Measurements of Solid Spheres Bouncing Off Flat Plates

Abstract

Recent years have seen a substantial increase of interest in the flows of granular materials whose rheology is dominated by the physical contact between particles and between particles and the containing walls. Considerable advances in the theoretical understanding of rapid granular material flows have been made by the application of the statistical methods of molecular gas dynamics (e.g., Jenkins and Savage (1983), Lun et al. (1984)) and by the use of computers simulations of these flows (e.g., Campbell and Brennen (1985), Walton (1984)). Experimental studies aimed at measurements of the fundamental rheology properties are much less numerous and are understandably limited by the great difficulties involved in trying to measure velocity profiles, solid fraction profiles, and fluctuating velocities within a flowing granular material. Nevertheless, it has become clear that one of the most severe Measurements of r Bouncing Off Flat Plate problems encountered when trying to compare experimental data with the theoretical models is the uncertainty in the material properties governing particle/particle or particle/wall collisions. Many of the theoretical models and computer simulations assume a constant coefficient of restitution (and, in some cases, a coefficient of friction). The purpose of the present project was to provide some documentation for particle/wall collisions by means of a set of relatively simple experiments in which solid spheres of various diameters and materials were bounced off plates of various thickness and material. The objective was to provide the kind of information on individual particle/wall collisions needed for the theoretical rheological models and computer simulations of granular material flows: in particular, to help resolve some of the issues associated with the boundary condition at a solid wall. For discussion of the complex issues associated with dynamic elastic or inelastic impact, reference is made to Goldsmith (1960) and the recent text by Johnson (1985).

Experimental study of the bouncing trajectory of a particle along a rotating wall

“…The random errors on the model particle angles are δθ = ±5 • . At the end of the plate (ejected radial position x e =25cm), the random errors on the radial velocity are an estimated δVx V x = Sondergaard et al 1990 [11] showed that the normal restitution coefficient decreases with the ratio of sphere diameter to plate thickness in agreement with the theory of Zener [12]. In this study, we use a plate with a sufficient thickness (5mm.)…”

Proposta experimental do estudo de colisões entre bolas de borracha e superfície plana

“…De acordo com Sondergaard et al [27], a partir dos resultados obtidos com lançamentos de bolas de aço com diâmetros de até 2,22 cm, há uma distância crítica entre a altura do lançamento da bola e a placa rígida a partir da qual o coeficiente de restituição permanece constante. Em distâncias inferioresà crítica, o coeficiente de restituiçãó e maior.…”

“…Também foi verificado que o coeficiente de restituição diminui com a velocidade de impacto e com á area de contato, pois estas são proporcionais (Equação 17). Não foi encontrado o valor limite da distância de lançamento como indicado em [27], mas em toda faixa de alturas de lançamento foi notada uma diminuição aproximadamente linear do coeficiente de restituição. Como em nossos experimentos foram usadas bolas de borracha com diâmetros superiores aos das bolas de aço usadas em [27],é possível que a distância crítica possa ser encontrada para lançamentos de alturas maiores.…”

Granular gases in mechanical engineering: on the origin of heterogeneous ultrasonic shot peening

“…But this would define an additional parameter µ corresponding to the Coulombic friction coefficient of the impacted surface. Experimental measurements of steel spheres bouncing on flat aluminum plates show [24] that the constant value of c T = 5/7 is mostly valid at small impact angles and under certain conditions up to θ ≃ 55 o . However, a more detailed analysis that should include the deformations and velocities associated with the elastic deformations of the surfaces is clearly beyond the scope and objectives of this paper.…”