Grain shape-equivalence method for compliant mechanics modeling and grinding force prediction in robotic belt grinding

Accurate mechanical modeling is essential for robotic belt grinding (RBG), a process characterized by compliant contact mechanisms that make force prediction particularly challenging. However, existing mechanical models predominantly focus on macroscale compliance while neglecting grain-scale compliant motion. Moreover, abrasive grains are typically idealized as regular shapes, overlooking the inherent stochasticity of real grain geometries. This study proposes a shape-equivalence method for modeling stochastic abrasive grains and develops a multiscale compliant force model for RBG. Specifically, an individual grain is represented as a polygonal pyramid with stochastic edges that is mathematically equivalent to a cone; this method unifies the treatment of grain geometries and streamlines the modeling process. The mathematical equivalence relationship for random grain shapes is further derived based on a grain-compliant contact model. By integrating grain geometric characteristics and progressive grain wear, an analytical mechanical model that captures both the static contact force and dynamic grinding force is established, thereby describing the transition from grain-workpiece compliant interaction to belt-workpiece elastic contact. Grinding experiments were conducted using abrasive belts with different grain shape distributions to validate the model. The results demonstrated reliable predictions of the tangential grinding force and its component characteristics. Additional analyses were performed to reveal how the tangential grinding force varies with wear time and grinding parameters.