Using DEM to investigate ball milling power draw, load behaviour and impact energy profile under various milling conditions

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Information about Using DEM to investigate ball milling power draw, load behaviour and...
Engineering

Published on November 2, 2014

Author: meschacbillkime

Source: slideshare.net

Description

Discrete element method modelling (DEM) has proven over many years to be a powerful tool for studying particulate systems within the mineral processing industry. DEM simulations were conducted to investigate the power draw, load behaviour and impacts energy profile of an experimental ball mill under different milling conditions. The variables that were regarded are mill rotational speed (% critical speed), ball size (mm), and lifter face angle (°). The DEM simulation results indicated that the grinding efficiency would be enhanced by use of 45° lifter face angle, 30 mm ball diameter and 80 % critical speed. The findings of this research work can be useful in guiding actual ball milling tests involving an ore sample.

1. Using DEM to investigate ball milling power draw, load behaviour and impact energy profile under various milling conditions M.B. Kime and M.H. Moys School of Chemical and Metallurgical Engineering, University of the Witwatersrand 1. Introduction •DEM is a numerical tool for modelling the behaviour of particulate systems. •Its mathematical fundamental relies on the knowledge of the contact forces applied on a given particle (particle - particle contact and particle - wall contact), and on solving the law of motion. In general, the particle motion equations are solved using the Newton’s law of motion. 2. Objectives •DEM simulations were conducted to investigate the power draw, load behaviour and impacts energy profile of an experimental ball mill under different milling conditions. 3. Experimental Procedure The DEM simulated mill was configured to match the environment inside the laboratory scale ball mill at Mintek. The DEM parameters used for the simulations are given in Table 3.1. 5. Discussion •Fig. 4.1 shows that the mill power draw increased gradually as the lifter face angle decreased from 90° to 45. •Fig. 4.2 (a) shows that the shoulder position increased gradually with the increase in the mill fractional speed. Higher shoulder and lower toe positions were obtained when simulating the mill with the 90° lifter face angle. •Fig. 4.2 (b) shows that mill simulated with 90° lifter face angles drew less mill power because of lots of ball cataracting onto the mill shell. •Fig. 4.3 shows that the mill simulated with 30 mm exhibited more impacts energy than the mill simulated with 20 mm balls. 6. Conclusion •Irrespective of lifter face angle considered, the peak power draw was found to be between 70 and 80 % critical speed. • The load behaviour and mill power draw were also found to be strong functions of ball size. • The DEM simulation did not take into account an ore sample properties, such as particle strength, the findings of this work need to be backed by actual experiment involving an ore sample. Acknowledgements •The authors acknowledge the financial support from Mintek for this research work. Reference • Cundall, P.A., Strack, O.D.L., 1979. A discrete numerical model for granular assemblies. Geothechnique, vol. 29, no. 1, pp. 47 – 65 4. Results 4.1 DEM prediction of the mill power draw 180 160 140 120 100 80 60 40 20 0 0 20 40 60 80 100 120 Power draw (W) Mill fractional speed (% Nc) 20 mm, L45 30 mm, L45 20 mm, L75 30 mm, L75 20 mm, L90 30 mm, L90 Figure 4.1 Effects of mill fractional speed and lifter face angle on the mill power draw 4.2 DEM prediction of the mill load behaviour } Shoulder positions } Toe positions 350 300 250 200 150 100 50 55 60 65 70 75 80 Media change angles (°) Mill fractional speed (% Nc) 90° lifter face angle 45° lifter face angle 75° lifter face angle Figure 4.2 (a) Variations of the toe and shoulder positions of the media charge with the percent fractional speed of the mill Figure 4.2 (b) DEM frames, particle paths for consecutive frames, position density plots (PDP) (ball diameter = 30mm) with 90° lifter face angle 100 90 80 70 60 50 40 30 20 10 0 2000 1500 1000 500 0 Frequency of collision (30 mm) Frequency of collision (20 mm) Density of Impact Energy (30 mm) Density of Impact Energy (20 mm) Cumulative Impact Energy (30 mm) Cumulative Impact Energy (20 mm) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Cumulative impact energy (%) Frequency of collisions Density of impacts energy (Joule) Impact classes energy (Joule) 4.3 Impact spectra Figure 4.3 Impact energy spectra as a function of ball size Parameters Ball-Ball contact Ball-Wall contact Coefficient of friction 0.4 0.5 Coefficient of restitution 0.4 0.5 Normal stiffness (kNm-1) 400 400 Shear stiffness (kNm-1) 300 300 Mill speed, [% critical speed] 10 - 100 Ball filling J, [%] 30 Ball density ρ, [kg m-3] 7800 Ball size d, [mm] 10, 20 and 30 Lifter geometry Number Shape Height [mm] Length [mm] Top width [mm] Bottom width [mm] Face angle [] 12 Trapezoidal 15 mm 400 mm 3 mm 33 mm 45 12 Trapezoidal 15 mm 400 mm 3 mm 20 mm 75 Measuring angles using the MB Ruler protractor: illustration Table 3.1 DEM parameters used for simulations

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