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Effect of design and operational parameters on particle morphology in ball mills
Accepted Manuscript Effect of design and operational parameters on particle morphology in ball mills
Farhad Moosakazemi, M.R. Tavakoli Mohammadi, M. Mohseni, M. Karamoozian, M. Zakeri PII: DOI: Reference:
S0301-7516(17)30127-8 doi: 10.1016/j.minpro.2017.06.001 MINPRO 3055
To appear in:
International Journal of Mineral Processing
Received date: Revised date: Accepted date:
20 December 2015 20 February 2017 4 June 2017
Please cite this article as: Farhad Moosakazemi, M.R. Tavakoli Mohammadi, M. Mohseni, M. Karamoozian, M. Zakeri , Effect of design and operational parameters on particle morphology in ball mills, International Journal of Mineral Processing (2017), doi: 10.1016/j.minpro.2017.06.001
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ACCEPTED MANUSCRIPT Effect of design and operational parameters on particle morphology in ball mills Farhad Moosakazemia1, M. R. Tavakoli Mohammadib, M. Mohsenic, M. Karamooziand,
School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran
TMU, Tehran, Iran c
Department of Mining Engineering, Tarbiat Modares University, Tehran, Iran
School of Mining, Petroleum & Geophysics Engineering, Shahrood University, Semnan, Iran
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d
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Mineral Processing Research Center, Academic Center for Education, Culture and Research (ACCER) on
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Abstract
Different factors involving in grinding of ore cause various breakage mechanisms. These different
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mechanisms differ the morphology of ground particles. In this study, the effect of ball mill types, feed sizes, and ball surface area have been investigated on the morphology of ground quartz particles using
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MBL cruise optical microscope and Olympus E-510 camera. Measured two-dimensional particle projection was expressed mathematically such as circularity, roundness and aspect ratio by ImageJ software. More than 20000 particles were morphologically measured for image analysis. Results show that circularity and
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roundness of ground particles are enhanced in an ordinary ball mill equipped with smooth liner (OBM). While higher aspect ratio of ground particles are achieved in cylindrical ball mill equipped with wavy liner
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(CBM). Consequently, the dominant breakage mechanism for OBM and CBM are abrasion and impact, respectively. Circularity and roundness values of coarse-grained ground particles are more than finegrained particles. The increase of ball surface area causes the increase of circularity as well as roundness
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b
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a
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M. Zakerib,
values and the decrease of aspect ratio value. Key words: Morphology, Circularity, Roundness, Aspect ratio, Ball mill, Breakage mechanism
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Corresponding author Tel. : +98 912 5544673 E-mail: [email protected]
ACCEPTED MANUSCRIPT 1. Introduction The demand for mineral deposits has been rising with the industrialization of the world. Every year, billions tons of metal ores, minerals, cement and other solid materials used in ceramics and chemical industries are subject to crushing and grinding by comminution
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equipment (Gupta and Sharma, 2014; Xiao et al., 2014).
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The shape and size of particles resulting from comminution process are dependent on
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many factors; including type of equipment, applied stress, retention time and materials
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properties. The effect of various comminution procedures such as crushing, ball, rod and autogenous grinding on particle shape have been investigated in number of research
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studies (Ahmed, 2010; Durney and Meloy, 1986; Hicyilmaz et al., 2005; Kursun and Ulusoy, 2006; Ulusoy and Yekeler, 2007; Ulusoy et al., 2004; Ulusoy et al., 2003;
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Vizcarra et al., 2011; Yekeler et al., 2004). Particles breakage in grinding equipment
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depends on the design and operational parameters (Ghassa et al., 2016). In fact, breakage
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mechanism determines particle shape in all comminution equipment. The main breakage mechanism is destructive breakage due to impact. However, other
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mechanisms such as abrasion and chipping play an important role in particle breakage,
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depending on the grinding conditions. It is often difficult to determine the mechanism and at least a combination of the two mentioned mechanisms simultaneously occur within the mill (Palaniandi et al., 2008; Ulusoy and Kursun, 2011). Sharp edges would be created as a result of destructive breakage, by the dominance of impact mechanism. Surface breakage occurs when the applied energy is not enough to break the particles into the separate parts. Thus, the dominant abrasion mechanism trims off the sharp edges of particles (Francioli, 2015).
ACCEPTED MANUSCRIPT The shape of particles plays an important role in subsequent processes such as manufacture, chemical engineering and material processing. The effects of particle morphology on performance of mineral processing methods have recently been considered. Particle shape analysis plays an important role in the behavior description of
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a particle in various separation processes. Durney and Meloy (1986) showed that by the
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behavior of different particle classes in these processes.
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detection of particle shape, it would be possible to develop better models to define the
For example, the shape of ground particles is an important physical criterion in particle-
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bubble attachment during flotation. The performance of flotation is dependent on the
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particles shape in accordance with basic model predictions (Anfruns, 1978). Based on the approach of determining gamma-c, elongated particles are more hydrophobic than round
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particles. Furthermore, the elongated particles have a higher recovery rate than round
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particles (Ulusoy and Kursun, 2011). The developed computational fluid dynamic models need to describe and add the particle shape parameters to better predict the kinetic rate
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constant of irregularly shaped particles (Koh et al., 2009).
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The particles shape also affects the physical separation methods. For malleable particles such as gold, the particles shape results from grinding process have significant effects on
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gravity separation efficiency (Ofori-Sarpong and Amankwah, 2011). Also, the importance of the shape of vanadium particles in primary separation using shaking table has been mentioned in a research (Zhao et al., 2013). Particle morphology is an important parameter in the behavior prediction of powder in various environments such as grinding, reaction, flotation, and agglomeration. The
ACCEPTED MANUSCRIPT particles geometry is also of particular importance in energy-consuming industries such as pharmaceutical industry, pigment production, ceramics, etc. (Ulusoy et al., 2003). Therefore, characterization of particle shape is essential to predict the performance of particles in various industries, including mineral processing. In this respect development
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of a proper shape in grinding equipment could be a new method in behavior optimization
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of mineral processing processes. In this paper, the effect of mill types, feed sizes, and ball
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surface area have been investigated on the shaping of particles.
2. Materials and Methods
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2.1. Materials and equipment
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In this study, the relatively pure quartz was used in two different sizes. Fine grain size of quartz (1-2 mm) and coarse grain size of quartz (3-5 mm) with bulk densities of 1.7 and
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1.45 (g/cm3), respectively, were used as feed sample. Quartz samples were kindly
following reasons:
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provided by a mine in the central part of Iran. These samples were chosen for the
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- Simple mineralogy and devoid of any particular complexity
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- Degree of freedom in large size - Being the major gangue in ore deposits The sample was ground (<74 μm) and riffled to obtain representative subsample for chemical analysis. Chemical compositions of main oxides in the samples are demonstrated in Table 1. X-ray Fluorescence (XRF) analysis was conducted using a Philips PW 2404 X-ray Fluorescence (Almelo, Netherlands) at Tarbiat Modares
ACCEPTED MANUSCRIPT University (Tehran, Iran). The sample mainly consists of SiO2 with the grade of 99.46% and major impurities are Al, Ca and Fe oxides. Batch grinding tests were carried out using a Denver ordinary ball mill equipped with smooth liner (OBM) and cylindrical ball mill equipped with wavy liner (CBM), as shown
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in Fig. 1. Characterization and operational conditions of the mills are illustrated in Table
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2.
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Three different steel ball size classes for the combination of 4 ball size distributions were chosen. These different distributions, their corresponding surface area, and also each ball
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diameter are presented in Table 3. The weight of each experiment ball charge was chosen
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to be quite equal.
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2.2. Methods
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The flow sheet used in this research is shown in Fig. 2. The samples of 740 and 670 g
CBM, respectively.
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from both fine- and coarse- grained feed sizes were chosen for grinding into OBM and
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Grinding carried out by 10% of ball charge filling for 10 minutes. Then, the ground ore
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was separated using a control sieve of 250 micron. The remained coarse particles (+250 micron) were weighed up to initial weight and ground again. Thus, the d80 of products of each mills were almost equal. The process continued until the weight of product with particles size less than 250 micron became about 100 g. Wet screening was applied to separate different size fractions of products (-250+210, -210+149, -149+105, -105+53, 53+37 micron). Finally, the particles dried in an oven at 70°C and weighed.
ACCEPTED MANUSCRIPT It is essential to use specific equipment to take appropriate images to determine the morphological parameters of particles size fractions by image analyzing. For this purpose, MBL cruise optical microscope and Olympus E-510 camera (China) were used. The plane objective lens of this microscope enabled the development of images with
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similar resolution at all levels. Moreover, the camera mounted on this microscope was
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equipped with a sensitive CCD with 10 effective megapixel image quality to provide
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more accurate representations of images. By placing the sample within the specific sample container and fixing of it using a special clip, the sample and container set were
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displaced under the objective lens by specific handlings crews in such a way that all the
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sections of powder were photographed. In order to increase the accuracy and reproducibility of data, the powder sample was changed two to three times and the
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imaging procedures were repeated as mentioned. Finally, the collection of photos taken
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from ground particles (~20000 particles) were subject to processing and analysis by Image-J software version 1.47 (Free of License) which performs based on particle
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projections obtained from the micrographs of particles.
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Generally, qualitative terms are used to describe the morphology of particle; however, these definitions cannot present an appropriate standard to describe morphology of
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particle and compare their morphological parameters. Therefore, the equations 1 to 3 have been applied to describe the morphological parameters of particles quantitatively. Circularity (C) mainly deals with characterizing the trimming off particle sharp edges. This parameter is described in equation 1: (1)
ACCEPTED MANUSCRIPT where A and P indicate the surface area and perimeter of particle, respectively (Little et al., 2015). Roundness (R) is defined by equation 2: (2)
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where DFeret represents the diameter equal to a diagonal distance of the farthest points on the particle from each other. The numerical range for this parameter lies between 0 and 1
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(Little et al., 2015). Thus, by increasing the roundness value, the particle shape would
(3)
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become close to a circle. The parameter of aspect ratio (AR) is expressed by equation 3:
where l and b are the length and width of a particle, respectively (Little et al., 2015;
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Stroeven, 2009).
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3. Results and discussion
The geometrical parameters for each test in different screen classes were calculated by
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ImageJ software. This method increases the accuracy and reduces error in determining
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the morphological parameters in comparison with simultaneous imaging of all particle sizes. The arithmetic average of each morphological parameter in all fractions was calculated for each test. Photomicrographs of quartz at different size fractions of OBM for test 1 are shown in Fig. 3. The image analyzing process is also shown in Fig. 4. Initially, the obtained images have been made binary by the software that means each pixel is stored as a single bit, i.e. a 0 or 1 (black or white). In some photomicrographs, particles are placed at the corner of images or on each other which caused that the
ACCEPTED MANUSCRIPT software to recognize them as a whole particle. Elimination of these kinds of particles has been performed to avoid calculating them. Then, image descriptors can be analyzed by Image-J software on binary images. Fig. 5 (a-f) shows the effect of ball charge
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distribution and feed sizes on particle morphologies.
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3.1. Circularity parameter
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Effect of ball charge distributions and feed sizes on changing circularity of particles for
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CBM and OBM is shown in Fig. 5 (a and b). According to the Fig. 5 (a), increasing ball surface area first reduced the circularity for both feed sizes but the circularity was then
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increased by a slight slope, such that the minimum value for fine- and coarse- grained
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feed is obtained in tests 2 and 3, respectively. The dominant breakage mechanism that eliminates the corners and sharp edges of the particles is abrasion (Gao and Forssberg,
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1995; Vizcarra et al., 2011). As can be seen from the graph, decreasing ball surface area
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caused reducing circularity with a high rate, which is subsequently increased by a low rate, indicating a reduction in the abrasion mechanism up to tests 2 and 3 for fine- and
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coarse- grained feed, respectively. Reducing the ball surface area directly reduced the
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ball-particle engagement, and then in tests 3 and 4 for fine-grained feed and test 4 for coarse-grained test, ball-particle entanglement type becomes different. In other words, steel balls for tests 3, 4 and 2, respectively for fine- and coarse-grained feed, hit the surface of particles within the ball with a stronger impact due to increased size. This initial impact on the surface caused contact of feed particles in the lower layer with each other due to reduction of primary impact force, resulting in circularity of the particles through an indirect abrasion mechanism (no contact between steel ball and particle). It
ACCEPTED MANUSCRIPT seems that direct abrasion capacity of particle-ball was eliminated more quickly due to larger surface of the majority of particles in fine-grained feed relative to ball surface. The abrasion mechanism occurred after test 2 caused circularity due to collision of ball with the surface of the material and subsequent energy transfer between the particles.
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In Fig. 5 (b), similar to CBM, first a downward trend at a rate faster than tests 1 to 3
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followed by an upward trend with a slower rate of tests 3 and 4 is observed for circularity
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due to the grinding of coarse-grained particles. This rapid rate indicated the reduction in strong abrasion effect on circularity resulting from direct collision between ball and
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particle, while the abrasion mechanism from initial impact of the ball on the surface of
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particles and subsequent energy transfer between the particles has a lower capacity to cause circularity. Moreover, reducing circularity value simultaneous with decreasing ball
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surface for both feed sizes are due to a lower available surface of balls to eliminate sharp
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particle angles and the balls of such dimensions are not fully capable of creating an indirect abrasion mechanism. The higher circularity value in coarse-grained feed relative
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to fine-grained feed probably indicates the reduced likelihood of ball-particle collision
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with increasing the surface area of the particles.
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3.2. Roundness parameter Effect of feed sizes and ball charge distributions on roundness parameter in the CBM and OBM are indicated in Fig. 5 (c and d), respectively. In all tests, the roundness of coarsegrained particles is higher than fine-grained particles. Due to lower surface of coarsegrained feed particles, these materials are more in contact with the balls and more influenced by grinding charges. Therefore, any combination of balls selectively converts
ACCEPTED MANUSCRIPT coarser feed particles to a round shape. As can be seen, changes in roundness are close to parabolic shape for both mills as well as both feed sizes. At the minimum points of tests 1 to 4, the abrasion mechanism is not due to direct ball-particle abrasion and it is inclined towards the impact of grinding load on feed surface and energy transfer between particles
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below the surface because of increasing ball size (reducing ball surface). In the minimum
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points, the impact mechanism is dominated over abrasion mechanism because of the ball
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size distribution as well as its movement. In the diagram of OBM, it can be seen that the maximum roundness value is in test 4, which has the lowest surface of balls among the
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tests. In this case, the abrasion mechanism through the impact of ball charge on the feed
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surface and energy transfer between particles below the surface (indirect abrasion) has caused the strongest effect on roundness value relative to direct abrasion mechanism. In
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CBM, there is a similar trend of changes in roundness, circularity as well as effect of the
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studied mechanisms.
3.3. Aspect ratio parameter
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Effect of feed sizes and ball dimensions on the morphological parameter of aspect ratio
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for CBM and OBM are represented in Fig. 5 (e and f), respectively. As observed in the study of previous morphological parameters, changing ball surface caused changing in the grinding mechanisms. According to these Figs., domination of impact mechanism (due to changes of ball size distributions and engagement pattern of particles) changed the particle shape from roundness to linear, up to test 3 for CBM and test 2 for OBM. Afterwards, the aspect ratio is decreased and breakage mechanism was changed for both feed sizes. It can be seen that the aspect ratio of fine-grained feed fraction was higher
ACCEPTED MANUSCRIPT than coarse-grained feed in all tests. This pattern indicates that fine-grained particles are more influenced by impact mechanism than coarse-grained ones. Aspect ratio and roundness parameters have opposite behaviors. It is clear that increasing of particle elongation lead to reduce its roundness and vice versa.
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3.4. Simultaneous comparison of mills
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In this section, the effect of mill types is described on the morphological parameters of
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particles in each size fractions Fig. 6 (a-f).
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Effect of ball charge distributions and mill types on parameter of particles circularity for fine- and coarse- grained feed are shown in Fig. 6 (a and b), respectively. As it can be
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seen, circularity of particles in all tests is higher for OBM than CBM, for both fine- and coarse-grained feeds. The difference of circularity depends on ball mill types. It shows
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the various breakage mechanisms over different tumbling mills.
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The roundness of particles has been evaluated in Fig. 6 (c and d). In all experiments,
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higher roundness value is occurred for OBM. The parameter of aspect ratio for fine- and coarse- grained feed are shown in Fig. 6 (e and
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f). The value of this parameter for CBM is more than OBM for all tests.
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The value of each morphological parameters of ground particles using minimum size of ball charge (test 1) are quite equals for both mills. In other words, the effect of mill types on particle shape could be negligible with increasing ball surface area. The comparison results of the effect of mill types on particles shape show that the abrasion is dominant breakage mechanism in the OBM due to sphere shape and smooth liner. In contrast, wavy liner and cylinder shape in the CBM causes dominant of impact mechanism relative to OBM. The wavy liner eliminates sharp angles and edges of
ACCEPTED MANUSCRIPT particles and causes higher circularity value. This liner changes the particle shape to circular (roundness parameter). CBM causes dominant mechanism of impact relative to OBM due to the presence of wavy liner as well as mill shape. Aspect ratio is a function of impact mechanism. The values of roundness and aspect ratio are quite equal in the case of
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applying ball charge with the most surface area. Thus, applying ball charge of small size,
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ball mills play no roles for creating mentioned particle morphologies.
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The mean of each morphological parameter in all tests for both mills are presented in Fig. 7 (a-c) in order to get a better comprehension. It can be seen that the values of circularity
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the aspect ratio is higher in CBM than OBM.
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and roundness parameters are higher for OBM in comparison to CBM and contrariwise,
For statistical discussion of the significance of process factors on particle morphology
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refer to Appendix.
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4. Conclusions
Breakage mechanisms in grinding process are affected by different factors. The effects of
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different factors included feed sizes, grinding media (ball surface area) and ball mill types
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on particle morphology have been studied in this paper. The results are as follows: 1. Different conditions evaluated in this study have created different mechanisms in particles grinding, which cause different morphological parameters. 2. Review of changes for morphological parameters indicated that changing the surface area of the balls causes changes in breakage mechanisms. Maximum ball surface area caused a high value of roundness and circularity, indicating the dominance of abrasion mechanism resulting from the ball-particle collision. With reducing the surface area of
ACCEPTED MANUSCRIPT steel balls in constant volume, the ball size is increased and changing particle-ball engagement causes dominance of impact mechanism. In this case, the value of roundness and circularity is minimum and aspect ratio is maximum in the majority of tests. Then, excessive reduction in surface area of balls caused a new mechanism of abrasion. This
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mechanism is a function of collision of ball charge with surface of feed within the mill.
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After this initial impact, a strong force is applied on the surface of feed particles due to
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the large size of balls and the transfer of this energy between the particles and particleparticle collisions caused grinding of materials with an abrasion mechanism.
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3. The higher values of roundness and circularity in the OBM and the higher value of
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aspect ratio in the CBM (at a specified feed size in most tests) are due to the type of liners. The smooth and wavy liners in the OBM and CBM, caused abrasion and impact as
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dominant mechanisms in grinding respectively.
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4. The effect of mill types on particle morphology is diminished with increasing ball surface area.
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5. Studies showed that the value of roundness and circularity parameters of coarse-
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grained feed is higher than fine-grained feed, but the aspect ratio of fine-grained particles is higher than coarse-grained particles; therefore, the dominant breakage mechanism of
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coarse-grained particles is abrasion relative to fine-grained particles.
Acknowledgment The authors wish to thank University of Shahrood and Academic Center for Education, Culture and Research (ACCER) on TMU for providing the possibility of conducting this research.
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Appendix The principles and basic equations of statistical analyses were discussed elsewhere (Dehghan et al., 2008; Tavakoli Mohammadi et al., 2015; Tripathy and Murthy, 2012).
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The data obtained from experiments inserted to Design Expert 7.0 software (DX-7) trial
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version for data validating and evaluating process parameters. Then the experimental
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results were fitted to some models including linear, 2 factor interactions (2FI), quadratic
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and cubic by the software. Each model was chosen on the basis of 95% confidence level (p-value<0.05) and higher F-value (Fisher variation ratio) among others. The best fits
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were achieved by linear models for circularity, roundness and aspect ratio and corresponding screening processes were represented in Table 4.
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The analysis of variance (ANOVA) was applied for the estimation of the significance of
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the models. From the p-values (<0.05) presented in Table 5 for circularity, roundness and
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aspect ratio, it can be concluded that all models and model terms are significant. Also, the values of 0.9344, 0.7079 and 0.7711 for R2 (correlation coefficient) for circularity,
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roundness and aspect ratio, respectively, indicate proper fitting of the models to
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experimental data. The signal to noise ratio was measured by adequate precision, which a ratio greater than 4 is favorable. All adequate precisions obtained, are greater than 4, indicating adequate signals. Therefore, the values of each shape parameter and their differences within experiments are significant. In this respect, process factors under investigation affect morphological parameters.
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List of Tables Table 1 Characterization and operational conditions of OBM and CBM
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Table 2 Physical characterization of the feed ore sample
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Table 3 Designed experiments with different ball charge distributions and surface area for
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both mills
Table 4 Sequential Model Sum of Squares [Type I] for morphological parameters
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Table 5 ANOVA results of regression models for morphological parameters
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Table 1 Chemical compositions of main oxides in head sample using XRF Component Weight (%) SiO2 99.46 Al2O3 0.31 Na2O 0.01 MgO 0.01 K2O 0.01 TiO2 0.011 MnO 0.001 CaO 0.06 Fe2O3 0.05 LOI 0.03
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Feed capacity (g) 740 670
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Table 2 Characterization and operational conditions of OBM and CBM Mill Types Length (mm) Diameter (mm) Liner configuration OBM 127 304.8 smooth CBM 355.6 177.8 wavy
Ball Charge (%) 10 10
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Table 3 Designed experiments with different ball charge distributions and surface area for both mills Ball size distributions in experiments (Test No.) Mill Ball Diameter 1 2 3 4 types sizes (mm) Small 19.72 48 0 0 0 OBM Medium 25.95 0 12 8 0 Large 31.68 0 5 7 12 Total surface area (cm2) 586.14 411.51 389.95 378.35 Small 19.72 44 0 0 0 CBM Medium 25.95 0 10 0 7 Large 31.68 0 5 11 6 Total surface area (cm2) 537.54 369.20 346.82 337.26
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F-Value
p-value
56.99 1.27 0.80 7.35
< 0.0001 0.3411 0.3976 0.0396
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13.47 2.99 13.38 1.02
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Table 4 Sequential Model Sum of Squares [Type I] for morphological parameters Factor Source S.S.α df M.S.β Mean vs Total 6.28 1 6.28 Linear vs Mean 1.632E-003 3 5.439E-004 2FI vs Linear 3.412E-005 3 1.137E-005 Circularity Quadratic vs 2FI 7.296E-006 1 7.296E-006 Cubic vs Quadratic 6.435E-005 4 1.609E-005 Residual 8.757E-006 4 2.189E-006 Total 6.28 16 0.39 Mean vs Total 7.19 1 7.19 Linear vs Mean 9.878E-004 3 3.293E-004 2FI vs Linear 1.492E-004 3 4.973E-005 Roundness Quadratic vs 2FI 1.809E-004 1 1.809E-004 Cubic vs Quadratic 4.597E-005 4 1.149E-005 Residual 3.157E-005 4 7.894E-006 Total 7.20 16 0.45 Mean vs Total 40.01 1 40.01 Linear vs Mean 0.010 3 3.500E-003 2FI vs Linear 1.557E-003 3 5.189E-004 Aspect ratio Quadratic vs 2FI 9.763E-004 1 9.763E-004 Cubic vs Quadratic 2.945E-004 4 7.362E-005 Residual 2.894E-004 4 7.235E-005 Total 40.02 16 2.50 α Sum of Squares. β Mean Square.
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Table 5 ANOVA results of regression models for morphological parameters Factor Source S.S.α df M.S.β F-Value p-value Model 1.632E-003 3 5.439E-004 56.99 < 0.0001 Aγ 4.029E-004 1 4.029E-004 42.22 < 0.0001 Bγ 3.342E-004 1 3.342E-004 35.01 < 0.0001 Cγ 5.656E-004 1 5.656E-004 59.27 < 0.0001 Circularity Residual 1.145E-004 12 9.544E-006 Cor Total 1.746E-003 15 R2 0.9344 Adeq. Precision 23.633 Model 9.878E-004 3 3.293E-004 9.69 0.0016 Aγ 1.684E-004 1 1.684E-004 4.96 0.0459 Bγ 4.912E-004 1 4.912E-004 14.46 0.0025 Cγ 2.016E-004 1 2.016E-004 5.93 0.0314 Roundness Residual 4.077E-004 12 3.397E-005 Cor Total 1.396E-003 15 R2 0.7079 Adeq. Precision 9.663 Model 0.010 3 3.500E-003 13.47 0.0004 Aγ 1.168E-003 1 1.168E-003 4.50 0.0555 Bγ 5.125E-003 1 5.125E-003 19.73 0.0008 γ C 2.911E-003 1 2.911E-003 11.21 0.0058 Aspect ratio Residual 3.117E-003 12 2.597E-004 Cor Total 0.014 15 R2 0.7711 Adeq. Precision 11.088 α Sum of Squares. β Mean Square. γ A, B and C are coded factors for ball surface area, feed sizes and ball mill types, respectively.
significant significant significant significant
significant significant significant significant
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List of Figures Fig. 1. Denver laboratory ball mills (OBM and CBM): (a) general view, (b) inside view Fig. 2. Process flow sheet Fig. 3. Photomicrographs of quartz (ground particles of OBM for fine-grained feed, test
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1): (a) -250+212, (b) -212+149, (c) -149+105, (d) -105+53, (e) -53+37 micron size
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Fig. 4. Image processing technique: (a) photomicrograph of quartz, (b) converted
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Fig. 5. Effect of ball charge distributions and feed sizes on morphological parameters: (a) effect of the variables on circularity of particles for CBM, (b) effect of the variables on
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circularity of particles for OBM, (c) effect of the variables on roundness of particles for CBM, (d) effect of the variables on roundness of particles for OBM, (e) effect of the
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variables on aspect ratio of particles for CBM, (f) effect of the variables on aspect ratio of particles for OBM
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Fig. 6. Effect of ball charge distributions and mill types on morphological parameters: (a) effect of the variables on circularity of fine-grained feed, (b) effect of the variables on
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circularity of coarse-grained feed, (c) effect of the variables on roundness of fine-grained feed, (d) effect of the variables on roundness of coarse-grained feed, (e) effect of the
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variables on aspect ratio of fine-grained feed, (f) effect of the variables on aspect ratio of coarse-grained feed
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Fig. 7. Comparison of various morphological parameters for both mills: (a), circularity, (b) roundness, (c) aspect ratio
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Fig. 3. Photomicrographs of quartz (ground particles of OBM for fine-grained feed, test 1): (a) 250+212, (b) -212+149, (c) -149+105, (d) -105+53, (e) -53+37 micron size fractions.
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Fig. 4. Image processing technique: (a) photomicrograph of quartz, (b) converted photomicrograph to binary image, (c) elimination of particles at the corner of image or overlapping each other.
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ACCEPTED MANUSCRIPT Highlights
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Effects of ball mill types, feed sizes and ball surface area on particle morphology have been examined. Different ball mills lead to various breakage mechanisms and morphologies. Coarse-grained ground particles are more round and circular. Circularity and roundness were increased as a result of increasing ball surface area.
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Farhad Moosakazemi, M.R. Tavakoli Mohammadi, M. Mohseni, M. Karamoozian, M. Zakeri PII: DOI: Reference:
S0301-7516(17)30127-8 doi: 10.1016/j.minpro.2017.06.001 MINPRO 3055
To appear in:
International Journal of Mineral Processing
Received date: Revised date: Accepted date:
20 December 2015 20 February 2017 4 June 2017
Please cite this article as: Farhad Moosakazemi, M.R. Tavakoli Mohammadi, M. Mohseni, M. Karamoozian, M. Zakeri , Effect of design and operational parameters on particle morphology in ball mills, International Journal of Mineral Processing (2017), doi: 10.1016/j.minpro.2017.06.001
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ACCEPTED MANUSCRIPT Effect of design and operational parameters on particle morphology in ball mills Farhad Moosakazemia1, M. R. Tavakoli Mohammadib, M. Mohsenic, M. Karamooziand,
School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran
TMU, Tehran, Iran c
Department of Mining Engineering, Tarbiat Modares University, Tehran, Iran
School of Mining, Petroleum & Geophysics Engineering, Shahrood University, Semnan, Iran
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Mineral Processing Research Center, Academic Center for Education, Culture and Research (ACCER) on
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Abstract
Different factors involving in grinding of ore cause various breakage mechanisms. These different
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mechanisms differ the morphology of ground particles. In this study, the effect of ball mill types, feed sizes, and ball surface area have been investigated on the morphology of ground quartz particles using
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MBL cruise optical microscope and Olympus E-510 camera. Measured two-dimensional particle projection was expressed mathematically such as circularity, roundness and aspect ratio by ImageJ software. More than 20000 particles were morphologically measured for image analysis. Results show that circularity and
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roundness of ground particles are enhanced in an ordinary ball mill equipped with smooth liner (OBM). While higher aspect ratio of ground particles are achieved in cylindrical ball mill equipped with wavy liner
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(CBM). Consequently, the dominant breakage mechanism for OBM and CBM are abrasion and impact, respectively. Circularity and roundness values of coarse-grained ground particles are more than finegrained particles. The increase of ball surface area causes the increase of circularity as well as roundness
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M. Zakerib,
values and the decrease of aspect ratio value. Key words: Morphology, Circularity, Roundness, Aspect ratio, Ball mill, Breakage mechanism
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Corresponding author Tel. : +98 912 5544673 E-mail: [email protected]
ACCEPTED MANUSCRIPT 1. Introduction The demand for mineral deposits has been rising with the industrialization of the world. Every year, billions tons of metal ores, minerals, cement and other solid materials used in ceramics and chemical industries are subject to crushing and grinding by comminution
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equipment (Gupta and Sharma, 2014; Xiao et al., 2014).
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The shape and size of particles resulting from comminution process are dependent on
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many factors; including type of equipment, applied stress, retention time and materials
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properties. The effect of various comminution procedures such as crushing, ball, rod and autogenous grinding on particle shape have been investigated in number of research
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studies (Ahmed, 2010; Durney and Meloy, 1986; Hicyilmaz et al., 2005; Kursun and Ulusoy, 2006; Ulusoy and Yekeler, 2007; Ulusoy et al., 2004; Ulusoy et al., 2003;
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Vizcarra et al., 2011; Yekeler et al., 2004). Particles breakage in grinding equipment
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depends on the design and operational parameters (Ghassa et al., 2016). In fact, breakage
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mechanism determines particle shape in all comminution equipment. The main breakage mechanism is destructive breakage due to impact. However, other
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mechanisms such as abrasion and chipping play an important role in particle breakage,
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depending on the grinding conditions. It is often difficult to determine the mechanism and at least a combination of the two mentioned mechanisms simultaneously occur within the mill (Palaniandi et al., 2008; Ulusoy and Kursun, 2011). Sharp edges would be created as a result of destructive breakage, by the dominance of impact mechanism. Surface breakage occurs when the applied energy is not enough to break the particles into the separate parts. Thus, the dominant abrasion mechanism trims off the sharp edges of particles (Francioli, 2015).
ACCEPTED MANUSCRIPT The shape of particles plays an important role in subsequent processes such as manufacture, chemical engineering and material processing. The effects of particle morphology on performance of mineral processing methods have recently been considered. Particle shape analysis plays an important role in the behavior description of
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a particle in various separation processes. Durney and Meloy (1986) showed that by the
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behavior of different particle classes in these processes.
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detection of particle shape, it would be possible to develop better models to define the
For example, the shape of ground particles is an important physical criterion in particle-
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bubble attachment during flotation. The performance of flotation is dependent on the
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particles shape in accordance with basic model predictions (Anfruns, 1978). Based on the approach of determining gamma-c, elongated particles are more hydrophobic than round
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particles. Furthermore, the elongated particles have a higher recovery rate than round
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particles (Ulusoy and Kursun, 2011). The developed computational fluid dynamic models need to describe and add the particle shape parameters to better predict the kinetic rate
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constant of irregularly shaped particles (Koh et al., 2009).
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The particles shape also affects the physical separation methods. For malleable particles such as gold, the particles shape results from grinding process have significant effects on
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gravity separation efficiency (Ofori-Sarpong and Amankwah, 2011). Also, the importance of the shape of vanadium particles in primary separation using shaking table has been mentioned in a research (Zhao et al., 2013). Particle morphology is an important parameter in the behavior prediction of powder in various environments such as grinding, reaction, flotation, and agglomeration. The
ACCEPTED MANUSCRIPT particles geometry is also of particular importance in energy-consuming industries such as pharmaceutical industry, pigment production, ceramics, etc. (Ulusoy et al., 2003). Therefore, characterization of particle shape is essential to predict the performance of particles in various industries, including mineral processing. In this respect development
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of a proper shape in grinding equipment could be a new method in behavior optimization
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of mineral processing processes. In this paper, the effect of mill types, feed sizes, and ball
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surface area have been investigated on the shaping of particles.
2. Materials and Methods
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2.1. Materials and equipment
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In this study, the relatively pure quartz was used in two different sizes. Fine grain size of quartz (1-2 mm) and coarse grain size of quartz (3-5 mm) with bulk densities of 1.7 and
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1.45 (g/cm3), respectively, were used as feed sample. Quartz samples were kindly
following reasons:
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provided by a mine in the central part of Iran. These samples were chosen for the
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- Simple mineralogy and devoid of any particular complexity
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- Degree of freedom in large size - Being the major gangue in ore deposits The sample was ground (<74 μm) and riffled to obtain representative subsample for chemical analysis. Chemical compositions of main oxides in the samples are demonstrated in Table 1. X-ray Fluorescence (XRF) analysis was conducted using a Philips PW 2404 X-ray Fluorescence (Almelo, Netherlands) at Tarbiat Modares
ACCEPTED MANUSCRIPT University (Tehran, Iran). The sample mainly consists of SiO2 with the grade of 99.46% and major impurities are Al, Ca and Fe oxides. Batch grinding tests were carried out using a Denver ordinary ball mill equipped with smooth liner (OBM) and cylindrical ball mill equipped with wavy liner (CBM), as shown
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in Fig. 1. Characterization and operational conditions of the mills are illustrated in Table
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2.
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Three different steel ball size classes for the combination of 4 ball size distributions were chosen. These different distributions, their corresponding surface area, and also each ball
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diameter are presented in Table 3. The weight of each experiment ball charge was chosen
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to be quite equal.
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2.2. Methods
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The flow sheet used in this research is shown in Fig. 2. The samples of 740 and 670 g
CBM, respectively.
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from both fine- and coarse- grained feed sizes were chosen for grinding into OBM and
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Grinding carried out by 10% of ball charge filling for 10 minutes. Then, the ground ore
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was separated using a control sieve of 250 micron. The remained coarse particles (+250 micron) were weighed up to initial weight and ground again. Thus, the d80 of products of each mills were almost equal. The process continued until the weight of product with particles size less than 250 micron became about 100 g. Wet screening was applied to separate different size fractions of products (-250+210, -210+149, -149+105, -105+53, 53+37 micron). Finally, the particles dried in an oven at 70°C and weighed.
ACCEPTED MANUSCRIPT It is essential to use specific equipment to take appropriate images to determine the morphological parameters of particles size fractions by image analyzing. For this purpose, MBL cruise optical microscope and Olympus E-510 camera (China) were used. The plane objective lens of this microscope enabled the development of images with
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similar resolution at all levels. Moreover, the camera mounted on this microscope was
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equipped with a sensitive CCD with 10 effective megapixel image quality to provide
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more accurate representations of images. By placing the sample within the specific sample container and fixing of it using a special clip, the sample and container set were
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displaced under the objective lens by specific handlings crews in such a way that all the
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sections of powder were photographed. In order to increase the accuracy and reproducibility of data, the powder sample was changed two to three times and the
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imaging procedures were repeated as mentioned. Finally, the collection of photos taken
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from ground particles (~20000 particles) were subject to processing and analysis by Image-J software version 1.47 (Free of License) which performs based on particle
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projections obtained from the micrographs of particles.
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Generally, qualitative terms are used to describe the morphology of particle; however, these definitions cannot present an appropriate standard to describe morphology of
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particle and compare their morphological parameters. Therefore, the equations 1 to 3 have been applied to describe the morphological parameters of particles quantitatively. Circularity (C) mainly deals with characterizing the trimming off particle sharp edges. This parameter is described in equation 1: (1)
ACCEPTED MANUSCRIPT where A and P indicate the surface area and perimeter of particle, respectively (Little et al., 2015). Roundness (R) is defined by equation 2: (2)
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where DFeret represents the diameter equal to a diagonal distance of the farthest points on the particle from each other. The numerical range for this parameter lies between 0 and 1
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(Little et al., 2015). Thus, by increasing the roundness value, the particle shape would
(3)
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become close to a circle. The parameter of aspect ratio (AR) is expressed by equation 3:
where l and b are the length and width of a particle, respectively (Little et al., 2015;
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Stroeven, 2009).
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3. Results and discussion
The geometrical parameters for each test in different screen classes were calculated by
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ImageJ software. This method increases the accuracy and reduces error in determining
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the morphological parameters in comparison with simultaneous imaging of all particle sizes. The arithmetic average of each morphological parameter in all fractions was calculated for each test. Photomicrographs of quartz at different size fractions of OBM for test 1 are shown in Fig. 3. The image analyzing process is also shown in Fig. 4. Initially, the obtained images have been made binary by the software that means each pixel is stored as a single bit, i.e. a 0 or 1 (black or white). In some photomicrographs, particles are placed at the corner of images or on each other which caused that the
ACCEPTED MANUSCRIPT software to recognize them as a whole particle. Elimination of these kinds of particles has been performed to avoid calculating them. Then, image descriptors can be analyzed by Image-J software on binary images. Fig. 5 (a-f) shows the effect of ball charge
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distribution and feed sizes on particle morphologies.
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3.1. Circularity parameter
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Effect of ball charge distributions and feed sizes on changing circularity of particles for
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CBM and OBM is shown in Fig. 5 (a and b). According to the Fig. 5 (a), increasing ball surface area first reduced the circularity for both feed sizes but the circularity was then
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increased by a slight slope, such that the minimum value for fine- and coarse- grained
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feed is obtained in tests 2 and 3, respectively. The dominant breakage mechanism that eliminates the corners and sharp edges of the particles is abrasion (Gao and Forssberg,
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1995; Vizcarra et al., 2011). As can be seen from the graph, decreasing ball surface area
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caused reducing circularity with a high rate, which is subsequently increased by a low rate, indicating a reduction in the abrasion mechanism up to tests 2 and 3 for fine- and
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coarse- grained feed, respectively. Reducing the ball surface area directly reduced the
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ball-particle engagement, and then in tests 3 and 4 for fine-grained feed and test 4 for coarse-grained test, ball-particle entanglement type becomes different. In other words, steel balls for tests 3, 4 and 2, respectively for fine- and coarse-grained feed, hit the surface of particles within the ball with a stronger impact due to increased size. This initial impact on the surface caused contact of feed particles in the lower layer with each other due to reduction of primary impact force, resulting in circularity of the particles through an indirect abrasion mechanism (no contact between steel ball and particle). It
ACCEPTED MANUSCRIPT seems that direct abrasion capacity of particle-ball was eliminated more quickly due to larger surface of the majority of particles in fine-grained feed relative to ball surface. The abrasion mechanism occurred after test 2 caused circularity due to collision of ball with the surface of the material and subsequent energy transfer between the particles.
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In Fig. 5 (b), similar to CBM, first a downward trend at a rate faster than tests 1 to 3
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followed by an upward trend with a slower rate of tests 3 and 4 is observed for circularity
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due to the grinding of coarse-grained particles. This rapid rate indicated the reduction in strong abrasion effect on circularity resulting from direct collision between ball and
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particle, while the abrasion mechanism from initial impact of the ball on the surface of
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particles and subsequent energy transfer between the particles has a lower capacity to cause circularity. Moreover, reducing circularity value simultaneous with decreasing ball
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surface for both feed sizes are due to a lower available surface of balls to eliminate sharp
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particle angles and the balls of such dimensions are not fully capable of creating an indirect abrasion mechanism. The higher circularity value in coarse-grained feed relative
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to fine-grained feed probably indicates the reduced likelihood of ball-particle collision
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with increasing the surface area of the particles.
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3.2. Roundness parameter Effect of feed sizes and ball charge distributions on roundness parameter in the CBM and OBM are indicated in Fig. 5 (c and d), respectively. In all tests, the roundness of coarsegrained particles is higher than fine-grained particles. Due to lower surface of coarsegrained feed particles, these materials are more in contact with the balls and more influenced by grinding charges. Therefore, any combination of balls selectively converts
ACCEPTED MANUSCRIPT coarser feed particles to a round shape. As can be seen, changes in roundness are close to parabolic shape for both mills as well as both feed sizes. At the minimum points of tests 1 to 4, the abrasion mechanism is not due to direct ball-particle abrasion and it is inclined towards the impact of grinding load on feed surface and energy transfer between particles
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below the surface because of increasing ball size (reducing ball surface). In the minimum
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points, the impact mechanism is dominated over abrasion mechanism because of the ball
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size distribution as well as its movement. In the diagram of OBM, it can be seen that the maximum roundness value is in test 4, which has the lowest surface of balls among the
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tests. In this case, the abrasion mechanism through the impact of ball charge on the feed
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surface and energy transfer between particles below the surface (indirect abrasion) has caused the strongest effect on roundness value relative to direct abrasion mechanism. In
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CBM, there is a similar trend of changes in roundness, circularity as well as effect of the
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studied mechanisms.
3.3. Aspect ratio parameter
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Effect of feed sizes and ball dimensions on the morphological parameter of aspect ratio
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for CBM and OBM are represented in Fig. 5 (e and f), respectively. As observed in the study of previous morphological parameters, changing ball surface caused changing in the grinding mechanisms. According to these Figs., domination of impact mechanism (due to changes of ball size distributions and engagement pattern of particles) changed the particle shape from roundness to linear, up to test 3 for CBM and test 2 for OBM. Afterwards, the aspect ratio is decreased and breakage mechanism was changed for both feed sizes. It can be seen that the aspect ratio of fine-grained feed fraction was higher
ACCEPTED MANUSCRIPT than coarse-grained feed in all tests. This pattern indicates that fine-grained particles are more influenced by impact mechanism than coarse-grained ones. Aspect ratio and roundness parameters have opposite behaviors. It is clear that increasing of particle elongation lead to reduce its roundness and vice versa.
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3.4. Simultaneous comparison of mills
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In this section, the effect of mill types is described on the morphological parameters of
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particles in each size fractions Fig. 6 (a-f).
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Effect of ball charge distributions and mill types on parameter of particles circularity for fine- and coarse- grained feed are shown in Fig. 6 (a and b), respectively. As it can be
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seen, circularity of particles in all tests is higher for OBM than CBM, for both fine- and coarse-grained feeds. The difference of circularity depends on ball mill types. It shows
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the various breakage mechanisms over different tumbling mills.
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The roundness of particles has been evaluated in Fig. 6 (c and d). In all experiments,
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higher roundness value is occurred for OBM. The parameter of aspect ratio for fine- and coarse- grained feed are shown in Fig. 6 (e and
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f). The value of this parameter for CBM is more than OBM for all tests.
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The value of each morphological parameters of ground particles using minimum size of ball charge (test 1) are quite equals for both mills. In other words, the effect of mill types on particle shape could be negligible with increasing ball surface area. The comparison results of the effect of mill types on particles shape show that the abrasion is dominant breakage mechanism in the OBM due to sphere shape and smooth liner. In contrast, wavy liner and cylinder shape in the CBM causes dominant of impact mechanism relative to OBM. The wavy liner eliminates sharp angles and edges of
ACCEPTED MANUSCRIPT particles and causes higher circularity value. This liner changes the particle shape to circular (roundness parameter). CBM causes dominant mechanism of impact relative to OBM due to the presence of wavy liner as well as mill shape. Aspect ratio is a function of impact mechanism. The values of roundness and aspect ratio are quite equal in the case of
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applying ball charge with the most surface area. Thus, applying ball charge of small size,
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ball mills play no roles for creating mentioned particle morphologies.
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The mean of each morphological parameter in all tests for both mills are presented in Fig. 7 (a-c) in order to get a better comprehension. It can be seen that the values of circularity
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the aspect ratio is higher in CBM than OBM.
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and roundness parameters are higher for OBM in comparison to CBM and contrariwise,
For statistical discussion of the significance of process factors on particle morphology
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refer to Appendix.
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4. Conclusions
Breakage mechanisms in grinding process are affected by different factors. The effects of
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different factors included feed sizes, grinding media (ball surface area) and ball mill types
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on particle morphology have been studied in this paper. The results are as follows: 1. Different conditions evaluated in this study have created different mechanisms in particles grinding, which cause different morphological parameters. 2. Review of changes for morphological parameters indicated that changing the surface area of the balls causes changes in breakage mechanisms. Maximum ball surface area caused a high value of roundness and circularity, indicating the dominance of abrasion mechanism resulting from the ball-particle collision. With reducing the surface area of
ACCEPTED MANUSCRIPT steel balls in constant volume, the ball size is increased and changing particle-ball engagement causes dominance of impact mechanism. In this case, the value of roundness and circularity is minimum and aspect ratio is maximum in the majority of tests. Then, excessive reduction in surface area of balls caused a new mechanism of abrasion. This
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mechanism is a function of collision of ball charge with surface of feed within the mill.
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After this initial impact, a strong force is applied on the surface of feed particles due to
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the large size of balls and the transfer of this energy between the particles and particleparticle collisions caused grinding of materials with an abrasion mechanism.
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3. The higher values of roundness and circularity in the OBM and the higher value of
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aspect ratio in the CBM (at a specified feed size in most tests) are due to the type of liners. The smooth and wavy liners in the OBM and CBM, caused abrasion and impact as
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dominant mechanisms in grinding respectively.
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4. The effect of mill types on particle morphology is diminished with increasing ball surface area.
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5. Studies showed that the value of roundness and circularity parameters of coarse-
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grained feed is higher than fine-grained feed, but the aspect ratio of fine-grained particles is higher than coarse-grained particles; therefore, the dominant breakage mechanism of
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coarse-grained particles is abrasion relative to fine-grained particles.
Acknowledgment The authors wish to thank University of Shahrood and Academic Center for Education, Culture and Research (ACCER) on TMU for providing the possibility of conducting this research.
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Appendix The principles and basic equations of statistical analyses were discussed elsewhere (Dehghan et al., 2008; Tavakoli Mohammadi et al., 2015; Tripathy and Murthy, 2012).
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The data obtained from experiments inserted to Design Expert 7.0 software (DX-7) trial
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version for data validating and evaluating process parameters. Then the experimental
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results were fitted to some models including linear, 2 factor interactions (2FI), quadratic
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and cubic by the software. Each model was chosen on the basis of 95% confidence level (p-value<0.05) and higher F-value (Fisher variation ratio) among others. The best fits
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were achieved by linear models for circularity, roundness and aspect ratio and corresponding screening processes were represented in Table 4.
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The analysis of variance (ANOVA) was applied for the estimation of the significance of
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the models. From the p-values (<0.05) presented in Table 5 for circularity, roundness and
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aspect ratio, it can be concluded that all models and model terms are significant. Also, the values of 0.9344, 0.7079 and 0.7711 for R2 (correlation coefficient) for circularity,
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roundness and aspect ratio, respectively, indicate proper fitting of the models to
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experimental data. The signal to noise ratio was measured by adequate precision, which a ratio greater than 4 is favorable. All adequate precisions obtained, are greater than 4, indicating adequate signals. Therefore, the values of each shape parameter and their differences within experiments are significant. In this respect, process factors under investigation affect morphological parameters.
ACCEPTED MANUSCRIPT References Ahmed, M. M., 2010. Effect of comminution on particle shape and surface roughness and their relation to flotation process. Int. J. Miner. Process. 94(3), 180-191. Anfruns, J.F., 1977. Rate of capture of small particles in flotation. Trans. Inst. Min.
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Vizcarra, T.G., Wightman, E.M., Johnson, N.W. and Manlapig, E.V., 2011. The effect of
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List of Tables Table 1 Characterization and operational conditions of OBM and CBM
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Table 2 Physical characterization of the feed ore sample
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Table 3 Designed experiments with different ball charge distributions and surface area for
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Table 4 Sequential Model Sum of Squares [Type I] for morphological parameters
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Table 5 ANOVA results of regression models for morphological parameters
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Table 1 Chemical compositions of main oxides in head sample using XRF Component Weight (%) SiO2 99.46 Al2O3 0.31 Na2O 0.01 MgO 0.01 K2O 0.01 TiO2 0.011 MnO 0.001 CaO 0.06 Fe2O3 0.05 LOI 0.03
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Feed capacity (g) 740 670
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Table 2 Characterization and operational conditions of OBM and CBM Mill Types Length (mm) Diameter (mm) Liner configuration OBM 127 304.8 smooth CBM 355.6 177.8 wavy
Ball Charge (%) 10 10
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Table 3 Designed experiments with different ball charge distributions and surface area for both mills Ball size distributions in experiments (Test No.) Mill Ball Diameter 1 2 3 4 types sizes (mm) Small 19.72 48 0 0 0 OBM Medium 25.95 0 12 8 0 Large 31.68 0 5 7 12 Total surface area (cm2) 586.14 411.51 389.95 378.35 Small 19.72 44 0 0 0 CBM Medium 25.95 0 10 0 7 Large 31.68 0 5 11 6 Total surface area (cm2) 537.54 369.20 346.82 337.26
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F-Value
p-value
56.99 1.27 0.80 7.35
< 0.0001 0.3411 0.3976 0.0396
9.69 1.73 18.67 1.46
0.0016 0.2299 0.0025 0.3624
13.47 2.99 13.38 1.02
0.0004 0.0881 0.0064 0.4935
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Table 4 Sequential Model Sum of Squares [Type I] for morphological parameters Factor Source S.S.α df M.S.β Mean vs Total 6.28 1 6.28 Linear vs Mean 1.632E-003 3 5.439E-004 2FI vs Linear 3.412E-005 3 1.137E-005 Circularity Quadratic vs 2FI 7.296E-006 1 7.296E-006 Cubic vs Quadratic 6.435E-005 4 1.609E-005 Residual 8.757E-006 4 2.189E-006 Total 6.28 16 0.39 Mean vs Total 7.19 1 7.19 Linear vs Mean 9.878E-004 3 3.293E-004 2FI vs Linear 1.492E-004 3 4.973E-005 Roundness Quadratic vs 2FI 1.809E-004 1 1.809E-004 Cubic vs Quadratic 4.597E-005 4 1.149E-005 Residual 3.157E-005 4 7.894E-006 Total 7.20 16 0.45 Mean vs Total 40.01 1 40.01 Linear vs Mean 0.010 3 3.500E-003 2FI vs Linear 1.557E-003 3 5.189E-004 Aspect ratio Quadratic vs 2FI 9.763E-004 1 9.763E-004 Cubic vs Quadratic 2.945E-004 4 7.362E-005 Residual 2.894E-004 4 7.235E-005 Total 40.02 16 2.50 α Sum of Squares. β Mean Square.
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Comment significant significant significant significant
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Table 5 ANOVA results of regression models for morphological parameters Factor Source S.S.α df M.S.β F-Value p-value Model 1.632E-003 3 5.439E-004 56.99 < 0.0001 Aγ 4.029E-004 1 4.029E-004 42.22 < 0.0001 Bγ 3.342E-004 1 3.342E-004 35.01 < 0.0001 Cγ 5.656E-004 1 5.656E-004 59.27 < 0.0001 Circularity Residual 1.145E-004 12 9.544E-006 Cor Total 1.746E-003 15 R2 0.9344 Adeq. Precision 23.633 Model 9.878E-004 3 3.293E-004 9.69 0.0016 Aγ 1.684E-004 1 1.684E-004 4.96 0.0459 Bγ 4.912E-004 1 4.912E-004 14.46 0.0025 Cγ 2.016E-004 1 2.016E-004 5.93 0.0314 Roundness Residual 4.077E-004 12 3.397E-005 Cor Total 1.396E-003 15 R2 0.7079 Adeq. Precision 9.663 Model 0.010 3 3.500E-003 13.47 0.0004 Aγ 1.168E-003 1 1.168E-003 4.50 0.0555 Bγ 5.125E-003 1 5.125E-003 19.73 0.0008 γ C 2.911E-003 1 2.911E-003 11.21 0.0058 Aspect ratio Residual 3.117E-003 12 2.597E-004 Cor Total 0.014 15 R2 0.7711 Adeq. Precision 11.088 α Sum of Squares. β Mean Square. γ A, B and C are coded factors for ball surface area, feed sizes and ball mill types, respectively.
significant significant significant significant
significant significant significant significant
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List of Figures Fig. 1. Denver laboratory ball mills (OBM and CBM): (a) general view, (b) inside view Fig. 2. Process flow sheet Fig. 3. Photomicrographs of quartz (ground particles of OBM for fine-grained feed, test
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1): (a) -250+212, (b) -212+149, (c) -149+105, (d) -105+53, (e) -53+37 micron size
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Fig. 4. Image processing technique: (a) photomicrograph of quartz, (b) converted
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Fig. 5. Effect of ball charge distributions and feed sizes on morphological parameters: (a) effect of the variables on circularity of particles for CBM, (b) effect of the variables on
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Fig. 6. Effect of ball charge distributions and mill types on morphological parameters: (a) effect of the variables on circularity of fine-grained feed, (b) effect of the variables on
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circularity of coarse-grained feed, (c) effect of the variables on roundness of fine-grained feed, (d) effect of the variables on roundness of coarse-grained feed, (e) effect of the
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Fig. 7. Comparison of various morphological parameters for both mills: (a), circularity, (b) roundness, (c) aspect ratio
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Name Feed Sample Ground Product Circulating Load Product Passing 250 micron screen Product Passing 38 micron screen Laboratory Ball Mill Control screen (250 micron) Control screen (38 micron)
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Fig. 3. Photomicrographs of quartz (ground particles of OBM for fine-grained feed, test 1): (a) 250+212, (b) -212+149, (c) -149+105, (d) -105+53, (e) -53+37 micron size fractions.
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Fig. 4. Image processing technique: (a) photomicrograph of quartz, (b) converted photomicrograph to binary image, (c) elimination of particles at the corner of image or overlapping each other.
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Effects of ball mill types, feed sizes and ball surface area on particle morphology have been examined. Different ball mills lead to various breakage mechanisms and morphologies. Coarse-grained ground particles are more round and circular. Circularity and roundness were increased as a result of increasing ball surface area.
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