# Design of Particle Dampers for Laser Powder Bed Fusion
## 1 Introduction  
The rapid development of systems in additive manufacturing towards ever-larger build spaces and build rates requires a rethink in product development [1]. In the future, the focus of Design for Additive Manufacturing (DfAM) will no longer be predominantly on components, but rather on assemblies [2, 3, 4, 5]. In the best case, the assembly can be manufactured in one piece, according to the principle of the one-piece machine [6]. In order to realise the goal of the one-piece machine as best as possible, a multitude of physical effects must be understood and integrated into the component: so-called effect engineering [7]. In the field of additive manufacturing, especially in powder bed-based processes, the effect of particle damping represents a hitherto little-researched but very effective method for reducing vibrations [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. Particle dampers produced by laser powder bed fusion (LPBF) can reduce vibrations by more than a factor of 20 in a wide frequency range [7, 10, 12]. In the field of product development, the use of additively manufactured particle dampers offers potential by solving the conflict between high stiffness and high damping [7, 8, 11]. For example, particles can be integrated in the area of the neutral fibre and components can be optimised in terms of mass, stiffness and damping. Since the mass, production time and costs hardly increase due to the functional integration of the particle damping effect in the field of additive manufacturing, this is also referred to as \"damping for free\" [7]. Due to numerous design parameters and interactions that are still not fully understood, research on additively manufactured particle dampers is still in its infancy [7]. As a result, detailed and universally valid design methods and tools do not yet exist. In addition, modelling is challenging due to highly non-linear properties [21, 22, 23]. Initial approaches to describing the effect of particle damping focus on limited parameter studies on additivelymanufactured primitives [7; 9; 10; 12; 13; 14; 16; 17]. Isolated demonstrators such as cutting tool holders, braking discs or motorcycle triple clamps have also been considered [8; 16; 18]. The studies have in common that the transferability of the findings to other applications is missing. However, the range of possible applications for particle dampers is large. For example, conventionally manufactured particle dampers are already used to reduce vibrations in electronics, either to protect the electronics from damage (rocket launch) or to ensure high-precision measurement tasks (optical applications) [24; 25]. In addition to mechanical vibrations, thermally induced vibrations are increasingly occurring in high-precision measurement tasks, which could be reduced by particle dampers [26]. Other areas of application are turbine components, antennas or surgical instruments [21]. This paper aims to identify the influence of excitation force, excitation frequency and cavity size on the effect of particle damping by developing a \(3^{3}\) full factorial experimental design. Beams are selected as test specimens, which are excited to vibrate from 10 to 180 N using an automated impulse hammer. The beams are manufactured in different dimensions in order to vary the natural frequency and thus characterise the frequency-dependent damping. Furthermore, in addition to the first bending mode, the higher modes are also evaluated. Thus, a frequency range from 500 Hz to 30,000 Hz can be analysed. Furthermore, it is to be analysed to what extent these findings are similar between the material classes of aluminium, steel and titanium. For this purpose, tests will be carried out on beams made of aluminium AlSi10 Mg, tool steel 1.2709 and titanium Ti6 Al4V. As a result of this contribution, these influencing parameters will be provided in the form of design curves. This should help the designer to reduce the vibration amplitudes to the desired level and to estimate the damping.