Ball Charge Research Articles

Numerical simulation of charge motion in ball mills — Lifter bar effect

This paper focuses on the use of a numerical tool known as the discrete element method (DEM) to study the motion of ball charge in ball mills. DEM is employed to simulate the motion of individual balls. While doing so, the effect of liner design on the grinding performance of the mill is studied. Two important factors, such as the configuration of the liner and the geometry of the lifting surfaces, are correlated with the overall mill performance. An attempt is made to show the effectiveness of the lifter bars in transmitting power from the mill, shell to the interior of the mill with particular emphasis on large diameter mills.

Modelling and simulation of ball mill wear

In the mineral processing industry, ball mills are used to reduce ore from one size distribution to another. Ball mill wear occurs as a result of the violent interactions within the ball charge. In the present article, a mathematical description of wear has been added to a ball charge motion model. Wear is associated with the comminution mechanisms found in the ball charge profile. It is assumed that ball mill wear occurs in each of three comminution zones, with adhesive wear found in the crushing and tumbling zones and abrasive wear arising in the grinding zone. Wear rates are proportional to the energy dissipated in these zones as predicted by the charge motion model. Three laboratory case studies are investigated followed by one full-scale example in a wet milling context. Simulation results are compared with experimental data from which real-system predictions are presented. The use of these results provides the possibility of optimizing ball mill performance while including the wear rate factor.

The discrete element method for the simulation of ball mills

The discrete element method (DEM) is a proven numerical technique for modelling the multibody collision behavior of particulate systems. This method is used here to study the motion of ball charge in tumbling mills. To get meaningful results, it is essential that the parameters involved in the model be carefully determined. These parameters embody essentially the material properties of the system: stiffness, damping, and friction. In this study, all the parameters are carefully determined experimentally for different operating mill conditions. A computer code based on DEM has been developed to model the motion of the balls in tumbling mills. The code incorporates a scheme to calculate the applied torque, and hence power input to the mill. A 55-cm ball mill is simulated for two different liner cross-sections— rectangular and triangular. Results of the simulations pertaining to applied torque are compared with the experiments. It is found that, with a particular model for the coefficient of friction, the predicted torque agrees well with the experiments.

Optimization of the make-up ball charge in a grinding mill

The combination of a grinding circuit simulator with a model of ball wear in a grinding mill leads to a method to calculate, with a preselected accuracy, the make-up ball charge that optimizes the operation with respect to a given objective for the grinding process. In the example shown, the best make-up ball charge, calculated with a 1% accuracy, increased the circuit capacity by 12% from the best monosized make-up ball charge.

Numerical Simulation of Ball Motion in a Tumbling Ball Mill.

The two dimensional motion of the individual balls in a tumbling ball mill was analyzed numerically by a Distinct Element Method using the extended Kelvin model composed of nonlinear spring and nonlinear dashpot. A parameter related to the coefficient of viscosity is determined from the data of imperfect restitution between ball and mill shell. The simulation of the dynamic motion of the individual balls is based on the nonlinear perfect elasticity, nonlinear viscosity and Newton's law of motion. The dynamic motion of balls during milling calculated was compared with the actual three dimensional motion of balls observed in a mill. The effects of ball charge fraction and mill speed on the impact velocity of balls estimated were also discussed.It can be concluded that the model simulation developed in the present study predicts approximately the actual motion of the balls in a tumbling mill. The motion reproduced from the simulation is strongly influenced by the ball charge fraction and mill speed. The impact frequency of the individual balls and their impact velocities at individual collisions can be estimated by the simulation technique proposed.

機械的合金化条件がＭ／Ａアルミニウム合金の機械的性質に及ぼす影響

A mixture of aluminum alloy powder, 2024, and 2 wt% of nickel powder has been mechanically alloyed in a vibratory ball mill to investigate the effects of process variables on mechanical properties of the consolidated products. It was found that ball charge and powder charge played important roles on tensile properties; in as-work-ed specimens, milling with lower ball charge or lower powder charge was desirable to achieve good results. In T6-treated specimens, however, higher ball charge gave rather good tensile properties. Changes in ball size and mill pot capacity showed little effect on tensile properties. Process control agent was another variable which played an important role on mechanical properties. Carbon and graphite were effective additives for improvement of tensile strength; both ambient and elevated (200°C) tensile strengths increased with their addition. Though addition of zinc stearate also brought an increase in room temperature strength, it was bad to ductility.

金属粉末の振動ボールミリングのモデルシミュレーション

The motion of each milling ball during vibratory ball milling of metal powders was simulated by a computer using one-. two- and three-dimensional models of a vibratory ball mill. In these models, the consumpton of impact energy of the balls by the micro-compaction of metal powder particles during impact was assumed to be equivalent to the energy loss by an imaginary viscosity given to the balls and mill container. As a result of the simulation by using the three models, it was found that the motion of the milling balls is strongly dependent on the ball charge fraction. With an increase in the ball charge, the impact frequency increased, while an average of impact velocity normal to each contact surface decreased.

遊星ミルの粉砕機構と限界粒度

To clarify the mechanism and characteristics of a planetary mill grinding, batch grinding experiments were carried out using several kinds of balls each with a different specific gravity and size. The motion of the grinding media in the mill was observed and analyzed by using multistroboscope photography connected to an image analyzer, and the pressure force acting on the mill wall by the grinding media was measured by using a special pressure sensor.A surging phenomenon consisting of a pendulum-like oscillation of the grinding media in the mill is observed. It is found that the compressive-abrasive motion of the ball charge on the compressed powder layer is effective in producing very fine particles.An optimum fractional ball filling of the mill was demonstrated by the experimental results. It was proved that optimum filling results in the maximum applied force and the greatest motion distance with the greatest oscillation frequency of the ball charge on the powder layer.It was also found that the smaller the size of grinding ball, the finer the ground product that can be obtained. The ratio of the largest remaining particle size to the ball size is about 3×10-3.

Relationship between breakage parameters and process variables in ball milling — An industrial case study

The performance of the secondary ball mill at the New Broken Hill Consolidated Ltd. concentrator is analysed using the perfect mixing model and an ore-specific breakage distribution function. This function was determined from single-particle breakage tests using a computer-monitored twin pendulum apparatus. The ratio of the breakage rate to the normalized discharge rate, r/d ∗ , determined for the ball mill using the ore-specific breakage distribution function for a range of grinding conditions is related to the mill power consumption. The mill power consumption is related to the percentage of mill volume occupied by the ball charge and to the percentage of solids in the mill feed.

Mill sizing for phosphate grinding in mills of 0.2 to 5 meters in diameter

The breakage parameters of phosphate ore were determined by batch first-ordering grinding studies in a laboratory ball mill according to the Austin, Klimpel, and Luckie procedures. The results were scaled to five larger mills of 0.56, 0.82, 3.36, 4.41, and 5 m in diameter assuming equilibrium ball charges for the full-scale mills. The results were used to predict product size distributions and capacities for batch grinding in the smaller mills and open-circuit grinding in the larger mills. The predicted capacities were in approximate agreement with experimental values except for the 5-m diam mill. The Bond method gave capacity predictions that were 45% to 150% too high.

A note on the prediction of specific rates of breakage for an equilibrium ball charge

A note on the prediction of specific rates of breakage for an equilibrium ball charge

Electrostatic disturbance forces on a three-axis drag-free sensor

The electrostatic analysis of a multiple-capacitance 3-axis drag-free sensor is presented in this paper. The instrument consists of a proof-mass (a dense metallic ball) floating freely inside a spherical cavity enclosed by the sensor plates and the shield. Since the ball and the cavity are not necessarily concentric, the problem in three-dimensional potential theory for electrostatics is solved by the method of boundary perturbations and specifically in terms of spherical harmonics. The capacitance outputs of the instrument and the electrostatic forces acting on the system are derived as non-linear functions of the ball position, ball charge and the sensor plate potentials. The instrument sensitivity and cross-coupling effects are discussed. The analysis may also be useful for electrostatic gyros and suspensions.

Dynamics of a spherical shell under a nonsymmetric internal pulse loading

These authors conduct experimental investigations of the elastic dynamic deformations of an air-filled spherical shell upon explosion of a lumped high energy charge in its cavity. A sketch illustrates the arrangement of the steel shell with ball charge and strain gauges; oscillograms show the pressure measurements on the outer and inner surfaces; and a table records shell strain as a function of eccentricity. The authors conclude that there is no connection between the build-up of vibrations and the disturbance in the central symmetry of the load.

Large Ball Mill Scale-Up Factors to be Studied Relative to Grinding Efficiency

Ball mills 5.5 m (18 ft) in diameter and larger tend to use energy delivered to the mill less efficiently than smaller diameter mills, particularly when the large mills carry 40% by volume ball charges. This paper will explore factors used in scaling up ball mills, showing where the advantages of one factor can possibly be negated by another factor. The paper will propose possible operating limits and areas for further study to establish selection and design limits.

Experience With Large Diameter Ball Mills at Bougainville Copper Ltd.

The performance of the nine 5.5 m diameter × 6.4 m mills (18 × 21 ft) initially installed at Bougainville Copper Ltd. did not meet the laboratory and pilot plant derived design expectations as measured by Bond Work Index. During the post-commissioning period, inefficient grinding of coarse material resulted in a build-up of large circulating loads and led to reduced throughputs because of pump and cyclone overloading. Installation of larger pumps and cyclones and development of an improved circuit control philosophy alleviated materials handling problems and permitted higher tonnages to be attained. Since 1977, plant throughput has been increased by installation of three additional mills. These are 0.9 m (2.9 ft) longer than the other nine and have a higher capacity. Developments in classification and mill speed-up, together with a finer ball mill feed size and substantial improvements to mill availability (99% in 1982) have further increased plant capacity. There is a continuing emphasis on improving grinding circuit efficiency in terms of throughput/grind. Current development work includes trials of graded ball charges, different liner profiles, and assessment of scalping/regrind proposals.

The Propagation of Blasts from Solid Explosives to two‐phase media

AbstractThe aim of this investigation is to determine the influence of the energy release from a combustible two‐phase media on the blast wave generated by an explosive charge, during the first stages of the process. For this purpose ball charges of “Composition B” were detonated in air, in pure nitrogen containing suspended solid particles of carbon, and in pure oxygen containing particles of aluminum and carbon. The blast wave's velocity was measured in all the media using fast frame camera 300,000 f.p.s. and streak photography at 2 mm/μs. The influence of release or absorption of energy by the medium was investigated by comparing experiments done in inert media with those conducted in combustible media while other parameters are kept constant.Kozorezov's triple isentrope model was compared to the results, and good agreement is found. The article contains detailed information on the experiments and the calculations performed.

The effect of high energy milling on the catalytic behaviour of manganese dioxide

A technique of dry high energy milling has been used to increase the catalytic activity of naturally occurring manganese dioxide powder. The effect of the basic milling parameters (ball charge, milling time and milling atmosphere) has been examined. The subsequent catalytic activity of the manganese dioxide powder has been assessed by quantitative measurement of the oxidation of carbon monoxide over a range of temperatures. A surface area increase alone did not explain the results, and hence a change in defect structure is suspected. The activity of a high purity synthetic manganese dioxide powder was reduced by the milling treatment.

Studies in vibration milling

The results of 300 experimental runs on vibration milling of soapstone, graphite, cXte, magnesite, rock phosphate, granite and zirX sand covering particle size range of (−0.25+0.10) to (−1.00+ 0.80) mm, density range of 2.29−4.59 g/cm 3, hardness range of 1–7 Mho's hardness number and surface energy range of 4.50–38.66 kg f m/m 2, are presented. The results obtained were used to determine (1) the effect of grinding characteristics (feed weight, feed particle size, ball charge, density of ball material, weight ratio and mill filling ratio), (2) the effect of material characteristics, (3) the comparative performance of vibration mill and ball mill, and to compare the specific surface areas produced by grindability apparatus, vibration mill and ball mill. Correlations for grinding energy consumption and rate of grinding are presented.

Fundamental Studies on the Ball Mill Crushing

The authors investigated the variation of crushing mechanism of a ball mill relative to mill speed, and found that crushing mechanism of the mill at 70 per cent of the critical speed was mainly represented by the impact compression. Whereupon they applied Eqs. (2)-(7)-relation between the crushing condition and the net work input to crushing by impact compression-to the ball mill crushing. By these Eqs., the authors' assumption on the effect of density, size and drop height of the ball on the capacity of the mill were proved to be nearly in accord with the expcrimental results.(a) The relation of the ball load to the capacity of the mill at the normal speed, i.c., 70 per cent of the critical speed, might be expressed by Eqs. (10)-(14). In case the total ball load is proportional to the weight of one ball at constant specific weight and constant number of balls, the relation is given by Eq. (10), but, when the ball load is proportional to the number of balls at constant specific weight and constant ball size, it is given by Eq. (11). On the other hand, in case the ball load is proportional to the specific weight at constant size and number of balls, it is given by Eq. (14).(b) The relation of the mill diameter to the capacity may be expressed by Eqs. (16) and (17). Of the two mills, having equal ball charge rate to the mill volume, but different diameters, the mill with the larger diameter has greater efficiency. So does the mill having the balls of smaller specific weight.

Part II: The Influence of the Powder Charge on Power Requirements

In Part II the relation between the relevant dynamic variables and the power required to drive a ball mill containing both balls and powder charge is established; this being an extension, to the practical case of a mill grinding a powder, of the results, given in Part I of the paper, of an investigation into the dynamics of a mill containing a ball charge only. By means of the results of Part II the power required to drive a mill, in which a granular material is being dry ground, may be calculated with an accuracy sufficient for design and operational purposes.