Profile accuracy and surface quality of microstructural array mold generated by ultra-precision machining are the premise of precision glass molding technology. Most optical applications of microstructural array mold need to obtain microstructures with sub-micron profile accuracy and nanoscale surface roughness. However, the structural characteristics of grinding wheel and array leads to the complexities of surface generation in envelope grinding. Experimental verification is time-consuming and laborious. In this paper, a multi-scale model is proposed to predict the surface topography of micro-aspherical-cylindrical structural array (MACSA) mold ground by different tool paths. Firstly, the ultrathin grinding wheel is reconstructed by considering the distribution characteristics of abrasive grains and the complex wheel profile. In this process, the grain distribution characteristics of the reconstructed grinding wheel are obtained by using the Johnson transformation the inverse Johnson transformation method. Then, a comprehensive model is established to understand the mechanism of the generation of the MACSA surface, which considers the wheel topography, the kinematics model of abrasive grains and the complex geometric conditions between tool and local surface profile in envelope grinding. The surface morphologies of MACSA obtained by simulation and experiment are coincident with each other very well. The simulation model is further verified by comparing the power spectral density (PSD) of the experimental and simulated surfaces. Based on the simulation and the experimental results, the effect of three tool path planning methods (constant step, constant arc length and constant scallop-height) on surface uniformity and profile accuracy is investigated to obtain a more uniform microstructural surface.

超精密加工产生的微结构阵列模具的型面精度和表面质量是精密玻璃成型技术的前提。微结构阵列模具的大多数光学应用需要获得具有亚微米轮廓精度和纳米级表面粗糙度的微结构。然而，砂轮和阵列的结构特点导致包络磨削中表面生成的复杂性。实验验证费时费力。在本文中，提出了一种多尺度模型来预测不同刀具路径下的微非球面圆柱结构阵列（MACSA）模具地面的表面形貌。首先，考虑磨粒的分布特征和复杂的砂轮轮廓，对超薄砂轮进行改造。在这个过程中，采用约翰逊变换和约翰逊逆变换的方法，得到了重构砂轮的晶粒分布特征。然后，建立一个综合模型来理解MACSA表面的生成机制，该模型考虑了砂轮形貌、磨粒运动学模型以及包络磨削中刀具与局部表面轮廓之间的复杂几何条件。模拟和实验得到的MACSA表面形貌非常吻合。通过比较实验和模拟表面的功率谱密度 (PSD)，进一步验证了模拟模型。基于仿真和实验结果，三种刀具路径规划方法（等步长、