Exploring Tumbling Mill Dynamics Through Sensor Development

Though inefficient, tumbling mills play an important role in modern mineral processing. By virtue of the mill's action, the internal forces make instrumentation of the mill difficult. One solution to this problem is the use of an instrumented ball. An instrumented ball, equipped with an accelerometer, rotation rate sensors and a temperature sensor has been built. The instrumented ball and a camera system are used to measure the state of the charge within a laboratory mill. Also, a discrete element model (DEM) of the laboratory mill, a type of simulation, is written. From the distributions and moments of the energy terms of the charge (the material within the mill), the simulation and experimental results are analyzed and compared. The moments are used to tune the DEM, such that the simulation results are in agreement with the experimental results. A model order, a measure of DEM accuracy, is defined. Based on concepts borrowed from thermodynamics and statistical mechanics, mill entropy is calculated. Critical behavior, similar to a phase transition, is observed in the entropy, mean energy and energy fluctuation. From this, another definition of the critical speed is introduced. The critical speed of the mill is defined as the speed about which the entropy, mean energy and energy fluctuations exhibit critical behavior. Unlike other definitions, which rest on geometric and dynamic analyses of the charge, this new definition is based on distributions and moments. Finally, areas requiring more research and development are presented.