We present a model for simulating normal forces arising during a grind-ing process in cement for single diamond grinding. Assuming the diamond to havethe shape of a pyramid, a very fast calculation of force and removed volume can beachieved. The basic approach is the simulation of the scratch track. Its triangle profileis determined by the shape of the diamond. The approximation of the scratchtrack is realized by stringing together polyhedra. Their sizes depend on both theactual cutting depth and an error implicitly describing the material brittleness.Each scratch track part can be subdivided into three three-dimensional simplicesfor a straightforward calculation of the removed volume. Since the scratched min-eral subsoil is generally inhomogeneous, the forces at different positions of theworkpiece are expected to vary. This heterogeneous nature is considered by sam-pling from a Gaussian random field.To achieve a realistic outcome the model parameters are adjusted applyingmodel based optimization methods. A noisy Kriging model is chosen as surrogateto approximate the deviation between modelled and observed forces. This devia-tion is minimized and the results of the modelled forces and the actual forces fromconducted experiments are rather similar.
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