A finite sliding model of two identical spheres under displacement and force control. Part II: dynamic analysis

Abstract

In Part I of the present study, the static analysis for the sliding of two identical spheres under displacement and force control was carried out. For linear and circular sliding trajectories, the contact traction evolution was analytically specified for both monotonic and reciprocal sliding regimes. Similarly, for the specified gravity loading, the driving force evolution and the sliding path were also determined. In the present Part II of the analysis, the dynamic response for the same sliding modes is presented. The contact traction and velocity evolutions are considered in detail. The analytical formulae are proposed for prediction of the tangential restitution coefficient, critical velocity, and time of contact for the displacement and load-controlled motions. The effects of loading and reloading in reciprocal sliding are also considered with account for the slip and sliding regimes. The generated results have practical aspects and can be implemented in modeling of the asperity and rough surface interaction, wear analysis and also in the development of the numerical discrete element method.

Modeling of combined slip and finite sliding at spherical grain contacts

“…Next, the sphere comes into contact with another bottom sphere and new contact activation begins. Such contact response was experimentally analyzed by Lukaszuk et al [16]. As it can be seen in Fig.…”

“…The tangential viscosity, artificially damping the oscillatory behavior of the sliding sphere during its slow down, is not considered. To this end, the application of the force-slip displacement law for the dynamical contact interaction has been demonstrated in the preceding work [16]. The contact condition is R − y 0 > 0 (where R = R 1 + R 2 , y 0 is the vertical coordinate of the sphere center), and it is supposed that the maximal overlap h 0 value is given; then, y 0 = R − h 0 = const.…”

“…In work [16], the main relationships for dynamic sphere motion have been derived for parameters related to two equal spheres. In these relationships, by applying substitutions k n = k * n and R 5/2 0 = R 5/2 / 4 √ 2 , the derived formulae can be adopted in the case of different radii spheres in contact.…”

“…The semi-analytical model for oblique impacts of elasto-plastic spheres was proposed and verified by FEM and experiments in [14]. In [15,16], analyzing the relative sphere motion along a specified linear trajectory without the initially activated contact zone, it was demonstrated that both normal and tangential forces vary proportionally, generating the continuing evolution of the sliding regime without the initial slip mode.…”