圆筒形容器中球形颗粒食品堆放压力和摩擦力的预测

Prediction of Pressure and Friction Force of Spherical Particulate Food in Cylindrical Container

本实验建立了圆筒形容器中球形颗粒食品的堆放模型来预测其堆放压力与摩擦力。首先假设相同尺寸的球形颗粒准六边形结构堆放。接着推导出颗粒的力的平衡方程和力的逐层传递方程,并给出颗粒间正压力、摩擦力、颗粒与容器间正压力逐层传递公式。数值计算结果表明,颗粒间正压力、颗粒与容器间正压力、颗粒间摩擦力随深度的增加而增大;颗粒间正压力、颗粒与容器壁间正压力随内摩擦角增大而减小,但颗粒间摩擦力、颗粒与容器底部间正压力随内摩擦角增大而增大,在同一个深度,颗粒间正压力、颗粒与容器间正压力随圆筒形容器的直径增大而增大;颗粒间正压力、颗粒与容器间正压力随圆筒形容器壁摩擦系数的增大而减小;颗粒间正压力、颗粒与容器壁间正压力随堆密度的减小而减小,但颗粒间摩擦力、颗粒与容器底部间正压力随堆密度的减小而增大;颗粒间正压力、颗粒与容器间正压力比颗粒间摩擦力大得多,是它的2.66～26.33倍,颗粒与容器底部间正压力比其上一层颗粒间的正压力及颗粒与容器壁间正压力大得多,是它们的1.74～1.89倍。

In this study, a model of particulate packing was established to predict pressure and friction force of spherical particulate food in cylindrical container. The model assumed that equal-sized spherical particles of food are parked in a quasihexagonal structure and divied into many layers. Force equilibrium and transfer equations were derived for each layer and solved consecutively to determine normal pressures and friction forces between two particles and between particle and container. The numerical results showed that as depth of particulate food increases the normal pressures and friction forces between two particles and between particle and container increase. As internal friction angle of particulate food increases, normal pressures between two particles and between particle and container wall decrease, but friction forces between two particles and normal pressures between particules and bottom of container increase. As diameter of container increases, normal pressures between particles and between particle and container increase in the same height. As coefficient of friction of container wall increases, normal pressures between two particles and between particle and container decrease. As apparent density of particulate food decreases, normal pressures between two particles and between particle and container wall decrease, but friction forces between two particles and normal pressures between particules and bottom of container increase. Normal pressures between two particles and between particle and container are 2.66 to 26.33 times of friction forces between two particles, and normal pressures between particules and bottom of container are 1.74 to 1.89 times of normal pressures between two particules and between particules and wall of container in the layer above bottom.