Responding to the variability and irregularity of the size and shape, and the uncertainty spatial location of abrasive in diamond wheel, this paper proposes a better virtual model of diamond grain and a workpiece model containing typical cracks,based on the method of random planes to segment the solid and truncated polyhedron in spherical coordinates. The FEM simulation and experiments are carried out on silicon nitride cutting with single diamond grain. The results show that a good agreement trend between simulations and measured results of grinding force. The relative error is less than 8%. The cutting force decreases with the increases of the rotational speed of the grinding wheel, while increasing along with the increases of the workpiece velocity and the cutting depths. The effect of cutting depth on cutting force is maximum.