A Critical Study of the Applicability of Rigid-Body Collision Theory

Abstract

This article deals with the collision of steel bars with external surfaces. The central issue of the article is the investigation of the fundamental concepts that are used to solve collision problems by using rigid body theory. We particularly focus on low velocity impacts of relatively rigid steel bars to test the applicability of these concepts.An experimental analysis was conducted to study the rebound velocities of freely dropped bars on a large external surface. A high speed video system was used to capture the kinematic data. The number of contacts and the contact time were determined by using an electrical circuit and an oscilloscope. Tests were performed by using six bar lengths and varying the pre impact inclinations and the velocities of the bars. The experimental results were used to verify the applicability of Coulomb's law of friction and the invariance of the coefficient of restitution in the class of impacts considered in this study.Then, given the unusual variation the coefficient of restitution as a result of changing pre impact inclinations, a theoretical model was developed to explain this variation. A discrete model of the bar was

Simulation of eddy-current separators

“…They explicitly verified that the assumption of Coulomb's law of dry friction, which is essential to Keller's theory, is satisfied for impact velocities of the order of a few meters per s and that the coefficient of restitution does not depend much on the particle size or the impact velocity. It was found in [18] that may depend strongly on the orientation of the particle, but this was attributed to the excitation of longitudinal vibrations of the particle. In the case of a metal particle-belt collision, the energy is absorbed by the belt rather than by the particle and the energy is absorbed locally, near the impact, independently of the shape and orientation of the particle.…”

“…In our study, was taken as a constant, independent of the size, shape, impact, velocity, or orientation of the particle. Such a simplification can be defended on the basis of a study by Stoianovici et al [18] who showed that the rigid body theory performs remarkably well as long as little of the energy is absorbed by the system as longitudinal vibrations of the particle. They explicitly verified that the assumption of Coulomb's law of dry friction, which is essential to Keller's theory, is satisfied for impact velocities of the order of a few meters per s and that the coefficient of restitution does not depend much on the particle size or the impact velocity.…”

Quasi-rigid objects in contact

“…More fundamentally, the coefficient of restitution is physically meaningful only for particles, and it has been difficult to define a suitable quantity for rigid bodies [MC95]. Even for something as simple as a metal rod, the measured coefficient of restitution can vary over most of the feasible range [SH96]. The other alternative is to introduce virtual springs and dampers at the contact points (e.g., [GPS94]), to remove the contact state sensitivity.…”

Energy absorption during compression and impact of dry elastic-plastic spherical granules

“…However, many different models were developed to describe the restitution coefficient of viscoelastic (Schafer et al [79], Stronge [88], Stoianovici and Harmuzlu [87]), viscoelastic-adhesive (Thornton and Ning), viscoelastic (Brilliantov [11]), elastic-perfectly plastic (Thornton [93], Wu et al [109]), elastic-perfectly plastic adhesive (Thornton and Ning [94]), elastic-perfectly plastic with hardening (Mangwandi et al [64]), elastic-plastic (Johnson [38]), elastic-viscoplastic (Adams et al [3]), plastic and viscoplastic (Walton and Braun [106]), elastic-adhesive (Thornton and Ning [94]) contacts. A review of these models is given in Table 1.…”