Two-way coupled MBD–DEM modeling and experimental validation for the dynamic response of mechanisms containing damping particles

Highlights

• Propose a coupled MBD-DEM model to solve granule-structure interaction problems.

• Validate the model by free vibration tests of mechanisms with damping particles.

• Produce reasonable to good agreement on the interaction behavior and load transfer.

• Adding damping particles to mechanisms reduces the acceleration amplitude.

Abstract

Damping particles can be used to attenuate vibrations in mechanisms. However, damping particles and mechanical parts interact in an extremely complex manner, which affects the energy dissipation of the mechanisms. This study proposes two-way coupled models based on Multi-Body Dynamics (MBD) and Discrete Element Method (DEM) to solve granule-structure interaction problems, and uses two sets of experiments to validate the numerical model. Subsequently, the validated coupled MBD–DEM model was used to further investigate the effects of cavity size and chamber number of particle dampers on the dynamic characteristics of mechanisms. Results show that the coupled MBD–DEM simulations reasonably agree with the corresponding experiments. In the mechanism with a particle damper, under the same mass but with different cavity sizes, the effect of vibration reduction follows the sequence: 1/4 box>1/8 box>1/16 box. Under the same mass but with different chamber numbers, the degree of damping follows the sequence: single-chamber box>double-chamber box>triple-chamber box. Adding damping particles to mechanisms does not affect the vibration period, but does reduce the acceleration amplitude.

Introduction

The suppression of vibrations has always been an important issue in mechanisms. Particle damping technology is a passive technology for the attenuation of vibration, where a certain number of particles are filled into the internal or additional cavities of a mechanism. When the mechanism vibrates, constant friction and collision between the particles and between the particles and the mechanical parts consume the vibration energy of the mechanism, thereby achieving a reduction in the vibration of the structure. This technology has advantages in its significant vibration reduction, resistance to high temperatures and harsh environments, small additional mass requirements, and a lesser effect on the configuration of the original mechanisms. It has been widely used in civil engineering [1], [2], [3], mechanical engineering [4], [5], [6], and aeronautical engineering [7]. In the following, the results of previous studies on particle damping in these fields are compared and presented.

One of the pioneering studies was conducted by Panossian [8], who proposed a closed particle damper concept and installed particle dampers comprised of varying particle materials on turbine blades. By using the standard vibration modal test, the reduction of blade vibration by the particle dampers was observed. Liu et al. [9] explored through physical experiments the vibration behavior of a disk container with a particle damper installed. The geometric size for optimum vibration reduction was determined by varying the diameter and thickness of the disk container. These investigators found that the particle damper mainly consumes system energy through friction between particles and between the particles and their container. Lu et al. [3] analyzed the dynamic behavior of a three-layer simple rigid frame with particle dampers subjected to historical seismic loads. Their experimental study revealed that properly designed particle dampers could greatly reduce the vibration energy of structural systems under the action of random earthquakes. Particle damping technology has been further applied to gear transmission systems. Xiao et al. [10] and Xiao et al. [11] placed particle dampers on the gears and conducted gear transmission tests, finding that a proper particle-filling ratio can greatly reduce the vibration of gear transmissions.

To understand the mechanism of vibration reduction for particle damping technologies, Wang et al. [12] and Lei and Wu [13] used a multiphase flow theory incorporating a damping mechanism to analyze the dynamic behavior of a cantilever beam with a particle damper. The reduction of vibrations of the cantilever beam was found to be greatly related to the damper position and the particle-filling ratio, and is mainly attributed to the collisions between the particles. Alternatively, the discrete element method (DEM) [14], a numerical method for modeling the motion of particles, can provide a deeper understanding of particle damping [15], [16], [17], [18]. Chen et al. [15] used the DEM to simulate the vibration behavior of a cylindrical rod with a particle damper. The parameter analysis revealed that particle size affects the friction and collision distribution of the energy dissipation mechanism, and that the particle-filling ratio has a significant effect on vibration reduction. Mao et al. [16] also used the DEM to simulate the vibration behavior of a cantilever beam with particle dampers and explored the effect of the filling ratio on vibration characteristics. Their results showed that the lower the filling ratio of the particle damper, the better the vibration reduction for the cantilever beam. Duncan et al. [17] simulated the dynamic behavior of a plate with a particle damper containing only one particle by using the DEM, reporting that the maximum degree of damping increases with the particle–structure mass ratio and the restitution coefficient. Machado et al. [18] adopted the DEM to predict the mechanical response of a bearing with a rigid or elastic housing. The DEM exhibits an excellent ability to describe accurately both elastic behavior and loading evolution in dynamic situations.

The contact between damping particles and mechanical parts has a complex interaction, affecting the energy dissipation and the effective vibration reduction for mechanisms. At present, this interaction has been rarely explored. The combining of related numerical methods can predict this complex interaction, clarify complex dynamic characteristics and nonlinear behavior, and lead to novel analysis methods. Multi-body dynamics (MBD) [19], [20], [21], [22] can model the dynamic behavior of rigid or elastic multi-body systems. Using the Euler–Lagrange principle, a mathematical model for the dynamics of multi-body systems can be established and then solved by a suitable numerical method. MBD has become a useful method for the kinematic analysis of multi-body systems [23,24]. Additionally, the DEM has been extensively used to simulate the motion and mechanical behavior of particles, and has recently been applied to solving problems related to particle damping technologies [5,[15], [16], [17], [18]]. To our knowledge, MBD or the DEM alone cannot address the interaction between damping particles and mechanical parts. This is because: (1) since contacting surfaces (mechanical parts) are assumed to be rigid bodies with no mass in the DEM, the DEM cannot describe the dynamic inertia properties of the mechanical parts; and (2) MBD is not equipped with a contact detection algorithm for particle-particle and particle-wall contacts, so MBD cannot currently describe the motion of thousands of particles. Consequently, it is essential to combine the two methods to simulate this complex interaction and further predict more accurately the vibration reduction mechanism. In the coupled MBD–DEM model, the mechanical parts are modeled by MBD, whilst the granular assemblies are modeled by the DEM. Both the mechanical parts and the discrete particles interact through contacts at the interfaces between them. The contact forces from the particle-wall contacts influence the motion of the mechanical parts, and relatively the mechanical parts drive the motion of the particles. It is indispensable for the coupling technique to apply the “particle forces” from the DEM on the mechanical parts, and feed the “movements” of the mechanical parts from MBD back to the DEM as a boundary for the particles. The development of the MBD–DEM coupling is only at the prototype stage. Lu et al. [2] and Coetzee et al. [25], two of the pioneers to develop the coupling technology, proposed simple prototypes, and subsequently, Barrios and Tavares [26] and Ahmad et al. [7] applied this coupling technology to mining engineering and aeronautical engineering, respectively. Lu et al. [27] developed a coupling model of a multi-degree-of-freedom vibration system and the DEM to predict the dynamic behavior of a three-layer simple rigid frame with particle dampers subjected to various seismic accelerations. This coupled model can reasonably predict the dynamic response of a simple frame with particle dampers. Lommen et al. [28] recently presented a framework for the development, numerical verification, and application of MBD–DEM coupling. Chung and Wu [29] further applied a coupled MBD–DEM simulation to analyze a gear transmission system containing damping particles. Their work also confirmed the vibration suppression effect in gear transmission systems and further demonstrated the feasibility of applying particle dampers to practical engineering.

From the above literature survey, it is evident that the interaction between damping particles and mechanical parts is extremely complicated. Only through reasonable and appropriate simulation techniques can the particle damping mechanism be accurately modeled. While the MBD–DEM coupling is a promising numerical method, it is still in the initial stage of development and concrete experimental validations for the MBD–DEM simulations are minimal. There is thus a question as to whether the coupled MBD–DEM model is capable of producing quantitative predictions rather than only qualitative representations for granule-structure interaction problems. The purpose of the present study is to validate the coupled MBD–DEM model against physical experiments and to explore the effects of the relevant parameters on the damping behavior via the validated model. Two sets of experiments were used to investigate the dynamic response of mechanisms with damping particles and to validate the coupled MBD–DEM model: a free vibration test of a particle-based thrust damper, taken from the experiment of Bai et al. [30], and a free vibration test of a mass-spring-damper-slide system with a particle damper, devised in the present study. These tests were conducted on a glass bead damper and a steel bead damper, respectively, and the corresponding coupled MBD–DEM simulations were performed. A comparison between the numerical simulations and the experiments is presented and discussed in this study. After the proposed coupled MBD–DEM model is validated, this study further investigates the effects of the relevant parameters of particle dampers on dynamic characteristics. The main and novel contributions of this study are: (1) concrete and rigorous experimental validation is provided for two-way coupled MBD–DEM models, facilitating the development of the coupled MBD–DEM theory; (2) a new mass-spring-damper-slide system with a particle damper is devised and an analytic method using coupled MBD–DEM models is proposed in the first place; (3) a multi-body system with joints and a particle damper, a slider-crank mechanism with a particle damper, is proposed and firstly analyzed using the coupled MBD–DEM model; and (4) new findings from the investigation for the effects of particle properties, cavity size, and chamber number are acquired.

In the following, the physical experiments, theory and implementation of the coupled MBD–DEM approach, model validation with the physical experiments, effects of the relevant parameters on the damping behavior, and finally a summary of the major findings are presented sequentially.