Mining, Metallurgy & Exploration

, Volume 36, Issue 1, pp 173–180 | Cite as

Breakage Behavior of Quartz Under Compression in a Piston Die

  • Abdel-Zaher M. A. AbouzeidEmail author
  • A. A. S. Seifelnassr
  • G. Zain
  • Y. S. Mustafa


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 high-pressure 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, xf/xp, 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.


Confined bed comminution Piston die Size reduction Quartz 

1 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 inter-particle interaction effects that are inevitable whenever a particulate system is ground in confined or loose beds [8, 9]. In particle-bed 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. Large-scale continuous grinding in the particle-bed mode is carried out in the newly invented choke-fed high-pressure grinding rolls [9, 14, 15, 16]. However, a completely confined particle-bed mode of grinding is difficult to attain in the high-pressure mill because of the well-known end effects that invariably result in leakage of some feed. Though with this discrepancy from completely confined-bed mode of breakage, the high-pressure mill is considered as an energy-saving 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 high-pressure mill is used [17]. The evolution concerning modeling of the high-pressure 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 piston-die press set-up 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 pre-assigned value. Therefore, the piston-die press set-up 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 feed mineral used in this study was quartz collected from Sapaloga, North Khartoum, Sudan. The sample was prepared by stage-crushing, in a laboratory jaw crusher followed by a roll crusher, down to minus 10 mm particle size. The crushed sample was sieved to produce a sufficient stock of several size fractions, namely − 10 + 6.3, − 6.3 + 4.75, − 4.75 + 3.35, − 3.35 + 2.36, − 2.36 + 1.70, − 1.70 + 1.18, and − 1.18 + 0.85 mm. A cell assembly, a piston die arrangement, was used to crush the quartz samples, see Fig. 1. A sample weight of 150 g was comminuted under a set of bed pressures ranging from 20 to 200 kN to generate a reasonable range of specific breakage energy inputs in the piston die.
Fig. 1

The piston die assembly: Dp diameter of piston (5.5 cm), Dc diameter of cylinder (5.55 cm), Lp length of piston (12.5 cm), Lc length of cylinder (11.55 cm), L1 measure length of the piston before compression, L2 measure length of piston after compression, (L1L2) displacement, dL, L initial height of bed sample, (a) before loading, and (b) after loading.

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 wet-dry 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/Xmax < 6, D/Xmax < 10, and D/H < 3, where H is the material bed height, D is the die diameter, and Xmax 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/cm3. 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.

It was observed, as expected, that the displacement is a function of the applied load, see Fig. 2, as expected, but what was not expected is that the displacement is a function of particle size where the displacement is consistently reduced as the material size fraction is reduced, i.e., the displacement is larger in the case of the coarser fractions than in the case of finer fractions. This is probably due to the fact that the interstitial voids within the material bed are larger in the case of coarser fractions (the bulk densities of all size fractions are practically the same, 1.43 g/cm3).
Fig. 2

The piston displacement, dL, as a function of the applied load for all the tested size fractions, the material weight is 150 g

As the particles of the coarse size fractions are broken while being compressed, the product particles move easily and fill in the large voids, and hence compacting the material bed volume. In the case of the fine fractions, the voids are smaller and friction opposing the movement of the product particles is higher, and hence compaction of the bed is less. This material behavior is reflected on the relative displacement of the piston, as shown in Fig. 3.
Fig. 3

The relative compression dL/L, of the material bed as a function of the applied load for the various size fractions, the material weight is 150 g

On the other hand, the rate of piston movement was faster in the case of the finer size fractions than in the case of the coarser ones, see Fig. 4. If we compare this trend, with respect to the size fractions and the relative compression discussed above, it can be concluded that the displacement, dL, was covered in a relatively shorter time in the case of the finer size fractions at all levels of loads.
Fig. 4

The rate of piston movement as a function of the applied load for each size fraction

These three variables: dL, dL/L compression ratio, and the rate of piston movement dL are plotted as a function of the applied load for the size fraction − 6.3 + 4.75 mm at material weight of 150 g. Figure 5 summarizes the trend of each of these parameters as the applied load varies from 20 to 200 kN.
Fig. 5

The piston displacement, dL, the relative compression, dL/L, and the rate of piston movement, dL cm/s for the size fraction − 6.30 + 4.75 mm

2.2.2 The Size Distributions of the Broken Product

The product size distribution of quartz compressed in a piston die is not like those obtained from ball mills or high-pressure grinding rolls (HPGR). The size distributions of material ground in ball mills follow the Gaudin-Schohmann size distribution with a reasonably long straight line portion in the fine size range and a convex portion near the top of the feed size at higher grinding times (higher energy levels) and a concave portion close to the top of the feed size at shorter grinding times [25]. The slope of the straight line portion (the distribution modulus) is constant for all grinding times (all energy levels) [19]. The product from the HPGR follows a convex shape all the way from the feed size to the finest size, when looked at from top, which indicates that most feed size particles are broken in a single pass through the roll mill, see Fig. 6a, b [19, 25].
Fig. 6

a Typical size distribution of the product from a ball mill (after Malghan, 1976). b Typical product size distribution from a HPGR (after Kapur et al., 1992)

The size distributions of the products from the piston die differ from the abovementioned distributions. They are fanning out, in straight lines, from the feed size towards the finer sizes at all applied loads (energy levels) for all size fractions tested (Fig. 7). The slope of the size distributions is a function of the applied loads (energy levels).
Fig. 7

Typical product size distributions from the piston die system for two feed sizes − 10 + 6.3 mm and − 1.7 + 1.18 mm

All of the distributions are reasonably normalizable with respect to the median size, X50, as shown in Fig. 8. This means that quartz is behaving the same in the confined piston die under all of the applied loads for all size fractions tested.
Fig. 8

Normalized size distributions for all size fractions at various loads

2.2.3 Specific Energy Consumption

As expected, the specific energy consumed for breaking the various size fractions increased as the applied load increased. The trend of the specific energy consumed as a function of the applied load increases as shown in Fig. 9. At any applied load, the specific energy expended is higher for the coarser size fraction. An explanation for this behavior is that the displacement is larger in the case of the coarser sizes than the finer sizes.
Fig. 9

The specific energy consumption as a function of the applied load for the various size fractions tested, the material load is 150 g

The extent of the increase in the specific energy consumption as a function of the mean fraction size at a load of 200 kN is presented in Fig. 10. The specific energy consumption increases as the median fraction size increases with slowing rate as the size gets coarser.
Fig. 10

The sp. energy consumed at 200 kN load as a function of the median fraction size of the feed material

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 log-log 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:

$$ \mathrm{Yi}=a\ {\left(\mathrm{xi}\right)}^{\upalpha \mathrm{i}} $$

That is to say, on log-log plot:

$$ \mathrm{Log}\ \mathrm{Yi}=b+\upalpha \mathrm{i}\ \log\ \mathrm{xi} $$

It was also found that αi is a linear function of energy, and can be expressed at:

$$ \upalpha \mathrm{i}=c+\beta\ \mathrm{Log}\ \mathrm{E} $$
By programming these relationships, b and c can be obtained, and hence the size distributions can be calculated at any expended energy in the piston die. Equation 3 is presented in Fig. 11 where the slope and the Y-intercept, c, can be obtained. Figure 12 presents the data and estimated points for a series of tests carried out on quartz of feed size − 6.3 + 4.75 mm at expended energy ranging from 1.27 J/g (20 kN) up to 23.2 J/g (200 kN). It can be seen that the calculated distributions match, to a good approximation the experimental points. It can be seen that the differences between the data points and the corresponding estimated values (the errors in estimation) increase at low expended energy (at 20 kN and 40 kN). This is probably due to the energy taken by the particulate bed for packing and rearrangement, which consumes a large amount of the applied energy and leaves little energy, at these low energy levels, for material breakage. This explains the large deviations between the estimated and the experimental points at low energy levels. In general, this model represents the breakage distribution of quartz broken in a piston die for various size fractions at different loads (energy levels) fairly well.
Fig. 11

Slope of the cumulative weight distribution versus the specific energy expended for quartz feed of size − 6.3 + 4.75 mm crushed by compression in a piston die

Fig. 12

The size distribution, measured and calculated, of quartz feed of size − 6.3 + 4.75 mm crushed by compression in a piston die

2.2.5 The Reduction Ratios of the Products

The reduction ration, X50f/X50p, as a function of the specific energy consumed for the breakage of some of the size fractions used in this study is shown in Fig. 13 for 150-g material samples. As expected, the slope of the relationship increases as the size fraction increases, i.e., the coarser size is more easily crushed in the die than the finer sizes. At size reduction of 2, the specific energy consumed was plotted as a function of the median fraction size, X50f, Fig. 14. It can be seen that the specific energy consumption in the piston die system decreases as the mean fraction size increases with a higher rate of decrease at the finer sizes. This finding confirms the results reported by Nad and Saramak [16] who found that the tensile strength decreases as the particle size increases with a higher rate of decrease at smaller sizes.
Fig. 13

The reduction ratio for some of the tested fractions as a function of the specific energy consumed

Fig. 14

The specific energy consumption, at a reduction ratio of 2, as a function of the mean fraction size

2.2.6 Percentage of Material Passing a Cut Size

The product material passing 0.85 mm was reported as a function of the specific energy consumed for various size fractions, see Fig. 15. The produced fine fraction increases as the specific energy increases for all tested size fractions. The product percent increases as the feed size decreases. This is because as the feed size approaches the cut size at the same specific energy, more crushed material will pass the cut size. At higher energy levels, the rate of increase of the product percent decreases as a result of the rapid decrease of the unbroken material in the fine sizes at higher energy levels. Figure 16 shows the decrease in product percent as the fraction size increases, as shown in Fig. 16, at a load of 200 kN.
Fig. 15

The product, − 0.85 mm material percent, as a function of the specific energy expended

Fig. 16

Minus 0.85 mm product percent as a function of the mean fraction size of the feed material

3 Conclusions

The breakage of quartz was studied in a piston die to give a better understanding of the fundamental breakage. Several size fractions (from 10 down to 1.18 mm) were used in this study. The applied load was varied from 20 to 200 kN. The following findings are reported:
  • 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, X50.

  • The cumulative size distributions can be represented by simple linear relationships on log-log 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, X50f/X50p, is in a reasonably linear function with the consumed specific energy. At the reduction ratio of 2, the specific energy consumption decreases non-linearly 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.


Compliance with Ethical Standards

Conflict of Interest

The authors declare that there is no conflict of interest.


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Copyright information

© The Society for Mining, Metallurgy & Exploration 2018

Authors and Affiliations

  1. 1.Faculty of EngineeringCairo UniversityGizaEgypt
  2. 2.Faculty of Petroleum and MineralsSuez UniversitySuezEgypt
  3. 3.Islamic UniversityKhartoumSudan

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