the depth of cut value. Based on analysis of Equation (2), we can see that angle \(\alpha\) depends on feed f and radius of insert \(\tau_{\varepsilon}\). From the analysis of Equation (3), we can observe that the \(\beta\) value depends on \(\mathrm{a_{p}}\) and \(\tau_{\varepsilon}\). Round inserts are produced in a wide range of diameters. For example, Sandvik Coromant produces round inserts: T-Max(r) P system RCMX type (cylindrical-Figure 2a) for 10, 12, 16, 20, 26, 32 mm diameter; and the CoroTurn(r) 107 system RCMT-type (cone shape--Figure 2b) for 05, 06, 08, 10, 12, 16, 20, 25, 32 mm diameter. Based on the practical range of insert dimensions used, graphs showing the effect of the radius of insert rand feed f on angle \(\alpha\) (Figure 3) and \(\mathrm{a_{p}}\) on angle \(\beta\) (Figure 4) were drawn. The in-depth SEWCE analysis of the phenomenon, based on the existing solutions for the diameters used, as shown in Figures 3 and 4 and the following figures, represents a significant advance compared with our previous work [28]. We can consider two main cases for replacing a worn edge section:  
* Complete, by rotating the insert through the angle \(\delta=\alpha+\beta\);
* Partial, by rotation of the insert through an angle contained within the limits \(2\alpha<\delta<\alpha+\beta\)  
Figure 1: Presentation of contact conditions between the cutting edge and workpiece surface. The total variation in the cutting-edge actuation can be obtained by turning the round end tip at a certain angle as can be equated by the formulation of \(\delta=\alpha+\beta\) (Figure 1)--the contact conditions between the tool and workpiece. However, this change does not ensure that the intensification of the work structure from the boundary of the cutting movement is cut off [1]. The theoretical number of edges that can be obtained for a full circuit cutting edge (360\({}^{\circ}\)) with full exchange of contact can be determined from the following formula [28; 29]:  
\[i=\frac{360}{\alpha+\beta} \tag{4}\]  
Graphs prepared using Equation (4) are presented in Figure 5.  
Figure 4: Effect of insert radius \(r_{e}\) and \(a_{\text{p}}\) on angle \(\beta\). Figure 3: Effect of insert radius \(r_{e}\) and feed f on angle \(\alpha\).