# Development of High-Power Ultrasonic System Dedicated to Metal Powder Atomization
## 4 Results and Discussion  
### Numerical Modelling  
In the first design phase, both components (plate and sonotrode) were analyzed and optimized separately to obtain the appropriate vibration mode at the assumed resonant frequency of 20 kHz. This simplified the design process using a modal analysis. After obtaining satisfactory results, in the next step, the tool elements were assembled and the the entire sonotrode assembly was analyzed using a harmonic analysis. These studies allowed us to determine the predicted distribution of vibration amplitude on the working surface of the sonotrode and determine the area with the highest amplitude of vibrations. It was also possible to determine the maximum stresses that occur in the material during operation. The harmonic analysis was carried out under conditions of forced vibrations in the contact area within the following components of the waveguide. Four models were analyzed, differing in the size of the working plate. The diameters of the plate were determined by the standing wavelength formed in the plate during resonance (-20 kHz). They were selected so that the smallest plate has one nodal point (with zero amplitude) and a diameter of 60 mm (Figure 5a). The larger plate, two-node one had a diameter of 108 mm (Figure 5b), the three-node plate had a diameter of 140 mm (Figure 5c) and the biggest, the four-node plate, had a diameter of 190 mm (Figure 5d). The calculations consisted of a modal analysis, necessary to design the appropriate geometry of the plate, and a harmonic analysis to determine the amplitudes of vibrations of the system. For all cases, the same sonotrode forcing (sinusoidal pressure with an amplitude of 50 MPa, which is the acceptable value for most types of materials) was used. In this way, it was possible to compare the effectiveness of the studied types of sonotrodes. The vibration amplitudes at selected points of the plates are listed below:  
* The maximum amplitudes of the single-node plate deflections in the deflection arrows, analyzed perpendicularly to the plate surface (57.3 \(\upmu\)m, 44.5 \(\upmu\)m)
* Maximum deflection amplitudes of a two-node plate in deflection arrows, analyzed perpendicularly to the plate surface (50.4 \(\upmu\)m, 22.3 \(\upmu\)m, 27.1 \(\upmu\)m)
* Maximum deflection amplitudes of the three-node plate in the deflection, analyzed perpendicularly to the plate surface (36.9 \(\upmu\)m, 32.5 \(\upmu\)m, 22.0 \(\upmu\)m, 27.7 \(\upmu\)m)  
Figure 4: The concepts of the oscillating systems for atomization: (**a**) 20 kHz system, (**b**) 70 kHz system, all dimensions are given in mm. * Maximum deflection amplitudes of the four-node plate in the deflection arrows, analyzed perpendicularly to the plate surface (32.1 \(\upmu\)m, 26.3 \(\upmu\)m, 19.2 \(\upmu\)m, 14.7 \(\upmu\)m, 17.3 \(\upmu\)m)  
Due to the predicted diameter of the melted metal stream by the TWAS process (in the range of 80-130 mm for the pre-defined stand-off distances of 100 to 300 mm), the smallest plates, with diameters of 60 mm and 108 mm, seem to be insufficient. However, they provide the highest level of amplitude (in the central part of the plate >50 \(\upmu\)m), which could have a significant impact on atomization efficiency. The sonotrode with a 190 mm working plate is sufficient for the assumed atomization conditions and the diameter of the melt stream, but it has the lowest amplitudes of the plate's deflections. Therefore, the selected solution here is a plate with a diameter of 140 mm. It meets both geometrical requirements, and provides a relatively high vibration amplitude of the plate surface. Taking into account the above conclusions, the calculations for a sonotrode with a natural frequency of 70 kHz were carried out for one diameter only, of 140 mm. This was also intended choice, giving a possibility of comparing both systems in future, in terms of properties of the obtained powders. The results of the calculation of the vibration distribution of the plate are shown below (Figure 6).