## 2 Materials and Methods
### Manufacturing Technology Project
#### 2.1.3 Developed Shape of Designed Cutting Blade  
For both bends, at the designed shape of the cutting blade, the initial length of the material was calculated. The lower the angle between the bent arms, the more the neutral layer is shifted to the bend axis. 1. The approximate calculation according to [30]:  
The developed length of the neutral layer arc for opening angles of \(\alpha\) = (90 to 150)\(\lx@math@degree\) can be calculated from the formula:  
\[L=0.01745\;\cdot\;\left(r+\frac{s}{2}\right)\cdot\;\left(180-\alpha\right)=0.01745\;\cdot\;\left(0.6+\frac{0.6}{2}\right)\cdot\;\left(180-135\right)=0.71 \;\mathrm{mm} \tag{6}\]where \(r\) (mm) is the inner radius of the curvature in the bending area, \(s\) (mm) is the thickness of the blank for bending, and \(\alpha\) (\({}^{\circ}\)) is the opening angle, i.e., between the bent arms. 2. The approximate calculation using the coefficient of neutral layer displacement in Autodesk Inventor 2023 software:  
The design cut blade shape (Figure 6) was constructed using Autodesk Inventor software and subsequently developed with the use of the coefficient \(k=0.44\), which considers the displacement of the neutral layer in the bending area and the consequent elongation of the material in the bending area. The value is valid for stainless steel, which can be used in other materials with higher tensile strength, which is the case for the heat-treated high-carbon steel strip 1.1274 according to [28] selected for the production of cutting blades. Developed length in the bending area:  
\[l=\varphi\cdot\frac{\pi}{180}\cdot(r+k\cdot s)=45\cdot\frac{\pi}{180}\cdot(0.6 +0.44\cdot 0.6)=0.68\;\mathrm{mm} \tag{7}\]  
where \(\varphi\) (\({}^{\circ}\)) is the bending angle, \(r\) (mm) is the inner radius of the curvature at the bending area, \(k\) (\(-\)) is the coefficient considering the neutral layer in the bending area, which is chosen in the range of 0.30 to 0.50 while larger values are used for large bending angles, and \(s\) (mm) is the thickness of the blank for bending. The coefficient considering the displacement of the neutral layer in the bending area has the following meaning:  
\[k=\frac{s_{\mathrm{v}}}{s} \tag{8}\]  
where \(s_{\mathrm{v}}\) (mm) is the distance of the neutral layer from the inner radius of curvature at the bending area, and \(s\) (mm) is the thickness of the blank for bending. 3. Precision calculation using the coefficient of neutral layer displacement:  
The neutral layer displacement coefficient can be calculated using the following equation:  
\[x=\left(0.642932593\cdot\frac{r}{s}\right)^{0.289311855}=\left(0.642932593 \cdot\frac{0.6}{0.6}\right)^{0.289311855}=0.882557986 \tag{9}\]  
The radius of the neutral layer:  
\[\rho=r+\frac{s}{2}\;\cdot\;x=0.6+\frac{0.6}{2}\;\cdot\;0.882557986\;=0.86476739 5\;\mathrm{mm} \tag{10}\]  
where \(r\) (mm) is the inner radius of the curvature in the bending area and \(s\) (mm) is the thickness of the blank for bending. Bend angle:  
\[\phi=180-\alpha\;=180-135\;=45^{\circ} \tag{11}\]  
Figure 6: Developed shape of the designed cutting blade of the oscillating cutter. where \(\alpha\) (\({}^{\circ}\)) is the opening angle, i.e., between the bent arms. Arc length of the neutral layer, i.e., developed length in the bending area:  
\[L=\phi\ \cdot\ \frac{\pi}{180}\ \cdot\ \rho=45\ \cdot\ \frac{\pi}{180}\ \cdot\ 0.864767395=0.68\ \text{mm} \tag{12}\]  
The exact value of the coefficient taking into account the displacement of the neutral layer in the bending area \(k\) to verify the method (b) listed above can be calculated using the displacement coefficient of the neutral layer of \(x\) calculated according to Equation (9):  
\[k=\frac{x}{2}=\frac{0.882557986}{2}=0.441278993 \tag{13}\]  
It follows from this that the use of the coefficient \(k\) = 0.44 in Autodesk Inventor software brought only a small difference that corresponds to the rounding to two decimal places.