Enhancing the dissipative properties of particle dampers using rigid obstacle-grids

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Abstract

Particle dampers (PDs) are becoming a popular alternative to conventional damping devices due to their simple design and their ability to dissipate energy over a wide frequency range. The energy dissipation in PDs takes place due to relative motion between solid particles within the PD enclosure. The degree of relative motion depends on various parameters, especially it is highly sensitive to vibration amplitude changes. Usually, the particle size is much smaller than that of the PD enclosure which, under low forcing conditions, leads to sub-optimal momentum transfer and thereby leads to lower energy dissipation. In this work a new approach is investigated, in which a complex 3D rigid obstacle-grid is deliberately introduced inside the PD enclosure in order to overcome the shortcomings of a conventional PD. In order to better understand the influence of various dissipation mechanisms, simulations were performed. The Discrete Element Method (DEM) is used to model the interactions between the solid particles and their surroundings. In the simulations, the rigid obstacle-grid is described using a triangular surface mesh and to speed-up the collision detection process, efficient bounding volume hierarchy data structures were used. Moreover, laboratory experiments were set up to test the validity of the simulation models. The experimental setup consists of an electromagnetic shaker used to excite, via elastic elements, a clamped beam on which a PD with a rigid obstacle-grid is mounted. The obstacle-grid used in the experiments is manufactured using a Stereolithography 3D printer. Simulations and experiments were observed to be in good agreement. Moreover, the damping performance of a PD with a rigid obstacle-grid is observed to be at least twice as good as a conventional PD. Visual observations indicate that particles which would have otherwise been hardly contributing to energy dissipation, move violently due to an obstacle-grid, and hence actively participate in the energy dissipation process. Furthermore, a numerical study indicates that the obstacle-grid cell-size has a profound effect on the dissipation, allowing it to be used as an additional parameter to tune the damping performance of PDs.

Introduction

The emphasis on lightweight construction is growing continuously. This, on one hand has led to the drastic reduction in weight of technical systems. On the other hand, it has made these technical systems more vulnerable to unwanted vibration than ever before. A particle damper (PD) is one way to attenuate these unwanted vibrations. A PD is a cavity usually filled with spherically shaped frictional particles. Due to their simple design and their flexible ability to dissipate energy over a wide frequency range, PDs have been used in various applications. For a detailed literature review on PDs and their applications see Ref. [[1], [2], [3], [4], [5], [6], [7]].

The energy dissipation in PDs mainly caused by relative motion between solid particles and their surroundings. The degree of the relative motion is particularly sensitive to changes in the forcing function, i.e.strong forcing leads to high energy dissipation (often up to 50% of input energy, see Ref. [8]). On the contrary, low forcing leads to drastically lower energy dissipation. Usually, the particle size is much smaller than the PD enclosure which, under low forcing conditions, leads to sub-optimal momentum transfer and thereby lower energy dissipation. There are several ways to constructively increase the degree of relative motion between solid particles and their surroundings. One way is to partially fill the PD container with a combination of solid and liquid filling [9,10]. However, an added liquid increases the (otherwise low) temperature dependence of PDs, which in turn makes it less applicable in extreme conditions. Another way to increase relative motion between solid particles is to subdivide the PD enclosure into multiple chambers to form a multi-unit particle damper [[11], [12], [13]]. In this case, since the solid particles are confined inside a number of smaller cavities, rather than a single large cavity, the bulk motion of particles is constructively prevented. Even though, this encourages more effective collisions and increases damping, the solid particles are still confined to their respective chambers, making them effective only for a particular amplitude range. Moreover, as the number of cavities increases the process of filling the cavities with a precise amount of particles can become increasingly tedious.

Another way to break collective motion of particles and promote relative motion is, to deliberately introduce rigid obstacles inside the PD enclosure [14]. The rigid obstacles investigated in Ref. [14], though geometrically very simple, had a notable increase in energy dissipated. Therefore, more complex obstacle structures, in form of a uniform rigid obstacle-grid, should aid distributed particle collisions and significantly increase the damping performance. Moreover, methods of additive manufacturing enable the generation of complex obstacle-grid structures within the PD cavity [15]. Since the energy dissipation in PDs depends on many parameters, performing experiments to find the optimal design is often time-consuming and expensive. It is seen in Ref. [16], that if designed inappropriately, uniform rigid obstacle-grids can even have a negative effect on the damping performance. Therefore, a simulation model to predict the damping behavior of PDs with a deliberately introduced obstacle-grid early in the design phase can be of great use.

There are different methods used to investigate particle dampers. Since the effectiveness of PDs is determined by dissipative collisions between particles and their surroundings, Lagrangian particle methods such as the Discrete Element Method (DEM) seems to be a good choice in order to adequately model a PD [11,14,[17], [18], [19], [20]]. In Ref. [14] the DEM was used to model PDs with simple rigid obstacle, where the obstacles were described using surface meshes consisting of triangular elements. As a consequence of the fact, that most particle simulation programs treat each mesh triangle as an individual element during collision detection, the computational overhead of simulating PDs with obstacle-grid consisting of several thousands of triangles can be expected to be extremely high [21]. In order to overcome this challenge, special treatment of the obstacle-grid geometry is necessary to reduce the number of required numerical operations. This can be achieved by using bounding volume hierarchical (BVH) data structures during the collision detection phase [22,23]. This kind of scheme is reducing the computational overhead of looping over all the mesh triangles of the obstacle-grid during the neighborhood search, even though a colliding particle comes in contact only with a few triangles at a particular instant.

The novel contribution of this paper lies in the fact that Discrete Element Method simulations in combination with bounding volume hierarchy based data structures could be used to model the complex interactions between the 3D obstacle-grid, involving thousands of mesh triangles, and the spherical balls. Moreover, this paper shows how such simulation models could be used to systematically investigate parameter changes, for instance the obstacle-grid cell-size, could affect the dissipation performance of PDs with obstacle-grids.

This paper is organized as follows. In Section 2, a DEM model including relevant simulation parameters, capable of reproducing the experiments is developed. In Section 3, a description of the laboratory apparatus is given, following which the experimental results comparing the dissipation performance of PDs with and without obstacle-grids are presented. In Section 4, the simulation models are validated against experimental data generated in Section 3. Furthermore, using simulation results a physical interpretation of the observed increased dissipation due to the deliberate introduction of an obstacle-grid is given. In Section 5, a numerical study to investigate the effect of obstacle-grid cell-size is presented. Finally, in Section 6 some concluding remarks are provided.

Section snippets

Discrete Element Method

The contacts between solid particles, the obstacle-grid, and PD container walls are modelled using the Discrete Element Method (DEM). The equations of motion of a single solid particle i is given by the Newton-Euler equations [26]midvidt=fi,Iidωidt+ωi×Iiωi=li.

In these equations, Ii is the inertia tensor, mi is the mass and fi and li are the external forces and torques acting on the particle i. The external force fi acting on a solid particle takes into account the forces due to gravity and due

Experimental setup and analysis

The laboratory apparatus consists of a horizontally mounted steel beam of dimensions 540 mm × 20 mm × 2 mm, which is rigidly clamped on one side as depicted in the schematic view in Fig. 2. The PD enclosure, weighing 58.8 g, is a transparent acrylic box of inner dimensions 35 mm × 35 mm × 20 mm, which is fixed to the side of the beam. This PD enclosure is filled with steel spheres of 2 mm diameter. The total mass of the spherical particles was kept constant at 0.03 kg throughout this

Simulating a particle damper with 3D-obstacle-grid

The focus of this section is to develop a simulation model in order to get a deeper insight on the geometrical effects of an obstacle-grid in a PD and to predict the influence of design changes on the damping performance without actually building an experimental prototype. In order to reliably predict the dissipative effects of a PD with obstacle-grid using numerical simulations, a variety of parameters, as mentioned in Section 2, should be taken into account. The most relevant parameters used

Influence of cell-size on damping performance

In this section, a numerical study is set up to investigate the effect of cell-size on the damping performance of a PD with an obstacle-grid. For this purpose, obstacle-grid geometries with two different cell-sizes, namely 5 mm and 8 mm, are investigated, as depicted in Fig. 9. In order to ensure a fair comparison, the PD is filled with the same amount (0.03 kg) of spherical steel particles for both simulation scenarios. Moreover, the same contact parameters identified in Section 4 are used for

Conclusion

In this paper, it is shown that the damping properties of a conventional particle damper can be significantly improved by deliberately introducing a rigid obstacle-grid. It was also shown that the Discrete Element Method (DEM) is able to adequately model the dynamics of PDs with rigid obstacle-grids. In order to build trust in the simulation models and to verify their ability to make reliable predictions, laboratory experiments were performed. The experimental setup consists of a PD in form of

CRediT authorship contribution statement

C. Gnanasambandham: Writing - original draft. F. Fleissner: Writing - review & editing. P. Eberhard: Writing - review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The results published in this article were partially compiled during the master thesis of Mr. Enrico Messori [32]. We would like to express our appreciation to him.

This research has received funding from the German Research Foundation (DFG) within the priority program SPP 1897 “Calm, Smooth and Smart: Neuartige Schwingungsbeeinflussung durch gezielt eingesetzte Dissipation” subproject EB195/25-1/2 “Partikeldämpfer - Schwingungsbeeinflussung durch verteilte Dissipation über komplexe

References (32)

  • G. Tomlinson et al.

    Damping characteristics of particle dampers - some preliminary results

    Proc. IME Part C J. Mech. Eng. Sci.

    (2001)
  • S. Chockalingam et al.

    Damping investigation in boring bar using hybrid copper-zinc particles

    J. Vib. Contr.

    (2017)
  • S. Knebler, Vibration Damper for Sport Racket, USPatent No. 5792011A,...
  • A. Floreani, Short Ski Having a Hollow Section Filled with Flowable Mass, USPatent No. 4778197,...
  • C. Gnanasambandham et al.

    Investigating the dissipative effects of liquid-filled particle dampers using coupled DEM-SPH methods

    Comput. Part. Mech.

    (2019)
  • C. Gnanasambandham et al.

    Modeling a Partially Liquid-Filled Particle Damper Using Coupled Lagrangian Methods

    (2019)
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