LIST OF SYMBOLS
2.1 Comminution Methods
Comminution methods can be broadly classified as single-particle comminution, loose-bed comminution and particle-bed comminution (Fuerstenau and Vazquez-Favela, 1997). Single-particle breakage can be achieved either by breaking particles individually in a testing machine or by breaking it in a rigidly mounted roll mill individually so that particles don’t interact with each other. The mode of loading in single particle breakage could be impact, shear or slow compression. Loose-bed comminution is achieved in grinding vessels where the energy is transferred to a loose bed of particles by grinding media. The common example for loose-bed comminution is the ball mill where the energy is transferred to particles by tumbling steel balls. This transfer mode makes loose-bed comminution the most inefficient size reduction method, since there exist non-productive collision events between ball and ball, ball and liner, particle and particle. Moreover, frictional losses could occur during tumbling motion of grinding media and particle bed. Particle-bed comminution is achieved by externally stressing a bed of particles. This external stress induces high interparticle stresses within the bed, which is responsible for the breakage of the particles. The inefficiency in particle-bed comminution arises from frictional losses due to the interaction between particles, and compaction or briquetting of fines produced (Fuerstenau et al., 2004).
5 2.1.1 High Pressure Grinding Rolls
A recently developed equipment for particle-bed comminution is the High Pressure Grinding Rolls (HPGR) which was invented in 1979. It was first developed by KHD® and Polysius® in Germany (Fuerstenau et al., 1993; Gutsche et al., 1993;
Schönert, 1988). At the beginning, it was utilized on industrial scale for the grinding of clinker and raw material in cement production. Since then, HPGR has been adopted into various size reduction processes including gold ore crushing prior to heap leaching; diamond ore crushing; iron ore pre-pelletizing, etc.
Breakage in HPGR is accomplished by passing the material through two counter-rotating rolls. One of the rolls rotates on a fixed axis while the other moves linearly with external pressure applied to the movable roll. The material is fed into the gap between the rolls through a feed hopper. As the material is nipped into the gap, it is compacted by external pressure. This external pressure on the particle bed induces high interparticle stresses on each particle, which causes breakage. It is estimated that these stresses are 40 to 60 times the external pressure applied (Schönert, 1988).
The operating principle of the HPGR is illustrated in Figure 2.1. As shown in Figure 2.1, three zones form during breakage in HPGR. The first zone is the acceleration zone where particles are nipped through the gap into the breakage zone. In this zone, densification of the particle bed occurs. Then, the bed is compacted and comminuted in the compression zone due to interparticle stresses acted on each particle. Lastly, the material bed expands and leaves the gap at the dilation zone (De, 1995).
The breakage behavior inside HPGR and the resultant product size distribution depend upon operating and material variables such as:
- External grinding pressure applied to the rolls - Roll diameter, roll speed, surface pattern of rolls
6 - Operating gap distance between rolls
- Particle size distribution, chemical composition and moisture content of the feed
Figure 2.1. Operating principle of HPGR (De, 1995)
2.1.2 Ball Mill
The most commonly used size reduction equipment in mineral processing and cement production is the ball mill. It is a cylindrical vessel containing steel balls and the material to be ground. It can be operated in either dry or wet condition.
Grinding is performed by rotating the mill such that the material is comminuted by the motion of loose grinding medium. When the mill is rotated at low rotational speeds, the balls move frequently in an inclined path where the balls are emerging, rolling down, and getting back to the surface, referred to as cascading state. At high rotational speeds, more balls are ejected from the ball bed, known as cataracting state. In the former case, the material bed is expanded between ball bed, and breakage is achieved by a series of collisions between balls. In the latter case, ejected balls fall onto ball bed, nipping and stressing the particles in between.
7
The complete explanation of grinding behavior in a ball mill is complex. It depends on material properties, mill environment, and operating variables such as:
- Physical and chemical characteristics of the feed such as particle size distribution, chemical composition of feed, etc.
- Ball diameter and ball density
- Mill diameter, mill length and lifter design
- The fraction of feed material filling the mill volume (powder loading) - The fraction of balls filling the mill volume (ball loading)
- Rotational speed of the mill - Dry or wet grinding condition - Mass transport and hold-up - Pulp density for wet grinding
It is necessary to define some test variables in order to describe the ball mill grinding conditions. In a ball mill, ball loading, ɸB, is defined as the fraction of the volume of ball bed in the mill volume, including porosity inside the ball bed. It is formulated as
ɸB = (Mb ρb ) Vm 1 (1-εb ) (1)
where Mball is the mass of balls (kg), ρball is the density of balls (kg/dm3), Vmill is the empty volume inside the mill and εball is the porosity of the ball bed, expressed as fraction. εball values for mono-size ball bed is generally taken as 0.4. Similarly, powder loading, fc, is defined as the fraction of the volume of feed material in the mill volume, including porosity inside powder bed. It is defined as
fc= (Mp ρp ) Vmill (1 (1-εp ) (2)
8
where Mpowder is the mass of powder to be ground (kg), ρpowder is the density of powder (kg/dm3), Vmill is the empty volume inside the mill (dm3) and εpowder is the porosity of the powder bed, expressed as fraction. Knowing the true density of the powder, εpowder can be estimated easily. ɸB and fc can be related with each other by defining the fraction of powder volume in the empty volume between balls, ɸM, by;
ɸM=fc (εball ) (3)
The number of balls and the weight of the feed material added to the batch mill can be computed easily after selecting ɸM and ɸB.
Critical speed, Nc, is also another variable affecting the mill performance. It is defined as the rotational speed of the mill above which balls start to centrifuge around the mill case (Austin et al., 1984). Thus, the tumbling motion of the balls does not occur above critical speed, i.e., no breakage occurs. The critical speed depends on mill diameter and ball diameter. It is expressed as;
N (rpm) =42.2 √D-d (4)
where D is the internal mill diameter and d is the maximum ball diameter in meters.
Rotational mill speed is determined as a fraction of critical speed, ɸc.