# Research on a Composite Power-Superimposed Ultrasonic Vibrator for Wire Drawing
## 3 Regulation Analysis of the Power-Superimposed Vibrator
### Transient Analysis and Driving Methods  
Transient analysis is a good indicator of the actual working status of the composite vibrator. The maximum amplitudes and the corresponding amplification ratio of the vibration system during a short period can be obtained. In this paper, the vibrator was driven by three separate transducers, all of which have exactly the same configuration and are distributed uniformly around the disc. Therefore, we need to study the influences of the driving signals in terms of their forms and the phase difference between them. In this paper we mainly studied the occasions where the driving signal is a sinusoidal voltage or a square wave voltage with the same phase or with a phase difference of 120\({}^{\circ}\)  
Figure 8: Harmonic response of the power-superimposing vibration system. (**a**) Longitudinal amplitude _vs._ frequency of the vibrator and transducers. (**b**) Radial amplitude _vs._ frequency in \(X\) and \(Y\) directions. Figure 7: Variation of resonant frequency with the disc’s radius. When the same sinusoidal voltage was applied across the PZTs of the three transducers in the simulation, the longitudinal and radial amplitudes of the vibrator and the longitudinal amplitudes of the transducer at their top surfaces could be obtained. Figure 9 shows the relevant results within 0.8 ms during the simulation period. From Figure 9a we can see that the longitudinal amplitude of the vibrator is much larger than that of the transducer, being 21.78 \(\upmu\)m and 5.13 \(\upmu\)m, respectively. The amplification ratio is 4.25, which is very different from the result obtained in harmonic analysis. This might be caused by the phase of driving signals. Figure 9b shows the radial amplitude of the vibration, which is negligible with a maximum value of 1.26 \(\upmu\)m. We tried to plot the movement trajectory of the point at the top surface, but it is chaotic. When sinusoidal voltages were applied with a phase difference of 120\({}^{\circ}\) between each other, the results are shown in Figure 10. It can be seen from Figure 10a that the longitudinal amplitude of the vibrator is still much larger than that of the transducer, at 43.75 \(\upmu\)m and 5.37 \(\upmu\)m, respectively. However, the amplification ratio has reached 8.15, which is really quite close to the result obtained in harmonic analysis. Therefore, it is better to apply sinusoidal voltages across the PZTs with an appropriate phase difference. Figure 10b shows the radial amplitudes of the vibrator in \(x\) and \(y\) directions with maximum values of 0.6 \(\upmu\)m and 1.1 \(\upmu\)m, which are negligible compared with that of longitudinal amplitude. Figure 10: Transient analysis of the power-superimposing vibration system driving by sinusoidal voltages with a phase difference of 120\({}^{\circ}\) between each other. (**a**) Longitudinal amplitude of vibrator and transducers. (**b**) Radial amplitude in \(X\) and \(Y\) directions. Figure 9: Transient analysis of the power-superimposing vibration system driving by sinusoidal voltages without phase difference (**a**) Longitudinal amplitude of vibrator and transducers; (**b**) Radial amplitude in \(Y\) direction. The movement trajectory of the point at its top end in _XY_ plan and _XZ_ plan were also plotted, as shown in Figure 11, where \(Z\) presents the longitudinal direction and _XY_ plan represents the radial directions. It can be found that the movement tracks of the points at the top end of the vibrator are ellipses, both in the _XY_ plane and in _XZ_ plane. Therefore, the contact points of the die and the titanium wire would have a similar movement trajectory, which means the composite vibrations of both longitudinal and radial direction were imposed on the drawing processes. According to references [16; 19], both forms of vibration exert a strong influence on the drawing process, and the composite vibration can produce better effects, including drawing force reduction and improved surface quality.