## 2 Fundamentals of the APofRCI Method, Taking into Account Torus Milling Cutter Cutting Blade Wear
### Active Cutting Edge Segment and Active Cutting Belt  
Basically, the inclination angle \(\delta\) is spread and determined in a plane perpendicular to the cutting speed vector \(v_{c}\) and passing through the contact point \(CP_{i}\) in the CWE, which is the common point of the outline of the machined surface and the cutting edge of the tool blade. The geometry of the cut layer is considered in the same plane. The geometrical parameters of the cut layer have a significant influence on the physical and technological effects of the cutting process, especially multi-axis milling. During multi-axis TPL-type milling using the torus milling cutter, the geometry of the cut layer has a characteristic shape, where, due to the kinematic-geometric system, the thickness of the cut layer \(h\) varies along the cutting edge, as shown in Figure 5a. The geometry of the cut layer is influenced by the radius of the round cutting insert \(r_{p}\), the feed per tooth \(f_{z}\), and the depth of cut \(a_{p}\). By considering the contact conditions in the CWE at the \(CP_{i}\) contact point, the angles \(X_{rci\_M}\), \(X_{rci\_E}\), and \(\psi_{rci}\) were determined to determine the maximum cross-sectional limits of the cut layer. Angle \(X_{rci\_M}\)--the angle defining the origin of the cross-section of the cut layer, as described in Equation (6). \[X_{rci\_M}=\sin^{-1}\biggl{(}1-\frac{a_{p}}{r_{p}}\biggr{)}, \tag{6}\]  
Figure 5: Multi-axis milling using the torus milling cutter: (**a**) cut layer geometry; (**b**) active cutting edge segment and active cutting belt. Angle \(X_{rcl,E}\)--the angle defining the end of the cross-section of the cut layer, as described in Equation (7). \[X_{rcl,E}=\frac{\pi}{2}+\sin^{-1}\left(\frac{f_{z}}{2r_{p}}\right), \tag{7}\]  
Angle \(\psi_{rcl}\)--working angle of the torus milling cutter, considered in the base plane of the round cutting insert at the \(CP_{i}\) contact point, as described in Equation (8). \[\psi_{rcl}=\left[\frac{\pi}{2}+\sin^{-1}\left(\frac{f_{z}}{2r_{p}}\right)-\sin ^{-1}\left(1-\frac{a_{p}}{r_{p}}\right)\right], \tag{8}\]  
Equation (8) is an important and rarely analyzed relationship in the literature. It acquires particular importance, especially under the conditions of finish machining, which takes place at very small values of depth of cut \(a_{p}\) and feed per tooth \(f_{z}\). Under these cutting conditions, the number of involved cutting blades (active blades) of the tool in the cutting process is \(z_{c}\leq 1\)[37]. Knowing the value of the angle \(\psi_{rcl}\) and having the given radius \(r_{p}\) of the round cutting insert, the length of the active segment of the cutting edge \(b\) can be calculated using Equation (9). \[b=\psi_{rcl}r_{p}, \tag{9}\]  
Thus, the active cutting belt can be determined (see Figure 5b) for a given inclination angle \(\delta\) in the CWE. During the movement of the tool, the tool is in contact with the workpiece on a temporary patch of the machined surface, which is called Cutter-Workpiece Engagement (CWE), and the material removed is the cut layer in the form of a chip. The CWE is located on the torus action surface of the tool within the adopted depth of cut \(a_{p}\). As the tool rotates about its axis, the CWE \(s_{CWE,i}\) at the contact point forms a belt \(s_{b,i}\), which was named the cutting belt, and is located on the action surface of the torus milling cutter. At any moment of cutting, the segment on the cutting edge that is inside the CWE is called the active segment of the cutting edge, i.e., the edge of the active segment is cutting at that moment. In addition, segments that are outside the CWE have been identified that are passive cutting edge segments, where the edge of the passive segment does not cut and is sharp. The angle parameter \(\psi_{rcl}\) in this work is used as the main parameter for the angular positioning of the round cutting insert in the torus milling cutter body, which is a new and original solution and the basis of the angular positioning method of the round cutting insert.