Frictional viscoelastic based model for spherical particles collision

In this paper, collision of two balls in three dimensions with regard to energy loss and friction is studied. This investigation intends to propose the procedure which can determine the condition of pure sliding, sliding with rolling or sticking, and rolling or sticking at the beginning of contact. Furthermore, the other aim of this research is to suggest the closed-form relation for post-collision angular and linear velocities in which the possibility of three regimes of impact, pure sliding, sliding with rolling, and pure rolling, are considered. In this investigation, viscous Hertz contact force describes the normal interaction force. Moreover, stick regime is not taken into account and during sliding, Coulomb friction is considered as a tangential force, which is endorsed by collision experimental data in case the collision regime is not stick regime. Considering aforementioned issues along with employing momentum conservation, the condition for the possibility of transformation of sliding to sticking or rolling during collision, and furthermore, the analytical relation for post-collision velocities are achieved. Eventually, in order to demonstrate the procedure of solving two balls collision, numerical examples are presented.