Model based optimization of a statistical simulation model for single diamond grinding

Abstract

We present a model for simulating normal forces arising during a grind- ing process in cement for single diamond grinding. Assuming the diamond to have the shape of a pyramid, a very fast calculation of force and removed volume can be achieved. The basic approach is the simulation of the scratch track. Its triangle profile is determined by the shape of the diamond. The approximation of the scratch track is realized by stringing together polyhedra. Their sizes depend on both the actual cutting depth and an error implicitly describing the material brittleness. Each scratch track part can be subdivided into three three-dimensional simplices for a straightforward calculation of the removed volume. Since the scratched min- eral subsoil is generally inhomogeneous, the forces at different positions of the workpiece 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 applying model based optimization methods. A noisy Kriging model is chosen as surrogate to approximate the deviation between modelled and observed forces. This devia- tion is minimized and the results of the modelled forces and the actual forces from conducted experiments are rather similar.