# Design of Particle Dampers for Laser Powder Bed Fusion
## 3 Experimental Methodology
### Test Plan  
A cuboid beam with a cuboid cavity is chosen to characterise the effect of particle damping. By positioning the beams on a longitudinal edge, support structures in the cavity can be dispensed with due to self-supporting structures (see Figure 5). The beams are thus manufactured horizontally. The basis of the experimental design is a \(3^{3}\) full factorial experimental design. This means that three influencing factors are analysed and each influencing factor has three supporting points. This results in a total of 27 parameter combinations. In order to be able to characterise the frequency-dependent course of the particle damping, the natural frequency of the beams is defined as the first parameter, which results from the geometric dimensions of the beams. The second influencing factor is the ratio \(\zeta\) between particle volume and beam volume and is thus an indirect description of how much particle mass in relation to the beam mass is in the beam. Here, beams with a cavity of 0% (fully-fused beam), 10% and 20% are examined. Figure 3: Frequency response function (FRF) left, circle-fit right, reprinted with permission from ref. [7]. Copyright Elsevier. As a third parameter, the material is varied. The largest application areas for the production of additively manufactured end products are aerospace and the automotive industry [48]. For aerospace, aluminium or titanium alloys are particularly relevant, especially for brackets, components for electronic mounting or turbine blades (titanium). In the automotive industry, aluminium can be used for motorcycle triple clamps or brake shoe holders, for example. Furthermore, steel alloys are relevant for the additive manufacturing of gears or brake discs in the automotive industry or also for cutting tool holders in plant engineering. It should be emphasised that the initial material of the particles and the beams must be the same and only the material combination as a whole can be changed. In total, three different material classes are varied, namely aluminium AlSi10 Mg, tool steel 1.2709  
Figure 4: Flow chart to characterise the effect of particle damping. Figure 5: Schematic representation of a particle filled beam on the building platform. and titanium Ti6 Al4V. In addition, two boundary conditions are introduced. The first boundary condition describes the length of the cavity and is defined as \(l_{\text{Cavity}}=0.8\)\(l_{\text{beam}}\). Additionally, the width ratio \(\xi=b_{\text{Cavity}}/b_{\text{beam}}\) of the cavity has to be specified and is defined as \(\xi=2.5\times\zeta\). Previous studies have shown that the frequency response functions of the beams made of AlSi10 Mg with dimensions of 10 \(\times\) 10 \(\times\) 200 mm\({}^{3}\) were strongly influenced by the effect of particle damping. This meant that the damping could not be reliably detected [7]. For this reason, a total of four interpolation points of the natural frequency are analysed in the experimental plan (see Table 1). In addition, two further parameters, the excitation force and the excitation direction, are varied during the experiment. The excitation force varies from 10 N to 180 N in steps of  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Batch**} & \multicolumn{3}{c}{**Outer Beam Dimensions in mm**} & \multicolumn{3}{c}{**Cavity Dimensions in mm**} & \multirow{2}{*}{**Cavity in \%**} \\ \cline{3-3} \cline{5-8}  & & & **Length** & & **Width** & & **Width** & **Height** & **Length** \\ \hline
1 & AlSi10 Mg & 1 & 200 & 20 & 20 & & Full material \\ \hline
12 & AlSi10 Mg & 3 & 200 & 10 & 10  
10 N to 100 N and in steps of 40 N to 180 N. However, these values are deviated from in individual cases if, for example, the acceleration sensor reaches its saturation limit. For the clear assignment and orientation of the beams during the test, the beam number and a coordinate system are printed on the front surfaces of all beams.