Separation performance of double deck banana screens – Part 1: Flow and separation for different accelerations

Minerals Engineering 22 (2009) 1218–1229

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Minerals Engineering journal homepage: www.elsevier.com/locate/mineng

Separation performance of double deck banana screens – Part 1: Flow and separation for different accelerations Paul W. Cleary a,*, Matthew D. Sinnott a, Rob D. Morrison b a b

CSIRO Mathematical and Information Sciences, Private Bag 33, Clayton South 3168, Australia Julius Kruttschnitt Mineral Research Center, The University of Queensland, Isles Rd., Indooroopilly, Qld 4068, Australia

a r t i c l e

i n f o

Article history: Received 4 March 2009 Accepted 3 July 2009 Available online 3 August 2009 Keywords: Screening Separation Discrete element method DEM Banana screen

a b s t r a c t Banana screens are often used for high capacity separation of iron ore, coal and aggregates into different size fractions. They consist of one or more curved decks that are fitted with screen panels with arrays of square or rectangular holes. The screen structure is vibrated at high frequency to generate peak accelerations of around 4–6g which separates particles flowing over each screen according to their size. Screens are often used to close comminution circuits and return specific size fractions of rock to different destinations such as pebble mills, crushers and back into the mills. All multi-deck screens are difficult to sample for intermediate products which makes measurement and optimization very difficult. Banana screens are even more difficult because the screen cut size varies with the varying slope of the decks. In this paper, the discrete element method (DEM) is used to simulate a full industrial scale double deck banana screen for a range of accelerations. The nature of the particle flow through this complex machine is explored for a range of peak accelerations. Critical aspects of the flow are linked to the separation performance. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction A large proportion of two of Australia’s most valuable export commodities – iron ore and coal – are processed using high capacity, curved, vibrating screens called ‘‘banana” screens because of their curved profile. These screens have many adjustable parameters and are much less well understood than conventional flat vibrating screens. They consist of one or more curved decks that are fitted with screen panels with arrays of square or rectangular holes. The screen structure is vibrated at high frequency to generate around 4–6g of acceleration. A dense stream of particles is loaded onto the upper end of the screen. They accelerate down the steeper early panels of the screen and slow as the panel angle decreases towards the discharge end. The material discharging from the top of the deck is the oversize and may become a coarse product or be crushed and recycled to the screen feed. The material falling through the deck can be further separated by additional decks below. Each lower deck returns a product stream and the material passing out through the bottom deck is the undersize. Screens are also often used to close comminution circuits and return specific size fractions of rock to different destinations such as pebble mills, crushers and back into the mills. The screen performance can strongly affect the overall circuit performance. * Corresponding author. Tel.: +61 3 9545 8005; fax: +61 3 9545 8080. E-mail address: [email protected] (P.W. Cleary). 0892-6875/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2009.07.002

Large banana screens are usually operated with a series of screen panels with different sizes and shapes of apertures. Because the screen produces only two or three products, it is very difficult to tell which panel selection strategies are most effective. Similar comments apply to wear of screen panels. Hence, a DEM study has much to recommend it in that significant quantitative data can be obtained about the relative contribution of each part of the screen. There is also a good chance that the exchange of energy between particles and each screen surface will provide at least an indicator of areas of high wear. DEM is also expected to be able to test a range of strategies for optimization of screen operating conditions, panel selection and wear minimization with a view to increasing capacity and availability. A major complexity is that the screen operation is strongly affected by particle shape. Hence the spheres and aggregations of spheres typically used for DEM simulations are not suited to this task. Parametrised super-quadric particles are used in a DEM model here to provide a flexible and more realistic class of particle shapes allowing detailed analysis of the banana screen performance. The aspect ratios of the particles have been measured for a range of ore types and should increase the degree of realism of the simulations. Much of the existing theoretical literature on granular screening is more than 20 years old. Prior to the maturation of analytical tools for studying particulate systems such as the discrete element method (DEM), it has been difficult to obtain fundamental insights

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into how bulk granular materials with large size distributions interact with moving screen deck surfaces and apertures. Standish (1985) considered the kinetics of particles in batch screening and found that the presence of oversize particles in the feed significantly enhanced screening rate. Standish et al. (1986) then extended the kinetics approach to determine the effect of certain operating variables (flow rate, deck inclination, deck speed, and degree of oversize) on the performance of a vibrating screen for sinter and coke particles. This study was the first to determine details of the screening of individual sizes based on the kinetic constants for each size. A method proposed by Nakajima et al. (1978) determined the shape and size distribution of non-spherical particles for square aperture screens. The Whiten and White (1977) model was unable to predict the screening sizes of non-spherical particles on slotted screens and so the Nakajima model was modified (Nakajima and Whiten, 1979) using an empirical probability function to give the fraction recovery of non-spherical particles in the oversize for rectangular aperture screens. Dehghani et al. (2002) replaced the empirical function in the Nakajima model with a probability equation depending on particle dimensions, and derived a regression function of operating variables for rectangular aperture screens for predicting screen efficiency. Soldinger (1999) considered particle transport in the shaken granular bed on the screen and its effect on the rate of passage through the screen. He developed a model to relate stratification in the vibrated bed for different particle sizes to the mass flow through a screen. From this, the transport of fine material into and out of the bottom layer adjacent to the screen could be related by determining the rates of stratification and transport through the screen. This model was extended (Soldinger, 2000) to account for the effects of material loading and particle size distribution on screening efficiency. Stratification rate was found to diminish with larger bed thickness, and when the fines proportion exceeded 60% of the size distribution due to fines plugging the holes between large particles. Passage through the screen was found to be more probable for larger beds, due to the reduced relative movement between bottom layer and screen. DEM now provides the ability to simulate screening applications for millions of particles by directly modelling the collisions between individual grains in the granular mass, and their passage through screen decks of very complex geometry. However, to date there are very few published DEM models of screens, and with the exception of Cleary and Sawley (2002) and Cleary (2004) who looked at a periodic section of a vibrating flat screen all of these are two dimensional. Li et al. (2002) used a linear-spring dashpot DEM model to consider the effect of bed depth on the screening of a binary mixture of different agricultural seeds. The seeds were modelled as two dimensional circular disks and the inclined screen deck as a series of equi-spaced, fixed DEM particles with voids in between. They found that larger bed depths necessitated a longer screen deck to maintain screen efficiency under increased loadings. In a broader numerical study, Li et al. (2003) demonstrated that large, oversize particles promote greater flow through the screen and near-mesh size particles tend to block or jam the apertures for finer material resulting in a sudden decrease in screening efficiency to almost zero. In this paper, DEM is used to simulate a full industrial scale double deck banana screen in three dimensions. A highly realistic screen geometry is used and realistic particle shapes are also used in the model. Flow patterns on each screen deck are predicted for a range of screen accelerations and two feed size distributions. The separation performance of each deck is then analysed and related to the structure of the flow and to the distribution of material within the screen. In the second part of this paper, detailed quantitative predictions of flow rates and residence time distributions for different size classes are used to understand the individual

contributions of each screen panel for each deck. The performance characteristics of each screen deck will be shown to be quite different. The stresses applied to the screen cloths by the flowing particles and the impact and abrasive wear on the screen surfaces will also examined. Finally, the energy absorbed by particles provides insight into the extent of particle degradation produced by transiting the screen. 2. Simulation technique The discrete element method is a numerical technique used to predict the behaviour of collision dominated particle flows. Each particle in the flow is tracked and all collisions between particles and between particles and boundaries are modelled. The particles are allowed to overlap and the extent of overlap is used in conjunction with a contact force law to give instantaneous forces from knowledge of the current positions, orientations, velocities and spins of the particles. Here we have used the simplest of the force laws which is the linear spring-dashpot model. The overlap Dx scaled by the spring constant k provides a repulsive force. The dashpot contributes an inelastic component to the collision. The damping coefficient C is determined from the specified coefficient of restitution for each combination of materials colliding. The spring and dashpot together define the normal force:

F n ¼ kDx þ C v n

ð1Þ

where vn is the normal component of the relative velocity at the contact point. In a similar way, the tangential force has an incremental spring based on the integrated tangential displacement and a dashpot for inelastic dissipation. The tangential force is then subject to the sliding Coulomb friction limit to give:

F t ¼ min



lF n ;

Z

kv t dt þ C v t

 ð2Þ

where vt is the tangential component of the relative velocity at the contact point and l is the coefficient of friction. A general review of DEM and its variants can be found in Barker (1994). The essential elements of the algorithm for the simulation procedure are: (1) A search grid regularly maintains a near-neighbour interaction list for all particle pairs and particle–boundary pairs that might participate in a collision in that given period. (2) For each timestep, this list is used to identify all collisions involving particles and boundary elements. The forces on particle pairs and boundaries are evaluated using the contact force model. (3) All the pair-wise collision forces and torques are summed to give net forces and torques. Forces from other forms of interaction can also be added in this step. Newton’s equations of motion and the matching kinematic equations are then integrated to give the changes in the position, speed, orientation and spin of the particles in response to these net forces and torques. Steps 2 and 3 are repeated sequentially stepping the system state forward in time until the search information is no longer valid. Then a new search (step 1) is performed to update the interaction list. This implementation of DEM has been used to model a broad variety of industrial granular flows (see Cleary, 2004; Cleary and Sawley, 2002; Cleary et al., 2008 for examples). More details of the implementation can be found in Cleary (1998). DEM simulations of real materials require more complex particle shape descriptions. The inclusion of shape is important for correctly predicting the failure and flow of granular solids.

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Spherical particle typically flow in an overly fluid like manner, have angles of repose that are too low and often incorrectly predict quantitative details of the flows. It is also reasonable to expect that the shape of particles will affect their ability to move through rectangular holes in a vibrating screen. A flexible class of shapes that balance increased realism with acceptable loss of computational speed is the super-quadric (SQ). This enables the angularity and aspect ratios of the particles to be included in the modelling allowing more realistic flow predictions. Super-quadrics are described by:

 x m a

þ

y m b

þ

zm c

¼1

ð3Þ

The resultant particles are somewhere between an ellipsoid and a rectangular box with the angularity/smoothness of the corners controlled by the choice of m (with m = 2 being ellipsoidal and large m being a box) and the aspect ratios being controlled by the ratios of the semi-major axes (b/a and c/a). These shapes were first used in two dimensions by Williams and Pentland (1992) and in three dimensions by Cleary (2004) which shows a number of examples of DEM using super-quadric shaped particles. 3. Two deck banana screen configuration and operation An industrial screen consists of several key components:  Frame  Motors  Base springs

 Top deck cloth  Bottom deck cloth  Supporting infrastructure A typical configuration is shown in Fig. 1a. The frame which is spring mounted on a base and which is free to move in response to the balance of forces created by the motors, gravity and the transient weight of the bed of material flowing through the machine. The driving motors (marked as M in Fig. 1a) are the complicated structure located at the top of the frame half way along the length of the screen. This consists of four heavy off center weights shaped as circular sectors that are located at the ends of two parallel shafts. The shafts are linked by a robust gear box to ensure their motions remain synchronised and are driven by the motor to rotate in opposite directions. The changing center of mass of these weights then forces the screen to move in a specific direction. As the weights rotate to the other side the screen is forced to move in the other direction. The phase difference between the two sets of rotating weights controls the shape of the motion generated by the screen motors. Here we use a linear motion directed at 45° upwards and towards the discharge direction. This is one of the most common types of screen motion and is often used for iron ore screens. This screen is 2.4 m wide by 6.1 m long and has two decks which allow the incoming particle stream to be separated into an oversize stream from the top deck, a product stream from the bottom deck and an undersize passing out the bottom of the machine. The decks consist of a series of linear sections which start with a

Fig. 1. Twin deck banana screen used in the DEM model: (a) overall schematic of the system including feeder and discharge chutes and conveyors, (b) cloth for the top deck, and (c) cloth for the bottom deck. M – driving motors. T – Top deck. B – Bottom deck. CT – top deck chute. CM – bottom deck chute. CU – Undersize chute.

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steeper inclination and which are then decreased progressively along the screen. This gives each deck a banana like shape after which the machine is named. The positions of the top and bottom decks are marked by the letters T and B in Fig. 1a. Particulate material is fed into the machine at the top right end of the machine as shown in Fig. 1a. In these simulations we use an inclined vibratory feeder to provide the feed stream. This is not shown in the configuration. Around 250 mm below the edges of the frame at the top end of the machine is a steel floor which leads to the start of the top deck cloth. A stream of feed material is poured into this part of the screen which fills up and acts as a rock box to reduce wear. Particles then start to flow from the rock box down onto the top deck of the screen. The top deck cloth is shown in Fig. 1b. It is called cloth but can be either steel or very tough polyurethane. The top deck has eight cloth panels across the width of the screen and five sets of panels along the length of the top deck. Each panel has an array of 2  7 rectangular holes, with each hole being 70 mm wide and 130 mm long (in the direction of flow along the screen. The top panels are inclined at 33°. The inclination of the panels decreases to 10° at the bottom. The cloth is geometrically very complex with 592 holes. As particles flow down along the top deck they accelerate with some particles smaller than the cloth aperture size being trapped and falling through to the bottom deck below. Particles that are not able to pass through the screen deck, either because they are too big to fit through the holes or because the flow did not provide them sufficient opportunity to reach and pass through the holes are discharged from the end of the top deck. A stream of these ‘oversized’ particles is then collected by the top deck chute (labeled as CT in Fig. 1a) where they are slowed and allowed to flow down onto the top deck oversize conveyor. This is directed away from the viewer in Fig. 1a so that the rear pulley around which the conveyor belt wraps is visible below the chute. The bottom deck has a similar overall structure, with a banana shape parallel to the top deck and five sets of panels along its length. The bottom deck cloth is shown in Fig. 1c. In this case there are four panels across the width of the screen and an array of 10  13 holes in each panel. This means there 2720 holes in the screen cloth that need to be fully resolved in the simulation. Each hole is 35  65 mm with the longer dimension in the direction of flow along the screen. The panel angles are the same as for the top deck. Note that there is no alignment of the positions of the top and bottom decks. Each panel is supported by structural supports in the frame which can impede the flow of particles that have passed through the top deck cloth, so all the internal structural elements of the screen frame need to be included in the simulations. Unlike for the top deck where the feed material enters at the start of the top deck, material falls onto the bottom deck along its entire length. This means that the loading and flow on the bottom deck are substantially different to the top deck. The bottom deck is fully enclosed and it is extremely difficult to photograph or measure anything about the dynamics of this critical part of the screen which is responsible for the separation of the screen product. The material falling from above collects on the bottom deck to form a flowing bed which again accelerates down the inclined slope of the cloth. Particles which are small enough can be trapped by the holes and fall through into the undersize collection chute (labeled CU in Fig. 1a) below the screen. These particles then discharge onto an undersize conveyor that passes directly under and parallel with the screen. Particles that are either too large to pass through the bottom deck cloth holes, or which do not have an opportunity because of their location in the flow discharge from the end of the bottom deck. These particles are collected by the bottom deck chute (labeled CM in Fig. 1a) where they are slowed and dropped down onto the middle conveyor. This is directed towards the viewer in Fig. 1a.

The cloth details for the top and bottom decks are summarised: Top deck     

8  5 panels 2  7 holes for most panels Total of 592 holes Each hole is 70  130 mm Panels inclination varies from 33° (top) to 10° (bottom)

Bottom deck     

4  5 panels 10  13 holes for most panel Total of 2720 holes Each hole is 35  65 mm Panels inclination varies from 33° (top) to 10° (bottom)

The aim of this screen is to divide the incoming particle stream into three outgoing streams; two streams of oversized material and a product stream which is the undersize of the bottom deck. Depending on the nature of what is being separated the product from the screen is one or more of these separated streams. An example of the use of a screen configured in this way would be for scalping crushed iron ore. The oversize material from the two screens would be returned to the crusher for further size reduction. The undersize iron ore product stream from this screen would be fed to a nominal 6 mm cut size product screen. The oversize and undersize of the product screen are designated as ‘‘lump” and ‘‘fines” which are saleable products. The apertures of the screens are chosen to target specified cut sizes for each stream. The sharpness of the cut of the top scalping deck is not critical as its function is to reduce the load of large particles reaching the bottom deck. The sharpness of cut of the bottom deck is critical as it not only determines the quality of the separation process, but it also controls the recovery of final products. This is critical to the operating performance of the plants using them. In the iron ore example if the bottom deck does not cut sharply, significant amounts of material that should be ‘product’ are returned for recrushing which increases the costs of processing, reduces capacity at the crusher to crush new material and will excessively reduce the size of the returned material creating unnecessary extra undersize material. Similarly, if the product screen does not operate efficiently, excess undersized material is sent to the product stream and reduces the capacity for real product to be processed and reduces the quality of the product by the inclusion of unwanted fine material – which may attract a price penalty if it exceeds a specified level. However, by far the most important economic factor is the screen capacity. Efficient removal of all saleable product increases the effective capacity of a closed circuit system. However, for any applications that use multi-deck screens, it is difficult to assess the quality of separation visually. A realistic DEM model should be able to reveal intermediate deck performance in detail. The key geometric and operating conditions of the screen are given in Table 1. The feed material used is a generic rock with a solid Table 1 Key geometric and operational parameters for the screen. Screen length Screen width # Decks Screen type Vibration frequency Vibration amplitude Vibration type Feed rate

6.1 m 2.4 m 2 Banana 1000 rpm 5.5–14 mm Linear at 45° 1000 tph

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Table 2 Feed particle size distribution. Class

Size range (mm)

Feed 1 composition (%)

Feed 2 composition (%)

1 2 3 4 5 6 7 8 9 10 11

200 to +140 140 to +100 100 to +70 70 to +60 60 to +49 49 to +42 42 to +35 35 to +28 28 to +22 22 to +18 18 to +15

5.0 5.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

5.0 5.0 10.0 10.0 10.0 10.0 10.0 7.5 7.5 7.5 17.5

density of 1400 kg/m3, a top size of 200 mm and bottom size of 15 mm. Two feed size distributions are used here and given in Table 2. Particle shape is critical for separation so the particles are modelled as super-quadrics. Their attributes are:  Blockiness uniformly distributed in the range 2.1–4.0 (round to moderately blocky).  Aspect ratio for the intermediate axis which is uniformly distributed in the range 0.85–1.0.  Aspect ratio for the short axis which is uniformly distributed in the range 0.7–1.0. The size distribution is determined by the length intermediate axis of the particles. This is used in quantitative reporting. Eighteen measurement planes are used to measure the particle size distributions, flow rates and residence times of particles passing through each screen panel and when entering or leaving the machine. The spring constant used in these simulations was 104 N/m. This gives very conservative mean overlaps of 0.35–0.45%. The Cundall number (number of particle timesteps per cpu second) is 40,000 and the Hopkins number (=Cu  average number of neighbours) is 200,000 on a 3.6 GHz single core cpu Pentium desktop computer. 4. Equilibrium particle flow on the vibrating screen The screen begins each simulation empty and particles are fed onto it from a vibrating feeder that is located above and to the right of the screen. The particles flow down into the rock box where they build up before flowing along the top screen and forming a bed. Smaller particles pass through the top deck and build up on the bottom screen. Some pass through the bottom screen to the undersize. Over time, there is an accumulation of material in each part of this multi-component system until the system reaches an equilibrium state. For this particular screen, the time to reach equilibrium is 13–20 s, which is more than 10 times the minimum residence time of particles in this system. The approach to equilibrium is evaluated by monitoring the number of particles, the mass of particles and the kinetic energy of the particles. When these have all become constant then the system is in equilibrium. The approach to equilibrium is not particularly useful for studying screen performance and so a detailed analysis of this is not included. 4.1. Flow for a peak acceleration of 14g Fig. 2 shows the particle flow on the vibrating screen for a high peak acceleration of 14g with feed size distribution 1. The top image shows particles coloured by speed and the bottom image shows particles coloured by size. In Fig. 2a, the broad particle distribution enters the front of the rock box from the vibrating feeder above. The material at the back of the rock box is stagnant (blue)

whilst the material at the front flows down and onto the screen at about 2 m/s. The combination of the strong forward vibration of the screen and the steep angle of the first panel causes the particles to accelerate along the top deck. The peak speeds of 4–5 m/s are reached in the middle of the screen (over panels 2 and 3) and then starts to decline during passage over the shallower angle of panel 4. Particles move at around only 2 m/s across the fifth panel and discharge from the top deck into the receiving chute at this speed. The receiving chute for the top deck captures the particles and drops them onto the higher of the discharge conveyors which is oriented orthogonal to the direction of flow on the top deck. This is the oversize stream of material that is nominally too coarse to pass through the top deck of the screen. Particles start to flow through the top deck of the screen once they have passed onto the first panel. The amount of material passing through this panel is very modest. The mass passing through the second panel is larger and a bed forms on the bottom deck. The high entry speed of the particles combined with collisional interaction with the rapidly vibrating bottom deck gives the particles high speeds of 2–5 m/s and produces a strongly dilated bed. The bed depth on the bottom deck increases along the screen with the thickest section resulting from particles passing through the top deck from the end panel. This is due to two main factors: (1) The bed on the top deck only becomes well enough stratified by the end panel and (2) the lower flow speed on the shallowest angle end panel allows the particles more time to pass through the screen apertures. The bottom deck is really only well loaded by the last panel. The slow build up of the bed and its dilated nature strongly inhibit the bottom deck from working effectively. Most of the separation occurs for the bottom deck around the last panel. This can be seen by the density of the undersize stream passing through each panel of the bottom deck. The undersize is collected by a large chute underneath the screen which funnels the particles falling through the bottom opening of the screen onto the bottom belt. The remaining particles on the middle deck form a stream which discharges into the middle chute and flows onto the middle conveyor. For these operating conditions the separation performance is visibly poor with a quite small undersize stream. The upper end of the bottom deck screen is seriously under-utilised because of the very low bed depth on the upper panels. The poor flow through the early panels of the top deck results from: (1) High particle speed which gives very short capture periods for the openings and (2) the need for fine material to percolate down through the flowing bed to reach the openings in the cloth. Fig. 2b shows the particles coloured by diameter with red being large, greens being intermediate and blues being fine material. Looking at the stream falling from the vibrating feeder it is clear that the material at the bottom is substantially blue finer material and that the coarser material sits above this. The motion of the feeder leads to strong vertical stratification of the particles. The counter-current feed arrangement, often used in industry, has the very unfortunate effect of depositing the finer material at the top surface of the bed on the top deck and the coarser material underneath adjacent to the cloth of the top deck. This means that the bed is maximally stratified in the wrong direction when it enters the first panel of the top deck. It takes some time for the bed flowing down the screen to become vertically stratified with the finer material near the deck and the coarser material near the free surface. This stratification process occurs by percolation of the finer

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Fig. 2. Particle distribution on the screen vibrating with 14g peak acceleration at two times during a vibration cycle for a particle bed that is in equilibrium for feed 1; coloured by (top) speed with red being high speed and blue being low, and (bottom) by particle size (red to green to blue for coarse to fine).

material through the shearing bed. There is a visible reduction of blue fine material along the length of the top screen deck. The upper half of this deck is dominated by blue colouring but the lower half is dominated by yellow and green shades. The very large but sparsely spaced red particles are distributed along the length of the bed and are predominantly at the free surface by the time the bed material reaches the fourth panel. The particles flowing through the top deck to form the bed on the bottom deck are entirely dark blue, light blue and green. The dilation of the bed in the upper half of the screen bottom deck makes it difficult to observe composition variation along the screen. The underflow consists of just dark and some light blue particles. The flow through the early panels of the bottom deck is very weak, with the majority of the separation occurring in the last two panels when a reasonable depth bed has finally formed. The quality of the separation is shown by the colours of the material on each of the product stream belts. Clearly all the coarser material has reported to the oversize stream (as intended) but there is also a

significant fraction of light blue material retained on the top deck that has not passed through the top deck screen. The middle stream ranges in colour from dark blue to yellow. This dark blue component should have reported to the undersize stream so the separation of the screen operating at 14g peak acceleration is well short of optimal. 4.2. Flow for a peak acceleration of 6g Fig. 3 shows the particle flow on the vibrating screen for a peak acceleration of 6g with feed size distribution 1. The top image shows the particles coloured by speed and the bottom image shows the particles coloured by size. The flow from the vibrating feeder into the rock box at the top of the screen is the same as previously since this is not influenced by the screen motion. The mass (and depth) of material in the rock box and consequently the initial bed depth when flowing onto the start of the first screen panel are increased for the lower acceleration. The bed again accel-

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Fig. 3. Particle distribution on the screen vibrating with 6g peak acceleration at two times during a vibration cycle for a particle bed that is in equilibrium for feed 1; coloured by (top) speed with red being high speed and blue being low, and (bottom) by particle size (red to green to blue for coarse to fine).

erates down the top deck with maximum speeds being reached over the third panel. The peak speed though is reduced from above 4.5 m/s to around 4.0 m/s with only the occasional freely falling large surface particle reaching higher speeds (coloured red). The volume of fast moving material (shown as the yellow through to red colours) is significantly reduced and the amount of ballistic material flying above the free surface of the bed is sharply reduced. The bed is much more coherent and its surface is much more sharply defined. Particles in a saltating layer above the bed surface are not able to size segregate and cannot be separated. The presence of a large dilated saltating surface bed (as can be seen in Fig. 2 for the 14g case) is likely to indicate that a screen is being operated at too high a peak acceleration. The reduced screen acceleration for the case in Fig. 3 also sharply slows the particles on the lower sections of the top deck with the speed on the critical last panel being reduced from around 2– 3 m/s (green) to around 1.0–1.5 m/s (light blue). This means that the residence times of the particles are sharply increased (by around a factor 2) significantly increasing the time of passage over

the individual apertures in the screen deck and therefore strongly increasing the opportunity for suitably sized particles to pass through the holes in the screen. The separation performance of the top deck has visibly been sharply improved. This is most noticeable in the much stronger flow of particles through the first two panels of the top deck leading to the much more rapid build up of a coherent bed on the bottom screen deck. The cloth is substantially obscured beyond half way along the first panel of the bottom deck and none of the third or later panel cloth is visible at all. The particles reach high speeds (red) as they fall between the screen decks but slow as soon as they join the bed on the bottom deck. The bed moves at around 1.5–2.5 m/s while travelling over the second and third panels which is much lower than the speed for the 14g case. The inclination decrease of the fourth panel appreciably slows the flow to around 1.0–1.5 m/s (light blue). With the further decrease in screen angle for the fifth panel the flow slows much further to around 0.5–1.0 m/s. There is a noticeable increase in bed thickness at the start of the fifth panel as the stream slows. This is enhanced by the very large flow rate of material falling from

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the fifth panel of the top deck above. The speed distribution along the bottom deck is quite different to that found for the top deck, except for the fifth panel where the flow speeds are similar. Examining the flow through the bottom deck screen and into the undersize collection chute, it is very clear that the volume of material being separated into the undersize stream is substantially higher for the 6g case than for the 14g case. There is already a significant flow through even the first panel and a reasonable amount of material deposited at the top of the undersize chute. The flow through the second and third panels is now quite strong. The flow through the last two panels of the bottom deck are now significantly higher than for the previous case where even the largest flow from the fifth panel was quite small. This demonstrates the strong non-linear sensitivity of screen separation performance with the peak acceleration. The lower flow speeds on the fifth panels of each deck mean that the discharge speeds are much lower and the flows into and through the collection chutes for each of the decks are much more ordered and fluid like. There is little sign of the dilute energetic particles flowing over the dilated material flowing through the chutes observed in the 14g acceleration case. The discharge onto the conveyor belts is then also much more ordered. The bed on the bottom deck builds up much faster for the 6g acceleration case than for the 14g case. But the bulk of the material entering the bottom deck bed still does so from the second half of the top deck. This means that the first half of the bottom deck, whilst now being used better than in the earlier case, appears to still be under-utilised. It is clear that one of the major design challenges for multi-deck screens is to maximise the utilisation of the bottom deck by most rapidly establishing a deep, stratified, shearing bed on top of it. Fig. 3b shows the particles now coloured by size for the 6g peak acceleration case. The feed stream is the same as for the previous 14g case (Fig. 2b). The most marked change is that the distribution of finer (blue) material is completely different. The finer material rapidly percolates away from the free surface leaving a bed that is rapidly dominated by medium to large particles. The majority of the very fine (dark blue material) disappears below the surface almost immediately. Over the second and third panels some light-mid blue material is still visible but is much reduced in volume. There is a further clear reduction in fine material (blue) over the fourth panel. There is essentially no visible sign of any blue material remaining in the bed as it travels over the fifth panel of the top deck. The particle bed is clearly much shallower here than for the previous panels. The material flowing onto the oversize conveyor still contains a small amount of fine material but is dominantly coloured yellow through to red, representing all the coarse fractions. This indicates that the cut size for the top deck has increased sharply with the reduction in peak acceleration. The fill level on the exit conveyor is significantly lower for the 6g case indicating that more material has been separated from the oversize product stream. The bed on the bottom deck is rapidly established and is predominantly blue with some green on the first panel. There is a clear and strong composition variation along the bottom deck with the green material becoming significant over the fourth panel. The yellow and green material dominate the bed composition over the fifth panel with only a modest amount of blue material remaining visible here. The composition variation along the bottom screen deck results from the finer material entering the bed earlier through panels 1–3 of the top deck, with the medium size material predominantly entering the bottom deck bed only over the last few panels. Similarly, the finer material having been on the bottom deck longer and having been well stratified by the third panel flows very easily through the apertures of the bottom deck. The combination of the coarser material arriving later onto the bottom deck

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bed along with the earlier separation of the finer fractions leads to highly visible size variation along this deck. The fill level on the exit conveyor for the bottom deck is significantly higher for the 6g case indicating that much more material has been separated into the main product stream. The material on this conveyor is also significantly coarser than for the previous case with the dominant colours now being yellow and green, with only a small amount of blue compared to the dominant blue to green colouration for the earlier case. 4.3. Flow for a peak acceleration of 5g Fig. 4 shows the particle flow on the vibrating screen when the peak acceleration is further reduced to 5g and using feed size distribution 2. The difference between the two feed sizes is that the distribution is mildly more heavily weighted towards the finer material. This is a bit more realistic but is not expected to be a particularly strong effect. The top image of Fig. 4 shows the particles coloured by speed and the bottom image shows the particles coloured by size. The flow from the vibrating feeder into the rock box at the top of the screen is the same as for the previous cases since this is not influenced by the screen motion. The flow through the screen is similar to that observed for the 6g peak acceleration (Fig. 3). The differences observed with the reduction of the acceleration from 6g to 5g are small compared to the differences found when decreasing from 14g. Nonetheless some minor differences are observed. The peak speed on the top surface of the top deck bed is slightly lower and the fraction of faster material (yellow through to orange) is reduced. There is more material trapped in the rock box and it moves more slowly. The slowing of the bed over the fourth panel of the top deck is much more pronounced with the lowest material in the bed being a much darker blue. This means that the bed material adjacent to the cloth which can be separated by this panel has much more time available to pass through the screen apertures. There is an appreciable increase in bed thickness at the start of the fifth panel as the stream slows to 0.5–1.0 m/s as compared to 1.0–1.5 m/s for the 6g case. This almost halving of the bed speed doubles the residence time distribution on this panel giving much more time for separation to occur. Otherwise the top deck bed structure is very similar to that of the 6g case. In particular, the bed is equally coherent with only scattered saltating surface particles flowing over a dense shearing bed. The bed on the bottom deck also moves with modestly reduced speed for the lower 5g acceleration. The bed now moves at around 1.0–1.5 m/s while travelling over the second and third panels. The inclination decrease of the fourth panel appreciably slows the flow to around 0.5–1.0 m/s (mid blue). With the further decrease in screen angle for the fifth panel the flow slows much further to around 0.5 m/s (darker blue). An appreciable increase in bed thickness is observed at the start of the fifth panel as the stream slows. There is a slight increase in the amount of material visible in the undersize collection chute compared to the 6g case, so the reduction in speed has improved the overall separation slightly. The speed distribution below the bottom deck and for the streams passing through the top and bottom deck chutes and onto the product conveyors are all unaffected as they are dominated by gravitational acceleration. Fig. 4b shows the particles coloured by size for the 5g peak acceleration case. Compared to the 6g case (Fig. 3b) there are some important differences. Firstly, the fine material deposited on the top surface of the bed remains there much longer. For the 6g case the agitation of the bed was enough for them to immediately fall below the surface. For the 5g case dark blue particles remain on or near the free surface until the end of the fourth panel. There

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Fig. 4. Particle distribution on the screen vibrating with 5g peak acceleration at two times during a vibration cycle for a particle bed that is in equilibrium for feed 2; coloured by (top) speed with red being high speed and blue being low, and (bottom) by particle size (red to green to blue for coarse to fine).

are however less dark blue particles visible deeper in the bed. The fine particles reaching the screen cloth are more able to pass through the apertures at the lower acceleration. This highlights the two key components of screen separation and their differing dependency on the screen acceleration: (1) Fine particles percolate through the dense shearing bed. Higher accelerations leading to more agitation of the bed and higher shear improve this component of screen flow. This is responsible for stratifying the bed and providing a layer of fine material adjacent to the screen cloth. (2) Particles smaller than the screen aperture size and which are close to the cloth must be captured by and pass through one of the screen cloth holes. This is dependent on the size and shape of the particle and on the flow. The faster the flow speed and the denser the bed above the cloth, the lower the chance of the particle being able to pass through an aperture.

From Figs. 3b and 4b it is clear that the 6g case provides more rapid stratification of the bed but is less good at the second stage where the particles pass through the screen. In comparison, the 5g case is less good at the bed stratification but offers better chances for separation of near-screen material. For optimal screen separation there must be a balance between these two separation components. Lower accelerations will shift the balance further towards the near-screen separation whilst weakening the bed stratification. So accelerations much less than 5g can be expected to reduce overall separation efficiency. At this preliminary stage we will not try to determine the precise optimal acceleration. For this screen geometry and this feed size material the 5g peak acceleration will be close to optimal. Another question that we will explore in the future is the degree of sensitivity of the optimal acceleration to changes in aperture size and particle size and shape distribution. There is also potential to include a DEM model of the crusher fed by the scalping screen oversize to allow interactive optimization of both units.

P.W. Cleary et al. / Minerals Engineering 22 (2009) 1218–1229 Table 3 Numbers, mass and kinetic energy of particles for different peak accelerations in the simulation configuration once it has reached equilibrium. Acceleration

Number of particles

Mass (tonnes)

Kinetic energy (kJ)

5g 6g

245,000 175,000

3.45 2.95

5.3 6.0

Returning to Fig. 4b we see that the separation of the fines from the top deck is substantially complete over the fourth panel and there is little blue material visible over any part of the fifth panel. Looking at the bottom deck we observe that there is more dark blue material both in the falling streams under panels 1 and 2 and in the bed. The bed is of similar size and density for the two

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cases (5g and 6g) but the material in the bed is clearly finer for the first three panels. By the fourth panel the bed is similar in composition. Over the fifth panel the bed actually looks coarser with more yellow and a small amount of orange material present. This reflects the slightly enhanced separation of coarse material by the fifth panel of the top deck and the enhanced loss of fine material through the bottom deck for the lower acceleration case. The material being collected in the undersize chute is dominated by the fines (blue) with a modest amount of green material. The volume of material collected and the fraction of dark blue finer material is slightly larger for the 5g case. So overall, the decrease in the peak acceleration from 6g to 5g has predominantly led to modest reductions in flow speeds, resulting in larger times available for particles to pass through holes in

Fig. 5. Surface speed of the particles contacting: (a) the frame, (b) the top deck cloth and, (c) the lower deck cloth, for the screen vibrating with 5g peak acceleration. Red is high speed, green is intermediate and dark blue is stationary.

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the screen decks. This is most marked for the fifth panels of both decks. The top deck bed experiences slower stratification but faster transport of fine particles through the screen cloth. This results in slightly larger volumes of finer material in the bottom deck product and undersize streams with a mild reduction in volume for the top deck product. This will correspond to a marginally sharper and coarser cut size for each deck. So the overall separation performance of the screen has been mildly increased by this reduction in peak acceleration. The mass of particles resident on the screen decks after 20 s was 1.56 tonnes for a 5g acceleration which was significantly higher than the 1.16 tonnes found for 6g acceleration. The lower acceleration was observed to lead to slower speeds over the screen decks. This increases particle residence times and thereby increases the load on the screen. Too high an acceleration leads to residence times that are too short to allow adequate separation. Accelerations that are too low lead to deep beds with limited particle mobility and result in poor separation. Table 3 gives further comparative details of these two cases. The total equilibrium mass in the simulated system (which includes particles on the feeder and on the discharge conveyors) is 2.95 tonnes for 6g acceleration. This increases to 3.45 tonnes for the 5g acceleration case. 0.4 tonnes of this 0.5 tonne increase occur for the material actually on the screen deck. There is only a slight change in the mass contained in the rest of the system. The 5g acceleration case has 245,000 particles (which for these simulation times and including particle shape is a significant size computation). The kinetic energy of the particles decreases from 6.0 kW to 5.3 kW when the acceleration is reduced from 6g to 5g. Considering the increasing particle mass this means that the average particle speed has decreased from around 2.02 m/ s to 1.75 m/s. This is the simplest quantification of the speed reduction of the particles produced by the decrease in screen peak acceleration. To help quantify the flow in different parts of the screen we show the two screen decks and the frame for the 5g acceleration case coloured by the surface contact speed of the particles. Fig. 5a shows the frame from the side. The front side of the screen has been removed to allow the velocity distribution on the internal surfaces to be seen. The green band above the location of the top deck shows that the bed travels at fairly uniform speed of 0.6–1.0 m/s near the edges of the screen (due to the friction of the frame sides). Note that this is lower than the particle speed observed in Fig. 4 because the particles are rotating in the shear zones adjacent to the wall which leads to lower contact velocities at the solid surfaces. Contact speeds are similar on the lengthwise structural beams that support the top deck screen cloth. The highest contact speeds are observed on the sides of the frames between decks as the edges of the falling streams of particles accelerate and contact the frame with surface speeds of around 1.5 m/s. Fig. 5b shows the average contact speed on the top deck screen cloth. This clearly shows that the highest speeds of 0.5 m/s are achieved at the bottom of the second and top of the third panels. The speeds on the first and fourth panels are similar ranging from 0.2 to 0.45 m/s. The deceleration of the bed over the shallower angle of the fifth panel is clearly visible with contact speeds observed being only around 0.1 m/s. This figure highlights the very non-uniform nature of the bed motion on the top deck. Fig. 5c shows the average contact speed on the bottom deck screen cloth. High speeds of around 0.5 m/s are observed around many of the holes in the first panel and a scattering of holes lower down. This is produced by the impact of the high speed particles falling from the top deck. Excluding these, the surface speed over most of the bottom deck is fairly uniform at around 0.2–0.3 m/s. The bed starts to slow over the second half of the fourth panel and slows sharply to around only 0.05 m/s over the fifth panel.

5. Conclusions DEM simulation of full size, double deck banana screens is now feasible. Models including the full geometry of the screen, its motion, and the shape of the particles can now be solved with more than 200,000 particles in reasonable computation times. Predictions of separation performance and of the flow through the screen are quite realistic. The DEM simulation offers insight into the operation of the ‘‘hidden” bottom deck. In this case, the separation on the second deck is found to be not ideal. The simulations reported here are a ‘‘proof of concept” and provide interesting insights. The next stage of this project will use measured plant conditions from an industrial screen as a base case. A comparative study of particle flow through screens operated at different peak accelerations 5g, 6g and 14g has been presented here. Common to these cases is the observation that the bottom deck appears to be under-utilised, although this is worse for higher accelerations. It is clear that one of the major design challenges for multi-deck screens is to maximise the utilisation of the bottom deck by most rapidly establishing a deep, stratified, shearing bed on top of it. The two key components of screen separation and their differing dependency on the screen acceleration are: 1. Fine particles percolate through the dense shearing bed: Higher accelerations lead to more dilation of the bed and to higher shear which improve this component of screen flow. This is responsible for more rapid stratification of the bed and provision of a layer of fine material adjacent to the screen cloth. 2. Particles smaller than the screen aperture size and which are adjacent to the cloth are captured by and pass through holes in the screen cloth. This process is dependent on the size and shape of the particle and on the flow. The faster the flow speed and the denser the bed directly above the cloth, the lower is the chance of a particle being able to pass through an opening. For optimal screen separation there must be a balance between these two separation components. Lower accelerations will shift the balance further towards the near-screen separation whilst weakening the bed stratification. So accelerations that are too low will reduce the separation efficiency. Conversely, accelerations that are too high will give residence times that are too short to allow particles to pass through screen deck apertures. The presence of a large dilated surface bed with significant amounts of energetic, airborne particles is likely to indicate that a screen is being operated at too high a peak acceleration. Overall, the 3D DEM method with realistic non-round particles offers an opportunity to seriously explore industrial scale screen performance in much more detail than is possible with traditional testing techniques – although good quality survey and wear measurements will be essential for verification of the DEM models. Acknowledgements This project is carried out under the auspice and with the financial support of the Centre for Sustainable Resource Processing, which is established and supported under the Australian Government’s Cooperative Research Centres Program. The authors would like to thank Toni Kojovic who provided screen panel details. References Barker, G.C., 1994. Computer simulations of granular materials. In: Mehta, A. (Ed.), Granular Matter: An Inter-Disciplinary Approach. Springer, Berlin.

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