Modeling virtual abrasive grain based on random ellipsoid tangent plane

In the previous studies about grinding simulation, most of the abrasive grain models are simple geometries. The shape and size of the abrasive grain are varied, which will lead to the difference between the simulation and the reality. To make the virtual abrasive grains closer to reality, a stochastic polyhedral abrasive particle modeling method based on the ellipsoid tangent plane is proposed. Based on the ellipsoid model, the vertex coordinate equations of abrasive grain are derived. The 3D normal distribution is used to generate uniform random tangent points on the ellipsoid. The shape characteristics of normal virtual abrasive grains were analyzed, and the abnormal abrasive grains were corrected. The diameter of the minimum enclosed ball is used to calculate the equivalent diameter of the abrasive grain. According to the normal distribution, the abrasive grain sizes are scaled to the actual sizes. The coordinate transformation makes the abrasive grains more diverse. Finally, the influence of each input parameter on the virtual abrasive grain shapes is analyzed. And the shape distribution of actual and virtual abrasive grains is compared. The results show that the abrasive grain shape distribution can be effectively controlled through different generation strategies, and the model can simulate the actual abrasive grains effectively through the specific input strategy.