To study the theoretical relationship between the ore fragmentation energy and the particle size, the multistage crushing test model of magnetite was constructed with the fractal geometry to simulate the general process of magnetite crushing from the initial particle size to the target particle size, and the theoretical relationship between the fragmentation energy and fragment size and fractal dimension was established. Results show that the multistage crushing of magnetite has fractal characteristics, the rate of particle size reduction in the multistage crushing process decreases, and the fractal dimension increases gradually to be a stable value. The cumulative unit fragmentation energy is affected by the fragment size and fractal dimension, which is defined as the ratio of the cumulative fragmentation energy to ore mass. With the increase in the median particle size of the fragments (), the cumulative unit fragmentation energy decreases in the form of exponential function. With the increase in the fractal dimension of the fragment size, the logarithm of the cumulative unit fragmentation energy increases linearly. The smaller the fragment size is, the faster the cumulative unit fragmentation energy changed with the fractal dimension. The larger the fractal dimension of the fragments is, the more significant change in the cumulative unit fragmentation energy with the fragment size is. The mathematical relationship between cumulative unit fragmentation energy, fragment particle size, and fractal dimension is determined.

中文翻译：

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磁铁矿矿石多级破碎过程中能量与粒度的分形关系


为了研究矿石破碎能与粒度之间的理论关系，利用分形几何构建了磁铁矿多级破碎试验模型，模拟了磁铁矿破碎从初始粒度到目标粒度的一般过程，并得到了理论模型。建立了破碎能与碎片尺寸和分形维数之间的关系。结果表明，磁铁矿多级破碎具有分形特征，多级破碎过程中粒度减小率减小，分形维数逐渐增大至稳定值。累积单位破碎能受碎块尺寸和分形维数的影响，定义为累积破碎能与矿石质量的比值。随着碎片中值粒径（）的增加，累积单位碎片能量以指数函数的形式减小。随着碎片尺寸分形维数的增加，累积单位碎片能量的对数线性增加。碎片尺寸越小，累积单位碎片能量随分形维数的变化越快。碎片的分形维数越大，累积单位碎片能量随碎片尺寸的变化越显着。确定了累积单位破碎能、碎片粒径和分形维数之间的数学关系。