مقاله ای دیگر با عنوان The impact of end-wall effect on the charge trajectory in tumbling model mills در مجله بین المللی International Journal of Mineral Processing منتشر شد. نویسندگان این مقاله آقایان دکتر مصطفی مالکی مقدم، مهندس علیرضا قاسمی، دکتر محسن یحیایی و دکتر صمد بنیسی هستند.
Direct observation of the charge shape and its motion in industrial mills is not possible, it is then customary to use transparent end, small-scale mills (i.e., model mills) to determine the charge trajectory directly by visualization methods. Because of a short length of the model mills, the end-wall effects could introduce a significant bias on the observed charge trajectories and shape. In this research, the end-wall effect was investigated by gradually increasing the model mill length and analysing the charge trajectory and shape variation at given operating conditions (i.e., ball filling, mill speed, liner type). The special design of the model mill with the diameter of 100 cm made it possible to increase the mill length in steps of 3.6 cm up to 21.6 cm. Four types of liners, five steel ball fillings (10, 15, 20, 25, 30% v/v) and three mill speeds (55, 70, 85% of critical speed) were tested. The results indicated that when the mill length was below 10.8 cm the end-walls prevented the charge from free falling. This resulted in lower impact point angles and lower power draws compared with the case of no end-wall effect. When the same experiments were performed using an iron ore instead of balls with the same size range, the impact of end-wall effect was more pronounced. For a mill length of 3.6 cm, an increase of 30% in the speed (from 55 to 85%) with the iron ore charge, the torque decreased by 41% (from 3.7 to 2.2 kgf·m) when mill filling was 30%. At the same operating conditions, when steel balls were used the torque decreased only by 19% (from 9 to 7.2 kgf·m). Three-dimensional DEM simulations also resulted in similar conclusions.
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