Mining Science and Technology (China) 21 (2011) 451–455

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Mining Science and Technology (China)

journal homepage: www.elsevier .com/locate /mstc

Screening efficiency and screen length of a linear vibrating screen using DEM3D simulation

Wang Guifeng, Tong Xin ⇑School of Mechanical Engineering and Automation, Huaqiao University, Xiamen 361021, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 October 2010Received in revised form 22 November 2010Accepted 26 December 2010

Keywords:Screen lengthScreening efficiencyDiscrete element method

1674-5264/$ - see front matter � 2011 Published bydoi:10.1016/j.mstc.2011.05.026

⇑ Corresponding author. Tel.: +86 595 22703657.E-mail address: ccq@hqu.edu.cn (X. Tong).

The effect of screen length on the screening efficiency of particles is studied under various single param-eter conditions including frequency, amplitude, vibration angle, and screen inclination. The Discrete Ele-ment Method (DEM) has been used to simulate the screening process. A functional relationship betweenscreening efficiency and screen length is established. It is shown that screening efficiency and screenlength have a complicated exponential relationship. Relationships between them are profoundly dis-cussed and conclusions are easily drawn: low values of the parameters do not benefit screening; screen-ing efficiency generally increases with screen length; screening efficiency reaches a plateau when theseparameters are in range frequently encountered in practical applications.

� 2011 Published by Elsevier B.V. on behalf of China University of Mining & Technology.

1. Introduction

Sieving and screening are widely used in industry as a unitoperation for large-scale separation of particles according to sizeand in the laboratory as a tool for the analysis of particle sizedistribution, usually at a small scale [1]. Sieving is one of the oldestand most widely employed physical size separation methods [2].Although this very ancient technique may be dated back tothousands of years ago, an insightful understanding of thistechnique has never been realized due to the complicated sizedistribution, and composition of industrial particulate solids. Thecomprehensive effect of particle motion under various operationalparameters and screen configurations further complicates thequestion [3]. A lack of advanced analytical and experimental tech-niques for the study of particulate systems has also hinderedprogress in this area. As a result, most published information onsieve and screen performance has been empirical in nature [4].

In the process of modeling batch sieving or continuous screen-ing, particulates that are generated, or stored, by a particle factoryfall off the outlet of the feeding hopper by the action of gravity andthen reach the surface of the screen. Oversize particles bouncealong the screen and the bulk of the undersize particles passthrough the apertures. Size classification occurs by presenting eachparticle to the screen surface. This is the simplest process ofscreening.

The screening process consists of two regions: a ‘‘crowded’’region and a ‘‘separated’’ region. At the beginning where particles

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are arriving the screen surface the accumulation of particles nearthe screen mesh causes the particles to be crowded and undersizedparticles must pass through gaps between the oversize particles.This is the ‘‘crowded’’ region. As particles travel along the screensurface more and more of the undersize particles pass throughthe apertures and the concentration of undersize particles in theflowing mixture near the screen mesh drops. The assembly ofparticles then behaves more dilute and loose. This marks thebeginning of the ‘‘separated’’ region. As the length of the screensurface increases there are more opportunities for particles topenetrate the apertures.

There are a large number of factors that affect screen conditionsand influence screening efficiency. Fortunately, the crucial effectsof discrete particle motion on screening efficiency have beenidentified by a number of researchers. These effects include grainsegregation in the material layer and the way undersize particlesapproach the sieve and ultimately pass through the apertures. Inaddition, vibration parameters, structural parameters and the feedrate also influence screening conditions and ultimately impactscreening efficiency. Vibration parameters consist of the ampli-tude, the frequency, and the vibration angle. Structural parametersinclude the width of the screen, the length of the screen, thediameter of the wire, the aperture size, and the screen inclination.

The effect of screen length on screening efficiency has beenstudied for a long time and numerous experts have drawn variousconclusions based on their experiments and experience. Li Zhengli-ang noted that an increase in screen length causes the screeningpoint to come back and the penetration diameter to increase [5].There was a peak in the screening efficiency over only a certainrange. Yin Shouren also stated that the choice of screen length

iversity of Mining & Technology.

452 G. Wang, X. Tong / Mining Science and Technology (China) 21 (2011) 451–455

should take the distribution of particles into account [6]. Finerparticles require a shorter length of screen surface. Zhao Yueminsuggested that screen length did not influence the probabilitydensity function for penetration but mainly determines the inter-cept boundary of the screened products [7]. Some researchers haveproposed, either from 2-D studies or experiments, that screenefficiency and screen length are subject to a diminishing exponen-tial distribution [8,9]. Increasing the length of the screen can bringscreening efficiency to 100%, theoretically.

This paper introduces the effect of screen length on screeningefficiency for an inclined screen surface under various singleparameter experiments using the Discrete Element Method(DEM). The results show that numerical simulation of screeninghas tremendous superiority over traditional methods.

2. DEM

The application of the Discrete Element Method (DEM) to vibra-tory screen analysis is a great improvement that was introduced byCundall and Strack [10] as a way to model the behavior of densesolid assemblies in soil. The sieving analysis initially employed a‘‘first-order rate law’’ to analyze screening, e.g.; the random pathmodel of Jansen and Glastonbury, which was only applicable toindependent particles [4]. Then ideas from Computational FluidDynamics (CFD) were adopted and the solids were treated as acontinuum. Finally, multiphase flow models using the, so called,Lagrangian approach or the DEM are now being developed wherethe motion of each individual particle is determined as a conse-quence of all the forces acting on it. The basic advantage of thismethod over continuum techniques is that it simulates effects atthe particle level and there is no need for global assumptions aboutthe assembly response, which is directly output from thesimulation.

The fundamental theory of particulate simulation uses the‘‘springs and dash pots’’ model to represent particle interactions,as shown in Fig. 1. This has been adopted in most of the currentDEM applications to particulate flows. Particles are assumed tobe cohesion-less elastic bodies and the microscopic particle–parti-cle and particle–boundary interactions are calculated along withthe evolution of the particle trajectories. The magnitude of thenormal force, Fn, and the tangential force, Ft , are:

Fn ¼ �kDxn þ Cvn ð1Þ

Ft ¼ �kDxt þ Cv t ð2Þ

where Dxn and Dxt are the particle displacements in the normal andtangential directions, vn and v t the relative velocities, k the stiffnessof the spring, and C the coefficient of viscous dissipation. Thenormal force is a spring that provides the repulsive force and a dashpot to dissipate a proportion of the relative kinetic energy. Thenormal damping coefficient, C, is chosen to give the required coeffi-

Fig. 1. Models of contact forces.

cient of restitution as defined by the ratio of the post-collisional topre-collisional normal components of the relative velocities

C ¼ 2cffiffiffiffiffiffiffiffiffiffiffimijkn

q; ð3Þ

where

c ¼ InðeÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip2 þ In2ðeÞ

q

andmij ¼

mimj

miþmjgives the reduced mass of particles i and j with

masses mi and mj. Once Ft surpasses the limiting friction forcethe particles slide over each other and the tangential force is thencalculated using the friction coefficient, f:

Ft ¼ �fFn ð4Þ

By knowing the various forces, which always include contactand gravitational forces, acting on the particles the velocity andthe trajectory of each individual particle may be computed by inte-gration over time.

Eqs. (1) and (2) show a linear relationship between the contactforces and the displacements, which takes the form of Hooke’s law.Seville et al., stated that the linear spring model is the simplestmathematical form, and it is fairly widely used [11]. Tsuji et al.,assumed a small value for the stiffness, k, of 800 N/m [12]. Thisallowed a large time step in the calculations while still producingrealistic particle motion with reduced computation times. For aDEM simulation the time step is vital and should be selected basedon trial runs. Different values are tried until a reasonable and sta-ble result is obtained. As a result of this a time step equal to, or lessthan, 5 � 10�7 s has been found sufficient to produce repeatableresults without introducing excessive particle motion caused byunrealistic particle collisions. The coefficient of viscous dissipation,C, is related to the coefficient of restitution that is one of the phys-ical properties of the particles, and can easily be obtained fromexperiments.

3. Simulation and discussion

3.1. Conditions of the simulation

A 3D DEM model (Fig. 2) was set up to simulate the screeningprocess for an angle of 21 degree as the screen inclination. Thescreen box is 160 mm long, 30.5 mm wide, and 80 mm high. Theboundary consists of a woven mesh with a wire diameter of0.7 mm and a square aperture 1 mm on a side. This provides anaperture that allows undersize particles to pass through it. Parti-cles fed onto the front section of the screen by gravity, via theparticle factory, fall to the screen mesh where some pass through

Fig. 2. Schematic layout of the vibration screening model.

Table 1Summary of modeling conditions.

Material property Poisson’s ratio Shear modulus Density

Particle 0.3 23 MPa 2678 kg/m3

Screen 0.29 79.92 GPa 7861 kg/m3

Collision property Coefficient of restitution Coefficient of static friction Coefficient of rolling frictionParticle–particle 0.1 0.545 0.01Particle–screen 0.2 0.5 0.01

Particle diameter Mean 0.5 and 1.0 mm Std. Dev. 0.45 Particle generation rate 50,000 particle/sScreen aperture 0.7 mm�0.7 mm Particle generation position Particle factory positioned randomlyScreen declination 21�

G. Wang, X. Tong / Mining Science and Technology (China) 21 (2011) 451–455 453

the apertures and become an underflow stream. Other particlesrebound along the screen surface and become the overflow stream.

This study employs a mixture of two different sized particles,which consists of bimodal normal distribution with individualmean diameters of 0.5 and 1.0 mm. The standard deviation indiameter is 0.45. The spherical particle density is 2687 kg/m3,which have similar properties to sands. The initial velocity calcu-lated from the feed was assigned to all the particles. At themoment of generation the particle velocity is assumed to bevx = vy = 0 and vz = –0.01 m/s. As a result of vibration the velocitiesin all three dimensions changes because the particles contact eachother and the screen surface. The conditions and parameters of themodel are listed in Table 1.

Simulations have been divided into four groups according to theparameters used. The first group was conducted using variousamplitudes: 0.5, 1.5, 2.55, 3.5, 4.49, 5.0, and 7.0 mm, while theother conditions were held constant. For the second the frequencywas varied: 10, 15, 20, 30, 40, 50, 60, and 70 Hz. Different vibrationangles of 10, 21, 32, 44, 51, 61, 71, 81, 90, and 100 degrees wereused for series three. Series four involved different inclinations:0, 10, 15, 20, 25, 30, 35, and 45 degrees.

Fig. 3. Screening efficiency curves for different frequencies

The length of the screen surface was 160 mm and it was evenlydivided into eight parts so the relationship between screen lengthand screening efficiency could be analyzed.

3.2. Screening efficiency versus screen length: varied frequency andvibration angle

Frequency mainly influences the bounce state of particles onthe screen surface. High frequency is benefit to penetration andto avoid blinding of particles. The vibration angle is defined asthe angle between the vibration direction and the screen surface.An appropriate vibration angle not only can improve well-propor-tioned bounce but also raise the screening efficiency.

The screening efficiency curves for different frequencies appearand efficiency curves for different screen inclinations appear in Fig3. As the frequency increases there are obvious changes in thecurves. Between 20 and 30 Hz, a commonly used range, the screen-ing efficiency increases at longer screen lengths one of which wasshown as Fig. 3a at 20 Hz. Fig. 3b shows that efficiency is almostproportional to screen length when the frequency is very high, over50 Hz. Lower frequencies, less than 10 Hz, give curves that are

and efficiency curves for different screen inclinations.

454 G. Wang, X. Tong / Mining Science and Technology (China) 21 (2011) 451–455

almost horizontal, see Fig. 3c. In this case a low peak emerged at ascreen length of 60 mm mainly due to the moment of the particlesfalling on the screen surface.

The vibration angle simulations are not exactly the same asthose where frequency was varied. Although the curves of screen-ing efficiency still increase with screen length the rate of increasechanges little varying from 10 to 91 degrees, see Fig. 3d and e.

It can be concluded that longer screen length increases screen-ing efficiency at each frequency or vibration angle. However,higher frequencies and vibration angles show more sensitivity tothis effect. The maximum screening efficiency identified bysimulations is in the range usually utilized in industrial screeningapplications. The identified frequency range is from 20 to 30 Hzand the vibration angle is from 30 to 60 degrees.

The main reason the maximum appears in this range is that lowfrequencies cannot sustain bouncing and the particles lack kineticenergy. At excessively high frequencies the particles had highkinetic energy and touched the screen surface for a shorter periodof time. Larger vibration angles extend the time of the particlesstay on the screen surface and raise penetration efficiency. Whenthe vibration angle is over 100 degrees the particles have a

0 40 80 120 16015

20

25

30

35

40

45

20

30

40

50

60

70

80

0 40 80 120

Diameters 0.5 0.60.7 0.8 0.9

Screen length (mm)

Scre

enin

g ef

fici

ency

(%

)

Screen length (mm)

Scre

enin

g ef

fici

ency

(%

)

0.50.6

0.7

0.8

0.9

(a) Amplitude 0.5 mm (b) Screen inclination 0

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

60

mm a b c d RelE%0.5 2.1936 0.6839 0.0160 4.1565 0.030620.6 2.1945 0.6741 0.0127 2.9374 0.021210.7 2.1860 0.6837 0.0107 3.1076 0.005350.8 2.2978 0.6705 0.0095 3.5484 0.005060.9 2.4566 0.6594 0.0088 4.5542 0.00764

200

Screen length (mm)

Scre

enin

g ef

fici

ency

(%

)

(d) Screen inclination 25 degrees

0 20 40 60 80

15

20

25

30

35

40

45

50

mm a0.5 2.4920.6 2.5720.7 2.5210.8 2.7100.9 2.475

Screen

Scre

enin

g ef

fici

ency

(%

)

(f) Screen inclination 3

Fig. 4. Efficiency vers

tendency to rebound, which then results in the ‘‘pollution’’ of over-size particles in the underflow area. This can be seen in Fig. 3f. Thescreen length of 60 mm is critical because at this point there is apeak and the screening efficiency becomes stable at longer lengths.In industrial screening applications only wet sieving of particlescontaining a mass of water employs a large vibration angle.

3.3. Screening efficiency versus screen length: varied amplitude andscreen inclination

Vibration amplitude mainly influences the kinetic energy of theparticles. Large amplitudes contribute to energy transportation andstratification and also make the particles bounce higher and further[13]. This is also an important influence on the required structuralstrength of the vibrating screen. Increased amplitude requires thestructural strength to be taken into account [14]. Inclination of thescreen is defined as the angle between a horizontal line and thescreen surface. Changes in inclination directly influence thehorizontal projection of the holes in the screen cloth and the velocityof the particles moving, or bounding, on the inclined surface [15].Large inclinations shrink the horizontal projection of the aperture

0 40 80 120 160

20

30

40

50

60

mm a b c d RelE%0.5 2.2033 0.7914 0.0143 4.4040 0.059930.6 2.0616 0.8038 0.0164 4.6289 0.033370.7 2.1818 0.7896 0.0159 4.7619 0.020840.8 2.2033 0.7914 0.0143 4.4040 0.010030.9 2.6703 0.7472 0.0156 3.7108 0.01253

160 200Screen length (mm)

Scre

enin

g ef

fici

ency

(%

)

0.50.6

0.7

0.8

0.9

degrees (c) Amplitude 2.55 mm

0 20 40 60 80 100 120 140 160 18010

20

30

40

50

mm a b c d RelE%0.5 1.7738 0.7648 0.0170 3.4302 0.014380.6 1.9711 0.7034 0.0162 3.1369 0.007590.7 2.0130 0.7040 0.0157 2.9049 0.004800.8 2.3092 0.6546 0.0121 3.0904 0.028450.9 2.9342 0.6014 0.0101 3.1791 0.02379

200

Screen length (mm)

Scre

enin

g ef

fici

ency

(%

)

(e) Amplitude 4.49 mm

100 120 140 160 180

b c d RelE%0 0.5140 -0.0120 5.4312 0.012762 0.4831 -0.0245 6.5146 0.013830 0.5364 -0.0030 5.5467 0.021809 0.5688 0.0093 4.7569 0.021762 0.6216 0.0142 3.6176 0.02592

200

length (mm)

5 degrees

us screen length.

G. Wang, X. Tong / Mining Science and Technology (China) 21 (2011) 451–455 455

and the horizontalcomponentof velocityrises. Penetrationprobabil-ities of the particles decrease in the normal direction and as a resultthis contributes to an increase in productivity.

Fig. 4a and b show the situation of small amplitude and screeninclination (an amplitude of 0.5 mm and an inclination of 0degrees). It can be seen that the screen length is important at60 mm because screening efficiency changes at this point. Fig. 4ashows that screening efficiency decreases as screen lengthapproaches 60 mm. Fig. 4b shows that screening efficiencyincreases as screen length approaches 60 mm. The main reasonamplitude affects efficiency is that the momentum of a fallingparticle increases the penetration probability and the particleshave little bounce after 60 mm. Over the range frequently usedin practice all of the screening efficiency curves are strictly convexbut the slopes become smaller. The rate of growth in screening effi-ciency decreases as can be seen in Fig. 4c and d (an amplitude of2.5 mm and an inclination of 25 degrees). Once the screen inclina-tion, or amplitude, surpasses a critical value (an amplitude of 3 mmor an inclination of 35 degrees) the curves of screening frequencyare almost proportional to the length of screen as illustrated inFig. 4e and f.

Finally, it appears that screen length is a benefit for the increasein screening efficiency in the amplitude and screen inclination sim-ulations. Note that amplitude and inclination play an importantrole in the simulations: longer screen lengths give higher screeningefficiency (approaching a theoretical 100% efficiency) in the ampli-tude and inclination simulations.

4. Establishment of a function relating screen length toscreening efficiency

The entire simulated data, including frequency, vibration angle,amplitude, and screen inclination simulations, were fit with a leastsquare method. A function describing how screening efficiencyvaries with screen length, at low relative errors, is:

y ¼ axbe�cxb þ d ð5Þ

where x is screen length (mm), y is screening efficiency (%) and a, b,c, and d are constant that change with particle diameter. The fittingcurves are depicted by the dotted line in Figs. 3a, b, d, e, and 4c, d, eand f. The constants and relative error (RelEs) are also shown inFigs. 3a, b, d, e, and 4c, d, e and f. This equation indicates that oncea goal for screening efficiency, such as 80%, has been established theminimum screen length required can be calculated. This is helpfulin the design of screening machinery.

5. Conclusions

(1) A function relating screening efficiency to screen length undervarious single parameter conditions (including frequency,amplitude, vibration angle, and screen inclination) was estab-lished from DEM 3D simulations. The results show that thefunction selected for fitting was excellent in accordance.

(2) When the parameters are extremely high or low (as shownin Figs. 3c, f, and 4a, and b) screening efficiency curves are

horizontal lines, i.e.; screen length has almost no effect onscreening efficiency. However, with the growth of theseparameters the screening efficiency increases with screenlength as shown in Figs. 3a, d, e, 4c, and d. However, the rateof growth becomes more and more stable. When the param-eters become very large (a frequency of approximately50 Hz, an amplitude of 5.0 mm, an vibration angle of 90degrees, or an inclination angle of 35 degrees) the screeningfrequency curves are almost proportional to the length ofscreen. In particular, optimal screening efficiency is obtainedwhen the parameters are in their frequently used range,which has been proved by many researchers and by practicalapplication.

(3) DEM-3D was conveniently and flexibly used for the simula-tions. One advantage of DEM is that it is convenient for cal-culating the number, position, and weight of the particles. Inaddition the motion and traces of the particles recurs duringscreening so the computational costs were significantlyreduced. It is expected that DEM has the ability to analyzeparticle stratification, penetration, and blinding.

Acknowledgments

The authors gratefully acknowledged the Special Topic Fund ofKey Science and Technology of Fujian Province (No. 2006HZ0002-2)for the financial support of these studies.

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