N. Djordjevic

Discrete element modelling of the influence of lifters on power draw of tumbling mills

Crushing and grinding are the most energy intensive part of the mineral recovery process. A major part of rock size reduction occurs in tumbling mills. Empirical models for the power draw of tumbling mills do not consider the effect of lifters. Discrete element modelling was used to investigate the effect of lifter condition on the power draw of tumbling mill. Results obtained with PFC3D code show that lifter condition will have a significant influence on the power draw and on the mode of energy consumption in the mill. Relatively high lifters will consume less power than low lifters, under otherwise identical conditions. The fraction of the power that will be consumed as friction will increase as the height of the lifters decreases. This will result in less power being used for high intensity comminution caused by the impacts. The fraction of the power that will be used to overcome frictional resistance is determined by the materials coefficient of friction. Based on the modelled results, it appears that the effective coefficient of friction for in situ mill is close to 0.1

Discrete element modelling of power draw of tumbling mills

Abstract The power required to operate large mills is typically 5–10 MW. Hence, optimisation of power consumption will have a significant impact on overall economic performance and environmental impact. Power draw modelling results using the discrete element code PFC3D have been compared with results derived from the widely used empirical model of Morrell. This is achieved by calculating the power draw for a range of operating conditions for constant mill size and fill factor using two modelling approaches. fThe discrete element modelling results show that, apart from density, selection of the appropriate material damping ratio is critical for the accuracy of modelling of the mill power draw. The relative insensitivity of the power draw to the material stiffness allows selection of moderate stiffness values, which result in acceptable computation time. The results obtained confirm that modelling of the power draw for a vertical slice of the mill, of thickness 20% of the mill length, is a reliable substitute for modelling the full mill. The power draw predictions from PFC3D show good agreement with those obtained using the empirical model. Due to its inherent flexibility, power draw modelling using PFC3D appears to be a viable and attractive alternative to empirical models where necessary code and computer power are available.

Origin of blast-induced fines

The generation of fines during blasting has intrigued researchers and practitioners for some considerable time. Fines are generally considered to be fragments smaller than 10 mm, but in some applications the cutoff size is more explicit. In the case of iron ore fines are considered to be particles less than 6.3 mm, and in the case of coal less than 1 mm. There is thus a need for a more general definition of fines. It is considered here that fines are particles that are much smaller than the median or mean fragment size produced by blasting and that they are also created predominantly by shear failure of the rock mass, whereas coarser particles are created by tensile failure of the rock. Tensile failure tends to be the dominant mode of blast-induced rock mass fragmentation on account of the inherently low tensile strength of a rock mass. The Kuz–Ram model for prediction of blast-induced fragmentation does not consider fines separately from the coarse particles.1 As result, its application almost always results in a significant underestimate of the amount of fines. The literature on blasting describes models that aim to predict the amount of fines. Some of these models are based on calculation of the extent of failure around the blasthole, using equations from the theory of elasticity for a thick-wall cylinder under static internal pressure2 combined with the Kuz–Ram model for coarse fragments. Another method is based on the testing of large rock lumps in a blast chamber.3 The fraction of fines is defined from the change of slope of the fragment size distribution when the distribution is presented in a double logarithm coordinate system. Extrapolation to in-situ conditions is based on the amount and type of explosive employed in the laboratory relative to that used in practice and makes use of the concept of strain energy factor coupled with the empirically derived part of the Kuz–Ram model. Although this approach clearly provides a sounder base for modelling, it also frequently underestimates the amount of fines found after blasting. The principal reason is associated with the representativeness of a large rock lump in relation to the in-situ rock mass. As part of blast fragmentation research projects the Julius Kruttschnitt Mineral Research Centre conducted a large number of small-scale blasting tests on rock and concrete samples. In the course of that work numerical modelling of the rock fragmentation process was also carried out with the continuum finite-difference code FLAC and discrete-element modelling code PFC3D.

Discrete element modelling of lifter stresses in tumbling mill

Abstract The discrete element code PFC3D has been used to model lifter stresses within a large tumbling mill. The intensity of the induced stresses (shear and normal) is directly proportional to the intensity of lifting action and liner/lifter wear. Results show that, for the modelled case, the magnitude of the stresses decreases as the number of lifters increase. Hence, longer intervals between relining can be expected for a mill with a larger number of lifters. However, it appears that beyond a critical number, a further increase in the number of lifters will not result in significant further reduction of stress. Distribution of the impact energy is also affected by the number of lifters. With very few lifters, the dominant form of energy consumption will be low intensity abrasion events. With larger numbers of lifters, high intensity impacts will be more frequent. Net power draw will be at a minimum for very small numbers of active lifters. As the number of lifters increases, power draw increases and eventually reaches a relatively stable value. Further work will be required to investigate the effect of lifter shape on the induced stresses. It appears to be possible to determine the number and shape of lifters that will result in the optimal power draw, while simultaneously minimising liner/lifter wear.