Experimental Research On The Relationship Between Line Fractal Dimension And Volume Fractal Dimension Of Crushing Material

The crushing particle materials, no matter particle size distribution or particle outline, are satisfied with statistical self-similarity and can be characterized by fractal dimension. In this paper, silicon oxide, feldspars and ores power are chosen as crushing materials to calculate the line fractal dimension and volume fractal dimension, thus verifying the relationship between them. Through particle size testing and image data analyzing of the crushing materials, we can get the line fractal dimension and volume fractal dimension. The main work includes the following aspects:(1) The particle materials crushing technology, materials characterization and the application of fractal theory in characterizing particle materials and measuring fractal dimensions is summarized.22 sample materials and 625 particle images of three kinds of crushing materials are tested respectively by the BT-9300H and BT-2000 Laser Particle Size Analyzer. Then with two methods, the experiment data is analyzed and processed.(2) The optimized method of R-R particle size distribution fitting curve of particle materials is discussed. The optimized parameters are characteristic diameter and correlation coefficient of linear regression analysis. The optimization result of the fitting curve is analyzed by the method of comparing the graphic representation and the characteristic parameters. On the basis of R-R distribution fractal theory model, proposed by research group, and MATLAB, the volume fractal dimension is achieved by compiling programs. The results show that volume fractal dimension can be used as a parameter to characterize the broken material.(3) Studying the determination of initial step size and the analysis and process method of particle image outline curve experimental data. Following the yard stick method model, proposed by research group, and MATLAB software, the line fractal dimension of crushing particle materials are achieved by compiling programs. The result shows that the particle image outline has fractal characteristics and is satisfied with statistical self-similarity, the fractal dimension can be a parameter, which characterizes the broken materials; the line fractal dimension fluctuation of the three kinds of materials is less than that of a single sample significantly. This indicates that the line fractal dimension, measured by the yard stick method, is reasonable and feasible.(4) Research in power spectrum method of experiment data of the particle image outline. Based on MATLAB software and the fractal theory of power spectrum, a program to get the line fractal dimension of crushing particle materials is compiled. The result shows that particle image outline has fractal characteristics and is satisfied with statistical self-similarity. The line fractal dimension, achieved by power spectrum method, can be a parameter characterizing the broken materials too; the maximum relative error between the power spectrum method and the yard stick method is 0.9408%; the line fractal dimension comparison of the two methods shows that the yard stick method is relatively stable. The power spectrum method is affected by many factors while analyzing and processing particle outline curve. The accuracy of the line fractal dimension is related to the nature of material.(5) According to the relationship between the line fractal dimension and the volume fractal dimension, we can get a line fractal dimension. It shows that the maximum relative error between the line fractal dimension, calculated with the relationship, and the fractal dimension, achieved with the yard stick method, is 2.1861%, while the maximum relative error between the line fractal dimension, calculated with the relationship, and the line fractal dimension, achieved with power spectrum method is 1.6231%. This testifies that the line fractal dimension model and the volume fractal dimension model are correct and reasonable.