用投影轮廓分维中位维表征颗粒群粗糙度的研究

Study on Projected Outline Fractal Dimension Mid-position Fractal Dimension Characterizing Particle Group's Degree of Roughness

为了表征颗粒群粗糙度,本文中构建了单颗粒投影轮廓分维数学模型,并以高精度数字光学显微系统为基础,测算了5种颗粒样品的单颗粒投影轮廓分维。结果表明,5种颗粒样品的单颗粒投影轮廓分维均值从小到大依次为:柴油汽车排气管沉积颗粒、碳黑颗粒、粉煤灰颗粒、石灰性褐土颗粒、河流沉积土壤颗粒。首次提出了"中位维"的概念以表征颗粒群粗糙度,计算了颗粒样品的中位维,其大小排序与投影轮廓分维均值一致,验证了将"中位维"作为表征颗粒群粗糙度的合理性。

In order to characterize the degree of rough of the particle group,a mathematical model to calculate the projected fractal dimensions of particle group was modeled. The projected outline fraetal dimensions of five kinds of particle group samples were measured and calculated based on a high precision digital optics micro-system. The results showed that the average values＇ size sequence of the projected fractal dimensions was diesel car exhaust pipe deposited particles,carbon black particles ,coal ash particles ,the lime drab soil particles and the topsoil of fiver sediment particles respectively. The conception of ＂mid-position fractal dimension＂ was put forward firstly to characterize the degree of roughness of particle group, and the values of the mld-position fractal dimensions are calculated, and their size sequence was in accordance with the projected fractal dimensions＇. So, the rationality of using the fractal dimension to characterize the roughness degree of particle group was proved.