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使用DME作为挖掘机铲斗填充物的数字模型南非Matieland7602 Privte Bag X1 Stellenbosch大学机械和机械电子工程部，收于2007年2月15日，校订版收于2009年2月25日，2009年5月8日接受，2009年6月25日在线提供。摘要挖掘机铲斗填充物是一种复杂的流动着的颗粒，对于包含的不同的机制的理解是非常重要的。这种抽象的元素方法对于模拟土壤装置间的相互作用是是一种有前途的方法，并且它也被用于模拟挖掘机铲斗的填充过程。有效的模拟是基于准确性，通过这种准确性模型预测出斗的拉力和不同流动区的变化。通过用经验的方法比较，DEM预测出较低的斗拉力但是一般的倾向总会精确的被模拟出。在铲掘的最后错误的预测拉力占20%。就质量而言，在观察和模拟流动区域的处置和从一个阶段转移到另一个具有良好的一致性。在所有的填充阶段，DEM能够准确的预测出颤抖中材料的体积并使误差保持在6%以内。1 引言 运载设备在农业业运载业和矿业中扮演者一个重要角色。这些装备在外形和功能上有很大的差异，但是大多土壤铲掘机器能够归为三种基本种类之一，这三种包括叶片式，割裂式，和斗容式。这篇文章主要介绍了使用抽象的元素方法作为铲掘机铲斗的填充物及DME。铲斗经常在运载机上出现。拉铲掘机经常用于从露天煤矿移走超重负荷的东西。它的移除暴露了沉积的煤使之被采掘。一辆拉铲掘机就像一台装载机一样，拥有一个超过100立方米的巨大铲斗并且有钢绳索调动着。拉铲掘机是采矿中很昂贵的但也是最为基本的一部分，并且在南非的采矿业的竞争中扮演这很重要的角色，在煤矿工业中拉铲掘机的效率每提高1个百分点，这就将会导致1百万的R的增长，每种拉铲掘机的年产量。铲斗也经常在液压铲掘机和装载铲挖机上找到。铲斗填充物是一种颗粒状的流动的东西。野外装备用于测量斗装物的仪器是非常昂贵和困难的。使用小的比例经验装配来评价斗的设计是可行的，但是这种方法代价高并且比例的有效性从在着问题。放大模拟实验的的结果从在这问题，因为并没有一个普遍的规定对于流动颗粒，因为他们是动态的。根据清单斗的填充物，在没有大的石块的情况下，在横轴方向上有很小的移动。流动的模型沿着十字口在拉力的方向上是填充的最重要方面，通过两倍容积的模型能够很好地分析出结果。Rowlands基于拉铲掘机铲斗填充的实验做出了相似的实验。根据Maciejewski et al.，在试验情况下当铲斗或推土机的挡板被讨论时，刨系状况只应用于一些畸变区域，用于这样工具的刨系方法只能用较低的准确度予于证实，Maciejewski et al.也研究这种在铲斗中刨系条件的假设。在铲斗中沙土和铲斗的动作被强制在两面透明的屏障之间。为了在这种斗进行测量，由于处于沙土与墙板之间的摩擦而作用于铲刀上的力不得不评估式忽略，对于拥有多齿的铲斗，他们展示出这些牙并不是作为单个的三维物体，而是作为一个宽的刀具建于模型。这种在如此多的牙之前的畸变模式被发现属于刨系畸变，最终作者总结出这是正确的对于特殊的粘合的沙土并且可能不会应用于其他材料。在这个研究中，铲斗拥有一个宽的嘴型，没有铲牙，并且是基于Maciejewski et al.的发现，刨系假设被制作并且二维的DEM模型被使用。用于模仿沙土和牙之间的相互作用的分析方法被限用于极微小的刀具动作和问题的假定几何形状。这些方法并没有期望是正确的对于先进掘土问题的后发展阶段的分析。这种分析方法是以Terzaghi的消极土壤压力理论和初步土壤衰减模式的假设。Cleary 使用DEM仿制拖线铲斗的填充物趋势被展出并且作了以下质量方面的比较。但是并没有实验结果被展示出与水有关的挖掘机斗得填充物的工艺被Maciejewski和Jarzebowski用于实验性的研究。他们的研究。他们的研究目标是为了挖掘过程和铲斗轨线的最优化，据演示最具活了有效地铲斗是一种。后部挡板的推力效果被消弱的铲斗。Owen et al.模仿出了3D的拖线铲斗填充物。在这种方法下，铲斗用于有限元法和DEM制作的沙土被模仿成簇的半圆被用于近似模仿出部分角度，这种铲斗沿着一条规定的线路。Esterhuyse和Rowland研究了实践性的大规模拖线铲斗填充物的动作。并且将焦点至于传动装置布局。颤抖形状和牙状。他们出示铲斗款高比例的方法和在填充铲斗所需拖拉距离方面的重要角色。用最短填充距离的铲斗被发现能够产生最高的峰值拉力。这个研究的最主要物体是证明DEM在预测铲斗的推力和材料流动模式的能力，DEM的结果将被在一个沙箱中与实验结果相比较。2抽象元素法抽象元素法是以被作为单个不连续粒状材料的动作模仿为依据的。DEM是最先由Cundall和Strack用于岩石力学的。在这一研究中，所有的模仿都是二维的并且使用商业DEM软件PFC进行操作。一个线性联系的模型在法线方向上使用一个弹性系数Kn，在剪切方向上使用一个弹性系数Ks。摩擦滑移在几何切线的方向上是允许存在的。用摩擦系数表示。衰减力作用于一个点，力的方向与该点的速度方向相反并且是按一定比例于最终作用该店的力衰减。对于得到一个详细的DEM描述，读者涉及到Cleary和Sawley，Gundall和Strack，Hogue和Zhang和Whiiten。3实验性的两个平行的玻璃仪表盘被安装于距沙土箱200mm处。铲斗外形轮廓被淡妆于一辆载重车，载重车市有一个球螺杆喝不进电动机带动的。完整的装配可设置一个角度相对于水平面如图2a所示。第一根杆被传动和固定为了使两根杆保持垂直第二根臂杆保持自由状态，便能够在垂直方向上移动。首先，反向重力在A点增加使铲斗的轮廓总重保持平衡，第二个臂杆集成。这会导致一个“失重”的铲斗。反重力之后被夹在B点来设置“有效的”铲斗重量。由于臂杆总是垂直的甚至操纵角为0度，高效的铲斗重量。由于臂杆总是垂直的甚至操纵角为0度，高效的铲斗重量总是垂直向下的。49.1N,93.2N，138.3N和202.1N的铲斗重量是常被使用的。当铲斗被拖在演示方向上，他也是自由的在垂直的方向上移动，作为有效地铲斗重量是和颗粒状物体作用于其他的力的一个结果。铲斗的底部边缘总是被安排平行于拖的方向和材料自由表面。这种动作类型像一个拖线型铲斗，这种铲斗在被拉的方向被一系列绳索所拖拉，但是在其他方向上的行动依旧是自由的。载有弹性负荷的聚四氟乙烯的绳子被用于封印介于铲斗轮廓和玻璃表盘之间的小口子。一种力传感器被设计并建造用于测量的铲斗的拉力。一系列标准被系于n条钢柱上。四种品系标准值的装置被用于测量在拉方向的力，其他力的组成部分不能被测出。力传感器被标定并且刻度的常规检测可避免测量上的渐变。在拖拉开始之前力传感器被调零。这种对于铲斗重量部分的补偿在拖拉方向进行着。铲斗的垂直换置被一线性多变不同种的转换器处置并且用作DEM模拟的输入。在实验和DEM模拟两者中，铲斗被给予了10mm/s的速度铲斗轮廓的尺寸数据。4DEM参数和数字模型图3展示出了系列被测量的谷物尺寸和同等重量DEM谷物。对一批给定尺寸的正常分类被用于创造部件簇。簇可以由增加2个或更多的部件到一起形成，以至于形成一个刚醒部件，粒子彼此之间被包含于簇中并且保持一定距离拥有簇的可以与任何延伸联系的同时发生的部件，不可能产生在这些部件之间。这些簇不能被破坏在模拟时，尽管力作用于他们，在模型中2000030000个簇部件被使用。一个定量过程，出现在另一张纸上，被发展用于不连贯的材料。部件尺寸，形状和密度由物理测量方法决定。研究所剪切检测和浓缩检测被检测被用于决定材料的内部摩擦角和-硬度。这些检测被数次重复，使用DEM模型在不同的部分摩擦系数和部分刚性系数。剪切检测和浓缩检测的结合能够用于决定一种独一无二的摩擦系数和刚度组。在使用中软件PFC20所谓的墙是常用于构建结构。检测装置和铲斗，与实验中的一尺寸大小一样，由墙建造而来，墙板是刚性的并且可移动根据规定的转弯和旋转速度。作用于墙的力和转折点不能够影响到墙板的动作。在整个试验中一个持续的10mm/s的拉速度被应用垂直移动被处理进行。垂直移动会受到安装角和实际的铲斗重量的影响。一种典型的结果在图4中展示出。除了起初的转变，垂直速度几乎是恒定的，并且随着铲斗重量的增加会变大。在DEM模型中，行进速度设置为10mm/s，并且经处理的垂直移动被读取从一个文件中并且应用于铲斗。建立于PFC20的标准功能适用于获得力和转折点，并且作用于各自的墙板和铲斗，且作为一个整体。重力的组成部分会相应的依据水平的装配做调整。5结果和讨论做关于流动模式的有关质量的比较是困难的。当比较材料的自由面时，一些比较能做出图5和图6展示出材料是如何流进铲斗的对于=0和=20这具有代表性。当比较磁疗自由表面的形状时，模拟能够预测出普通的形状在填充的起初阶段。但是模拟无法精准的预测出自由表面在最后的填充阶段。曲线与实验的自由表面相适应，并且覆盖了很多的图5和图6的结果，介于两个自由面最大的不同就是沿着垂直于行进的方向进行调节测量，两种测量制形成，一种是DEM预测出的较高堆积高度，另一种是DEM预测出较低高度。被测量出的价值和位置在图中已经表明。将名义上零件尺寸作为10mm,DEM预测的堆积高度的精准性在1.54.5倍之间。图7展示了典型的从实验和模拟中获得的拉力。在实验开始时获得较大变化的拉力在大多时能被观察出但是无法解释并需要进一步的研究。从这个结果看，DEM模型在拉力中占据一般的倾向是很清晰的。但预测出较低的价值与测量价值比较起来。超过完整的800mm的移动，模型可预测出比测量力低1550N的力。在最终的推动误差为20%。介于聚四氟乙烯的绳索和玻璃表盘的摩擦力药效。颗粒物与盘的边缘之间的摩擦力可能也会影响测试的结果。这些摩擦力可能不能够被测出或包含于2D的DEM的模型并且可能是模型低估拉力的原因。拖拉能量是被定义为拉力移动曲线下的面积。使用不同的装置角和实际上的铲斗重量Wb，拉力能量E700 超过了700mm的移动量在图8中被比较。第一个发现：能够做到的是随着实际铲斗的重量增加，一个给定的，将有一个线性增长在所需的拉力能量上。一个近似的调查显示随着铲斗重量的增加，铲斗被进一步插入材料中，这将引起一个较高的拉力当与一个较轻的铲斗比较时。第二个能够发现的是随着的增加，在拉力能上力会减小。实际的铲斗重量Wb总是垂直向下动作，如图2C,以至于正常的力将铲斗插入材料中是由Wb*cos决定。因此，随着角的增加，将会使得铲斗插入材料的力减小，这会引起拉力能的减少。但与使用的较低的的结果线比较时。DEM模拟能够占领普通趋势。但是他预测出的拉力能低于被测值。这一现象的原因是由于预测的拉力太低因为不包含颗粒物与玻璃表盘之间的摩擦力。无论怎样，它将依旧可能使用模拟结果用于填充物的质量最优化。使用模拟结果能够明确有多大的力施加于各铲斗。如图9中的铲斗被分解为6个部分。图片显示出以一定的比例的力施加于每一个部分。从开始起升到位移200mm。总力主要施加于开口处和底部部分。当材料开始流过铲斗时，其他部分也开始发挥作用，首先是内部曲线，最后是前端部分，低于5%的力作用于顶端部分。这远远低于施加于底部的力，施加底部的力占总力的30%。造成这一现象的原因是铲斗内部材质，几乎没有相对运动并且顶部端面所受的压力只是由铲斗自身的重力所决定的。在完全填充的过程中20%30%的拉力施加于开口处。这就表现出开口和牙的设计是至关重要的。众所周知开口的长度或牙和铲角是影响铲斗填充物的重要因素。Rowland使用谷物、豌豆、和玉米的混合物在他的2维探测装置上。填充物的动作的观察结果导致了一个理论的发展。这一理论描述了流动的特征和材料进入铲斗的模式。Rowland称这一概念为剪切区理论。他观察到确切的剪切平面形成在不同移动材料固体之间。这些剪切刨平面可根据内部装置和自身的不同填装阶段调节方位和位置。这一概括出的理论如图10所示。不同的流动区域，由Rowland命名，在图上标注。相对于铲斗的材料移动由箭头所标注。6结论这份报告的目的是为了说明具体的元素方法能够预测挖掘机填充过程的准确性。进入到铲斗的材料的模式因为材料之间的相互作用而产生的拉力，能量需求和铲斗填充效率和实验结果和方法相比较。这种研究局限于松散的填充物材料和二维模型。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)./locate/jterraAvailable 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 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 theFig. 6. Bucket filling results with rig angle h = 20?.222C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227remainder of the drag (Fig. 10b and c). At steeper dragangles, the material flows more rapidly towards the rearbecause of the added gravitational assistance. This effectcan 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 inthe active flow zone ramps up and over the initial laminarlayer. Some of the material in the initial laminar layer failsand 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.1002003004005006007008000ExperimentSimulation250200Drag force N 15010050Displacement in drag direction mm Fig. 7. Typical bucket drag forces with rig angle h = 10? and a bucketweight Wb= 138.3 N. = 0 = 10 = 20 Experiment Simulation 40 40220200 180160140120WbN 10080 60 506070 80100 120 110 90E700 J Fig. 8. Bucket drag energy E700as a function of the bucket weight Wbfordifferent rig angles h.010020030040050060070080000.10.20.30.40.5Displacement mm Drag force ratio FrontInner curveTopLip Bottom Outer curve LipTopBottomFrontInner curveOuter curveFig. 9. Bucket drag force distribution with h = 10?.Active dig zone Initial laminar layer Active dig zone Initial laminar layerActive flow zone Virgin material Active dig zone Dead loadActive flow zone Initial laminar layer Shear lineShear line Shear line Dead load shear line Virgin material Virgin material bcaFig. 10. The Shear Zone Theory according to Rowlands 2.C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227223It 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 different 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 each100 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 effect the average velocity ratio over ashort period.The flow regimes as predicted by the Shear Zone Theoryare indicated on the figure. The three pictures correspondFig. 11. Flow regions using the particlebucket displacement ratio.224C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227to the three pictures given in Fig. 10. After a displacementof 100 mm, the active dig zone is clearly visible with0.40 6 PDR 0.65. The initial laminar layer moves intothe bucket with 0.10 6 PDR 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 0.10 6 PDR 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-ment of 800 mm, the bulldozing effect 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 differentstages 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 differ-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 completelyfilled in 23 bucket-lengths. With an increase of the rigangle from 0? to 10?, 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 20? 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 Wb? 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 fillpercentage.The comparison between experimental and DEM fillpercentages is summarised in Fig. 13. Using three rigangles h = 0?, 10? and 30? and two effective 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 effect 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 = 0?. Forh = 20?, the DEM model predicts additional material inthe back of the bucket which can be explained by the differ-ence in the final fill state as seen in Fig. 6 at a displacementof 800 mm.0.511.522.50102030405060708090100Displacement bucket lengthBucket fill % = 0 = 10 = 20 Fig. 12. Bucket fill percentage as a function of bucket displacement fordifferent rig angles. = 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 N102030Experimental %405060010203040Simulation %5060- 6% + 6% Fig. 13. Comparison between experimental and DEM fill percentages.C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 2172272256. 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-sionless 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
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