硅酸盐学报

基于分形理论表征工程陶瓷磨削表面

作者：张彦斌1 林滨1 梁小虎2 亓振良1

单位：1. 工程陶瓷与加工技术教育部重点实验室天津大学天津 300072 2. 天津市特种设备监督检验技术研究院天津 300192

关键词：工程陶瓷分形理论表面形貌磨削加工

分类号：

出版年,卷(期):页码：2013,41(11):1558-1563

DOI：

摘要：

将分形几何理论应用于工程陶瓷磨削表面表征中，通过对盒维数法、变分法、小波变换法及差平均法四种计算分形维数的方法对比发现，变分法最适合计算工程陶瓷磨削表面的分形维数。对各向同性和各向异性的三维分形模型进行了研究，同时考虑到磨削加工表面具有纹理，故用各向异性的仿真表面与实测表面进行对比验证了变分法的有效性。并对金属、氧化锆、氧化铝、氮化硅四种材料磨削轮廓的算术平均偏差Ra和分形维数进行计算，发现Ra与分形维数D之间不是一一对应的关系，陶瓷材料的同一表面测量数次的Ra变化会较大，而分形维数值基本上不变。而且，对于工程陶瓷磨削表面，分形维数高时，纹理精细而密集；分形维数低时，纹理粗大而稀疏。

Fractal method is introduced to characterize the ground surface of engineering ceramics. This work compared four methods to calculate the profile dimension, i.e., box dimension, variation method, wavelet transform method and different-average law method. The results show that the variation method is suitable to calculate the fractal dimension of engineering ceramics ground surface. By the texture, the anisotropic fractal model is suitable to simulate ceramics surface morphology. The validity of the variation method was examined via the comparison of the simulated surface and measured surface. Finally, the fractal dimension of four material specimens, i.e. steel, zirconia, alumina, and silicon nitride was determined. The results show that surface roughness Ra is not correlated to the fractal dimension. Ra will vary even for the same surface after the repeated measurements. However, the fractal dimension does not change. Besides, the texture in engineering ceramics ground surface is fine and dense, at a great fractal dimension. The texture is sparse and coarse at a low fractal dimension.

基金项目：

国家自然科学基金资助项目(51075296)。

作者简介：

参考文献：

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