# Design of Particle Dampers for Laser Powder Bed Fusion
## 4 Results
### Particle Damped Beams
#### 4.2.4 Second Measurement Campaign  
In the following, the 10 \(\times\) 10 \(\times\) 200 mm\({}^{3}\) beams of AlSi10 Mg and the 8.4 \(\times\) 8.4 \(\times\) 169 mm\({}^{3}\) of 1.2709 are analysed. A CT scan for a beam made of 1.2709 with a cavity of 20% is shown in Figure 9. It can be seen that the cavity is almost completely filled with powder. Due to the limitations of the accelerometer, only forces up to a maximum of 100 N can be analysed. Figure 10a,b shows a selection of three frequency response functions each for an excitation force of \(F_{z}\) = 50 N. By means of the impulse hammer excitation, a frequency range up to 30,000 Hz can be analysed. The evaluation of the measurement results showed, for all particle-damped beams, both for AlSi10 Mg and 1.2709, that all frequency response functions of the first mode do not look like a classical resonance peak, as it is known from an equivalent 1 degree of freedom model. Figure 10c,d shows two exemplary frequency response functions of the particle damped beams with a cavity of 20% and an excitation force of \(F_{z}\) = 10 N. When using the circle-fit method to evaluate the measurement results, it was found that instead of one circle, two intertwined circles were characterised. This is an indication of further resonances in the examined frequency range, so that the circle-fit method is not suitable for the evaluation of this mode. Repositioning the beams on the foam did not change the characteristics either. By comparing the frequency responses, however, a clear reduction of the amplitude by up to 97% due to the effect of particle damping can be demonstrated (see Table 4). For this reason, the amplitude reduction was calculated for each excitation force and the factor of the amplitude reduction multiplied by the damping value of the fully-fused beams (Figure 10e,f). This made it possible to derive an equivalent damping. Figure 9: CT scan of a powder-filled beam made from 1.2709, outer dimensions: 8.4 \(\times\) 8.4 \(\times\) 169 mm\({}^{3}\), parameter 43, material: 1.2709. Figure 10: Frequency response functions and force-dependent damping characteristics (1 st, 3 rd and 5 th mode) Left: outer dimensions: 10 \(\times\) 10 \(\times\) 200 mm\({}^{3}\), parameter 12–14, material: AlSi10 Mg, right: outer dimensions: 8.4 \(\times\) 8.4 \(\times\) 169 mm\({}^{3}\), parameter 43–45, material: 1.2709. In the following, the focus of the evaluation is placed on the third bending mode. For this purpose, detailed damping curves as a function of different excitation forces are shown in Figure 10g.h. For the third modes, it is noticeable that no more side resonances occur and the damping can again be reliably characterised with the circle-fit method. For the beams made of AlSi10 Mg with a cavity of 10%, a direction-dependent damping characteristic is evident, whereas this does not occur for the beams made of 1.2709. The force-dependent damping curve for the beams with a cavity of 20% is approximately identical for the beams made of AlSi10 Mg and 1.2709. In addition, a larger cavity leads to higher damping for both materials. The course of the damping could be described by a hyperbolic function. In the fifth mode of the fully-fused beams made of AlSi10 Mg, the frequency response functions for all force levels show a side resonance. As a result, the amplitudes of the particle-damped beams are consistently higher than those of the fully-fused beams. In the seventh mode, no pronounced resonance could be detected for the fully-fused beam. Consequently, the amplitudes of the particle-damped beams are also consistently higher than those of the fully-fused beams. For the fifth mode of the beams from 1.2709, the damping of the fully-fused beams for an excitation in y-direction is strongly fluctuating (see Figure 11). It can be seen that the effect of particle damping in the y-direction does not make a significant contribution. On the other hand, there is an increase in damping for excitation in the \(z\)-direction. It is noticeable that the damping is higher for a small cavity.