105:
light fraction segregated from shredded solid waste, thereby increasing the quality of the product fuel. In addition, trommel screens are used for the treatment of wastewater. For this particular application, solids from the entering flow will settle onto the screen mesh and the drum will rotate once the liquid reaches a certain level. The clean area of the screen is submerged into the liquid while the trapped solids fall onto a conveyor which will be further processed before removal.
2539:
rate is unknown beyond this point. A phenomenon exist below 2° such that for a given set of operating conditions, decreasing the inclination angle will increase the bed depth resulting in a lower screening efficiency. However it will also simultaneously increase the residence time, which results in an increase in the screening efficiency. It is unsure which effect will be more dominant at inclination angles less than 2°.
50:
179:
susceptible to plugging and blinding, especially when different sized screen apertures are in series. Plugging is when material larger than the aperture may become stuck or wedged into the apertures and then may be forced through which is undesirable. Blinding is when wet material clump up and stick to the surface of the screen. The vibrations in the vibrating screens reduce the risk of plugging and blinding.
233:
materials like trommel screens. However, it is common for the gyratory separators to separate either dry or wet materials only. This is because there are different parameters for the gyratory screen to have the best separation efficiency. Therefore, two separators would be required for the separation of dry and wet materials, while one trommel screen would be able to do the same job.
46:. It consists of a perforated cylindrical drum that is normally elevated at an angle at the feed end. Physical size separation is achieved as the feed material spirals down the rotating drum, where the undersized material smaller than the screen apertures passes through the screen, while the oversized material exits at the other end of the drum.
2001:
123:
industries use trommel screens to sort dry food of different sizes and shapes. The classification process will help to achieve the desired mass or heat transfer rate and avoid under or over-processing. It also screens tiny food such as peas and nuts that are strong enough to resist the rotational force of the drum.
2478:
At higher feed flow rates, smaller-sized particles at the lower layer of the packed bed are able to be screened at designated apertures and remaining small-sized particles adhere to larger particles. On the other hand, it is easier for smaller-sized particles to pass through the granules thickness in
2538:
Since screening efficiency is directly proportional to the length of the trommel, a shorter trommel screen would be needed at a smaller inclination angle to achieve a desired screening efficiency. It is suggested that the inclination angle should not be below 2° because the efficiency and production
2426:
This occurs when the rotational velocity of drum is low. The particles are lifted slightly from the bottom of the drum before tumbling down the free surface as shown in Figure 8. As only smaller- sized filter granules near the wall of the trommel body are able to be screened, this results in a lower
1630:
Two simplifying assumptions are made in the equation presented in this section for the residence time of materials in a rotating screen. First, it is assumed that there is no slippage of particles on the screen. In addition, the particles dislodging from the screen are under free fall. When the drum
223:
Curved screens are able to separate finer particles (200-3000 μm) than trommel screens. However, binding may occur if the particle size is less than 200 μm which will affect the separation efficiency. The screening rate of a curved screen is also much higher than the trommel screen as the
143:
As for the screens, perforated plate screens or mesh screens are usually used. Perforated plate screen are rolled and welded for strength. This design contains fewer ridges which makes it easier for the cleaning process. On the other hand, mesh screen are replaceable as it is susceptible to wear and
62:
Trommel screens can be used in a variety of applications such as classification of solid waste and recovery of valuable minerals from raw materials. Trommels come in many designs such as concentric screens, series or parallel arrangement and each component has a few configurations. However depending
246:
One of the main process characteristics of interest is the screening rate of the trommel. Screening rate is related to the probability of the undersized particles passing through the screen apertures upon impact. Based on the assumption that the particle falls perpendicularly on the screen surface,
187:
A grizzly screen is a grid or set of parallel metal bars set in an inclined stationary frame. The slope and the path of the material are usually parallel to the length of the bars. The length of the bar may be up to 3 m and the spacing between the bars ranges from 50 to 200 mm. Grizzly screens
2547:
In the wastewater treatment industry, the solids that exit the trommel will be compressed and dewatered as they travel along the conveyor. Most often a post-washing treatment such as a jet wash will be used after the trommel screen to break down faecal and unwanted semi-solid matter. The volume of
178:
However more material can be screened at once for a vibrating screen compared to a trommel screen. This is because only one part of the screen area of the trommel screen is utilised during the screening process whilst the entire screen is used for a vibrating screen. Trommel screens are also more
232:
Finer particle sizes (>40 μm) are able to be separated with the gyratory separator than with a trommel screen. The size of the gyratory screen separator can be adjusted through removable trays, whereas the trommel screen is usually fixed. Gyratory separators can also separate dry and wet
139:
For an inclined drum, objects are being lifted and then dropped with the help of lifter bars to move it further down the drum which the objects will otherwise roll down slower. Furthermore, the lifter bars shake the objects to segregate them. Lifter bars will not be considered in the presence of
104:
Trommel screens are used by the municipal waste industry in the screening process to classify sizes of solid waste. Besides that, it can also be used to improve the recovery of fuel-derived solid waste. This is done by removing inorganic materials such as moisture and ash from the air-classified
131:
One of the available designs of trommel screens is concentric screens with the coarsest screen located at the innermost section. It can also be designed in parallel in which objects exit one stream and enter the following. A trommel in series is a single drum whereby each section has different
122:
Other applications of trommel screens can be seen in the screening process of composts as an enhancement technique. It selects composts of variable size fractions to get rid of contaminants and incomplete composted residues, forming end products with a variety of uses. Besides this, the food
113:
Trommel screens are also used for the grading of raw materials to recover valuable minerals. The screen will segregate minuscule materials which are not in the suitable range of size to be used in the crushing stage. It also helps to get rid of dust particles which will otherwise impair the
2474:
According to Ottino and
Khakhar, increasing the feed flow rate of particles resulted in a decrease in screening efficiency. Not much is known about why this occurs, however, it is suggested that this effect is influenced by the thickness of filter granules packed in the trommel body.
135:
The trommel screen has many different configurations. For the drum component, an internal screw is fitted when the placement of the drum is flat or elevated at an angle less than 5°. The internal screw facilitates the movement of objects through the drum by forcing them to spiral.
196:
The material of construction of the bars is usually manganese steel to reduce wear. Usually, the bar is shaped in such a way that its top is wider than the bottom, and hence the bars can be made fairly deep for strength without being choked by lumps passing partway through them.
2465:
As the rotational velocity increases further, cataracting motion will transition to centrifuging motion which will result in a lower screening efficiency. This is due to particles attaching to the wall of the rotating drum caused by centrifugal forces as shown in Figure 10.
224:
whole surface area of the screen is utilised. Furthermore, for curved screens, the feed flows parallel to the apertures. This allows any loose material to break up from the jagged surface of the larger materials, resulting in more undersized particles passing through.
2535:, as illustrated in Figure 7. However, this is at a cost of a lower screening efficiency. On the other hand, decreasing the inclination angle will result in a much longer residence time of particles within the trommel system which increases the screening efficiency.
214:
Roller screens are preferred to trommel screens when the feed rate required is high. They also cause less noise than trommel screens and require less head room. Viscous and sticky materials are easier to be separated using a roller screen than with a trommel screen.
2514:
When designing the trommel screen, it should be taken into account that higher inclination angle would result in a higher production rate of particles. A higher inclination angle would result in a higher production rate due to an increase in particle velocity,
2487:
Increasing the area of material exposed to screening allows more particles to be filtered out. Therefore, features that increase the surface area will result in a much higher screening efficiency and production rate. The larger surface area can be increased by
2087:
Trommel screens are used widely in industries for its efficiency in material size separation. The trommel screening system is governed by the rotational velocity of the drum, mass flow rate of feed particles, size of the drum and inclination of trommel screen.
205:
A coarse feed (say from a primary crusher) is fed at the upper end of the grizzly. Large chunks roll and slide to the lower end (tail discharge), while small lumps having sizes less than the openings in the bars fall through the grid into a separate collector.
174:
Trommel screens are cheaper to produce than vibrating screens. They are vibration free which causes less noise than vibrating screens. Trommel screens are more mechanically robust than vibrating screens allowing it to last longer under mechanical stress.
1846:
1733:
90:
of the drum, mass flow rate of feed particles, size of the drum, and inclination of trommel screen. Depending on desired application of trommel screen, a balance has to be made between the screening efficiency and production rate.
2448:
while smaller granules stay near the screen surface, thereby allowing smaller filter granules to pass through. This motion generates turbulent flow of particles, resulting in a higher screening efficiency compared to slumping.
86:. Therefore, design rules are often used in place of the governing equations in the design of a trommel screen. When designing a trommel screen, the main factors affecting the screening efficiency and production rate are the
1312:
2443:
As rotational velocity increases, slumping transitions to cataracting motion where particles detach near the top of the rotating drum as shown in Figure 9. Larger granules segregate near the inner surface due to the
1439:
2409:
With varying rotational velocities, the effect of screening efficiency and production rate varies according to different types of motion mechanisms. These mechanisms include slumping, cataracting and centrifuging.
1584:
528:
refers to the rectangular dimension of the aperture. After determining the probability of passage of a given size interval of particles through the screen, the fraction of particles remaining in the screen,
1042:
1631:
rotates, particles are kept in contact with the rotating wall by centrifugal force. As the particles reach near the top of the drum, the gravitational force acting in the radial direction overcomes the
1068:
Apart from screening rate, another characteristic of interest is the separation efficiency of the trommel screen. Assuming that the size distribution function of the undersized particles to be removed,
470:
2401:, the particles are retained within the rotating drum. Larger granules will be retained inside the trommel screen until the desired aperture is met and follows the same particle behaviour.
748:
836:
308:
2919:
Lau, S.T.; Cheung, W.H.; Kwong, C.K.; Wan, C.P.; Choy, K.K.H.; Leung, C.C.; Porter, J.F.; Hui, C.W.; Mc Kay, G. (2005). "Removal of batteries from solid waste using trommel separation".
2097:
1457:
Therefore, the separation efficiency, which is defined as the ratio of the fraction of particles removed to the total fraction of particles in the feed, can be determined as follows:
2458:
2436:
2303:
2243:
2419:
1996:{\displaystyle t_{r}={\frac {L\cdot (360-4\alpha +229.2\cdot \cos \alpha \cdot \sin \alpha )}{48\cdot {n}\cdot {r}\cdot \tan \beta \cdot \cos \alpha \cdot (\sin \alpha )^{2}}}}
607:
2990:
Richardson, J.F. Harker, J.H. Backhurst, J.R. (2002). "Coulson and
Richardson's Chemical Engineering Volume 2 - Particle Technology and Separation Processes (5th Edition)".
2399:
2359:
2947:
Neikov, O. D. Stanislav, I. Mourachova, I. B. Gopienko, V.G. Frishberg, I.V. Lotskot, D.V. (2009) "Handbook of Non-Ferrous Metal
Powders: Technologies and Applications".
1796:
670:
1635:, causing the particles to fall from the drum in a cataracting motion. The force components acting on the particle at the point of departure is illustrated in Figure 6.
3123:
West, G. Fookes, P.G. Lay, J. Sims, I. Smith, M.R. Collis, L. (2001). "Aggregates: Sand, Gravel and
Crushed Rock Aggregates for Construction Purposes (3rd Edition)".
2196:
2077:
82:
of particles in the screen. These equations could be applied in the rough calculation done in initial phases of a design process. However, design is largely based on
1836:
2176:
2149:
1646:
1150:
1123:
1096:
930:
881:
2533:
2122:
2057:
2037:
1816:
1769:
1170:
901:
643:
547:
526:
506:
384:
364:
344:
144:
tear compared to perforated screen. In addition, screw cleaning work for this design is more intensive as objects tend to get wedged in the mesh ridges.
1180:
2857:
Chen, Yi-Shun; Hsiau, Shu-San; Lee, Hsuan-Yi; Chyou, Yau-Pin; Hsu, Chia-Jen (2010). "Size separation of particulates in a trommel screen system".
1838:
is the angle of inclination of the drum. Hence, the residence time of particles in the rotating screen can be determined from the equation below:
766:
An alternative way of expressing the fraction of particles remaining in the screen is in terms of the particle weight, which is given as follows:
1338:
1465:
645:
is the number of impingements of the particles on the screen. After making the assumption that the number of impingements per unit time,
3152:
952:
2884:
Glaub, J.C., Jones, D.B. & Savage, G.M. (1982). "The Design and Use of
Trommel Screens for Processing Municipal Solid Waste",
2198:
to be the angle between the particle motion and vertical component, the vertical and horizontal velocities can now be written as:
2104:
Considering the mesh sizes of the rotating drum are larger than particle sizes as shown in Figure 7, the particle motion velocity
400:
3103:
Warren, John L. (1978). "The use of a rotating screen as a means of grading crude refuse for pulverization and compression".
3167:
3147:
2912:
2639:
63:
on the application required, trommels have several advantages and limitations over other screening processes such as
2830:
Alter, Harvey; Gavis, Jerome; Renard, Marc L. (1981). "Design models of trommels for resource recovery processing".
1330:
Furthermore, the total number fraction of particles within this size range in the feed can be expressed as follows:
686:
147:
The screen's aperture comes in either square or round shape which is determined by many operating factors such as:
2905:
Hester, R.E. & Harrison, R.M. (2002). "Environmental and Health Impact of Solid Waste
Management Activities".
774:
255:
3172:
79:
78:
Some of the main governing equations for a trommel screen include the screening rate, screening efficiency and
3095:
Tarleton, S. Wakeman, R. (2006) "Solid/Liquid
Separation: Equipment Selection and Process Design: Equipment".
1065:
Screening efficiency can be calculated using mas weight in the following way E=c(f-u)(1-u)(c-f)/f(c-u)^2(1-f)
188:
are typically used in mining to limit the size of material passing into a conveyance or size reduction stage.
72:
3162:
3130:
Wills, B.A Napier-Munn, T. (2011) "Wills' Mineral
Processing Technology: An Introduction to the Practical".
3081:
392:) holds for both square and circular apertures. However, for rectangular apertures, the equation becomes:
2266:
2206:
557:
3157:
2364:
2324:
1602:
There are a number of factors that affect the separation efficiency of the trommel, which include:
1774:
648:
17:
1728:{\displaystyle \alpha ={\cos ^{-1}}({\frac {r{\cdot }\omega _{t}^{2}}{g{\cdot }\cos \beta }})}
883:
is the weight of a given size interval of particles remaining in the screen at any given time
68:
2877:
Fellows, P. J. (2009). "Food
Processing Technology - Principles and Practice (3rd Edition)".
2181:
2062:
64:
3015:
1821:
3011:
2964:
2154:
2127:
1128:
1101:
35:
1072:
906:
857:
8:
2983:
Pichtel, J. (2005). "Waste
Management Practices: Municipal, Hazardous, and Industrial",
2968:
2851:
Brentwood Recycling Systems (2013). "Trommels 101: Understanding Trommel Screen Design"
2518:
2107:
2042:
2022:
1801:
1754:
1155:
886:
628:
532:
511:
491:
369:
349:
329:
154:
The aperture area. Round aperture contributes to a smaller area than square-shaped one.
2955:
Ottino, J. M.; Khakhar, D. V. (2000). "Mixing and Segregation of Granular Materials".
2891:
Gupta, A. Yan, D. (2006) "Mineral Processing Design and Operation - An Introduction".
3116:
3056:
2936:
2843:
2445:
2124:
can be broken down into two velocity components consisting of the vertical component
1638:
The departure angle, α can be determined through a force balance, which is given as:
1632:
3112:
3077:
3051:
3046:
3034:
3019:
2972:
2928:
2866:
2839:
87:
43:
2976:
2100:
Figure 7: Relationship between the velocities and the sieve behaviour of particles
3024:
2999:
2932:
3068:
Stessel, Richard Ian; Kranc, S. C. (1992). "Particle Motion in Rotary Screen".
1307:{\displaystyle P(x_{0},x_{m})=\int _{x_{0}}^{x_{m}}f(x)\cdot (1-(1-p)^{n})\,dx}
2870:
2548:
the solid will decrease up to 40% depending on the properties before removal.
3141:
2059:
refers to the rotation of the screen in terms of revolutions per minute and
3060:
2940:
2850:
2703:
2361:, the particles escape through the mesh in the rotating drum. However, if
386:
refers to the ratio of aperture area to the total screen area. Equation (
2898:
Halder, S.K. (2012) "Mineral Exploration: Principles and Applications".
1434:{\displaystyle F({x_{0}},{x_{m}})=\int \limits _{x_{0}}^{x_{m}}f(x)\ dx}
164:
1579:{\displaystyle E(x_{0},x_{m})={\frac {P(x_{0},x_{m})}{F(x_{0},x_{m})}}}
114:
performance of the subsequent machineries in the downstream processes.
2096:
1098:, is known, the cumulative probability of all particles ranging from
83:
2457:
49:
2435:
39:
932:
is the initial weight of the feed. Therefore, from equations (
2418:
1037:{\displaystyle {\dfrac {dW(t)}{dt}}=\sigma _{t}ln(1-P)W(t)\,}
2859:
Chemical Engineering and Processing: Process Intensification
2499:
Increasing the size of the apertures and number of apertures
3088:
Sutherland, K.S. (2011) "Filters and Filtration Handbook".
465:{\displaystyle P=(1-{\dfrac {d}{a}})(1-{\dfrac {d}{A}})Q\,}
2091:
132:
apertures size arranged from the finest to the coarsest
366:
refers to the size of aperture (diameter or length) and
2502:
Reducing the number of gaps/area between the apertures
3039:
Journal of the Air & Waste Management Association
2521:
2367:
2327:
2269:
2209:
2184:
2157:
2130:
2110:
2065:
2045:
2025:
1849:
1824:
1804:
1777:
1757:
1649:
1468:
1341:
1183:
1158:
1131:
1104:
1075:
957:
955:
909:
889:
860:
794:
777:
689:
651:
631:
560:
535:
514:
494:
444:
420:
403:
372:
352:
332:
275:
258:
165:
Advantages and limitations over competitive processes
247:the probability of passage, P, is simply given as
2913:Johnsons Screens (2011). "Inclined Rotary Screens"
2527:
2505:Using lifting bars to increase spread of particles
2393:
2353:
2297:
2237:
2190:
2170:
2143:
2116:
2071:
2051:
2031:
1995:
1830:
1810:
1798:is the rotational velocity in radians per second,
1790:
1763:
1727:
1578:
1433:
1306:
1164:
1144:
1117:
1090:
1036:
924:
895:
875:
830:
742:
664:
637:
601:
541:
520:
500:
464:
378:
358:
338:
302:
38:machine used to separate materials, mainly in the
3035:"Laboratory Investigation of a New Trommel Model"
2918:
2856:
151:The required dimension of the undersized product.
99:
3139:
2829:
2461:Figure 10: Centrifuging motion in rotating drum
1625:
236:
2496:Increasing the length and diameter of the drum
743:{\displaystyle V(t)=(1-P)^{\sigma _{t}^{t}}\,}
2954:
2404:
227:
3067:
2812:
2810:
2542:
2509:
2422:Figure 8: Slumping motion in a rotating drum
831:{\displaystyle V(t)={\dfrac {W(t)}{W(0)}}\,}
303:{\displaystyle P=(1-{\dfrac {d}{a}})^{2}Q\,}
140:heavy objects as they may break the screen.
3032:
3000:"Numerical experiments in screening theory"
2782:
2780:
2778:
2776:
2774:
944:), the screening rate can be expressed as:
3033:Stesscl, Richard Ian; Cole, Keith (1996).
2755:
2753:
2689:Wills & Napier-Munn 2011, pp. 196-200.
2439:Figure 9: Cataract motion in rotating drum
2079:refers to the departure angle in degrees.
157:The magnitude of the agitation of product.
3050:
3023:
2807:
2798:
2762:
2725:
2723:
2713:
2711:
1297:
1033:
827:
739:
598:
461:
299:
2789:
2771:
2732:
2572:
2570:
2479:the trommel system at lower feed rates.
2456:
2434:
2417:
2095:
2082:
1060:
48:
3082:10.1061/(ASCE)0733-9399(1992)118:3(604)
2750:
2741:
2685:
2683:
2681:
2679:
2677:
2667:
2665:
1606:Speed of rotation of the trommel screen
94:
14:
3140:
3102:
2997:
2720:
2708:
2699:
2697:
2695:
2635:
2633:
2623:
2621:
2619:
2617:
2615:
2613:
2611:
2609:
2607:
2605:
2590:Chen, Y.S. et al. 2010, pp. 1214-1221.
2092:Particle rotational velocity behaviour
1818:is the gravitational acceleration and
34:, also known as a rotary screen, is a
2747:Tarleton & Wakeman 2006, pp. 1-78
2586:
2584:
2582:
2567:
117:
108:
71:, roller screens, curved screens and
2674:
2662:
2653:
2593:
2260:
2200:
1840:
1640:
1459:
1332:
1174:
946:
768:
680:
551:
394:
249:
126:
2692:
2630:
2602:
2482:
2298:{\displaystyle V_{x}=V\sin \theta }
2238:{\displaystyle V_{y}=V\cos \theta }
1618:Number and size of screen apertures
1612:Residence time in the rotating drum
169:
24:
3105:Resource Recovery and Conservation
2717:Richardson et al. 2002, pp. 57-58.
2644:
2579:
2558:
25:
3184:
2659:Hester & Harrison 2002, p. 75
2564:Stessel et al. 1996, pp. 558-568.
2469:
241:
182:
44:solid-waste processing industries
3070:Journal of Engineering Mechanics
2957:Annual Review of Fluid Mechanics
2576:Stessel et al. 1992, pp. 604-619
602:{\displaystyle V(n)=(1-P)^{n}\,}
218:
209:
3153:Mechanical biological treatment
2729:West et al. 2001, pp. 116 – 124
2452:
191:
3052:10.1080/10473289.1996.10467491
2786:Alter et al. 1981, pp. 223-240
2650:Warren, J. L. 1978, pp. 97-111
2627:Glaub et al. 1982, pp. 447-457
2599:Lau et al. 2005, pp. 1004-1012
2430:
2394:{\displaystyle V_{y}<V_{x}}
2354:{\displaystyle V_{y}>V_{x}}
1981:
1968:
1917:
1872:
1722:
1671:
1570:
1544:
1536:
1510:
1498:
1472:
1419:
1413:
1375:
1345:
1294:
1285:
1272:
1263:
1257:
1251:
1213:
1187:
1085:
1079:
1030:
1024:
1018:
1006:
972:
966:
919:
913:
870:
864:
820:
814:
806:
800:
787:
781:
718:
705:
699:
693:
589:
576:
570:
564:
455:
434:
431:
410:
287:
265:
100:Municipal and industrial waste
13:
1:
2977:10.1146/annurev.fluid.32.1.55
2823:
2816:Ottino et al. 2000, pp. 55-91
2039:refers to the screen length,
346:refers to the particle size,
3125:Geological Society of London
3117:10.1016/0304-3967(78)90032-X
3004:Astronomy & Astrophysics
2933:10.1016/j.wasman.2005.04.009
2844:10.1016/0166-3097(81)90051-1
2738:Gupta & Yan 2006, pp. 29
2311:
2251:
2009:
1741:
1626:Residence time in the screen
1615:Angle of inclination of drum
237:Main process characteristics
27:Machine separating materials
7:
3168:Material-handling equipment
2759:Sutherland 2011, pp. 97-209
2704:Brentwood Recycling Systems
2413:
1791:{\displaystyle \omega _{t}}
1621:Characteristics of the feed
1592:
1447:
1320:
1050:
940:
934:
844:
756:
674:
665:{\displaystyle \sigma _{t}}
615:
478:
388:
316:
10:
3189:
3148:Waste treatment technology
3025:10.1051/0004-6361:20034516
2907:Royal Society of Chemistry
2832:Resources and Conservation
2405:Particle motion mechanisms
228:Gyratory screen separators
200:
73:gyratory screen separators
57:
2886:Cal Recovery Systems, Inc
2871:10.1016/j.cep.2010.09.003
2795:Pichtel 2005, pp. 182-185
2671:Fellows 2009, pp. 113-114
2543:Example of post-treatment
2510:Inclination angle of drum
2151:and horizontal component
1152:that are separated after
672:, is constant, equation (
2915:Retrieved 7 October 2013
2853:Retrieved 5 October 2013
2804:Shaviv 2004, pp. 801-811
2768:Halder 2012, pp. 223-251
2551:
1172:impingements is simply:
3016:2004A&A...418..801S
2191:{\displaystyle \theta }
2072:{\displaystyle \alpha }
53:Figure 1 Trommel screen
3173:Solid-solid separation
2529:
2462:
2440:
2427:screening efficiency.
2423:
2395:
2355:
2299:
2239:
2192:
2172:
2145:
2118:
2101:
2073:
2053:
2033:
1997:
1832:
1831:{\displaystyle \beta }
1812:
1792:
1765:
1729:
1580:
1435:
1409:
1308:
1166:
1146:
1119:
1092:
1038:
926:
897:
877:
832:
744:
666:
639:
603:
549:, can be found using:
543:
522:
502:
466:
380:
360:
340:
304:
54:
2530:
2460:
2438:
2421:
2396:
2356:
2300:
2240:
2193:
2173:
2171:{\displaystyle V_{x}}
2146:
2144:{\displaystyle V_{y}}
2119:
2099:
2083:Design and heuristics
2074:
2054:
2034:
1998:
1833:
1813:
1793:
1766:
1730:
1581:
1436:
1381:
1309:
1167:
1147:
1145:{\displaystyle x_{m}}
1120:
1118:{\displaystyle x_{0}}
1093:
1061:Separation efficiency
1039:
927:
898:
878:
833:
745:
667:
640:
604:
544:
523:
503:
467:
381:
361:
341:
305:
52:
3163:Industrial processes
2519:
2365:
2325:
2267:
2207:
2182:
2155:
2128:
2108:
2063:
2043:
2023:
1847:
1822:
1802:
1775:
1771:is the drum radius,
1755:
1647:
1466:
1339:
1181:
1156:
1129:
1102:
1091:{\displaystyle f(x)}
1073:
953:
925:{\displaystyle W(0)}
907:
887:
876:{\displaystyle W(t)}
858:
775:
687:
649:
629:
558:
533:
512:
492:
401:
370:
350:
330:
256:
95:Range of application
36:mechanical screening
2998:Shaviv, G. (2004).
2969:2000AnRFM..32...55O
2879:Woodhead Publishing
1699:
1247:
736:
88:rotational velocity
2525:
2463:
2441:
2424:
2391:
2351:
2295:
2235:
2188:
2168:
2141:
2114:
2102:
2069:
2049:
2029:
1993:
1828:
1808:
1788:
1761:
1725:
1685:
1576:
1431:
1304:
1219:
1162:
1142:
1115:
1088:
1034:
985:
922:
893:
873:
828:
825:
740:
722:
662:
635:
599:
539:
518:
498:
462:
453:
429:
376:
356:
336:
300:
284:
118:Other applications
109:Mineral processing
55:
2927:(10): 1004–1012.
2865:(11): 1214–1221.
2528:{\displaystyle V}
2446:Brazil nut effect
2319:
2318:
2259:
2258:
2117:{\displaystyle V}
2052:{\displaystyle n}
2032:{\displaystyle L}
2017:
2016:
1991:
1811:{\displaystyle g}
1764:{\displaystyle r}
1749:
1748:
1720:
1633:centrifugal force
1600:
1599:
1574:
1455:
1454:
1424:
1328:
1327:
1165:{\displaystyle n}
1058:
1057:
984:
896:{\displaystyle t}
852:
851:
824:
764:
763:
638:{\displaystyle n}
623:
622:
542:{\displaystyle V}
521:{\displaystyle A}
501:{\displaystyle a}
486:
485:
452:
428:
379:{\displaystyle Q}
359:{\displaystyle a}
339:{\displaystyle d}
324:
323:
283:
127:Designs available
65:vibrating screens
16:(Redirected from
3180:
3158:Mining equipment
3120:
3085:
3064:
3054:
3029:
3027:
2980:
2944:
2921:Waste Management
2874:
2847:
2838:(3–4): 223–240.
2817:
2814:
2805:
2802:
2796:
2793:
2787:
2784:
2769:
2766:
2760:
2757:
2748:
2745:
2739:
2736:
2730:
2727:
2718:
2715:
2706:
2701:
2690:
2687:
2672:
2669:
2660:
2657:
2651:
2648:
2642:
2640:Johnsons Screens
2637:
2628:
2625:
2600:
2597:
2591:
2588:
2577:
2574:
2565:
2562:
2534:
2532:
2531:
2526:
2483:Size of the drum
2400:
2398:
2397:
2392:
2390:
2389:
2377:
2376:
2360:
2358:
2357:
2352:
2350:
2349:
2337:
2336:
2313:
2304:
2302:
2301:
2296:
2279:
2278:
2261:
2253:
2244:
2242:
2241:
2236:
2219:
2218:
2201:
2197:
2195:
2194:
2189:
2177:
2175:
2174:
2169:
2167:
2166:
2150:
2148:
2147:
2142:
2140:
2139:
2123:
2121:
2120:
2115:
2078:
2076:
2075:
2070:
2058:
2056:
2055:
2050:
2038:
2036:
2035:
2030:
2011:
2002:
2000:
1999:
1994:
1992:
1990:
1989:
1988:
1940:
1932:
1920:
1864:
1859:
1858:
1841:
1837:
1835:
1834:
1829:
1817:
1815:
1814:
1809:
1797:
1795:
1794:
1789:
1787:
1786:
1770:
1768:
1767:
1762:
1743:
1734:
1732:
1731:
1726:
1721:
1719:
1709:
1700:
1698:
1693:
1684:
1675:
1670:
1669:
1668:
1641:
1594:
1585:
1583:
1582:
1577:
1575:
1573:
1569:
1568:
1556:
1555:
1539:
1535:
1534:
1522:
1521:
1505:
1497:
1496:
1484:
1483:
1460:
1449:
1440:
1438:
1437:
1432:
1422:
1408:
1407:
1406:
1396:
1395:
1394:
1374:
1373:
1372:
1359:
1358:
1357:
1333:
1322:
1313:
1311:
1310:
1305:
1293:
1292:
1246:
1245:
1244:
1234:
1233:
1232:
1212:
1211:
1199:
1198:
1175:
1171:
1169:
1168:
1163:
1151:
1149:
1148:
1143:
1141:
1140:
1124:
1122:
1121:
1116:
1114:
1113:
1097:
1095:
1094:
1089:
1052:
1043:
1041:
1040:
1035:
999:
998:
986:
983:
975:
958:
947:
931:
929:
928:
923:
902:
900:
899:
894:
882:
880:
879:
874:
846:
837:
835:
834:
829:
826:
823:
809:
795:
769:
758:
749:
747:
746:
741:
738:
737:
735:
730:
681:
671:
669:
668:
663:
661:
660:
644:
642:
641:
636:
617:
608:
606:
605:
600:
597:
596:
552:
548:
546:
545:
540:
527:
525:
524:
519:
507:
505:
504:
499:
480:
471:
469:
468:
463:
454:
445:
430:
421:
395:
385:
383:
382:
377:
365:
363:
362:
357:
345:
343:
342:
337:
318:
309:
307:
306:
301:
295:
294:
285:
276:
250:
170:Vibrating screen
160:Cleanup of drum.
21:
3188:
3187:
3183:
3182:
3181:
3179:
3178:
3177:
3138:
3137:
2826:
2821:
2820:
2815:
2808:
2803:
2799:
2794:
2790:
2785:
2772:
2767:
2763:
2758:
2751:
2746:
2742:
2737:
2733:
2728:
2721:
2716:
2709:
2702:
2693:
2688:
2675:
2670:
2663:
2658:
2654:
2649:
2645:
2638:
2631:
2626:
2603:
2598:
2594:
2589:
2580:
2575:
2568:
2563:
2559:
2554:
2545:
2520:
2517:
2516:
2512:
2485:
2472:
2455:
2433:
2416:
2407:
2385:
2381:
2372:
2368:
2366:
2363:
2362:
2345:
2341:
2332:
2328:
2326:
2323:
2322:
2274:
2270:
2268:
2265:
2264:
2214:
2210:
2208:
2205:
2204:
2183:
2180:
2179:
2162:
2158:
2156:
2153:
2152:
2135:
2131:
2129:
2126:
2125:
2109:
2106:
2105:
2094:
2085:
2064:
2061:
2060:
2044:
2041:
2040:
2024:
2021:
2020:
1984:
1980:
1936:
1928:
1921:
1865:
1863:
1854:
1850:
1848:
1845:
1844:
1823:
1820:
1819:
1803:
1800:
1799:
1782:
1778:
1776:
1773:
1772:
1756:
1753:
1752:
1705:
1701:
1694:
1689:
1680:
1676:
1674:
1661:
1657:
1656:
1648:
1645:
1644:
1628:
1564:
1560:
1551:
1547:
1540:
1530:
1526:
1517:
1513:
1506:
1504:
1492:
1488:
1479:
1475:
1467:
1464:
1463:
1402:
1398:
1397:
1390:
1386:
1385:
1368:
1364:
1363:
1353:
1349:
1348:
1340:
1337:
1336:
1288:
1284:
1240:
1236:
1235:
1228:
1224:
1223:
1207:
1203:
1194:
1190:
1182:
1179:
1178:
1157:
1154:
1153:
1136:
1132:
1130:
1127:
1126:
1109:
1105:
1103:
1100:
1099:
1074:
1071:
1070:
1063:
994:
990:
976:
959:
956:
954:
951:
950:
908:
905:
904:
888:
885:
884:
859:
856:
855:
810:
796:
793:
776:
773:
772:
731:
726:
721:
717:
688:
685:
684:
656:
652:
650:
647:
646:
630:
627:
626:
592:
588:
559:
556:
555:
534:
531:
530:
513:
510:
509:
493:
490:
489:
443:
419:
402:
399:
398:
371:
368:
367:
351:
348:
347:
331:
328:
327:
290:
286:
274:
257:
254:
253:
244:
239:
230:
221:
212:
203:
194:
185:
172:
167:
129:
120:
111:
102:
97:
69:grizzly screens
60:
28:
23:
22:
15:
12:
11:
5:
3186:
3176:
3175:
3170:
3165:
3160:
3155:
3150:
3136:
3135:
3128:
3121:
3100:
3093:
3086:
3076:(3): 604–619.
3065:
3045:(6): 558–568.
3030:
3010:(3): 801–811.
2995:
2988:
2981:
2952:
2945:
2916:
2910:
2903:
2896:
2889:
2882:
2875:
2854:
2848:
2825:
2822:
2819:
2818:
2806:
2797:
2788:
2770:
2761:
2749:
2740:
2731:
2719:
2707:
2691:
2673:
2661:
2652:
2643:
2629:
2601:
2592:
2578:
2566:
2556:
2555:
2553:
2550:
2544:
2541:
2524:
2511:
2508:
2507:
2506:
2503:
2500:
2497:
2493:
2492:
2484:
2481:
2471:
2470:Feed flow rate
2468:
2454:
2451:
2432:
2429:
2415:
2412:
2406:
2403:
2388:
2384:
2380:
2375:
2371:
2348:
2344:
2340:
2335:
2331:
2317:
2316:
2307:
2305:
2294:
2291:
2288:
2285:
2282:
2277:
2273:
2257:
2256:
2247:
2245:
2234:
2231:
2228:
2225:
2222:
2217:
2213:
2187:
2165:
2161:
2138:
2134:
2113:
2093:
2090:
2084:
2081:
2068:
2048:
2028:
2015:
2014:
2005:
2003:
1987:
1983:
1979:
1976:
1973:
1970:
1967:
1964:
1961:
1958:
1955:
1952:
1949:
1946:
1943:
1939:
1935:
1931:
1927:
1924:
1919:
1916:
1913:
1910:
1907:
1904:
1901:
1898:
1895:
1892:
1889:
1886:
1883:
1880:
1877:
1874:
1871:
1868:
1862:
1857:
1853:
1827:
1807:
1785:
1781:
1760:
1747:
1746:
1737:
1735:
1724:
1718:
1715:
1712:
1708:
1704:
1697:
1692:
1688:
1683:
1679:
1673:
1667:
1664:
1660:
1655:
1652:
1627:
1624:
1623:
1622:
1619:
1616:
1613:
1610:
1607:
1598:
1597:
1588:
1586:
1572:
1567:
1563:
1559:
1554:
1550:
1546:
1543:
1538:
1533:
1529:
1525:
1520:
1516:
1512:
1509:
1503:
1500:
1495:
1491:
1487:
1482:
1478:
1474:
1471:
1453:
1452:
1443:
1441:
1430:
1427:
1421:
1418:
1415:
1412:
1405:
1401:
1393:
1389:
1384:
1380:
1377:
1371:
1367:
1362:
1356:
1352:
1347:
1344:
1326:
1325:
1316:
1314:
1303:
1300:
1296:
1291:
1287:
1283:
1280:
1277:
1274:
1271:
1268:
1265:
1262:
1259:
1256:
1253:
1250:
1243:
1239:
1231:
1227:
1222:
1218:
1215:
1210:
1206:
1202:
1197:
1193:
1189:
1186:
1161:
1139:
1135:
1112:
1108:
1087:
1084:
1081:
1078:
1062:
1059:
1056:
1055:
1046:
1044:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1011:
1008:
1005:
1002:
997:
993:
989:
982:
979:
974:
971:
968:
965:
962:
921:
918:
915:
912:
892:
872:
869:
866:
863:
850:
849:
840:
838:
822:
819:
816:
813:
808:
805:
802:
799:
792:
789:
786:
783:
780:
762:
761:
752:
750:
734:
729:
725:
720:
716:
713:
710:
707:
704:
701:
698:
695:
692:
659:
655:
634:
621:
620:
611:
609:
595:
591:
587:
584:
581:
578:
575:
572:
569:
566:
563:
538:
517:
497:
484:
483:
474:
472:
460:
457:
451:
448:
442:
439:
436:
433:
427:
424:
418:
415:
412:
409:
406:
375:
355:
335:
322:
321:
312:
310:
298:
293:
289:
282:
279:
273:
270:
267:
264:
261:
243:
242:Screening rate
240:
238:
235:
229:
226:
220:
217:
211:
208:
202:
199:
193:
190:
184:
183:Grizzly screen
181:
171:
168:
166:
163:
162:
161:
158:
155:
152:
128:
125:
119:
116:
110:
107:
101:
98:
96:
93:
80:residence time
59:
56:
32:trommel screen
26:
9:
6:
4:
3:
2:
3185:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3149:
3146:
3145:
3143:
3133:
3129:
3126:
3122:
3118:
3114:
3110:
3106:
3101:
3098:
3094:
3091:
3087:
3083:
3079:
3075:
3071:
3066:
3062:
3058:
3053:
3048:
3044:
3040:
3036:
3031:
3026:
3021:
3017:
3013:
3009:
3005:
3001:
2996:
2993:
2989:
2987:, Boca Raton.
2986:
2982:
2978:
2974:
2970:
2966:
2962:
2958:
2953:
2950:
2946:
2942:
2938:
2934:
2930:
2926:
2922:
2917:
2914:
2911:
2908:
2904:
2901:
2897:
2894:
2890:
2887:
2883:
2880:
2876:
2872:
2868:
2864:
2860:
2855:
2852:
2849:
2845:
2841:
2837:
2833:
2828:
2827:
2813:
2811:
2801:
2792:
2783:
2781:
2779:
2777:
2775:
2765:
2756:
2754:
2744:
2735:
2726:
2724:
2714:
2712:
2705:
2700:
2698:
2696:
2686:
2684:
2682:
2680:
2678:
2668:
2666:
2656:
2647:
2641:
2636:
2634:
2624:
2622:
2620:
2618:
2616:
2614:
2612:
2610:
2608:
2606:
2596:
2587:
2585:
2583:
2573:
2571:
2561:
2557:
2549:
2540:
2536:
2522:
2504:
2501:
2498:
2495:
2494:
2491:
2490:
2489:
2480:
2476:
2467:
2459:
2450:
2447:
2437:
2428:
2420:
2411:
2402:
2386:
2382:
2378:
2373:
2369:
2346:
2342:
2338:
2333:
2329:
2315:
2308:
2306:
2292:
2289:
2286:
2283:
2280:
2275:
2271:
2263:
2262:
2255:
2248:
2246:
2232:
2229:
2226:
2223:
2220:
2215:
2211:
2203:
2202:
2199:
2185:
2163:
2159:
2136:
2132:
2111:
2098:
2089:
2080:
2066:
2046:
2026:
2013:
2006:
2004:
1985:
1977:
1974:
1971:
1965:
1962:
1959:
1956:
1953:
1950:
1947:
1944:
1941:
1937:
1933:
1929:
1925:
1922:
1914:
1911:
1908:
1905:
1902:
1899:
1896:
1893:
1890:
1887:
1884:
1881:
1878:
1875:
1869:
1866:
1860:
1855:
1851:
1843:
1842:
1839:
1825:
1805:
1783:
1779:
1758:
1745:
1738:
1736:
1716:
1713:
1710:
1706:
1702:
1695:
1690:
1686:
1681:
1677:
1665:
1662:
1658:
1653:
1650:
1643:
1642:
1639:
1636:
1634:
1620:
1617:
1614:
1611:
1608:
1605:
1604:
1603:
1596:
1589:
1587:
1565:
1561:
1557:
1552:
1548:
1541:
1531:
1527:
1523:
1518:
1514:
1507:
1501:
1493:
1489:
1485:
1480:
1476:
1469:
1462:
1461:
1458:
1451:
1444:
1442:
1428:
1425:
1416:
1410:
1403:
1399:
1391:
1387:
1382:
1378:
1369:
1365:
1360:
1354:
1350:
1342:
1335:
1334:
1331:
1324:
1317:
1315:
1301:
1298:
1289:
1281:
1278:
1275:
1269:
1266:
1260:
1254:
1248:
1241:
1237:
1229:
1225:
1220:
1216:
1208:
1204:
1200:
1195:
1191:
1184:
1177:
1176:
1173:
1159:
1137:
1133:
1110:
1106:
1082:
1076:
1066:
1054:
1047:
1045:
1027:
1021:
1015:
1012:
1009:
1003:
1000:
995:
991:
987:
980:
977:
969:
963:
960:
949:
948:
945:
943:
942:
937:
936:
916:
910:
890:
867:
861:
848:
841:
839:
817:
811:
803:
797:
790:
784:
778:
771:
770:
767:
760:
753:
751:
732:
727:
723:
714:
711:
708:
702:
696:
690:
683:
682:
679:
677:
676:
657:
653:
632:
619:
612:
610:
593:
585:
582:
579:
573:
567:
561:
554:
553:
550:
536:
515:
495:
482:
475:
473:
458:
449:
446:
440:
437:
425:
422:
416:
413:
407:
404:
397:
396:
393:
391:
390:
373:
353:
333:
320:
313:
311:
296:
291:
280:
277:
271:
268:
262:
259:
252:
251:
248:
234:
225:
219:Curved screen
216:
210:Roller screen
207:
198:
189:
180:
176:
159:
156:
153:
150:
149:
148:
145:
141:
137:
133:
124:
115:
106:
92:
89:
85:
81:
76:
74:
70:
66:
51:
47:
45:
41:
37:
33:
19:
3131:
3124:
3108:
3104:
3096:
3089:
3073:
3069:
3042:
3038:
3007:
3003:
2991:
2984:
2960:
2956:
2948:
2924:
2920:
2906:
2899:
2892:
2885:
2878:
2862:
2858:
2835:
2831:
2800:
2791:
2764:
2743:
2734:
2655:
2646:
2595:
2560:
2546:
2537:
2513:
2486:
2477:
2473:
2464:
2453:Centrifuging
2442:
2425:
2408:
2320:
2309:
2249:
2103:
2086:
2018:
2007:
1750:
1739:
1637:
1629:
1601:
1590:
1456:
1445:
1329:
1318:
1067:
1064:
1048:
939:
933:
853:
842:
765:
754:
673:
624:
613:
487:
476:
387:
325:
314:
245:
231:
222:
213:
204:
195:
192:Construction
186:
177:
173:
146:
142:
138:
134:
130:
121:
112:
103:
77:
61:
31:
29:
2431:Cataracting
2178:. Denoting
678:) becomes:
3142:Categories
3111:: 97–111.
2824:References
84:heuristics
2985:CRC Press
2963:: 55–91.
2293:θ
2290:
2233:θ
2230:
2186:θ
2067:α
1978:α
1975:
1966:⋅
1963:α
1960:
1954:⋅
1951:β
1948:
1942:⋅
1934:⋅
1926:⋅
1915:α
1912:
1906:⋅
1903:α
1900:
1894:⋅
1885:α
1879:−
1870:⋅
1826:β
1780:ω
1717:β
1714:
1707:⋅
1687:ω
1682:⋅
1663:−
1651:α
1609:Feed rate
1383:∫
1279:−
1270:−
1261:⋅
1221:∫
1013:−
992:σ
724:σ
712:−
654:σ
583:−
441:−
417:−
272:−
3132:Elsevier
3097:Elsevier
3090:Elsevier
3061:28065125
2992:Elsevier
2949:Elsevier
2941:15979869
2900:Elsevier
2893:Elsevier
2414:Slumping
3012:Bibcode
2965:Bibcode
938:) and (
201:Working
58:Summary
40:mineral
18:Trommel
3059:
2939:
2019:where
1751:where
1423:
854:where
625:where
488:where
326:where
2552:Notes
2321:When
1891:229.2
3057:PMID
2937:PMID
2379:<
2339:>
903:and
508:and
42:and
3113:doi
3078:doi
3074:118
3047:doi
3020:doi
3008:418
2973:doi
2929:doi
2867:doi
2840:doi
2287:sin
2227:cos
1972:sin
1957:cos
1945:tan
1909:sin
1897:cos
1876:360
1711:cos
1659:cos
1125:to
3144::
3107:.
3072:.
3055:.
3043:46
3041:.
3037:.
3018:.
3006:.
3002:.
2971:.
2961:32
2959:.
2935:.
2925:25
2923:.
2863:49
2861:.
2834:.
2809:^
2773:^
2752:^
2722:^
2710:^
2694:^
2676:^
2664:^
2632:^
2604:^
2581:^
2569:^
2312:13
2252:12
2010:11
1923:48
1742:10
75:.
67:,
30:A
3134:.
3127:.
3119:.
3115::
3109:3
3099:.
3092:.
3084:.
3080::
3063:.
3049::
3028:.
3022::
3014::
2994:.
2979:.
2975::
2967::
2951:.
2943:.
2931::
2909:.
2902:.
2895:.
2888:.
2881:.
2873:.
2869::
2846:.
2842::
2836:6
2523:V
2387:x
2383:V
2374:y
2370:V
2347:x
2343:V
2334:y
2330:V
2314:)
2310:(
2284:V
2281:=
2276:x
2272:V
2254:)
2250:(
2224:V
2221:=
2216:y
2212:V
2164:x
2160:V
2137:y
2133:V
2112:V
2047:n
2027:L
2012:)
2008:(
1986:2
1982:)
1969:(
1938:r
1930:n
1918:)
1888:+
1882:4
1873:(
1867:L
1861:=
1856:r
1852:t
1806:g
1784:t
1759:r
1744:)
1740:(
1723:)
1703:g
1696:2
1691:t
1678:r
1672:(
1666:1
1654:=
1595:)
1593:9
1591:(
1571:)
1566:m
1562:x
1558:,
1553:0
1549:x
1545:(
1542:F
1537:)
1532:m
1528:x
1524:,
1519:0
1515:x
1511:(
1508:P
1502:=
1499:)
1494:m
1490:x
1486:,
1481:0
1477:x
1473:(
1470:E
1450:)
1448:8
1446:(
1429:x
1426:d
1420:)
1417:x
1414:(
1411:f
1404:m
1400:x
1392:0
1388:x
1379:=
1376:)
1370:m
1366:x
1361:,
1355:0
1351:x
1346:(
1343:F
1323:)
1321:7
1319:(
1302:x
1299:d
1295:)
1290:n
1286:)
1282:p
1276:1
1273:(
1267:1
1264:(
1258:)
1255:x
1252:(
1249:f
1242:m
1238:x
1230:0
1226:x
1217:=
1214:)
1209:m
1205:x
1201:,
1196:0
1192:x
1188:(
1185:P
1160:n
1138:m
1134:x
1111:0
1107:x
1086:)
1083:x
1080:(
1077:f
1053:)
1051:6
1049:(
1031:)
1028:t
1025:(
1022:W
1019:)
1016:P
1010:1
1007:(
1004:n
1001:l
996:t
988:=
981:t
978:d
973:)
970:t
967:(
964:W
961:d
941:5
935:4
920:)
917:0
914:(
911:W
891:t
871:)
868:t
865:(
862:W
847:)
845:5
843:(
821:)
818:0
815:(
812:W
807:)
804:t
801:(
798:W
791:=
788:)
785:t
782:(
779:V
759:)
757:4
755:(
733:t
728:t
719:)
715:P
709:1
706:(
703:=
700:)
697:t
694:(
691:V
675:3
658:t
633:n
618:)
616:3
614:(
594:n
590:)
586:P
580:1
577:(
574:=
571:)
568:n
565:(
562:V
537:V
516:A
496:a
481:)
479:2
477:(
459:Q
456:)
450:A
447:d
438:1
435:(
432:)
426:a
423:d
414:1
411:(
408:=
405:P
389:1
374:Q
354:a
334:d
319:)
317:1
315:(
297:Q
292:2
288:)
281:a
278:d
269:1
266:(
263:=
260:P
20:)
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