Abstract
A simplified analytical model of tangential contact engagement, sliding and separation of two elastic, identical spheres is developed assuming the kinematically induced sphere motion trajectory or load controlled sliding motion. The evaluation of driving force during contact sliding motion is determined for both monotonic and reciprocal sliding motion. The analytical formulae and diagrams of driving force versus sliding path are specified for linear and circular paths. The sliding trajectories are also determined for the load controlled programs. The results presented can be applied in the experimental testing of frictional response of contacting bodies, in a wear study of rough surfaces or in the contact interaction analysis of granular material during flow. The results can also be relevant for the development of the discrete element method widely applied in simulation of granular material flow, where the sliding regime conditions prevail in grain contact interaction.
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References
Mindlin R.D., Deresiewicz H.: Elastic spheres in contact under varying oblique forces. J. Appl. Mech. 20, 327–344 (1953)
Lubkin J.L.: The torsion of elastic spheres in contact. J. Appl. Mech. 18, 183–187 (1951)
Deresiewicz H.: Contact of elastic spheres under an oscillating torsional couple. J. Appl. Mech. 21, 52–56 (1954)
Walton K.: The oblique compression of two elastic spheres. J. Mech. Phys. Solids 35, 213–226 (1978)
Vu-Quoc L., Zhang X.: An accurate and efficient tangential force-displacement model for elastic frictional contact in particle-flow simulations. Mech. Mater. 31, 235–269 (1999)
Segalman J.D., Starr J.M., Heinstein H.V.: New approximations for elastic spheres under an oscillating torsional couple. J. Appl. Mech. 72, 705–710 (2005)
Dobry R., Ng T.-T., Petrakis E., Seridi A.: General model for contact law between two rough spheres. J. Eng. Mech. ASCE 117, 1365–1381 (1991)
Jarzębowski A., Mróz Z.: On slip and memory rules in elastic, friction contact problems. Acta Mech. 102, 199–216 (1994)
Aleshin V., VanDen Abeele K.: Hertz–Mindlin problem for arbitrary oblique 2D loading: General solution by memory diagrams. J. Mech. Phys. Solids 60, 14–36 (2012)
Thornton C., Yin K.K.: Impact of elastic spheres with and without adhesion. Powder Technol. 65, 153–166 (1991)
Di Renzo A., Di Maio F.P.: An improved integral non-linear model for the contact of particles in distinct element simulations. Chem. Eng. Sci. 60, 1303–1312 (2005)
Łukaszuk, J., Molenda, M., Horabik, J., Wiącek, J.: Method of measurement of coefficient of friction between pairs of metallic and organic objects. Acta Agrophys. 13, 407–41 (in Polish) (2009)
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Balevičius, R., Mróz, Z. A finite sliding model of two identical spheres under displacement and force control—part I: static analysis. Acta Mech 224, 1659–1684 (2013). https://doi.org/10.1007/s00707-013-0839-9
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DOI: https://doi.org/10.1007/s00707-013-0839-9