磨屑破碎及分布的多重分形模拟

基于多重分行理论和磨屑尺寸分布的统计自相似性，建立了磨屑破碎过程的多重分形模型，以数论和矩阵2种方式对磨屑破碎过程和分布进行了论述，并利用多重分形模型对具体工况下磨屑破碎过程和分布进行了模拟，并将模拟结果与实验统计结果进行了对比分析．结果表明，该模型能够较精确的描述磨屑的破碎过程和分布，具有静态（磨屑分布）和动态（磨屑破碎过程）二重性；根据多重分形分形维数表达式所求出的分形维数具有惟一性，体现了多重分形表征磨屑破碎过程和分布的惟一性；该模型对磨屑破碎过程和分布的描述和预测基本不受测量仪器分辨率和取样长度的影响，因而比传统基于统计分析的模型更为合理和有效．

Multiple Fractal of Fragmentizing Process and Distribution of Wear Particles

Based on the multiple fractal theory and the self-comparability of wear particles,a multiple fractal model of the fragmentizing process of an original wear particle was proposed using number and matrix theory.The fragmentizing course and distribution of wear particles were simulated by the multiple fractal model,and the simulant and actual test results were compared.The results show that the multiple fractal model can be used to describe fragmentizing course and distribution of wear particles accurately on static state(contribution of wear particles) and dynamic state(fragmentizing course);the calculated result by multiple fractal dimension formula was one and only,which shows clear fractal characteristic.The multiple fractal model can describe and prognosticate the wear particles fragmentizing and distribution more reasonably and effectively than traditional models based on statistics.