Optimization model of charge motion in tumbling ball mills

The basic motion equations of ball media in tumbling ball,mills are analyzed. The influence of slippage of the charge, and the effect of liner lifter upon the charge motion are discussed. A general mathematical model for optimizing the charge motion is established. Taking the operation parameters of the tumbling ball mill, speed ratio, filling ratio and radius of ball media as design variables, and the total collision energy of ball media per unit time as the objective function, operation parameters are optimized under constraints on the power, motion, collision energy and boundary conditions of the variables. An example of optimum design is given which show that the total collision energy of ball media per unit time under the optimized operation parameters is increased 41.3%, the operation speed can reach 85.4% critical speed, and the filling ratio of ball media can reach 54%.