Breakage Behavior of Quartz Under Compression in a Piston Die
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Abstract
The main forces acting on minerals in conventional size reduction units are compression, impact, attrition, and/or abrasion. Usually a combination of these forces shares the breakage action of the minerals with one or more of these forces dominating the breaking action, depending on the machine used. The present work concentrates on the behavior of quartz when stressed with compression force in a confined piston die. Several size fractions within the size range minus 10 mm to plus 0.85 mm were compressed in the piston die. The measured parameters are compression load, bed thickness, displacement as a result of compression, rate of displacement, and the size distribution of the products. It was found that the size distributions are, to some extent, different from those produced by the ball mill or the highpressure roll mill. This is mainly because of the differences in the type of the acting forces in each case. It was also found that the cumulative weight of the distributions is reasonably normalizable with respect to the median particle size of the product. The specific energy expended is inversely proportional to the median size of the products, and the reduction ratios, x_{f}/x_{p}, are directly proportional to the applied compression force, and hence, to the specific energy expended. A simple model is suggested for predicting the particle size distribution as a function of the expended energy. The calculated values of the size distributions match fairly well with the experimental values, except at the very low energy levels, where most of the energy expended is consumed in the rearrangement and packing of the particles in the confined space with little or no breakage.
Keywords
Confined bed comminution Piston die Size reduction Quartz1 Introduction
In the mining industry, the energy value chain starts at the mine face and extends to the processes of smelting and refining. The main component of this value chain is comminution, which accounts for 30–70% of all energy used in the mining industry [1, 2]. Comminution is the term given to processes that reduce particle sizes in a wide range of applications including minerals, cement, pharmaceutical, and chemical industries. In the mineral industry, it begins with the blasting of rocks in the mine and is then further achieved through crushing and grinding. Comminution unit operations are used throughout the minerals industry for the purpose of liberating valuable minerals, creating reactive surface area, and producing desirable particle size distributions. It has been reported that about 3% of the world’s electrical energy is consumed by grinding [3]. Approximately 50–80% of the total energy consumption in a mineral processing plant is utilized by comminution equipment [4] rendering comminution as an energy intensive process. The relationship between the comminution energy and the product size obtained for a given feed size has been researched extensively over the last century. Size reduction operations from an integral part of almost every operation in mineral processing and its importance and significance arise from the fact that comminution is highly energy demanding and also very inefficient. Therefore, there is a large potential for financial improvements, and even a 10% increase in energy saving in size reduction would warrant a major scientific and technological research effort [5]. An efficient comminution process will be associated with increased recovery rates of any ore and make possible the utilization of low grade ores in order to satisfy the world demand for materials, especially those in short supply in the near future. Keeping these factors in mind, even a small gain in improving comminution energy efficiency can have a substantial impact on the operating cost of the processing plant. Therefore, the interest in the improvement of comminution through a better understanding of its fundamental aspects and the more rational and meaningful performance evaluation remains undiminished. Improvements in comminution efficiency should be directed not only towards the development of machines that enhance energy utilization but also towards the design of grinding operations that make optimal use of existing machines. In size reduction processes, the focus is primarily on the interrelated phenomena of energy absorption, energy utilization, reduction ratio, grind limit, and size distributions of the comminuted product. It has been reported that the energy utilization in conventional size reduction machines is only a fraction of what is achieved in breaking single particles under slow compression [5, 6, 7]. This decrease in process efficiency can be attributed to a number of interrelated causes inherent to the design and operating conditions of size reduction machines and the interparticle interaction effects that are inevitable whenever a particulate system is ground in confined or loose beds [8, 9]. In particlebed comminution (confined mode), unlike most conventional grinding mills (unconfined mode), energy is transferred directly to the charge mass and breakage occurs by very high stresses, generated locally, at the contact points between the particles of the tightly compressed bed [10, 11, 12, 13]. For this reason, among others, significantly enhanced energy efficiency is realized when a confined bed of particles is comminuted under sufficiently high compressive loads. Largescale continuous grinding in the particlebed mode is carried out in the newly invented chokefed highpressure grinding rolls [9, 14, 15, 16]. However, a completely confined particlebed mode of grinding is difficult to attain in the highpressure mill because of the wellknown end effects that invariably result in leakage of some feed. Though with this discrepancy from completely confinedbed mode of breakage, the highpressure mill is considered as an energysaving unit of size reduction compared with the conventional tumbling mills. It is possible to achieve energy savings of more than 50% of the specific energy commonly known to be consumed for size reduction of mineral commodities in conventional ball mills, when a highpressure mill is used [17]. The evolution concerning modeling of the highpressure mill technology is reviewed recently [18]. In addition, this mode of grinding reduces contamination of the product with iron during grinding. This latter feature saves steel wear consumption and produces clean products needed for subsequent processes in some special applications. For detailed fundamental investigation of this grinding mode in the laboratory, the batch process in a pistondie press setup has some advantages over the continuous process in a pressure mill. Substantially smaller feed sample is required and the rate at which the bed is compressed can be fixed at a preassigned value. Therefore, the pistondie press setup provides a convenient and versatile tool for the study and analysis of the absorption, dissipation, and utilization of the grinding energy; size spectra of the ground product; and virtual cessation of further size reduction at high pressures [10, 19, 20, 21, 22, 23, 24].
The present paper attempts to characterize the breakage properties of a brittle rock, quartz, at different size fractions when compressed at various loads in a confined piston die. This is to understand the interaction between the various variables affecting the breakage behavior of a brittle solid in a confined zone. Application of the results may lead to improving the energy efficiency in the size reduction units utilizing compression as the main stressing force.
2 Experimental Work
2.1 Material, Equipment, and Procedure
The assembly was loaded in a laboratory compression machine equipped with a load cell. The piston having a diameter of 5.5 cm was snugly fitted into the die, 5.55 cm diameter, to make a fully confined particle bed. The particle beds were compressed at a slow rate of loading which varies with the applied load {3 mm/s at the lowest load (20 kN), and 1 mm/s at the highest load (200 kN)} up to the desired maximum force level. Piston displacements were measured at the end of the unloading cycle using a vernier caliper, and the loading time was measured using a digital stop watch from the start to the desired load. After load is released, the comminuted bed was discharged and soaked in water to disperse the agglomerated fines. The dispersed sample was then subjected to standard wetdry sieve analysis.
2.2 Results and Discussion
2.2.1 The Performance of the Cell (Piston Die)
According to Gutsche [19], there are restrictions on the dimensional ratios for meaningful interpretation of the piston die results. These restrictions are H/X_{max} < 6, D/X_{max} < 10, and D/H < 3, where H is the material bed height, D is the die diameter, and X_{max} is the maximum particle size of the loaded material. During the course of this work, these restrictions were fulfilled, where the maximum particle size was 10 mm, and the maximum bed height was 4.37 cm at sample weight of 150 g and bulk density of 1.43 g/cm^{3}. The bulk density of all sizes is practically the same provided the particle shape in all quartz sizes is the same, and attrition and abrasion are minimal in a hard material such as quartz.
The measured parameters in this investigation, as a result of the applied loads, are the displacement, dL, and the time taken by the piston from the start to the assigned load in seconds. The calculated parameters are the relative compression, dL/L, the specific energy associated with the above measurements, and the compression rate, dL/time.
2.2.2 The Size Distributions of the Broken Product
2.2.3 Specific Energy Consumption
2.2.4 Estimation of the Size Distribution
In all the size distributions of quartz produced as a result of compression in the piston die, it was observed that the loglog plots of the cumulative weight percent as a function of particle size are straight lines at all energies applied and sizes tested. Figure 7 above is a demonstration of this observation. This feature suggested that the size distributions can be expressed as:
That is to say, on loglog plot:
It was also found that αi is a linear function of energy, and can be expressed at:
2.2.5 The Reduction Ratios of the Products
2.2.6 Percentage of Material Passing a Cut Size
3 Conclusions

The piston displacement increased with increasing feed size, the relative compaction increased slightly with the feed size, and the rate of piston movement decreased with increasing feed particle size.

The size distribution of the product is different from those of ball mills or HPGR and fans out in straight lines from the feed size down to the fine size fraction for the various specific energy inputs. The size distributions follow similar criterion with respect to the median size, X_{50}.

The cumulative size distributions can be represented by simple linear relationships on loglog plots. The slope of the linear relationship is a function of the energy consumed for breaking the feed material. This slope is used to predict the size distribution at any expended energy.

The specific energy consumption increases with increasing the load, and the specific energy consumption, at 200 kN load, increases with increasing feed size, but the rate of increase decreases with increasing the material size.

The reduction ratio, X_{50f}/X_{50p}, is in a reasonably linear function with the consumed specific energy. At the reduction ratio of 2, the specific energy consumption decreases nonlinearly with the feed size fraction.

The material passing a cut size for all the size fractions increases as a function of the specific energy consumption. The product percent, represented here by the minus 0.85 mm cut size, decreases dramatically with increasing feed size.
Notes
Compliance with Ethical Standards
Conflict of Interest
The authors declare that there is no conflict of interest.
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