# Design of Particle Dampers for Laser Powder Bed Fusion
## 4 Results
### Particle Damped Beams
#### 4.2.3 First Measurement Campaign  
In the following, the 5 \(\times\) 5 \(\times\) 200 mm\({}^{3}\) beams made of AlSi10 Mg and the 4.2 \(\times\) 4.2 \(\times\) 169 mm\({}^{3}\) made of 1.2709 are analysed. Due to the limitations of the accelerometer, only forces up to 20 N and 25 N can be analysed. Figure 8a,b shows a selection of three frequency response functions each for an excitation force of \(F_{z}\) = 20 N. More detailed damping curves are shown as a function of different excitation forces and for the first, third and fifth mode in Figure 8c-h. The local maxima (resonances) in Figure 8a,b represent the odd bending modes. The local minima (anti-resonances) represent the even bending modes. Since the acceleration sensor is located at a vibration node for the even bending modes, only the odd bending modes can be evaluated. Using impulse hammer excitation, a frequency range of up to 18,000 Hz can be excited for the beams made of AlSi10 Mg and up to 25,000 Hz for the beams made of 1.2709. It can be seen that the effect of particle damping is effective over the frequency range investigated. Table 3 shows the percentage reduction in amplitude due to the effect of particle damping compared to the fully-fused beam. However, the damping effect decreases from the second mode onwards. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Material** & **Parameter** & **1** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** & **23** & **25** \\ \hline \multirow{3}{*}{AlSi10 Mg} & \(m_{\text{B}}\) [g] & 212.20 & 53.75 & 48.45 & 50.85 & 13.95 & 13.05 & 12.5 & 159 & 144.2 & 151.2 & 197.6 & 193.05 \\ \cline{2-13}  & \(m_{\text{P}}\) [g] & 0 & 0 & 5.45 & 2.48 & 0 & 1.89 & \(-\)0 & 0 & 17.00 & 8.1 & 6.62 & 23.29 \\ \cline{2-13}  & \(\eta\) [\%] & 1 & 1 & 50.70 & 46.05 & 1 & 67.74 & \(-\)1 & 1 & 53.46 & 50.94 & 31.20 & 54.88 \\ \hline \multirow{3}{*}{**Material**} & **Parameter** & **40** & **41** & **42** & **43** & **44** & **45** & **46** & **47** & **48** & **49** & **50** & **51** \\ \cline{2-13}  & \(m_{\text{B}}\) [g] & 343.90 & 360.53 & 384.00 & 87.55 & 91.05 & 93.68 & 21.75 & 22.65 & 23.75 & 261.95 & 273.75 & 288.45 \\ \cline{2-13}  & \(m_{\text{P}}\) [g] & 36.70 & 14.93 & 0 & 12.61 & 6.74 & 0 & 2.75 & 1.28 & 0 & 31.19 & 14.15 & 0 \\ \cline{2-13}  & \(\eta\) [\%] & 47.79 & 38.88 & 1 & 67.28 & 71.93 & 1 & 57.89 & 53.68 & 1 & 54.06 & 49.04 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Beam mass \(m_{\text{B}}\), particle mass \(m_{\text{P}}\) and packing density \(\eta\) of the beams. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Powder** & **Damped Beam** & **1 st Mode** & **3 rd Mode** & **5 th Mode** & **7 th Mode** & **9 th Mode** \\ \hline AlSi10 Mg & 10\% cavity & 32\% & 48\% & 75\% & 76\% & - \\ \hline AlSi10 Mg & 20\% cavity & 42\% & 75\% & 68\% & 58\% & - \\ \hline
1.2709 & 10\% cavity & 62\% & 91\% & 48\% & 14\% & \(-\)49\% \\ \hline
1.2709 & 20\% cavity & 69\% & 96\% & 77\% & 59\% & 63\% \\ \hlineFigure 8: Frequency response functions and force-dependent damping characteristics (1 st, 3 rd and 5 th mode) Left: outer dimensions: 05 \(\times\) 05 \(\times\) 200 mm\({}^{3}\), parameter 15–17, material: AlSi10 Mg, right: outer dimensions: 4.2 \(\times\) 4.2 \(\times\) 169 mm\({}^{3}\), parameter 46–48, material: 1.2709. Figure 8 also shows that the damping of the particle-damped beams increases significantly from the first to the third bending mode. Subsequently, the damping for all beams, except for the AlSi10 Mg beam with a 10% cavity, decreases again for higher modes. From the results, it can be concluded that for the beams made of steel, a larger cavity consistently leads to higher damping than a smaller cavity. For the AlSi10 Mg alloy, which is subject to strong fluctuations especially in the \(z\)-direction, no general statement can be made. Some of the damping curves show a characteristic curve, which can be described by a functional relationship. The damping curves are fitted by a hyperbolic function.