中文摘要：

建立球形磨粒在空间随机运动的数学模型,提出创建三维砂轮数值模型的方法。提取仿真砂轮的表层磨粒以生成虚拟砂轮形貌,依据振动模型确定的磨粒中心坐标,将球形磨粒转化为不规则六面体进行统计分析。以单点金刚石笔为修整工具,建立修整模型并将其引入砂轮形貌生成过程之中。利用激光传感器测量实际砂轮形貌的磨粒分布规律,并将试验统计数据与同特征的仿真结果相比较,分析两结果之间的区别和联系。通过计算磨粒突出高度、磨粒间距等评价参数,讨论砂轮形貌修整前后的差异,测量和仿真的结果表明：在初始砂轮形貌中,磨粒突出高度呈正态分布,修整后则近似均匀分布,大部分磨粒间距分布在0.2～0.6 mm,为进一步探讨砂轮形貌对磨削工件的影响提供了依据。

英文摘要：

Based on the random spatial movement of grains, a numerical approach is proposed for a grinding wheel 3D model while regarding the shape of grains as a sphere. The grains located on the grinding wheel surface are extracted to generate a visual topology as a function of x, y, z and the sphere grain model is converted into an irregular hexahedron. The dressing process is modeled as well in terms of a single point diamond. This grinding wheel characters are calculated through measuring its topology with a laser sensor, which are used to experimentally validate the simulation results. The estimated parameters for grinding wheels, such as grains protrusion height, grains spacing, are compared to discuss the difference between the experimental and numerical results. The frequency of grains protrusion height is approximately normal distribution prior to being dressed, and it is conditionally converted into uniform distribution after dressing. The spacing represented by most grains is from 0.2 mm to 0.6 mm. This grinding wheel model and its corresponding dressing approach are successfully validated, and that provides a valuable basis for investigating its effect on the ground workpiece surface.