A modified three-dimensional quasi-wet discrete element method (DEM), which is constructed by adding the drag force and buoyancy and the velocity dependence of the friction coefficient of a ball to a conventional dry DEM model, is proposed for analyzing the impact energy of balls in wet ball-milling processes. A comparison of the calculated ball motion in water as the liquid medium with the experimental results demonstrated the validity of the proposed model. The friction coefficient decreased with the increase in the vessel rotational speed and was expressed as a function of the rotational speed and loading amount of the balls. The velocity dependence of the friction coefficient was similar to the variation in the friction coefficient with the sliding velocity, as derived from the lubrication theory. A numerical analysis of the impact energy distribution in the vessel showed that relatively high-impact energies of the balls were intensively generated near the vessel wall, indicating that the wet ball-milling processes were controlled by the impact energy between the ball and the wall. Our model can contribute to reducing the calculation load for simulating the ball motion in wet ball-milling processes compared with the coupling models such as DEM-CFD.

提出了一种改进的三维准湿离散元方法（DEM），该方法通过将阻力和浮力与球的摩擦系数的速度相关性添加到常规干DEM模型中来构造，以分析冲击能量在湿式球磨过程中的球。将水作为液体介质的水球运动与实验结果进行了比较，证明了该模型的有效性。摩擦系数随着容器转速的增加而减小，并表示为球的转速和负载量的函数。摩擦系数的速度依赖性类似于润滑理论中摩擦系数随滑动速度的变化。对容器中冲击能量分布的数值分析表明，在容器壁附近强烈产生了较高的冲击能量，这表明湿式球磨过程受球与壁之间的冲击能量控制。与DEM-CFD之类的耦合模型相比，我们的模型可以帮助减少用于模拟湿式球磨过程中球运动的计算量。