Grinding machines used mineral processing

Grinding action

Industrial grinding machines used in the mineral processing industries are mostly of the tumbling mill type. These mills exist in a variety of types – rod, ball, pebble autogenous and semi-autogenous. The grinding action is induced by relative motion between the particles of media – the rods, balls or pebbles. This motion can be characterized as collision with breakage induced primarily by impact or as rolling with breakage induced primarily by crushing and attrition. In autogenous grinding machines fracture of the media particles also occurs by both impact (self breakage) and attrition.

The relative motion of the media is determined by the tumbling action which in turn is quite strongly influenced by the liners and lifters that are always fixed inside the shell of the mill. Liners and lifters have two main purposes:

• Liners protect the outer shell of the mill from wear – liners are renewable.
• Lifters prevent slipping between the medium and slurry charge in the mill and the mill shell. Slippage will consume energy wastefully but more importantly it will reduce the ability of the mill shell to transmit energy to the tumbling charge. This energy is required to cause grinding of the material in the mill. The shape and dimensions of the lifters control the tumbling action of the media.

The tumbling action is difficult to describe accurately but certain regions in the mill can be characterized in terms of the basic pattern of motion of material in the mill.

The motion of an individual ball in the charge is complicated in practice and it is not possible to calculate the path taken by a particular particle during station of the charge. However the general pattern of the motion of the media can be simulated by discrete element methods which provide valuable information about the dynamic conditions inside the mill.

The impact energy spectrum in a mill

The energy that is required to break the material in the mill comes from the rotational energy that is supplied by the drive motor. This energy is converted to kinetic and potential energy of the grinding media. The media particles are lifted in the ascending portion of the mill and they fall and tumble over the charge causing impacts that crush the individual particles of the charge. The overall delivery of energy to sustain the breakage process is considered to be made up of a very large number of individual impact or crushing events. Each impact event is considered to deliver a finite amount of energy to the charge which in turn is distributed unequally to each particle that is in the neighborhood of the impacting media particles and which can therefore receive a fraction of the energy that is dissipated in the impact event. Not all impacts are alike. Some will be tremendously energetic such as the impact caused by a steel ball falling in free flight over several meters. Others will result from comparatively gentle interaction between media pieces as they move relative to each other with only little relative motion. It is possible to calculate the distribution of impact energies using discrete element methods to simulate the motion of the media particles including all the many collisions in an operating mill. The distribution of impact energies is called the impact energy spectrum of the mill and this distribution function ultimately determines the kinetics of the comminution process in the mill.

The Continuous Mill

Industrial grinding mills always process material continuously so that models must simulate continuous operation. Suitable models are developed in this section.

The population balance model for a perfectly mixed mill.

The equations that describe the size reduction process in a perfectly mixed ball mill can be derived directly from the master population balance equation that was developed in Chapter 2. However, the equation is simple enough to derive directly from a simple mass balance for material in any specific size class.

Mixing Characteristics of Operating Mills

In practice operating mills do not conform particularly well to the perfectly mixed pattern because there is considerable resistance to the transport of material, both solids and water, longitudinally along the mill. This type of behavior can be modeled quite well by several perfectly mixed segment in series with discharge from the last segment being restricted by a post classifier. The size distribution in the material that leaves each segment can be calculated by repeated application of equation successively to each mixed segment in turn. The product from the first segment becomes the feed to the next and so on down the mill. The number of mixed sections and their relative sizes can be determined from the residence-time distribution function in the mill. Residence distribution functions have been measured in a number of operating ball, pebble and autogenous mills and it is not unusual to find that three unequal perfectly mixed segments are adequate to describe the measured residence-time distribution functions. Usually the last segment is significantly larger than the other two. This is consistent with the behavior of a post classifier that holds up the larger particles at the discharge end of the mill which are then thrown quite far back into the body of the mill.

It has been suggested in the literature that a further refinement to the mixed-region model can be achieved by the use of a classification action between each pair of segments, but since it is impossible to make independently verifiable measurements of such interstage classifications, this refinement cannot be used effectively.

Models for Rod Mills

The physical arrangement of rods in the rod mill inhibits the effective internal mixing that is characteristic of ball mills. The axial mixing model for the mixing pattern is more appropriate than that based on the perfectly-mixed region. When axial mixing is not too severe in the mill, an assumption of plug flow is appropriate. In that case the population balance model for the batch mill can be used to simulate the behavior of the rod mill with the time replaced by the average residence time in the mill which is equal to the holdup divided by the throughput.

The Population Balance Model for Autogenous Mills

Four distinct mechanisms of size reduction have been identified in fully autogenous mills: attrition, chipping, impact fracture and self breakage. Attrition is the steady wearing away of comparatively smooth surfaces of lumps due to friction between the surfaces in relative motion. Chipping occurs when asperities are chipped off the surface of a particle by contacts that are not sufficiently vigorous to shatter the particle. Attrition and chipping are essentially surface phenomena and are commonly lumped together and identified as wear processes. Impact fracture occurs when smaller particles are nipped between two large particles during an impact induced by collision or rolling motion. Self breakage occurs when a single particle shatters on impact after falling freely in the mill. Rates of breakage and the progeny spectrum formed during these processes differ considerably from each other and each should be modeled separately.

A fifth breakage mechanism occurs in a semi-autogenous mill when particles are impacted by a steel ball. Breakage and selection functions that describe this mechanism can be modeled in a manner similar to those used for the ball mill.