Power Relationships for Tumbling Mills (8915eaf8-774a-4e16-9e73-503ef0b75ba7)

Based on a simplified model for the motion of particulate materials in horizontal, rotating cylinders, approximate expressions have been derived relating the power consumption of a tumbling mill to its dimensions and speed of rotation and to the amount and nature of the charge. The basic assumptions underlying the model are that there is no slip between the charge and the mill shell, that the free surface of the charge remains essentially planar during rotation, and that there is no transfer of momentum from the material flowing down the free surface back to the mill shell. The relationships formulated from this model have been shown to be in excellent agreement with experimental results taken from the literature. While the requirements of the model are most clearly met at low speeds of rotation, the results appear to be valid even for speeds up to 70-80% of the critical speed. Poorer agreement between theory and experiment is found when the charge consists of relatively large particles (balls) and when the filling of the mill exceeds 50% of the available volume. Qualitative explanations of these deviations have been offered.