Dimensionality In Ball Mill Dynamics

Introduction The theoretical analysis of tumbling mill energetics and performance has largely neglected mill dimensionality, and, in particular, the importance of the length/diameter (L/D) ratio. This is in spite of the fact that practice varies substantially: geographically, for semi-autogenous and autogenous mills, as between North America and South Africa/Scandinavia, and historically, for overflow ball mills, for which the L/D ratio has increased significantly from the earliest small mills to the largest mills currently. The present study is concerned primarily with the influence of the L/D ratio on the design and operation of overflow ball mills, on the occurrence of the overload phenomenon, and on the limits, if any, it may impose on mill capacities because of critical pulp axial velocity limits. It will be shown that the shape factor is of major importance in this area and that its adjustment to the extent that this is practical should remove the diameter limitations previously postulated for this mill type. Dimensionality in mill design Ball mill shape factors in the period prior to 1927 (Taggart, 1927) averaged 1.1/1 for 29 center discharge mills and 1.0/1 for 30 peripheral discharge mills. With the resumption of new plant construction after the 1930s depression, the Morenci concentrator continued the 1/1 ratio with its 3.1 x 3.1 m (10 x 10 ft) mills. The ratio was increased progressively from then on, reaching 1.6 and 1.8/1 for the largest overflow mills currently. As shown recently (Arbiter, 1989), this is in sharp contrast to autogenous and SAG mill shapes, for which the ratio averages 0.4 in North America. On the other hand, South African practice, starting at the turn of the century with autogenous mills having 4/1 ratios, moved toward 1/1 until recently, when a 2.5/ 1 ratio mill was installed. The reasons given for such divergent practice for mill shape factors are in some respects contradictory and generally inconclusive. The most complete discussion from a practical viewpoint (Dor and Bassarear, 1982) is limited to primary SAG and autogenous mills. Considerations of ball mill dimensionality have had a twofold direction. On the one hand, it has been argued that ball mill efficiencies should increase with increasing diameter and that the specific energy for a particular grind should be reduced accordingly. An inadvertent test of this idea at the Bougainville operation (Burns and Erskine, 1983) resulted in drastic underpowering, which led to failure to reach design capacity until additional mills were installed. This can be taken as strong evidence against any increase in efficiency with diameter. In another direction, it has been argued (Arbiter and Harris, 1982, 1983) that there is a limit to ball mill diameters because of the demonstrable limit to axial flow velocities evident in the overload phenomenon, which as a fact is incontrovertible. But that it places a limit on mill diameters overlooks the evidence given below that appropriate variation in the L/D ratio will permit major increases in diameter, limited only by constructional or economic factors. The present study was directed toward quantifying the overload phenomenon through examination of the influence of mill dimensionality variation and mill operating variables on its occurrence. It is shown that varying the operating conditions, specifically the load fraction and the fraction critical speed, can reduce the risk of overload for existing operations; while appropriate decreases in the L/D ratio can minimize the risk in the design of new circuits. Ball mill overload Ball mill overload is a consequence of the approach to a critical velocity with increasing feed rates or circulating loads. Although the effect has been known for over 50 years, there have been no previous attempts to quantify it. The following description of the ball mill as a flow system is the preliminary to a quantitative analysis: 1) In the absence of a ball load, axial flow of pulp through a mill resembles open channel flow, except for disturbances near the shell due to shell/lifter rotation. 2) For a given ball load (Lf), the void fraction available for pulp hold-up (H) for the ascending portion of the load is approximately 0.4 Lf. In the descending portion, it is greater than this and increases with fraction critical speed (Fc) because of load expansion. 3) Increasing the feed rate increases pulp hold-up and progressively fills the available void space. At a critical flow rate, which depends on system geometry, hydraulic head and pulp rheology, void filling reaches its limit; a pool forms rapidly and fills available space outside the ball load and up to the overflow level. Prior to this, pulp discharges mainly along the ascending rim of the overflow. 4) For a small mill (Lo et al., 1990), it has been shown that with increasing feed rates the critical filling is at or near 50% of the mill volume. Power drops rapidly when this level is reached, as required by the torque formula. 5) The transition to overload is associated with the following phenomena: a) The decrease in power draw. b) Damping of mill sound. c) Reduced comminution of coarser feed sizes, probably due to reduced direct impact in the presence of a pool. d) Increased circulating loads, which further intensify the overload, and increased density of cyclone underflows, which can lead to roping. e) Conditions beyond overload are not known because feed rates are not delibelrately increased beyond this point. f) The existence of the phenomenon limits the capacity of a mill with a fixed set of operating conditions and can prevent the balancing of hard ore feed rate decreases by increases in soft ore rates.