Analysis of oblique rebound using a redefinition of the coefficient of tangential restitution coefficient

Abstract A redefinition of the coefficient of tangential restitution based on the separation of friction and restitution effects is presented. Using this modified coefficient of tangential restitution and the usual definitions of the coefficients of normal restitution and sliding friction, a description of oblique impacts in both stick and slip regimes is obtained. This, description, which is tested with available rebound data in literature, avoids sharp (apparent) variations in the coefficient tangential restitution with impact angle and can justify anomalous results reported by Calsamiglia et al. (1999) .

[1]  Melany L. Hunt,et al.  Oblique particle–wall collisions in a liquid , 2004, Journal of Fluid Mechanics.

[2]  François Rioual,et al.  Experimental study of the bouncing trajectory of a particle along a rotating wall , 2009 .

[3]  Raymond M. Brach,et al.  Friction, Restitution, and Energy Loss in Planar Collisions , 1984 .

[4]  A. Doménech Non-smooth modelling of billiard-and superbilliard-ball collisions , 2008 .

[5]  A. Ruina,et al.  A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations , 1998 .

[6]  Analysis of two-disc collisions , 1993 .

[7]  Colin Thornton,et al.  A semi-analytical model for oblique impacts of elastoplastic spheres , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  Ahmad H. Kharaz,et al.  The measurement of particle rebound characteristics , 2000 .

[9]  T Pöschel,et al.  Coefficient of tangential restitution for viscoelastic spheres , 2008, The European physical journal. E, Soft matter.

[10]  A. Ruina,et al.  Anomalous Frictional Behavior in Collisions of Thin Disks , 1999 .

[11]  Agba D. Salman,et al.  An experimental study of the elastic rebound of spheres , 2001 .

[12]  Stefan Heinrich,et al.  Energy absorption during compression and impact of dry elastic-plastic spherical granules , 2010 .

[13]  Michel Y. Louge,et al.  Measurements of the collision properties of small spheres , 1994 .

[14]  J. N. Fawcett,et al.  THE REBOUND OF ELASTIC BODIES IN OBLIQUE IMPACT , 1977 .

[15]  A. Chatterjee,et al.  Anomalous Frictional Behavior in Collisions of Thin Disks Revisited , 2008 .

[16]  T. Kane,et al.  An explicit solution of the general two-body collision problem , 1987 .

[17]  L. Vu-Quoc,et al.  An elastoplastic contact force–displacement model in the normal direction: displacement–driven version , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  Andrés D. Orlando,et al.  Effect of rolling friction on binary collisions of spheres , 2010 .

[19]  Loc Vu-Quoc,et al.  An accurate elasto-plastic frictional tangential force-displacement model for granular-flow simulations: Displacement-driven formulation , 2007, J. Comput. Phys..

[20]  M. Oda,et al.  Rolling Resistance at Contacts in Simulation of Shear Band Development by DEM , 1998 .