An experimental study of the elastic rebound of spheres

Kharaz, Ahmad H.; Gorham, D.A.; Salman, Agba D.

doi:10.1016/s0032-5910(01)00283-2

Cited by 172 publications

(96 citation statements)

References 19 publications

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“…36a. However, the coefficient of tangential restitution decreases with target inclination and reaches a minimum at an to that observed by Dong and Moys [18], Kharaz et al [46] for different solid particles and it could be explained by transition from rolling at small angles to sliding at large angles.…”

Section: The Tangential Restitution Coefficientmentioning

confidence: 52%

“…If the contact force exceeds the yield point, the coefficient of restitution can decrease with increasing impact velocity, which was shown in many experimental studies [21,23,46,64,86] and described with the models [73,94].…”

Section: Significant Factors Affecting the Restitution Coefficientmentioning

confidence: 98%

“…To describe the oblique impact the measurements are carried out at different impact angles, in the range from 0 • to 90 • . The additional information about the impact behaviour can be obtained from rebound angle and the angular speed of rotation created during the rebound [46,18].…”

Section: Measurement Of the Restitution Coefficient Of A Granulementioning

confidence: 99%

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

et al. 2010

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The discrete modelling and understanding of the particle dynamics in fluidized bed apparatuses, mixers, mills and others are based on the knowledge about the physical properties of particles and their mechanical behaviour during slow, fast and repeated stressing. In this paper model parameters (modulus of elasticity, stiffness, yield pressure, restitution coefficient and strength) of spherical granules ( γ -Al 2 O 3 , zeolites 4A and 13X, sodium benzoate) with different mechanical behaviour have been measured by single particle compression and impact tests. Starting with the elastic compression behaviour of granules as described by Hertz theory, a new contact model was developed to describe the force-displacement behaviour of elastic-plastic granules. The aim of this work is to understand the energy absorption during compression (slow stressing velocity of 0.02 mm/s) and impact (the impact velocity of 0.5-4.5 m/s) of granules. For all examined granules the estimated energy absorption during the impact is found to be far lower than that during compression. Moreover, the measured restitution coefficient is independent of the impact velocity in the examined range and independent of the load intensity by compression (i.e. maximum compressive load). In the case of repeated loading with a constant load amplitude, the granules show cyclic hardening with increasing restitution coefficient up to a certain saturation in the plastic deformation. A model was proposed to describe the increase of the contact stiffness with the number of cycles. When the load amplitude is subsequently increased, further plastic deformation takes place and the restitution coefficient strongly decreases.

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Section: The Tangential Restitution Coefficientmentioning

confidence: 52%

Section: Significant Factors Affecting the Restitution Coefficientmentioning

confidence: 98%

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

et al. 2010

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“…It was suggested that the basic energy dissipation mechanism at high impact velocities is plastic deformation. More recently, accurate measurements of the coefficient of restitution have been made by Kharaz et al (2001) for the impact of 5 mm elastic (aluminium oxide) spheres on thick plates of steel and aluminium alloy over a wide velocity range. The variations in the coefficient of restitution with impact velocity were reported.…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical model for oblique impacts of elastoplastic spheres

Thornton

2008

Proc. R. Soc. A.

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Results of finite-element analysis (FEA) of oblique impacts of elastic and elastic, perfectly plastic spheres with an elastic flat substrate are presented. The FEA results are in excellent agreement with published data available in the literature. A simple model is proposed to predict rebound kinematics of the spheres during oblique impacts. In this model, the oblique impacts are classified into two regimes: (i) persistent sliding impact, in which sliding occurs throughout the impact, the effect of tangential (elastic or plastic) deformation is insignificant and the model reproduces the well-established theoretical solutions based on rigid body dynamics for predicting the rebound kinematics and (ii) non-persistent sliding impact, in which sliding does not occur throughout the impact duration and the rebound kinematics depends upon both Poisson's ratio and the normal coefficient of restitution (i.e. the yield stress of the materials). For non-persistent sliding impacts, the variation of impulse ratio with impact angle is approximated using an empirical equation with four parameters. These parameters are sensitive to the values of Poisson's ratio and the normal coefficient of restitution, but can be obtained by fitting numerical data. Consequently, a complete set of solutions is obtained for the rebound kinematics, including the tangential coefficient of restitution, the rebound velocity at the contact patch and the rebound rotational speed of the sphere during oblique impacts. The accuracy and robustness of this model is demonstrated by comparisons with FEA results and data published in the literature. The model is capable of predicting complete rebound behaviour of spheres for both elastic and elastoplastic oblique impacts.

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“…Coefficients of restitution describe the ratio of the normal (or tangential) velocity component of the center of mass before and after an impact (e.g. Kharaz et al, 2001). Parameter values for various surface types are retrieved from the literature (e.g., Azzoni and de Freitas, 1995;Chau et al, 2002;Schweigl et al, 2003;Heidenreich, 2004).…”

Section: The Rockfall Modelmentioning

confidence: 99%

Evaluation of a 3-D rockfall module within a forest patch model

Rammer

Brauner

Dorren

et al. 2010

Nat. Hazards Earth Syst. Sci.

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Abstract. Many slopes in the Alps are prone to rockfall and forests play a vital role in protecting objects such as (rail) roads and infrastructure against rockfall. Decision support tools are required to assess rockfall processes and to quantify the rockfall protection effect of forest stands. This paper presents results of an iterative sequence of tests and improvements of a coupled rockfall and forest dynamics model with focus on the rockfall module. As evaluation data a real-size rockfall experiment in the French Alps and two 2-D rockfall trajectories from Austria and Switzerland were used. Modification of the rebound algorithm and the inclusion of an algorithm accounting for the sudden halt of falling rocks due to surface roughness greatly improved the correspondence between simulated and observed key rockfall variables like run-out distances, rebound heights and jump lengths for the real-size rockfall experiment. Moreover, the observed jump lengths and run-out distances of the 2-D trajectories were well within the stochastic range of variation yielded by the simulations. Based on evaluation results it is concluded that the rockfall model can be employed to assess the protective effect of forest vegetation.

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An experimental study of the elastic rebound of spheres

Cited by 172 publications

References 19 publications

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

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

A semi-analytical model for oblique impacts of elastoplastic spheres

Evaluation of a 3-D rockfall module within a forest patch model

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