Keywords: discrete element method, mining mill, balls, grinding.

A mill is a mechanical system and its objective is to make a diminution of size of a determined material that is introduced in its interior. Geometrically a mill, is a cylinder that is made rotate on its axial axis, at a speed so that it allows to generate in his interior four types of movements; the first corresponds to a zone of cataract, the second to a cascade, the third to a zone of recirculation and the fourth made up of a shared in common movement to the mill. In the zone of cataract and cascade, it is possible to clearly appreciate that there is a direct bonding between the elements; therefore an impact takes place that generates stopping levels of forces, causing the rupture of the elements. In order to improve the process, spherical elements of a determined material (steel balls) were placed in it, in order that these stuck to the material and were mixed with them in all the zones. This simple device has been transformed nowadays into the main system of milling, although others of different nature exist.

Nowadays a great amount of paradigms in the operation of the mills exists due to the great importance that these have in the conminution process. For example in the process of copper obtaining, a mill of SAG type can process 3000 ton per day, which translated into resources, is in the order of USS 20,000 per hour. These numbers have allowed the development of a great amount of technology and modalities of operation that experience has demonstrated not being extrapolables to other mills even those of the same geometric characteristics, and mainly to the materials that they process which are different. Nowadays it is accepted like usual practice, for example, to operate the mill to its maximum power. The base of this paradigm is whether the form of the material to the interior of the mill causes a load that must have the maximum of eccentricity and therefore a great torsor moment on the axis of the mill, which causes a high consumption of power. Another one of paradigms, which has not enjoyed much acceptance, is in using balls of great size; the base of this application consists that the balls of greater size when falling of high altitude cause a greater energy of impact. The paradigms have a defensible sustenance, but they have unfortunately not been validated scientifically due to the impossibility of observing the kinematics and dynamics of the movement in a direct form, and on the other hand to make models in laboratories; these are not scalable, the use of a life size mill is not possible either, due to the high cost that it would involve to make a series of measurements, since it would be necessary to remove the mill from the line of production.

The object of this work is to know in detail the physics of the problem from computational simulations; it emphasizes the distribution of energy that is used in the conminution process. The behaviour of the energy consumed by the impact among ball-mineral, mineral-mineral, mineral-coating studies and ball-coating, for four different cases of operation, corresponds to the SAG type mill whose main dimensions are 36´ of diameter by 18´ of length.

The mathematical model that captures the movement of the particulate material and balls is based on the Discreet Elements Method (MED) developed among others by Mishrra [1], Cundall et. al. [2], In essence the MED is divisible in three great problems that is to say: Problem of Movement, Problem of Impact, Problem of Collision; these problems live simultaneously and are of different nature, has as a result the Lagrangian description of the movement of each particle and therefore all the dynamic kinematics variables of the problem are known.

Different conditions of operation have been evaluated and the variable dynamic kinematics and that satisfactorily fulfill the initial conditions and boundary conditions by means of the computational simulation, have been determined and it is possible to conclude that:

The presented qualitative results allow to recognize zones of segregation of the material product of the movement of the load. The balls of great size are located in the zone of smaller speed and they do not put under particles of material to impacts. For the used conditions of operation it is possible to observe that the action that exerts the balls on the material is the one that more energy develops; therefore the condition of semiautogenous improves the process of milling for this mill. When visualizing the values of power consumed by the different studied cases, one can conclude that it is possible to save the order of 0.5 single MW changing to the conditions of speed and filling level in small amounts. The conditions of operation jointly studied with the geometry of a lifter and granulometer of the material do that the blow of balls with the coatings is minimum. This condition diminishes the possibility of breakage of grills or lifters.

1

B.K. Mishra, "Study of media mechanics in tumbling mills by the Discrete Element Method". Ph D Tesis Department of Engineering Metalurgical of University from Utah, March, 1991.

2

P.A. Cundall, "Computer Simulation of Dense Sphere Assemblies", in Micromechanics of Granular Materials pp 113-123 M. Satake and J.T. Jenkins Eds, Elsevier Science, Amsterdam, 1988.

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