Abstract:  The bounding sphere was usually used to detect the collision of grinding grains in the virtual grinding wheel modeling methods. When the bounding spheres were in contact， there was still a large gap between the abrasive grains， which resulted in a big difference between the virtual and actual grinding wheel surfaces. To solve this problem， a virtual grinding wheel modeling method was proposed based on convex polyhedron collision detection. The mathematical model of the random positions of abrasive grains on the grinding wheel surface was derived in detail. The interferences of grains were judged based on the convex polyhedron collision detection method， and the virtual grinding wheel was finally generated. The virtual grinding wheel surfaces generated by convex polyhedron and bounding sphere collision detections were compared. The improved method may generate virtual grinding wheel with 60% volume fraction of abrasive grains， while the original method may not generate virtual grinding wheel with more than 50% volume fraction of abrasive grains. The results indicate that the improved method may generate a virtual grinding wheel with a higher abrasive volume fraction and more randomness surface. Finally， the virtual grinding wheel surfaces were compared with the actual grinding wheel surfaces， and results show that the virtual grinding wheel surface has the characteristics of actual grinding wheel surface. 

Key words: virtual grinding wheel, random grain, convex polyhedron, collision detection

摘要： 虚拟砂轮建模时大多采用包围球对磨粒进行碰撞检测，而包围球相互接触时凸多面体磨粒之间仍存在间隙，导致虚拟砂轮表面与实际砂轮表面差异较大，影响后续磨削过程仿真的准确性。针对这一问题，提出了一种基于凸多面体碰撞检测的虚拟砂轮建模方法。推导了砂轮表面磨粒随机位置的数学模型，基于凸多面体碰撞检测判断磨粒干涉状况，最终生成虚拟砂轮。对基于凸多面体和包围球碰撞检测方法生成的虚拟砂轮表面进行对比分析，发现前者的磨粒位置更具随机性，且可以生成磨粒率为60%的虚拟砂轮，后者则不能生成磨粒率大于50%的虚拟砂轮。最后将虚拟砂轮与真实砂轮进行对比分析，结果表明虚拟砂轮与真实砂轮的表面特征一致，证明了该方法的优越性。

关键词: 虚拟砂轮, 随机磨粒, 凸多面体, 碰撞检测