Multi-layer kinematics and collision energy in a large-scale grinding mill-the largest semi-autogenous grinding mill in China

Using the largest semi-autogenous grinding mill in China as a model, collision energy was analyzed on the basis of the multi-layer kinematics of the steel balls. First, the kinematic equation of the steel balls was obtained by considering the multi-layer characteristics of the steel balls. Second, the collision energy of the inner-layer steel balls was addressed according to its kinematic characteristics. Finally, the total collision energy per unit time was obtained. Results show that the leaving angle decreases as the mill speed ratio increases and as the radius ratio increases, but the leaving velocity increases linearly. Moreover, a discontinuity point of the tangential collision velocity occurs at an angle factor beta = 0, and the angle factor b is divided into two intervals: [-3, 0] and [0, 1.5]. The leaving angles corresponding to a tangential velocity equal to zero are calculated to be 1.185 and 0.7854 rad in the two intervals. In addition, the sum collision velocity increases when b is less than zero, but it decreases sharply above zero. The maximum total collision energy per unit time occurs at 84.2% of the mill speed corresponding to the optimal mill speed ratio.