On The Mathematical Description Of High-energy Ball Milling Process

High-energy ball milling has broadly used in the preparation of nano-materials, which is categorized into mechanical alloying and mechanical milling. The core object of the theoretical research on high-energy ball milling is to predict the properties of outcome powders, given coefficient of the milling system and property of input materials. A major difficulty of modeling High-energy milling process is its strong nonlinearity, which is believed caused by small-particle effect and cumulative effect.In this study, a nonlinear milling model is constructed with energy efficiency curve as a nonlinear factor of grinding equation, which use fractal dimension as an independent variable to characterize small-size and cumulative effect of particle size distribution. The model is developed from the Markov chain theory and mass balance model of ball milling process.The model is then processed numerical simulation for particulate of single-phase materials with breakage matrices generated from simplified assumptions of ideal brittle and ductile materials. Two simulation models has been build: model 1 with single fractal dimension, and model 2 with two fractal dimensions as coefficient of milling process. The result showed effectiveness of fractal dimension in describing the complexity of powder materials under milling, and priority of model 2 than model 1 with high flexibility and significant representativeness to describe the evolution of particle size distribution and surface area in milling process.Employing ideal assumptions of phase transformation and mechanical alloying, this model is then used to describe the process of phase transformation of two-phase materials and the process of mechanical alloying. By watching the evolution of particle size distribution, surface area and fractal dimension, the physics property is determined and the mechanism of mechanical alloying is characterized.