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The numerical modelling of excavator bucket fi lling using DEM C.J. Coetzee*, D.N.J. Els Department of Mechanical and Mechatronic Engineering, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa Received 15 February 2007; received in revised form 25 February 2009; accepted 28 May 2009 Available online 25 June 2009 Abstract The fi lling of an excavator bucket is a complex granular fl ow problem. In order to optimize the fi lling process, it is important to under- stand the diff erent 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 fi lling process of an excavator bucket. Model validation was based on the accuracy with which the model predicted the bucket drag force and the development of the diff erent fl ow regions. Compared to experimental measure- ments, DEM predicted lower bucket drag forces, but the general trend was accurately modelled. At the end of the fi lling process the error in predicted drag force was 20%. Qualitatively, there was a good agreement between the observed and the modelled fl ow regions in terms of position and transition from one stage to the other. During all stages of fi lling, DEM was able to predict the volume of material inside the bucket accurately to within 6%. ? 2009 ISTVS. Published by Elsevier Ltd. All rights reserved. 1. Introduction Earthmoving equipment plays an important role in the agricultural, earthmoving and mining industries. The equipment is highly diverse in shape and function, but most of the soil cutting machines can be categorised into one of three principal classes, namely blades, rippers and buckets (shovels). This paper focuses on the numerical modelling of excavator bucket fi lling using the discrete element method (DEM). Buckets are found on a number of earthmoving machin- ery. Draglines are used to remove blasted overburden from open cut mines. Its removal exposes the coal deposits beneath for mining. A dragline is a crane-like structure with a huge bucket of up to 100 m3in volume suspended by steel ropes. Draglines are an expensive and essential part of mine operations and play an important role in the com- petitiveness of South African mines. In the coal mining industry it is generally accepted that a 1% improvement in the effi ciency of a dragline will result in an R1 million increase in annual production per dragline 1. Buckets are also found on hydraulic excavators, loaders and shovel excavators. The fi lling of a bucket is a complex granular fl ow prob- lem. Instrumentation of fi eld equipment for measuring bucket fi lling is diffi cult and expensive. It is possible to use small-scale (usually 1/10th scale) experimental rigs to evaluate bucket designs 1,2 but they are expensive and there are questions regarding the validity of scaling 3,4. To scale-up results from model experiments is problematic since there are no general scaling laws for granular fl ows as there are for fl uid dynamics 5. According to Cleary 5 the fi lling of buckets, in the absence of very large rocks, is observed to be relatively two-dimensional with little motion in the transverse direc- tion. The fl ow pattern along a cross-section of the bucket in the drag direction is the most important aspect of fi lling and can be analysed satisfactorily using two-dimensional models. Rowlands 2 made similar observations based on dragline bucket fi lling experiments. According to Maciejewski et al. 6, in practical cases when 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 tools can be assumed only with limited accuracy. Maciejewski 0022-4898/$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). Available online at Journal of Terramechanics 46 (2009) 217227 Journal of Terramechanics et al. 6 also investigated the assumption of plane strain conditions in soil bins where the soil and tool motion is constrained between two transparent walls. For measure- ments in such a bin, the force acting on the tool due to the 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 separate three-dimensional objects but as one wide tool built up from several modules. The deformation pattern in front of such an assembly of teeth was found to be plane strain deformation. The authors, however, concluded that this was true for the particular cohesive soil (sandy clay) and may not apply to other (especially rocky and brittle) mate- rials. In this study the bucket had a full-width lip with no teeth and based on the fi ndings 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 infi nitesimal motion of the tool and the given geometry of the problem. These methods were not expected to be valid for the analysis of the subsequent stages of advanced earth digging problems 12. The analyt- ical methods are based on Terzaghis passive earth pressure theory and assumptions of a preliminary soil failure pattern 13. Complicated tool geometry (such as buckets) and large deformations cannot be modelled using these methods 14. The discrete element method is a promising approach to model soil-implement interaction and can be used to over- come some of the diffi culties encountered by analytical methods 15. In DEM, the failure patterns and material deformation are not needed in advance. The tools are mod- elled using a number of fl at walls and the complexity of the tool geometry does not complicate the DEM model. Large deformation in the granular material and the development of the granular material free surface are automatically han- dled by the method. Cleary 5 modelled dragline bucket fi lling using DEM. Trends were shown and qualitative comparisons made, but no experimental results were presented. The process of hydraulic excavator bucket fi lling was investigated experi- mentally by Maciejewski and Jarzebowski 12. The aim of their research was optimization of the digging process and bucket trajectories. It is shown that the most energy effi cient bucket is the one where the pushing eff ect of the back wall is minimized.Owenetal.21modelled3Ddraglinebucketfi ll- ing. In there approach, the bucket was modelled with the fi nite element method and the soil with DEM. Ellipsoids and clumped spheres were used to approximate the particle angularity. The bucket followed a prescribed path. Esterhuyse 1 and Rowlands 2 investigated the fi lling behaviour of scaled dragline buckets experimentally with the focus on rigging confi guration, bucket shape and teeth spacing. They have shown that the aspect ratio of the bucket (width to depth) plays and important role in the drag distance needed to fi ll a bucket. The bucket with the shortest fi ll distance was found to produce the highest peak drag force. The main objective of this study was to demonstrate the ability of DEM to predict the drag force on the bucket and the material fl ow patterns that develop as the bucket fi lls up. The DEM results were compared to experiments per- formed in a soil bin. 2. The discrete element method Discrete element methods are based on the simulation of the motion of granular material as separate particles. DEM was fi rst applied to rock mechanics by Cundall and Strack 16. In this study, all the simulations were two-dimensional andperformedusingcommercialDEMsoftwarePFC2D17. A linear contact model was used with a spring stiff ness kn in the normal direction and a spring stiff ness ksin the shear direction (Fig. 1). Frictional slip is allowed in the tangential directionwithafrictioncoeffi cientl.Thedampingforceacts on a particle in the opposite direction to the particle velocity and is proportional to the resultant force acting on the par- ticle with a proportionality constant (damping coeffi cient) C 17. For a detailed description of DEM, the reader is referred to Cleary and Sawley 18, Cundall and Strack 16, Hogue 19 and Zhang and Whiten 20. 3. Experimental Two parallel glass panels were fi xed 200 mm apart to form the soil bin. The bucket profi le was fi xed to a trolley which was driven by a ball screw and stepper motor. The Friction kn ks Fig. 1. DEM contact model. 218C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227 complete rig could be set at an angle h to the horizontal as shown in Fig. 2a. The fi rst arm was then rotated and fi xed such that both arms remained vertical. The second arm remained free to move in the vertical direction. First, coun- terweights were added at position A (Fig. 2a) to balance the combined weight of the bucket profi le and the second arm assembly. This resulted in a weightless” bucket. Counterweights were then added at position B to set the eff ective” bucket weight. Since arm 2 was always vertical even for rig angles other then zero, the eff ective bucket weight always acted vertically downwards (Fig. 2c). Bucket weights 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 as a result of the eff ective bucket weight and the force of the grains acting on it. The bottom edge of the bucket was always set to be parallel to the drag direction and the mate- rial free surface. This type of motion resembles that of a dragline bucket which is dragged in the drag direction by a set of ropes, but with freedom of motion in all other directions 2. Spring loaded Tefl on wipers were used to seal the small opening between the bucket profi le and the glass panels. A force transducer was designed and built to measure the drag force on the bucket. A set of strain gauges was bonded to a steel beam of which the position is shown in Fig. 2a. The set of four strain gauges was used to measure the force in the drag direction. Other force components were not measured. The force transducer was calibrated and the calibration checked regularly to avoid drift in the measure- ments. For rig angles other than zero, the force transducer was zeroed before the drag commenced. This compensated forthecomponentofthebucketweightthatactedinthedrag direction. The vertical displacement of the bucket was mea- sured with a linear variable diff erential transformer (LVDT) andusedasinputtotheDEMsimulation. Inboththeexper- imentsandtheDEMsimulationsthebucketwasgivenadrag velocity of 10 mm s?1 . The dimensions of the bucket profi le are shown in Fig. 2b. In this study corn grains were used. Although the corn grains are not real soil, Rowlands 2 observed that seed grains are suitable for experimental testing and closely resemble natural soil fl ow into dragline buckets. 4. DEM parameters and numerical model Fig. 3 shows the range of measured grain dimensions and the equivalent DEM grain. A normal distribution within the range of dimensions given was used to create the clumped particles. Clumps can be formed by adding two or more particles (discs in 2D and spheres in 3D) together to form one rigid particle, i.e. particles included in the clump remain at a fi xed distance from each other 17. Particles within a clump can overlap to any extent and contact forces are not generated between these parti- cles. Clumps cannot break up during simulations regardless of the forces acting upon them. In the model 20,00030,000 clumped particles were used. A calibration process, presented in another paper, was developed for cohesionless material. The particle size, shape and density were determined from physical measurements. The laboratory shear tests and compressions tests were used to determine the material internalfriction angleandstiff ness respectively. These tests were repeated numerically using DEM models with diff erent sets of particle friction coeffi - cientsandparticle stiff ness values.Thecombinationofshear testandcompressiontestresultscouldbeusedtodeterminea unique set of particle friction and particle stiff ness values, Table 1. A Direction of drag Direction of vertical motion 2nd Arm 1st Arm B Force transducer 100 mm 200 mm 150 mm Max volume 35 mm 45 WbcosWb Counter weights a bc Fig. 2. Experimental setup. 5 - 9 8 - 12 5 - 6 4 - 5 3 - 6 R 2.5 - 4.5 R 1.5 - 3.0 3.0 - 5.0 a b Fig. 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) 217227219 In the software used, PFC2D, so-called walls are used to build structures. The test rig and the bucket, with the same dimensions as in the experiment, were built from walls. The walls are rigid and move according to prescribed transla- tional and rotational velocities. The forces and moments acting on the walls do not infl uence the motion of the wall. During the experiments a constant drag velocity of 10 mm s?1was applied while the vertical displacement was measured. The vertical displacement was infl uenced by both the rig angle and the eff ective 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 given setup, and increased with an increase in bucket weight. In the DEM model, the drag velocity was set to 10 mm s?1 and the measured vertical displacement was read from a data fi le and applied to the bucket. Standard functions build into PFC2Dwere used to obtain the forces and moments acting on individual walls and on the bucket as a whole. For rig angles other than zero, the rig was kept horizontal but the gravity compo- nents were set accordingly. 5. Results and discussion It is diffi cult to make quantitative comparisons regard- ing fl ow patterns. When comparing the material free surface, some comparisons could however be made. Figs. 5 and 6 show how the material fl owed into the bucket for rig 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 the initial stages of fi lling. The simulations however failed to accurately predict the material free surface during the fi nal stages of fi lling. Curves were fi tted to the experimental free surface and overlaid on the numerical results in Figs. 5 and 6. The max- imum diff erence between the two free surfaces (heap height) was measured along the direction perpendicular to the drag direction. Two measurements were made, one where DEM predicted a higher heap height, and one measurement where DEM predicted a lower heap height. The values and the positions where they were measured are indicated in the fi gures. Taking the nominal particle size as 10 mm, DEM predicted the heap height accurately within 1.54.5 particle diameters. Fig. 7 shows typical drag forces obtained from experi- ments and simulations. The large jump in the drag force at the beginning of the experiment was observed in most of the runs and could not be explained and needs further investigation. From this result, it is clear that the DEM model captured the general trend in drag force, but it pre- dicted lower values compared to the measured values. Over the complete drag of 800 mm, the model predicted a force which was 1550 N lower than the measured force. At the end of the drag the error was 20%. The frictional force between the Tefl on 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 forces between the grains and the side panels would also have an infl uence on the measured results. These frictional forces could not be measured or included in the 2D DEM model and might be the reason why the model predicts lower drag forces 6. The drag energy was defi ned as the area under the drag forcedisplacement curve. Making use of diff erent rig angles h and eff ective bucket weights Wb, the drag energy E700up to a displacement of 700 mm is compared in Fig. 8. The fi rst observation that could me made was that with an increase in eff ective bucket weight, for a given rig angle h, there was a linear increase in required drag energy. A closer investigation showed that with an increase in bucket weight, the bucket was forced deeper into the material which caused a higher drag force when compared to a bucket with less weight. The second observation that can be made is that with an increase in the rig angle, there is a decrease in drag energy. The eff ective bucket weight Wbalways acted vertically Table 1 Summary of corn properties and DEM parameters used. Macro propertyMeasuredDEM Internal friction angle23?24? Angle of repose25 2?24 1? Bulk density778 kg m?3778 kg m?3 Confi ned bulk modulus1.60 MPa1.52 MPa Material-steel friction14?14? Calibrated DEM properties Particle stiff ness, kn= ks450 kN/m Particle density, qp855 kg/m3 Particle friction coeffi cient, l0.12 Other properties Damping, C0.2 Model width0.2 m 0100200300400500 Drag displacement mm 600700 20 40 60 80 100 Vertical displacement mm 120 Wb= 202.1 N 138.3 N 93.2 N 49.1 N Fig. 4. Measured vertical displacement of the bucket with h = 10? and four values of eff ective bucket weight Wb. 220C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227 downward (Fig. 2c) so that the normal force pushing the bucket into the material is given by Wb? cos (h). Thus, with an increase in rig angle, there is a decrease in the normal force pushing the bucket into the material. This caused a reduction in the drag force, and hence a reduction in the drag energy, when compared to results using a