Dynamic simulation of particle‐filled hollow spheres

Abstract

We are simulating a new lightweight material that could potentially be used in several technical applications, such as machine casings to rapidly damp vibrations, reducing wear and tear. This is achieved by employing embedded hollow spheres that are filled with a granular material, such as a ceramic powder. Energy is dissipated via friction caused by the interaction of particles with each other and with the sphere wall. The present dynamic simulation is based on a leapfrog algorithm, a time integration method used in molecular dynamics. Modifications, such as reflecting boundary conditions, are introduced to adapt the scheme to the field of granular materials. Motivation and Technical ApplicationsLimited fossil fuel supply and increasing awareness of climate change has led to a raise in demand of highly efficient means of transportation and industrial equipment. These can be constructed to be more efficient, e.g. by reducing their mass. The Fraunhofer Institute for Advanced Manufacturing Technology in Dresden, Germany is developing a new type of lightweight material that uses particle filled hollow spheres that are embedded within technical structures [1]. While the particles add to the overall weight, the material still shows a highly desirable dampening-to-weight ratio. When the structure is vibrating, e.g. due to engine operation, the particles can help to suppress these vibrations by quickly converting kinetic energy to heat through friction arising from collisions of the particles with each other and with the hull of the sphere [2]. This new material could be deployed in machine casings to reduce wear and tear. The benefits include lower maintenance cost and noise reductions. Computational MethodsTo simulate the dynamics of a large number of particles inside a hollow sphere, discrete element methods can be used. This allows to track each individual particle with respect to its position, velocity and rotational state. Modern molecular dynamics (MD) methods are capable of simulating large numbers of particles. Starting from a typical MD code that is aimed at the thermodynamic behavior of macroscopic fluid phases, some adaptations are required. For instance, MD usually considers periodic boundary conditions for the simulation volume. In the present scenario, the particles must interact with the boundary of the simulation volume to allow for energy transfer by vibration and particle impact. Additionally, most implementations only allow for a limited number of shapes for the simulation volume, such as a cuboid. We based our algorithm on a MD code co-developed at the Chair of Thermodynamics and Energy Technology, University of Paderborn [3]. Newton's equations of motion are at the core of the computations. For the equation of translational motion and the equation of rigid body rotational motion we considerHere, F i , m i , a i and x i are the forces acting on a particle i, the particle mass, the acceleration and position, while θ i , τ i , I i and α i are the angular orientation, torque, moment of inertia tensor...