# Design of Particle Dampers for Laser Powder Bed Fusion
## 5 Discussion  
This paper shows for the first time a comparison between damping characteristics of the material classes of aluminium (AlSi10 Mg) and steel (1.2709) in a frequency range from 500 to 30,000 Hz. It can be shown that the results correlate well between the material classes. The strong frequency- and force-dependent course of the damping is striking for both material classes. For high forces from 100 N, however, a constant damping curve related to the excitation force can be determined for both material classes. This constant damping measure is suitable as a design variable for determining the frequency-dependent damping. However, it should be taken into account that up to approx. 1300 Hz, the force-dependent damping increases until the asymptote is reached and decreases from 1300 Hz. Figure 15 shows the frequency-dependent damping factor (damping of the particle-damped beams in relation to the damping of the fully-fused beams) for the first to the third mode. It is noticeable that the damping factor for the beams made of 1.2709 is significantly higher. This is mainly due to the lower damping of the fully-fused beams made of 1.2709 compared to the beams made of AlSi10 Mg. Thus, with the same damping factor of the particle-damped beams of 1.2709 to AlSi10 Mg, the damping factor of 1.2709 can be higher. It can be seen that an increase in the damping factor can be realised for the first two modes by means of the effect of particle damping. However, the optimum in the damping factor of both material classes around 2000 Hz is striking. At lower frequencies, the deflection is greater for the same acceleration. Consequently, the beam deflection may be much greater than the relative movement between the particles and the beam. [PERSON] et al. already stated that the limit value of the minimum excitation \(X_{0}\times f^{2}\) should be greater than 3.5 m/s\({}^{2}\)[49]. On the other hand, the particle deflection is too small at frequencies above 10,000 Hz. Thus, there is an optimum in the frequency range, here at 2000 Hz. Another explanation for the low damping effect at 650 Hz may be related to parasitic friction in the mounting on foam, so that the fully-fused beam already shows increased damping. To evaluate this influence, the measurements could be repeated again for beams suspended on strings. Further, in investigations by [PERSON] et al., it was found that for an impulse hammer excitation of walls (clamped on one side) the effect of particle damping at 767 Hz for a cavity of approx. 20% provides only a small added value [9]. Higher modes could be damped much better in [PERSON] et al., but the higher modes of the walls differ significantly from the bending modes of the beams investigated here, so the measurements can only be compared with each other to a limited extent. Figure 14: Force-dependent damping characteristics—1 st mode, parameter 40–42, material: 1.2709, outer dimensions: 20 \(\times\) 20 \(\times\) 200 mm\({}^{3}\), left: one hit per excitation force, right: five hits per excitation force. The frequency response functions of the bending modes at 1300 Hz are striking in the second measurement campaign. The frequency response functions of the beams made of AlSi10 Mg as well as for 1.2709 show chaotic movements. A possible explanation could be stick-slip effects due to friction. These stick-slip effects depend on the excitation force and excitation frequency [50,51], which coincidentally occur more strongly with exactly this parameter combination. Another explanation could also be possible effects of dynamic vibration absorption, since the particle cluster has a large number of natural frequencies. One of the natural frequencies of the particle cluster could coincide with that of the beam in the parameter combination. The \(3^{3}\) full factorial experimental design presented here should be extended in further work. In particular, further support points should be investigated for the natural frequency.