Contact Mechanics and Coefficients of Restitution

Thornton, Colin; Ning, Zemin; Wu, Chuanyu; Nasrullah, Mohammed Z.; Li, Long-yuan

doi:10.1007/3-540-44506-4_9

Cited by 56 publications

(22 citation statements)

References 11 publications

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“…In other words, for a given impact angle and impact speed, the rebounding kinematics of the sphere can be determined once e n and f are known (Brach 1988(Brach , 1991. Many studies have been carried out to investigate the normal coefficient of restitution e n during elastoplastic impacts, and the rebound behaviour of elastoplastic spheres during normal impacts is well established (Johnson 1987;Thornton 1997;Thornton & Ning 1998;Kharaz et al 2001;Li et al 2000Li et al , 2002Thornton et al 2001;Wu et al 2003a). The impulse ratio can be determined by measuring the initial and rebound velocities at the sphere centre (Brach 1988(Brach , 1991Cheng et al 2002).…”

Section: Theoretical Aspectsmentioning

confidence: 99%

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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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Section: Theoretical Aspectsmentioning

confidence: 99%

“…The corresponding rebound kinematics for EE impacts are shown in figures 9-11. In these figures, data reported in the literature (Maw et al 1976;Kharaz et al 2001;Thornton et al 2001) are also superimposed. It is clear that our FEA results are in good agreement with the published data.…”

Section: Impact Of An Elastic Sphere With An Elastic Substrate (Ee Immentioning

confidence: 99%

A semi-analytical model for oblique impacts of elastoplastic spheres

Thornton

2008

Proc. R. Soc. A.

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“…Poppe et al 2000b,a;Gundlach & Blum 2015) and small aggregates thereof , several dust collision experiments were performed by observing aggregates of higher masses and at higher relative velocities (see the review by Blum & Wurm (2008), and the collision model by Güttler et al (2010)). Several of these experiments were combined with the Hertz and Thornton et al (2001) contact theories (e.g. by Güttler et al 2010;Kothe et al 2013) resulting in a dust collision model.…”

Section: Introductionmentioning

confidence: 99%

Low-velocity collision behaviour of clusters composed of sub-millimetre sized dust aggregates

Brisset

Heißelmann

Kothe

et al. 2017

A&A

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Context. The experiment results presented apply to the very first stages of planet formation, when small dust aggregates collide in the protoplanetary disc and grow into bigger clusters. In 2011, before flying on the REXUS 12 suborbital rocket in 2012, the Suborbital Particle and Aggregation Experiment (SPACE) performed drop tower flights. We present the results of this first microgravity campaign. Aims. The experiments presented aim to measure the outcome of collisions between sub-mm sized protoplanetary dust aggregate analogues. We also observed the clusters formed from these aggregates and their collision behaviour. Methods. The experiments were performed at the drop tower in Bremen. The protoplanetary dust analogue materials were micrometresized monodisperse and polydisperse SiO 2 particles prepared into aggregates with sizes between 120 µm and 250 µm. One of the dust samples contained aggregates that were previously compacted through repeated bouncing. During three flights of 9 s of microgravity each, individual collisions between aggregates and the formation of clusters of up to a few millimetres in size were observed. In addition, the collisions of clusters with the experiment cell walls leading to compaction or fragmentation were recorded. Results. We observed collisions amongst dust aggregates and collisions between dust clusters and the cell aluminium walls at speeds ranging from about 0

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“…For the collision behaviors between the coal gangue particles and the impact-contact problems between the coal gangue particles and the hydraulic support metal plate, through the theories, simulations and experiments [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], and other methods, many scholars have carried out similar studies on the contact behavior between particles [20] and the contact behavior between particles and plates [21][22][23][24][25] in the early stage, which provides the basis for the research of the collision behavior between coal gangue particles or between the coal gangue and the hydraulic support in the top-coal caving. Jackson et al [26] investigated the restitution coefficient of the impacting elastic-perfectly plastic spheres.…”

Section: Introductionmentioning

confidence: 99%

Study on the Vibroimpact Response of the Particle Elastic Impact on the Metal Plate

Yang

Wan

2019

Shock and Vibration

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In order to study the contact and vibration response in the reciprocating impact between coal gangue particles and metal plate, on the basis of the Hertz contact theory, L-N contact model, and the Lagrange equation, this paper established an impact-contact model when the particles free falling to vertically impacts on the metal plate. The variable damping simulation method is proposed, and the accuracy of the variable damping simulation in the medium reciprocating collision is verified by combining the constant damping simulation, the variable damping simulation, and the falling body impact-contact model. The functional relationship between the damping term and the initial impact velocity in Adams simulation is also obtained. Then, through the rigid-flexible coupling method which is combined by Adams and Hypermesh, the three types of variable damping simulations are conducted: the simulation that the free-falling rigid rock sphere impact on the rigid metal plate, the simulation that the elastic rock sphere impact on the rigid metal plate, and the simulation that the elastic rock sphere impact on the elastic metal plate, respectively. Furthermore, contact and vibrate responses of the rock sphere and the metal plate in the three types of the simulation are studied. The results show that the impact-contact response of the rock sphere obtained from the simulation that the elastic rock sphere impact on the elastic metal plate is more accurate. After the flexible treatment of the rock sphere and the metal plate, most of the system energy is consumed during the impact. The conclusions will provide a theoretical calculation method for the medium vertical reciprocating impact and a theoretical basis for the setting of the damping term in Adams simulation and support the research basis for the study of the impact behavior between coal gangue particles and the metal plate.

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Contact Mechanics and Coefficients of Restitution

Cited by 56 publications

References 11 publications

A semi-analytical model for oblique impacts of elastoplastic spheres

A semi-analytical model for oblique impacts of elastoplastic spheres

Low-velocity collision behaviour of clusters composed of sub-millimetre sized dust aggregates

Study on the Vibroimpact Response of the Particle Elastic Impact on the Metal Plate

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