Analysis of dynamic similarity and energy-saving mechanism of the grinding process in a horizontal planetary ball mill

• Fundamental motion equation, impact time and detaching trajectory were gotten.
• Equal impact potential energy brings equal grinding effect.
• Two types of mills were compared through dynamic similarity principles.
• Quantitative relationships of these two mills were acquired after comparison.

In this paper, we discretized the ball motion in a horizontal planetary ball mill, the fundamental equation of the relative motion and the detaching trajectory were analyzed, and the impact time was approximately formulated. We performed experiments on impact comminution and observed that an equal impact potential energy causes an equal grinding effect. Based on theoretical analysis, comparing the horizontal planetary ball mill whose planetary factor is z with the traditional ball mill through dynamic similarity principles, the results show that when dynamic similarity exists and when the grinding outputs of each mill are equal to each other, the radius of horizontal planetary ball mill is z−1/4 times as the radius of a traditional ball mill. If the impact potential energies of the balls in these two mills are the same, the impact stress of the balls in a horizontal planetary ball mill is z times as in a dynamic similarity traditional ball mill. To determine the equal grinding effect, the energy consumption of a horizontal planetary ball mill is z−3/8 times as that of traditional ball mill.

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