Identification of energy efficiency of ore grinding and the liner wear by a three­phase motion of balls in a mill

We have analytically derived an equation that relates the technological parameters of a ball mill, grinding material, to the parameters of a rod primary converter of energy efficiency of ore grinding. By using a method of applying a basic rod primary converter with a large cross-sectional area, at the side end of which large pieces of ore are destroyed at balls impacts, and an additional rod converter with identical parameters and a smaller cross-sectional area, which interacts only with balls, we have achieved invariance in determining the energy efficiency of ore grinding by a ball mill to a change in the motion speed of grinding bodies. We have analytically derived a mathematical model of energy-saving ore grinding by a ball mill with a three-phase motion of grinding bodies, invariant to a change in the length of rods during wear. The model can estimate the energy efficiency of grinding larger pieces of ore based on the resulting volume of crushed large-lump material. The mathematical model includes such constants as the cross-sectional areas of rod primary converters, the initial length of rod primary converters, the length of a basic section of strain gauges arrangement, the value for Young's modulus of the primary converters' material, as well as the changing constants that are defined by the ground material. In addition, the dependence has been derived analytically for determining the length of a main rod primary converter, based on which one can estimate the height of a liner, which wears out in the course of operation. We have devised a functional circuit for the automated control system of energy efficiency of ore grinding by a ball mill that makes it possible to obtain estimation parameters using modern microprocessor tools. According to the devised circuit, one can build algorithms for determining the volume of ore to be crushed, as well as the thickness of a liner in a ball mill, which open up an avenue for developing software products. Computer simulation has proven the possibility of applying the proposed method in order to estimate energy efficiency of ore grinding by a ball mill with a three-phase ball motion. We have established high sensitivity of the proposed approach to a deviation in energy efficiency of ore grinding from the best value. A possibility to estimate the parameter with a relative error of ±2.5 % has been confirmed.