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On the tangential restitution problem: independent friction–restitution modeling

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An Erratum to this article was published on 15 November 2014

Abstract

A single modeling of impact in terms of independent contributions of tangential restitution and friction is presented and tested with available literature data. Using this formulation, a description of oblique rebound of a homogenous sphere on a infinitely massive wall is obtained for both stick and gross slip regimes of impact using the same set of coefficients of restitution (normal and tangential) and friction based on the consideration of tangential forces at impact without viscose nor adhesive effects. This formulation which avoids sharp (apparent) variations in the coefficient of tangential restitution on the incident angle, provides a justification of several experimental results considered as anomalous in literature.

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Abbreviations

\(R\) :

Sphere radius (m)

\(m\) :

Sphere mass (kg)

u, v :

Pre- and post-impact center of mass velocities of the rebounding sphere (m/s)

U, V :

Pre- and post-impact velocities of the contacting point

\(\varvec{\upomega }, \varvec{\Omega }\) :

Pre- and post-impact angular velocities of the sphere (rad/s)

\(e_\mathrm{n}, e_\mathrm{t}\) :

Coefficients of normal and tangential restitution defined in the IFR model relative to the velocities of the contact point

\(e_\mathrm{t}\)(AFR):

‘Apparent’ coefficient of tangential restitution defined in the AFR model relative to the velocities of the contact point

\(e_\mathrm{t}\)(AFR, CM):

‘Apparent’ coefficient of tangential restitution defined in the AFR model relative to the mass center velocities

\(\mu \) :

Coefficient of sliding friction

\(\mathbf{J}_\mathbf{en}, \mathbf{J}_\mathbf{et}\) :

Normal and tangential impulses due to restitution (kg m/s)

\(\mathbf{J}_\mathbf{f}\) :

Impulse due to friction (kg m/s)

n,t :

Normal and tangential unit vectors (m)

\(\gamma , \delta \) :

Angles of incidence and rebound (deg)

\(\psi _{1}\) :

Tangential to normal pre-rebound velocity ratio

\(\psi _{2}\) :

Tangential post-rebound velocity to normal pre-rebound velocity ratio

\(\varepsilon _\mathrm{rot}\) :

Ratio between the post-impact rotational energy and the initial kinetic energy

\(\varepsilon _\mathrm{trans}\) :

Ratio between the post-impact translational energy and the initial kinetic energy

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Acknowledgments

Financial support is gratefully acknowledged from the Spanish government (MEC) Project CTQ2011-28079-CO3-02 which is also supported with ERDF funds.

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  1. Department of Analytical Chemistry, University of Valencia, Dr. Moliner, 50, 46100 , Burjassot, València, Spain

    Antonio Doménech-Carbó

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Correspondence to Antonio Doménech-Carbó.

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Doménech-Carbó, A. On the tangential restitution problem: independent friction–restitution modeling. Granular Matter 16, 573–582 (2014). https://doi.org/10.1007/s10035-014-0507-3

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