Motion analysis of a tumbling ball mill based on non-linear optimization

Non-linear optimization, a technique of numerical analysis, is applied to motion analysis of ball media in a tumbling ball mill. The basic principles of optimization are explained. The motion equations of ball media are established. The point of maximum energy is computed, and this maximum energy is 2.34% greater than the energy at the point of maximum falling height. The distribution graph of media collision energy shows that this is a multi-limit problem. We propose to define the total potential energy of charge as the accumulation of energy of all dropping points. Optimization of the parameters related to the total potential energy demonstrates that the point of maximum total potential energy does not depend on the mill size. The operation parameters are optimized with the total collision energy of the ball media per unit time as the objective function. The total collision energy of the ball media per unit time under the optimal operation parameters is increased significantly.