小型電動(dòng)播種機(jī)設(shè)計(jì)

喜歡這套資料就充值下載吧。資源目錄里展示的都可在線預(yù)覽哦。下載后都有，請(qǐng)放心下載，文件全都包含在內(nèi)，圖紙為CAD格式可編輯，【有疑問咨詢QQ:414951605 或 1304139763】 The numerical modelling of excavator bucket filling using DEMC.J. Coetzee*, D.N.J. ElsDepartment of Mechanical and Mechatronic Engineering, University of Stellenbosch, Private Bag X1, Matieland 7602, South AfricaReceived 15 February 2007; received in revised form 25 February 2009; accepted 28 May 2009Available online 25 June 2009AbstractThe filling of an excavator bucket is a complex granular flow problem. In order to optimize the filling process, it is important to under-stand the different mechanisms involved. The discrete element method (DEM) is a promising approach to model soil-implement inter-actions and it was used in this study to model the filling process of an excavator bucket. Model validation was based on the accuracy withwhich the model predicted the bucket drag force and the development of the different flow regions. Compared to experimental measure-ments, DEM predicted lower bucket drag forces, but the general trend was accurately modelled. At the end of the filling process the errorin predicted drag force was 20%. Qualitatively, there was a good agreement between the observed and the modelled flow regions in termsof 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%.? 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 ofexcavator bucket filling using the discrete element method(DEM).Buckets 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 miningindustry it is generally accepted that a 1% improvementin the efficiency of a dragline will result in an R1 millionincrease in annual production per dragline 1. Bucketsare 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 difficult 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.To scale-up results from model experiments is problematicsince there are no general scaling laws for granular flows asthere 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 ondragline 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. Maciejewski0022-4898/$36.00 ? 2009 ISTVS. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.jterra.2009.05.003*Corresponding author. Tel.: +27 21 808 4239; fax: +27 21 808 4958.E-mail address: ccoetzeesun.ac.za (C.J. Coetzee) online at Journal of Terramechanics 46 (2009) 217227JournalofTerramechanicset 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 difficulties 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 andbucket trajectories. It is shown that the most energy efficientbucket is the one where the pushing effect 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 theshortest fill distance was found to produce the highest peakdrag force.The 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 a spring stiffness knin the normal direction and a spring stiffness ksin the sheardirection (Fig. 1). Frictional slip is allowed in the tangentialdirectionwithafrictioncoefficientl.Thedampingforceactson a particle in the opposite direction to the particle velocityand is proportional to the resultant force acting on the par-ticle with a proportionality constant (damping coefficient)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. ExperimentalTwo 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 model.218C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227complete 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 theeffective” bucket weight. Since arm 2 was always verticaleven for rig angles other then zero, the effective 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 effective 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. Aforce transducer was designed and built to measure the dragforce on the bucket. A set of strain gauges was bonded to asteel beam of which the position is shown in Fig. 2a. Theset of four strain gauges was used to measure the force inthe drag direction. Other force components were notmeasured. The force transducer was calibrated and 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-sured with a linear variable differential transformer (LVDT)andusedasinputtotheDEMsimulation. Inboththeexper-imentsandtheDEMsimulationsthebucketwasgivenadragvelocity of 10 mm s?1. 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.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 for cohesionless material. The particle size, shapeand density were determined from physical measurements.The laboratory shear tests and compressions tests were usedto determine the material internalfriction angleandstiffnessrespectively. These tests were repeated numerically usingDEM models with different sets of particle friction coeffi-cientsandparticle stiffness values.Thecombinationofsheartestandcompressiontestresultscouldbeusedtodetermineaunique set of particle friction and particle stiffness values,Table 1.ADirection of drag Direction of vertical motion 2nd Arm1st ArmBForce transducer 100 mm200 mm150 mm Max volume 35 mm45WbcosWbCounter weights abcFig. 2. Experimental setup.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).C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227219In 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 s?1was applied while the vertical displacementwas measured. The vertical displacement was influencedby both the rig angle and the effective 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 s?1and 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 difficult 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 = 0? and h = 20?, 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 difference 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.The 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 theend 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 different rigangles h and effective 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 effective 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 anincrease in the rig angle, there is a decrease in drag energy.The effective bucket weight Wbalways acted verticallyTable 1Summary of corn properties and DEM parameters used.Macro propertyMeasuredDEMInternal friction angle23?24?Angle of repose25 2?24 1?Bulk density778 kg m?3778 kg m?3Confined bulk modulus1.60 MPa1.52 MPaMaterial-steel friction14?14?Calibrated DEM propertiesParticle stiffness, kn= ks450 kN/mParticle density, qp855 kg/m3Particle friction coefficient, l0.12Other propertiesDamping, C0.2Model width0.2 m0100200300400500Drag displacement mm60070020406080100Vertical displacement mm120Wb= 202.1 N138.3 N93.2 N 49.1 N Fig. 4. Measured vertical displacement of the bucket with h = 10? andfour values of effective bucket weight Wb.220C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227downward (Fig. 2c) so that the normal force pushing thebucket into the material is given by Wb? 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.Using 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 bucketFig. 5. Bucket filling results with rig angle h = 0?.C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227221and 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 ZoneTheory. 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 different stages of the filling pro-cess itself. The generalised theory is shown in Fig. 10. Thedifferent 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