An analytical model to study the effect of asperity geometry on forces in ploughing by an elliptical asperity

An analytical ploughing model is used to compute the forces on a rigid, elliptical, i.e. ellipsoid and elliptic-paraboloid shaped, asperity sliding through a rigid-plastic substrate as a function of its axes size, ellipticity ratio and sliding orientation. The normal force due to the plastic deformation of the substrate and the tangential force due to the shearing of the asperity-substrate interface are calculated from the surface normal vector and the tangent vector along the direction of plastic flow. The elemental forces are integrated over the boundaries of the asperity-substrate contact to obtain the individual force components. In this way, an analytical model to study the effect of asperity geometry on ploughing forces has been developed and compared with the available theories.