Application status of discrete element method in grinding equipment research and parameter optimization
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摘要: 介紹了離散元法（DEM）在磨礦領域的應用背景；解釋了DEM中Hertz-Mindlin 接觸模型和顆粒黏結模型的基本原理；分類綜述了DEM在球磨機、攪拌磨機和自磨機/半自磨機等三類磨礦設備及參數優化研究中的應用現狀；指出了DEM在磨礦領域研究中的獨特優勢及其發展方向。Abstract: Grinding is an important link in the process of mineral processing. This is because whether the useful minerals in the ore can fully dissociate the monomers and the particle size meets the sorting requirements have a decisive effect on the beneficiation index. Over the last two decades, the discrete element method (DEM) has become an important tool for understanding comminution fundamentals and providing theoretical guidance for the design, optimization, and operation of comminution devices. DEM is now widely used in industries where comminution is critical. The application of DEM in simulating fracture, breakage, crushing, milling and equipment wear has become increasingly extensive and complex, resulting in tremendous changes in the understanding of the grinding process. In this article, the application background of DEM in the field of grinding was introduced; the basic principles of two commonly used models in DEM, the Hertz-Mindlin contact model, and the bonding particle model, were explained. Subsequently, the application status of DEM in ball mills, stirring mills and self-mill/semi-automatic mills, and other three types of grinding equipment and parameter optimization research were summarized. Finally, it further pointed out the unique advantages of DEM in the field of grinding and its development direction.
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Key words:
- discrete element method /
- ball mill /
- stirring mill /
- autogenous mill /
- semiautogenous mill
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表 1 接觸模型中使用的彈簧剛度和阻尼系數
Table 1. Spring stiffness and damping coefficients used in the contact model
Coil type Normal direction Tangential direction Spring stiffness constant, K $ {K_{\text{n}}} = \dfrac{4}{3}{E^*}\sqrt {{R^*}{\delta _{\text{t}}}} $ $ {K_{\text{t}}} = 8{G^*}\sqrt {{R^*}{\delta _{\text{n}}}} $ Damping coefficient, C $ {C_{\text{n}}} = 2\sqrt {\dfrac{5}{6}} \dfrac{{\ln \varepsilon }}{{\sqrt {{{\ln }^2}\varepsilon + {{\text{π}} ^2}} }}\sqrt {{m^*}2{E^*}\sqrt {{R^*}{\delta _{\text{n}}}} } $ $ {C_{\text{t}}} = 2\sqrt {\dfrac{5}{6}} \dfrac{{\ln \varepsilon }}{{\sqrt {{{\ln }^2}\varepsilon + {{\text{π}} ^2}} }}\sqrt {{K_{\text{t}}}{m^*}} $ 
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