Material removal by fixed abrasives following curved paths

This paper proposes a method for computing the removal of material as the abrasive tool follows a path on a three-dimensional surface. The method assumes that the pressure distribution is Hertzian at the contact between the tool and the surface and that the abrading rate follows the Archard wear law. The focus is on the effect of the path curvature on the profile of material removal. Simulation examples are included to illustrate the proposed method. Results indicate that the material removal profile is affected by the geodesic radius of curvature of the tool path. When the radius is large, the profile is almost parabolic. As the radius is reduced, the location of maximum material removal is shifted towards the centre of the geodesic curvature. Moreover, the location can be at the bound of the profile for very small values of the radius.