Modeling breakage of monodispersed particles in unconfined beds

Mathematical models of grinding mills and crushers are undergoing significant advances in recent years, demanding ever more detailed information characterizing ore response to the mechanical environment. In a mechanistic model of a comminution machine, the type of characterization data used should cover, as much as possible, the conditions found inside the size reduction machines. This applies to the particle size, the stressing energy and rates that particles are subject to, the breakage mechanism and the level of interaction of the particles during stressing, which all must be described appropriately. Whereas, a very large number of experimental techniques and published data exist that allows understanding and quantitatively describing the response of single particles to stressing, comparatively little information exists on the breakage of particles contained in beds. The present work investigates breakage of particle beds impacted by a falling steel ball in unconstrained conditions, such as those that are likely to be found in tumbling mills. The influences of particle size, impact energy, ball size and bed configuration are investigated for selected materials and a mathematical model is proposed that describes the influence of all these variables. The key element of this model is that it allows predicting breakage in monolayer unconfined particle beds with a combination of single-particle breakage data and functions that describe energy partition and volume of material captured in the bed. This model has been calibrated and validated using data from quartz, granulite, limestone and a copper ore, with good agreement.

Research highlights► A model that describes breakage in monolayer particle beds has been developed on the basis of information from single-particle breakage and quantitative descriptions of volume captured and energy split among particles captured. ► It predicts breakage in beds that range from an individual particle to a monolayer bed. ► It allows estimating the volume of the contact area as a function of ball diameter and stiffness, particle size and material strength and stiffness. ► The model developed describes the decreasing fracture probability of particles as they are positioned away from the impact.