Modelling of Grain Motion for Three-body Abrasion

Surface formation for three-body abrasion is essentially more difficult to model than for two-body abrasion. In contrast to grains embedded in the polishing pad and therefore time-invariant tool geometry for two-body abrasion, here a variable tool geometry is prevailing as a result of the rolling abrasive grains. Nevertheless, three-body abrasion is an important abrasive process in the surface finishing of glass and ceramics and the modelling of the surface formation for mechanical abrasive machining with loose grains is required for a better process understanding and enhanced process design.The modelling of the surface formation for three-body abrasion is dealt with by splitting the integral removal volume under the polishing pad into the removal of single grains and distributing the total polishing force according to the interaction of individual grains with the workpiece material. This new methodical approach intends to determine the material removal in discrete time steps for every grain and further on the generated new surface topography. Data from polishing experiments like concentration and form of abrasives, polishing load, surface topography and integral removal are applied to set up this analytic-empiric model. Crucial elements of this model are the geometry of single grains, their rolling motion under load and the principle of material removal. In this paper the simulation of the rolling motion of single abrasive grains using a numerical time step model is introduced.