Analytical Modelling of Combined Slip and Sliding Modes in Contact Interaction of Two Spherical Grains

The analytical modelling of coupled slip and sliding contact response of two elastic spheres is presented for the kinematically imposed sphere centre relative motion trajectories. One sphere is assumed as a fixed, the other translating along a specified trajectory and remaining in contact condition. Two cases are considered, the first is corresponding to a linear trajectory with the contact engagement in the combined slip-sliding mode, the other is related to the contact initiation by normal loading and subsequent motion along an inclined linear trajectory. The formulae and diagrams of the evolution of driving force along the sliding path in terms of main contact geometry parameters were analytically specified. Further extensions and applications of the analysis can be envisaged in the creation of the translation controlled apparatus for the measurements of friction and restitution coefficients for the pair of spherical grains.