On geometry and kinematics of abrasive processes: The theory of aggressiveness

Due to the stochastic nature of the abrasive-tool topography, abrasive processes are difficult to model and quantify. In contrast, their macro geometry and kinematics are usually well defined and straightforwardly controlled on machine tools. To reconcile this seeming contradiction, a novel unifying modelling framework is defined through the theory of aggressiveness. It encompasses the arbitrary geometry and kinematics of a workpiece moving relative to an abrasive surface. The key parameter is the point-aggressiveness, which is a dimensionless scalar quantity based on the vector field of relative velocity and the vector field of abrasive-surface normals. This fundamental process parameter relates directly to typical process outputs such as specific energy, abrasive-tool wear and surface roughness. The theory of aggressiveness is experimentally validated by its application to a diverse array of abrasive processes, including grinding, diamond truing and dressing, where the aggressiveness number is correlated with the aforementioned measured process outputs