An analytical model to study the effect of asperity geometry on forces in ploughing by an elliptical asperity. (September 2019) - Mishra, Tanmaya; de Rooij, Matthijn; Shisode, Meghshyam; Hazrati, Javad; Schipper, Dirk J.
Abstract: 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. Highlights: The model computes forces on an elliptical asperity ploughing a substrate due to substrate deformation and interfacial shear. Normal and tangent vectors for an asperity surface element calculated in terms of its projected areas in polar coordinates. Elemental forces integrated over the contact region to compute net force on ellipsoidal and elliptic-paraboloid asperities. Friction forces acting on elliptical asperities are compared with cases of similar asperity geometries in the literature. Effect of asperity size, ellipticity ratio and orientation in regard to sliding direction on ploughing forces is discussed.