Experimental Quantification of Impact Force and Energy for Mechanical Activation in Vibratory Ball Mills

This research study develops and validates a force model linking vibratory ball mill parameters such as milling frequency, ball/vessel material, fill ratio, and geometry to measurable impact forces. Using embedded piezoresistive sensors, we measured real-time force ensembles and compared results with an adjusted Hertzian contact model, finding strong agreement. Simulations showed minimal kinetic differences between using mean force and full force distributions for simple reactions. Applying the model to the Knoevenagel condensation of vanillin and barbituric acid revealed that higher milling frequencies yield diminishing energy efficiency, highlighting the need for an optimal balance between collision intensity and productive energy use.

本研究构建并验证了一款力模型，该模型将振动球磨机（vibratory ball mill）的关键参数——研磨频率、球磨介质/罐体材质、装填率及几何构型——与可量化的冲击力建立关联。本研究通过嵌入式压阻式传感器（piezoresistive sensors）采集实时力系综数据，并将实测结果与修正后的赫兹接触模型（Hertzian contact model）进行比对，二者契合度极佳。模拟实验表明，针对简单反应，采用平均力与完整力分布开展计算时，动力学差异极小。将该模型应用于香兰素（vanillin）与巴比妥酸（barbituric acid）的克诺文格尔缩合反应（Knoevenagel condensation）后发现，研磨频率越高，能源效率的提升幅度越趋平缓，这凸显出需在碰撞强度与有效能源利用之间寻求最优平衡的必要性。