外文翻譯--利用DEM法對挖掘機(jī)鏟斗填充進(jìn)行數(shù)值模擬 英文版

*,formexcavatorof position and transition from one stage to the other. During all stages of filling, DEM was able to predict the volume of material insidethe bucket accurately to within 6%.excavator bucket filling using the discrete element method(DEM).industry it is generally accepted that a 1% improvementin the eciency of a dragline will result in an R1 millionincrease in annual production per dragline 1. BucketsTo scale-up results from model experiments is problematicsince there are no general scaling laws for granular flows asdragline bucket filling experiments.According to Maciejewski et al. 6, in practical caseswhen the motion of a bucket or bulldozer blade is dis-cussed, plane strain conditions apply only in some defor-mation regions. The plane strain solution for such toolscan be assumed only with limited accuracy. Maciejewski*Corresponding author. Tel.: +27 21 808 4239； fax: +27 21 808 4958.E-mail address: ccoetzeesun.ac.za (C.J. Coetzee).Available online at Journal of Terramechanics 46JournalBuckets are found on a number of earthmoving machin-ery. Draglines are used to remove blasted overburden fromopen cut mines. Its removal exposes the coal depositsbeneath for mining. A dragline is a crane-like structurewith a huge bucket of up to 100 m3in volume suspendedby steel ropes. Draglines are an expensive and essential partof mine operations and play an important role in the com-petitiveness of South African mines. In the coal miningthere are for fluid dynamics 5.According to Cleary 5 the filling of buckets, in theabsence of very large rocks, is observed to be relativelytwo-dimensional with little motion in the transverse direc-tion. The flow pattern along a cross-section of the bucket inthe drag direction is the most important aspect of fillingand can be analysed satisfactorily using two-dimensionalmodels. Rowlands 2 made similar observations based onC211 2009 ISTVS. Published by Elsevier Ltd. All rights reserved.1. IntroductionEarthmoving equipment plays an important role in theagricultural, earthmoving and mining industries. Theequipment is highly diverse in shape and function, but mostof the soil cutting machines can be categorised into one ofthree principal classes, namely blades, rippers and buckets(shovels). This paper focuses on the numerical modelling ofare also found on hydraulic excavators, loaders and shovelexcavators.The filling of a bucket is a complex granular flow prob-lem. Instrumentation of field equipment for measuringbucket filling is dicult and expensive. It is possible touse small-scale (usually 1/10th scale) experimental rigs toevaluate bucket designs 1,2 but they are expensive andthere are questions regarding the validity of scaling 3,4.The numerical modelling of excavatorC.J. CoetzeeDepartment of Mechanical and Mechatronic Engineering, UniversityReceived 15 February 2007； received in revisedAvailable onlineAbstractThe filling of an excavator bucket is a complex granular flow problem.stand the dierent mechanisms involved. The discrete element methodactions and it was used in this study to model the filling process of anwhich the model predicted the bucket drag force and the developmentments, DEM predicted lower bucket drag forces, but the general trendin predicted drag force was 20%. Qualitatively, there was a good agreement0022-4898/$36.00 C211 2009 ISTVS. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.jterra.2009.05.003bucket filling using DEMD.N.J. Elsof Stellenbosch, Private Bag X1, Matieland 7602, South Africa25 February 2009； accepted 28 May 200925 June 2009In order to optimize the filling process, it is important to under-(DEM) is a promising approach to model soil-implement inter-bucket. Model validation was based on the accuracy withof the dierent flow regions. Compared to experimental measure-was accurately modelled. At the end of the filling process the errorbetween the observed and the modelled flow regions in /locate/jterra(2009) 217227ofTerramechanicsThe main objective of this study was to demonstrate theability of DEM to predict the drag force on the bucket andthe material flow patterns that develop as the bucket fillsup. The DEM results were compared to experiments per-formed in a soil bin.2. The discrete element methodDiscrete element methods are based on the simulation ofthe motion of granular material as separate particles. DEMwas first applied to rock mechanics by Cundall and Strack16. In this study, all the simulations were two-dimensionalandperformedusingcommercialDEMsoftwarePFC2D17.A linear contact model was used with aspring stiness knin the normal direction and a spring stiness ksin the sheardirection (Fig. 1). Frictional slip is allowed in the tangentialdirectionwithafrictioncoecientl.Thedampingforceactsonaparticleintheoppositedirectiontotheparticlevelocityand is proportional to the resultant force acting on the par-ticle with a proportionality constant (damping coecient)C 17. For a detailed description of DEM, the reader isreferred to Cleary and Sawley 18, Cundall and Strack16, Hogue 19 and Zhang and Whiten 20.3. ExperimentalTerramechanics 46 (2009) 217227et al. 6 also investigated the assumption of plane strainconditions in soil bins where the soil and tool motion isconstrained between two transparent walls. For measure-ments in such a bin, the force acting on the tool due tothe friction between the soil and the sidewalls has to be esti-mated or neglected. They have shown that for a high num-ber of teeth on the bucket, the teeth do not act as separatethree-dimensional objects but as one wide tool built upfrom several modules. The deformation pattern in frontof such an assembly of teeth was found to be plane straindeformation. The authors, however, concluded that thiswas true for the particular cohesive soil (sandy clay) andmay not apply to other (especially rocky and brittle) mate-rials. In this study the bucket had a full-width lip with noteeth and based on the findings by Maciejewski et al. 6,the assumption of plane strain was made and two-dimen-sional DEM models were used.Analytical methods 711 used to model soiltool inter-action are limited to infinitesimal motion of the tool andthe given geometry of the problem. These methods werenot expected to be valid for the analysis of the subsequentstages of advanced earth digging problems 12. The analyt-ical methods are based on Terzaghis passive earth pressuretheory and assumptions of a preliminary soil failure pattern13. Complicated tool geometry (such as buckets) and largedeformations cannot be modelled using these methods 14.The discrete element method is a promising approach tomodel soil-implement interaction and can be used to over-come some of the diculties encountered by analyticalmethods 15. In DEM, the failure patterns and materialdeformation are not needed in advance. The tools are mod-elled using a number of flat walls and the complexity of thetool geometry does not complicate the DEM model. Largedeformation in the granular material and the developmentof the granular material free surface are automatically han-dled by the method.Cleary 5 modelled dragline bucket filling using DEM.Trends were shown and qualitative comparisons made, butno experimental results were presented. The process ofhydraulic excavator bucket filling was investigated experi-mentally by Maciejewski and Jarzebowski 12. The aim oftheir research was optimization of the digging process andbuckettrajectories.Itisshownthatthemostenergyecientbucket is the one where the pushing eect of the back wall isminimized.Owenetal.21modelled3Ddraglinebucketfill-ing. In there approach, the bucket was modelled with thefinite element method and the soil with DEM. Ellipsoidsand clumped spheres were used to approximate the particleangularity. The bucket followed a prescribed path.Esterhuyse 1 and Rowlands 2 investigated the fillingbehaviour of scaled dragline buckets experimentally withthe focus on rigging configuration, bucket shape and teethspacing. They have shown that the aspect ratio of thebucket (width to depth) plays and important role in thedrag distance needed to fill a bucket. The bucket with the218 C.J. Coetzee, D.N.J. Els/Journal ofshortest fill distance was found to produce the highest peakdrag force.Two parallel glass panels were fixed 200 mm apart toform the soil bin. The bucket profile was fixed to a trolleywhich was driven by a ball screw and stepper motor. TheFrictionknksFig. 1. DEM contact plete rig could be set at an angle h to the horizontal asshown in Fig. 2a. The first arm was then rotated and fixedsuch that both arms remained vertical. The second armremained free to move in the vertical direction. First, coun-terweights were added at position A (Fig. 2a) to balancethe combined weight of the bucket profile and the secondarm assembly. This resulted in a weightless” bucket.Counterweights were then added at position B to set theeective” bucket weight. Since arm 2 was always verticaleven for rig angles other then zero, the eective bucketweight always acted vertically downwards (Fig. 2c). Bucketweights of 49.1 N, 93.2 N, 138.3 N and 202.1 N were used.When the bucket was dragged in the direction as indi-cated, it was also free to move in the vertical direction asa result of the eective bucket weight and the force of thegrains acting on it. The bottom edge of the bucket wasalways set to be parallel to the drag direction and the mate-rial free surface. This type of motion resembles that of adragline bucket which is dragged in the drag direction bya set of ropes, but with freedom of motion in all otherdirections 2.Spring loaded Teflon wipers were used to seal the smallopening between the bucket profile and the glass panels. Aforcetransducerwasdesignedandbuilt tomeasurethedragforce on the bucket. A set of strain gauges was bonded to asteel beam of which the position is shown in Fig. 2a. Thecalibration checked regularly to avoid drift in the measure-ments. For rig angles other than zero, the force transducerwas zeroed before the drag commenced. This compensatedforthecomponentofthebucketweightthatactedinthedragdirection. The vertical displacement of the bucket was mea-suredwithalinearvariabledierentialtransformer(LVDT)andusedasinputtotheDEMsimulation.Inboththeexper-imentsandtheDEMsimulationsthebucketwasgivenadragvelocity of 10 mm sC01. The dimensions of the bucket profileare shown in Fig. 2b.In this study corn grains were used. Although the corngrains are not real soil, Rowlands 2 observed that seedgrains are suitable for experimental testing and closelyresemble natural soil flow into dragline buckets.C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227 219set of four strain gauges was used to measure the force inthe drag direction. Other force components were notmeasured. The force transducer was calibrated and theADirection of drag Direction of vertical motion 2ndArm1stArmBForce transducer 100 mm200 mm150 mm Max volume 35 mm45WbcosWbCounter weights abcFig. 2. Experimental setup.4. DEM parameters and numerical modelFig. 3 shows the range of measured grain dimensionsand the equivalent DEM grain. A normal distributionwithin the range of dimensions given was used to createthe clumped particles. Clumps can be formed by addingtwo or more particles (discs in 2D and spheres in 3D)together to form one rigid particle, i.e. particles includedin the clump remain at a fixed distance from each other17. Particles within a clump can overlap to any extentand contact forces are not generated between these parti-cles. Clumps cannot break up during simulations regardlessof the forces acting upon them. In the model 20,00030,000clumped particles were used.A calibration process, presented in another paper, wasdeveloped forcohesionlessmaterial. Theparticle size,shapeand density were determined from physical measurements.Thelaboratorysheartestsandcompressionstestswereusedtodeterminethematerialinternalfrictionangleandstinessrespectively. These tests were repeated numerically usingDEM models with dierent sets of particle friction coe-cientsandparticlestinessvalues.Thecombinationofsheartestandcompressiontestresultscouldbeusedtodetermineaunique set of particle friction and particle stiness values,Table 1.5 - 98 - 125 - 64 - 53 - 6R 2.5 - 4.5 R 1.5 - 3.0 3.0 - 5.0 abFig. 3. (a) Physical grain dimensions and (b) DEM grain model.Dimensions in (mm).In the software used, PFC2D, so-called walls are used tobuild structures. The test rig and the bucket, with the samedimensions as in the experiment, were built from walls. Thewalls are rigid and move according to prescribed transla-tional and rotational velocities. The forces and momentsacting on the walls do not influence the motion of the wall.During the experiments a constant drag velocity of10 mm sC01was applied while the vertical displacementwas measured. The vertical displacement was influencedby both the rig angle and the eective bucket weight. A typ-ical result is shown in Fig. 4. Except for the initial transi-tion, the vertical velocity was nearly constant, for a givensetup, and increased with an increase in bucket weight. Inthe DEM model, the drag velocity was set to 10 mm sC01end of the drag the error was 20%. The frictional forcebetween the Teflon wipers and the glass panels was mea-sured in a run without grains. This frictional force was sub-tracted from the measured drag force. Frictional forcesbetween the grains and the side panels would also havean influence on the measured results. These frictional forcescould not be measured or included in the 2D DEM modeland might be the reason why the model predicts lower dragforces 6.The drag energy was defined as the area under the dragforcedisplacement curve. Making use of dierent rigangles h and eective bucket weights Wb, the drag energyE700up to a displacement of 700 mm is compared in Fig. 8.The first observation that could me made was that withan increase in eective bucket weight, for a given rig angleh, there was a linear increase in required drag energy. Acloser investigation showed that with an increase in bucketweight, the bucket was forced deeper into the materialwhich caused a higher drag force when compared to abucket with less weight.The second observation that can be made is that with an220 C.J. Coetzee, D.N.J. Els/Journal of Terramechanand the measured vertical displacement was read from adata file and applied to the bucket.Standard functions build into PFC2Dwere used toobtain the forces and moments acting on individual wallsand on the bucket as a whole. For rig angles other thanzero, the rig was kept horizontal but the gravity compo-nents were set accordingly.5. Results and discussionIt is dicult to make quantitative comparisons regard-ing flow patterns. When comparing the material freesurface, some comparisons could however be made. Figs.5 and 6 show how the material flowed into the bucket forrig angles of h =0C176 and h =20C176, respectively. When com-paring the shape of the material free surface, the simula-tions were able to predict the general shape during theinitial stages of filling. The simulations however failed toaccurately predict the material free surface during the finalstages of filling.Curves were fitted to the experimental free surface andoverlaid on the numerical results in Figs. 5 and 6. The max-imum dierence between the two free surfaces (heapheight) was measured along the direction perpendicularto the drag direction. Two measurements were made, onewhere DEM predicted a higher heap height, and onemeasurement where DEM predicted a lower heap height.Table 1Summary of corn properties and DEM parameters used.Macro property Measured DEMInternal friction angle 23C176 24C176Angle of repose 25 2C176 24 1C176Bulk density 778 kg mC03778 kg mC03Confined bulk modulus 1.60 MPa 1.52 MPaMaterial-steel friction 14C176 14C176Calibrated DEM propertiesParticle stiness, kn= ks450 kN/mParticle density, qp855 kg/m3Particle friction coecient, l 0.12Other propertiesDamping, C 0.2Model width 0.2 mThe values and the positions where they were measuredare indicated in the figures. Taking the nominal particlesize as 10 mm, DEM predicted the heap height accuratelywithin 1.54.5 particle diameters.Fig. 7 shows typical drag forces obtained from experi-ments and simulations. The large jump in the drag forceat the beginning of the experiment was observed in mostof the runs and could not be explained and needs furtherinvestigation. From this result, it is clear that the DEMmodel captured the general trend in drag force, but it pre-dicted lower values compared to the measured values. Overthe complete drag of 800 mm, the model predicted a forcewhich was 1550 N lower than the measured force. At the0 100 200 300 400 500Drag displacement mm600 70020406080100Vertical displacement mm120Wb= 202.1 N138.3 N93.2 N 49.1 N Fig. 4. Measured vertical displacement of the bucket with h =10C176 andfour values of eective bucket weight Wb.ics 46 (2009) 217227increase in the rig angle, there is a decrease in drag energy.The eective bucket weight Wbalways acted verticallyTerramechanC.J. Coetzee, D.N.J. Els/Journal ofdownward (Fig. 2c) so that the normal force pushing thebucket into the material is given by WbC1 cos (h). Thus, withan increase in rig angle, there is a decrease in the normalforce pushing the bucket into the material. This caused areduction in the drag force, and hence a reduction in thedrag energy, when compared to results using a lower rigangle. The DEM simulations were able to capture the gen-eral trends, but it predicted drag energies lower than themeasured. The reason for this is that the predicted dragforces were too low due to the exclusion of the frictionforces between the grains and the glass panels. It would,however, still be possible to use the simulation results forqualitative optimization of bucket filling.Fig. 5. Bucket filling resultsics 46 (2009) 217227 221Using the simulation results it was possible to identifyhow much of the total force was exerted on each of thebucket sections. In Fig. 9 the bucket was divided into sixsections. The graphs show, as a ratio of the total dragforce, the force on each of the sections. From the startup to a displacement of 200 mm (25% of total displace-ment) the total force acted mainly on the lip and the bot-tom section. As material started to flow into the bucket,the other sections came into play, first the inner curveand finally the front section. Less than 5% of the forceacted on the top section. This was far less than the bottomsection (30%). The reason for this is that the material insidethe bucket showed little movement relative to the bucketwith rig angle h =0C176.Terramechan222 C.J. Coetzee, D.N.J. Els/Journal ofand the pressure on the top section was only due to theweight of the material inside the bucket. On the bottomsection, the pressure was due to the combined weight ofthe material inside the bucket and the weight of the bucketitself. During the complete filling process, 2030% of thedrag force acted on the lip. This shows that the design ofthe lip and teeth is important. It is well known that thelength of the lip/teeth and the angle of attack are importantfactors influencing bucket filling 2 .Rowlands 2 made use of mixtures of millet, peas andcorn in his 2D test rig. The observation of the filling behav-iour led to the development of a theory that describes theflow characteristics and patterns of material entering thebucket. Rowlands 2 named this concept the Shear ZoneFig. 6. Bucket filling resultsics 46 (2009) 217227Theory. He observed that definite planes of shear (rupture)formed between distinct moving material regimes. Theseshear planes changed orientation and location dependingon initial setup and during dierent stages of the filling pro-cess itself. The generalised theory is shown in Fig. 10. Thedierent flow regions, as named by Rowlands 2, are indi-cated on the figure. The movements of the material relativeto the bucket are indicated by the arrows.The virgin material remains largely undisturbed until thefinal third of the drag during which bulldozing” occurs.The initial laminar layer flows into the bucket during thefirst third of the drag (Fig. 10a). After entering to a certaindistance, this layer fails at the bucket lip and subsequentlybecomes stationary with respect to the bucket for thewith rig angle h =20C176.100 200 300 400 500 600 700 8000ExperimentSimulation250200Drag force N 15010050Displacement in drag direction mm Fig. 7. Typical bucket drag forces with rig angle h =10C176 and a bucket0 100 200 300 400 500 600 700 80000.4Displacement mm Drag force ratio Lip Bottom Outer curve LipTopBottomOuter curveFig. 9. Bucket drag force distribution with h =10C176.Active dig zone Initial laminar layer Active dig zone Initial laminar layer Active flow zone Shear lineVirgin material Virgin material baC.J. Coetzee, D.N.J. Els/Journal of Terramechanremainder of the drag (Fig. 10b and c). At steeper dragangles, the material flows more rapidly towards the rearbecause of the added gravitational assistance. This eectcan be seen by comparing Figs. 5 and 6.With the laminar layer becoming stationary, a new zone,the active flow zone, develops (Fig. 10). In this zone, thematerial displacement is predominantly in the verticaldirection. The active dig zone is located above the teethand bucket lip. This area develops as material starts toenter the bucket and increases in size after failure of the ini-tial laminar layer. In this zone, the virgin material fails andeither flows into the bucket as part of the laminar layerduring the first part of filling or moves into the active flowzone during the latter part of filling.The dead load that has resulted from live” material inweight Wb= 138.3 N.the active flow zone ramps up and over the initial laminarlayer. Some of the material in the initial laminar layer fails = 0 = 10 = 20 Experiment Simulation 40 40220200 180160140120WbN 10080 60 506070 80100 120 110 90E700J Fig. 8. Bucket drag energy E700as a function of the bucket weight Wbfordierent rig angles h.0.5FrontInner curveTopFrontInner curveics 46 (2009) 217227 223and starts to form part of the dead load (Fig. 10c). Duringexperiments and while the material was flowing, a definiterupture or shear line could be observed here. With anincrease in drag angle, the active dig zone and active flowzone tended to join into one continuous band.Virgin material Active dig zone Dead load Active flow zone Initial laminar layer Shear line Shear line Dead load shear line cFig. 10. The Shear Zone Theory according to Rowlands 2.Terramechan224 C.J. Coetzee, D.N.J. Els/Journal ofIt should be noted that Fig. 10 only shows three stagesof the filling process, but in reality there is a gradual tran-sition from one stage to the next. It should also be notedthat this is a generalised theory and there will be variationsin the results when dierent materials and bucket geome-tries are used. During experiments two definite shear linescould be observed. The one extended from the tip of thelip up to the free surface. This is named the cutting shearline. The second line is the one between the initial laminarlayer and the dead load, called the dead load shear line.Making use of DEM and investigating the flow regionsfurther, the following procedure was devised. The bucketwas moved through the material and paused” after eachFig. 11. Flow regions using the particlebucics 46 (2009) 217227100 mm. The displacement vector of each particle was thenset to be zero after which the bucket was given a furtherdisplacement of 1015 mm (13 particle lengths). The par-ticle displacement ratio PDR was defined as the ratio of themagnitude of the particle absolute displacement vector tothe magnitude of the bucket absolute displacement vector.The particles were then coloured according to their individ-ual PDR values. A PDR equal to unity means that the par-ticle is moving with the bucket. The result is shown inFig. 11. This is in eect the average velocity ratio over ashort period.The flow regimes as predicted by the Shear Zone Theoryare indicated on the figure. The three pictures correspondket displacement ratio.to the three pictures given in Fig. 10. After a displacementof 100 mm, the active dig zone is clearly visible with0.406PDR 0.65. The initial laminar layer moves intothe bucket with 0.106PDR 0.25. This corresponds wellto the flow zones shown in Fig. 10a.After 500 mm, the characteristic V” shape of the activeflow zone can be seen with 0.106PDR 0.25. Althoughthe PDR is relatively low, the displacement is predomi-nantly in the vertical direction. The active dig zone is stillpresent and in the back of the bucket, the initial laminarlayer starts to become stationary relative to the bucket.This is visible by the PDR values that increase towardsthe back of the bucket. This corresponds well to the flowzones shown in Fig. 10b.After 800 mm the existence of the dead load shear line isclearly visible. When compared to Fig. 10c, the active flowzone and active dig zone cannot be distinguished from thedead load. The reason for this is that at a bucket displace-percentage.The comparison between experimental and DEM fillpercentages is summarised in Fig. 13. Using three rigangles h =0C176,10C176 and 30C176 and two eective bucketweights Wb= 49.1 N and 138.3 N, the fill percentagewas calculated at displacements of 100, 200, 300, 400,500, 600 and 700 mm. The 42 data points were plottedand the two lines indicate that in all cases, except fortwo, the DEM results were within 6% of the experi-mental results.In practice, the bucket is rotated to prevent the majorityof the material to fall out when the bucket is disengaged.This principle is depicted in Fig. 14 where, at the end ofits displacement, the bucket was lifted out of the materialand kept at the rig angle. The eect of bucket orientationis clear on the amount of material that the bucket couldhold. Again, the experimental free surface outline is shownon the DEM results with good agreement for h =0C176. Forh =20C176, the DEM model predicts additional material inthe back of the bucket which can be explained by the dier-C.J. Coetzee, D.N.J. Els/Journal of Terramechanment of 800 mm, the bulldozing eect is large and over-shadows the other flow zones.Dragline bucket optimization is very important in termsof force and energy requirements and cycle time. In someapplications it would be advantageous to fill the bucketusing the minimum amount of energy. In other applica-tions, it would be advantageous to fill the bucket as quicklyas possible to decrease cycle time 1. To investigate fillrates, images from the experiment were taken at dierentstages of filling, the outline of the material digitized, andthe volume of material inside the bucket calculated andexpressed as a percentage of the maximum bucket volume.The maximum bucket volume of 0.0146 m3is defined inFig. 2b. Using the DEM results, the same procedure wasfollowed and the results compared.Fig. 12 shows the experimental results using three dier-ent rig angles. The bucket fill percentage is plotted againstbucket displacement in terms of bucket-lengths. In thedragline industry, the target is to get the bucket completely0.511.5 2 2.50102030405060708090100Displacement bucket lengthBucketfill % = 0 = 10 = 20 Fig. 12. Bucket fill percentage as a function of bucket displacement fordierent rig angles.filled in 23 bucket-lengths. With an increase of the rigangle from 0C176 to 10C176, there is a slight increase in fill percent-age towards the latter stages of filling. This is due to thefact that when material is disturbed, it flows more easilyinto the bucket. When the rig angle is further increasedto 20C176 there is, however, a decrease in fill percentage. A fur-ther investigation showed that with an increase in rig angle,the bucket displacement into the material is less. It hasbeen shown that the force perpendicular to the materialsurface is given by WbC1 cos (h). Hence, with an increasein the rig angle, the force component forcing the bucketto dig in, decreases. When this force component decreases,the penetration depth of the bucket into the material isreduced and the bucket scoops up less material. Whenthe bucket scoops up less material, there is a decrease in fill = 0, Wb= 49.1 N = 10, Wb= 49.1 N = 20, Wb= 49.1 N = 0, Wb= 138.3 N = 10, Wb= 138.3 N = 20, Wb= 138.3 N10 20 30Experimental %40 50 60010203040Simulation %5060- 6% + 6% Fig. 13. Comparison between experimental and DEM fill percentages.ics 46 (2009) 217227 225ence in the final fill state as seen in Fig. 6 at a displacementof 800 mm.Terramechanics 46 (2009) 2172276. ConclusionsThe main objective of this paper was to demonstratehow accurately the discrete element method can predictthe process of excavator bucket filling. The flow patternsof material entering the bucket, drag force acting on bucketdue to material interaction, energy requirements and thebucket fill rates were compared to experimental observa-tions and measurements. The study was limited to cohe-Fig. 14. The eect of bucket orientation226 C.J. Coetzee, D.N.J. Els/Journal ofsionless granular material and two-dimensional models.The conclusions of the paper are:1. Comparing the material free surface, DEM can accu-rately model the flow of material into the bucket duringthe initial stages of filling. During the latter stages of fill-ing DEM, however, fails to accurately predict the mate-rial free surface.2. DEM can accurately predict the general trend in bucketdrag force. Over the complete drag of 800 mm DEMpredicts a drag force 1550 N lower than the measuredvalues. The maximum measured drag force is 250 Nwhile DEM predicts a maximum drag force of 200 N.3. DEM fails to accurately predict the drag energy. Thegeneral trends are however correct and it is shown thatthe drag energy increases linearly with an increase inbucket weight.4. Based on the DEM results, between 20% and 30% of thetotal bucket force acts on t