# Research on a Composite Power-Superimposed Ultrasonic Vibrator for Wire Drawing
## 3 Regulation Analysis of the Power-Superimposed Vibrator  
### Modal Analysis and Harmonic Analysis  
In order to study the variation of the vibrator's characteristic with structural parameters more precisely, FE models need to be built in the first step. Considering the complexity of the composite ultrasonic vibration system, the FE model was established by APDL command in ANSYS, as is shown in Figure 2. In the FE model, the PZTs were meshed with the SOLID 226 element, while the rest were meshed with the SOLID 186 element. The material of piezoelectric ceramic sheets is PZT8 and the material of the rear cover of the transducer is steel 45. The material for the rest parts of the vibrator is duralumin alloy 70A04, as mentioned. The rear ends of the transducers and the back end of the vibrator were constrained in all DOF. Through conducting the model analysis with a frequency range of 20-30 kHz, we determined the resonant frequencies and the corresponding vibration modes, the six lowest orders of which are shown in Table 2.  
We can obtain the longitudinal mode of the composite vibrator at the frequency of 21911.5 Hz and the displacements at its top end are as shown in Figure 6. The stress contour also shows that the vibrator has mainly deformed in the longitudinal direction.  
We also studied the influence of structural parameters on the inherent frequency of the composite power-superimposed vibration system. Figure 7 shows the various regulations of the vibrator's inherent frequency along with the disc's radius when the diameter of the inner bore \(d\) is \(\Phi 3\) mm and \(\Phi 5\) mm respectively. It can be seen that when the inner bore size remains unchanged, the resonant frequency decreases remarkably with the increase of the radial size of the disc. When the disc's radius is less than 65 mm, the resonant frequency increases as the bore size decreases, but not significantly. Considering the convenience of manufacturing, the bore size was set to \(\Phi 5\) mm.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Order** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Frequency/Hz & 20,096 & 21,912 & 22,855 & 22,859 & 23,474 & 23,476 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Resonant frequencies of the power-superimposed vibrator at the six lowest orders.  
Figure 6: Longitudinal mode of the vibrator at 21.9 kHz.  
In order to get the amplification ratio between the composite power-superimposed ultrasonic vibration system and the transducers, harmonic simulations were conducted on them. A voltage of 100 V and 21911 Hz was applied across the PZT ceramics. We can obtain the maximum amplitude of the longitudinal vibration at the end of the vibrator and the transducer respectively, as Figure 8a shows, and therefore calculate the amplification ratio between them. It can be seen that the amplitude reaches 401.1 \(\upmu\)m, which is much larger than that of the transducers (40.9 \(\upmu\)m). The amplitude factor can be as high as 9.83, which implies the excellent performance of the vibrator. The amplitude of the vibrator in the \(x\) and \(y\) direction are very small compared with that in longitudinal direction, as is shown in Figure 8b. It can be seen that the maximum values are 81 \(\upmu\)m and 41 \(\upmu\)m, respectively, and it occurs almost at an identical resonant frequency to that of the longitudinal vibration.