## 2 Materials and Methods of Determining the Design of the Proposed Solutions
### Cutting Insert Stress Simulation  
Equipping the cutting insert with the channel leads to the formation of rake and flank walls (Figure 8). The smaller thickness of the rake wall improves heat dissipation through the channel since most of it comes from the highest temperature zone, located on the insert's rake face. The flank wall perceives the main cutting force component, acting perpendicularly on the rake face. Based on the Mitsubishi Materials specifications, the flank wall thickness was set as 0.75 mm. The rake wall thickness (Figure 8, variable \(H\)) was determined by simulating the application of the cutting force to the insert. Values ranging from 0.95 to 0.55 mm in 0.05 mm increments were selected as possible thickness H. The stress simulation logic corresponded to a linear static analysis. A scheme of the simulated milling process is shown in Figure 9. SUS304 stainless steel was simulated as the machined material. The cutting insert model was mounted on the carbide plate model attached to the cartridge model body, as shown in Figure 10. The carbide plate and cartridge models were assumed to be absolutely solid, without regard to the characteristics of the materials or any influence on the final stress simulation results. The tested insert material's physical properties are provided in Table 3. The models were fixed through the back surface of the cartridge to simulate its installation in the tool holder. The cutting force was divided into three components, \(F_{z}\), \(F_{x}\), and \(F_{y}\). As an additional condition, gravity was applied in the direction opposite to the component \(F_{x}\). The width of the component application area corresponded to the simulated value of the tool feed rate, and the height of the area was equal to the depth of cut. The value of the cutting force component \(F_{z}\) was calculated using the following equation [23]:  
\[F_{z}=\frac{10C_{p}t^{x}s_{z}^{y}B^{n}z}{D^{q}n^{w}}K_{mp}, \tag{1}\]  
where \(C_{p}\), \(x\), \(y\), \(q\), and \(w\) are coefficients determined by the tool design and machined material. \(t\) is the depth of cut in mm. \(s_{z}\) is the tool feed rate in mm/tooth. \(B\) is the cutting width of 50 mm within the adopted milling process scheme. \(n\) is the spindle speed in rpm Under the conditions of machining stainless steel, the speed coefficient \(w\) was 0, which equated any value of speed to 1.0. Consequently, the spindle speed was not taken into account during the calculation. \(K_{mp}\) is the coefficient of the machined material's characteristics, determined by the following equation:  
\[K_{mp}=\left(\frac{\sigma^{B}}{750}\right)^{0.3}, \tag{2}\]  
where \(\sigma^{B}\) is the tensile strength of the machined material, equating to 505 MPa for SUS304 (AISI304 [24]). The cutting force components \(F_{x}\) and \(F_{y}\) for the utilized mill type were calculated using the equations below:  
\[F_{x}=0.55F_{z} \tag{3}\]  
\[F_{y}=0.40F_{z} \tag{4}\]  
Determination of the values of the components \(F_{z}\), \(F_{x}\), and \(F_{y}\) was carried out based on three variants of the tool feed rate \(s_{z}\) and three variants of the depth of cut \(t\), through the combination of which nine cutting modes were obtained. The obtained cutting modes with the calculated component values are shown in Table 4.  
The cutting insert material is similar in physical characteristics to tungsten carbide and belongs to the brittle category. Consequently, when testing the front wall thickness \(H\) variants, the stresses on the insert were evaluated based on the obtained maximum and minimum values of the principal stresses \(P_{1}\), \(P_{2}\), and \(P_{3}\). Subsequently, the obtained values were used to calculate the factor of safety. The factor of safety was determined by using three failure criteria: (a) _Mohr-Coulomb_[25], (b) limit on \(P_{1}\  
Figure 10: Stress simulation setup.