蓝宝石单晶精密磨削表面形貌的分形行为研究

如何合理有效地评价光学晶体微结构表面质量，是目前光学元件精密制造与应用领域面临的重要问题。基于分形理论，采用三维和二维盒计数方法对蓝宝石单晶磨削表面形貌进行了分析，结果表明磨削表面的三维分形维数Ds与表面粗糙度呈反比关系，而且三维分形维数越高表面纹理越精细，三维分形维数越低表面缺陷越多。磨削表面截面轮廓的二维分形维数DL分布规律可以反映材料去除方式的变化。当二维分形维数DL沿磨削方向呈强对称分布时，该磨削表面为延性域去除；若呈弱对称性或不规则分布，则该磨削表面为脆性域去除。研究证实了分形方法不仅可用于综合表征蓝宝石磨削表面形貌，还可用于揭示蓝宝石磨削表面的材料去除机理。

Research on Fractal Behavior of Surface Topography in Precision Grinding of Monocrystal Sapphire

At present, how to evaluate the quality of precision ground surface of optical crystals reasonably and effectively is an important problem for the field of optical element processing and its application. A three dimension (3D) and two dimension (2D) box-counting fractal analysis methods are used to analyze ground monocrystal sapphire surface topography. The results obtained show that the 3D fractal dimension Ds shows a negative correlation with the surface roughness parameter Ra. As the Ds are higher, its topography is more exquisite. For the ground surface with smaller Ds, the pronounced surface defects are exhibited in ground surface. The change of material removal mode can be implied from the distribution of 2D cross-sectional profile fractal dimension DL.。 When the 2D fractal dimension is highly symmetry along the grinding direction, the material removal mode is ductile. When the 2D fractal dimension is weakly asymmetry or irregular distribution, the material removal mode is brittle. This study indicates that the fractal method can not only be used for comprehensive characterization of ground monocrystal sapphire, but also be used to reveal the material removal mechanism of ground monocrystal sapphire.