## 3 Optimization of the Developed Ultrasonic Cutting Horn  
### Sensitivity Analysis  
We performed sensitivity analysis of the proposed block-type horn. Figure 5 shows the input parameters of the \(x\)-axis position of the slot, the \(z\)-axis position of the slot, width, thickness of the side part, thickness of the middle part and thickness of the lower part. Table 2 shows the upper and lower limit of each input parameters. The output parameters were the 1 st frequency isolation, 2 nd frequency isolation, gain and displacement uniformity. The sensitivity analysis was performed in the following steps: (1) a design-of-experiments (DOE) table is established by the optimal space filling method; (2) modal and harmonic analysis of every sample point are performed to complete the DOE table; (3) the response surface is formulated by a neural network method; and (4) the sensitivity analysis is performed using the response surface. Figure 6 shows the 1 st and the 2 nd frequency isolation according to the variation of the \(x\)-axis position of the slot, \(z\)-axis position of the slot, width, thickness of the side part, thickness of the middle part and thickness of the lower part. The thickness of the side part has the greatest influence on the 1 st frequency  
Figure 4: Simulated displacement at the lower face of the initial block-type horn model.  
isolation and decreases as the thickness increases. The effect of the thickness of the side part also has the greatest influence on the 2 nd frequency isolation, which decreases as the thickness of side part increases. Figure 7 shows the displacement uniformity and gain according to the variation of the \(x\)-axis position of slot, the \(z\)-axis position of the slot, width, thickness of the side part, thickness of the middle part and thickness of the lower part. The \(z\)-axis position of the slot and the thickness of the side part have the great influence on the displacement uniformity. The displacement uniformity increases as the \(z\)-axis position of the slot decreases to negative or the thickness of the side part increases. The \(z\)-axis position of the slot and the thickness of the middle part have the great influence on the gain. The gain increases as the \(z\)-axis position of the slot decreases to negative or the thickness of the middle part increases. The result of the sensitivity analysis shows that every design variable influences the output parameters differently, but the most critical variable among them was the thickness of the side part.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Name** & **Symbol** & **Lower Boundary** & **Upper Boundary** \\ \hline x-axis position of slot [mm] & \(sp_{x}\) & 18.4 & 23.4 \\ z-axis position of slot [mm] & \(sp_{z}\) & 42.0 & 49.0 \\ Width [mm] & \(w\) & 61.5 & 64.5 \\ Thickness of side part [mm] & \(th_{sid}\) & 21.5 & 25.0 \\ Thickness of middle part [mm] & \(th_{mid}\) & 18.0 & 19.5 \\ Thickness of lower part [mm] & \(th_{low}\) & 16.0 & 16.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Lower and upper limits of the design variables.  
Figure 5: Design parameters of a block-type ultrasonic cutting horn.  
Figure 6: The 1 st order trend lines of the frequency isolations according to the variation of the design parameters of the ultrasonic cutting horn.  
Figure 7: The 1 st order trend lines of the displacement uniformity and gain according to the variation of the design parameters of the ultrasonic cutting horn.