小型果樹(shù)移栽機(jī)及其鏟斗組件的仿真分析【棗樹(shù)移栽機(jī)】【說(shuō)明書+CAD+SOLIDWORKS+仿真】,棗樹(shù)移栽機(jī),說(shuō)明書+CAD+SOLIDWORKS+仿真,小型果樹(shù)移栽機(jī)及其鏟斗組件的仿真分析【棗樹(shù)移栽機(jī)】【說(shuō)明書+CAD+SOLIDWORKS+仿真】,小型,果樹(shù),移栽,及其,組件,仿真,分析,棗樹(shù) * , form excavator of position and transition from one stage to the other. During all stages of filling, DEM was able to predict the volume of material inside the bucket accurately to within 6%. excavator bucket filling using the discrete element method (DEM). industry it is generally accepted that a 1% improvement in the eciency of a dragline will result in an R1 million increase in annual production per dragline 1. Buckets To scale-up results from model experiments is problematic since there are no general scaling laws for granular flows as dragline bucket filling 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 * 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 Journal 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 m 3 in 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 there are for fluid dynamics 5. According to Cleary 5 the filling 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 flow pattern along a cross-section of the bucket in the drag direction is the most important aspect of filling and can be analysed satisfactorily using two-dimensional models. Rowlands 2 made similar observations based on C211 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 are also found on hydraulic excavators, loaders and shovel excavators. The filling of a bucket is a complex granular flow prob- lem. Instrumentation of field equipment for measuring bucket filling is dicult 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. The numerical modelling of excavator C.J. Coetzee Department of Mechanical and Mechatronic Engineering, University Received 15 February 2007; received in revised Available online Abstract The filling of an excavator bucket is a complex granular flow problem. stand the dierent mechanisms involved. The discrete element method actions and it was used in this study to model the filling process of an which the model predicted the bucket drag force and the development ments, DEM predicted lower bucket drag forces, but the general trend in predicted drag force was 20%. Qualitatively, there was a good agreement 0022-4898/$36.00 C211 2009 ISTVS. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jterra.2009.05.003 bucket filling using DEM D.N.J. Els of Stellenbosch, Private Bag X1, Matieland 7602, South Africa 25 February 2009; accepted 28 May 2009 25 June 2009 In 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 with of the dierent flow regions. Compared to experimental measure- was accurately modelled. At the end of the filling process the error between the observed and the modelled flow regions in terms (2009) 217227 of Terramechanics The main objective of this study was to demonstrate the ability of DEM to predict the drag force on the bucket and the material flow patterns that develop as the bucket fills 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 first applied to rock mechanics by Cundall and Strack 16. In this study, all the simulations were two-dimensional andperformedusingcommercialDEMsoftwarePFC 2D 17. A linear contact model was used with aspring stiness k n in the normal direction and a spring stiness k s in the shear direction (Fig. 1). Frictional slip is allowed in the tangential directionwithafrictioncoecientl.Thedampingforceacts onaparticleintheoppositedirectiontotheparticlevelocity and 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 is referred to Cleary and Sawley 18, Cundall and Strack 16, Hogue 19 and Zhang and Whiten 20. 3. Experimental Terramechanics 46 (2009) 217227 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 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 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 diculties 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 flat 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 filling using DEM. Trends were shown and qualitative comparisons made, but no experimental results were presented. The process of hydraulic excavator bucket filling was investigated experi- mentally by Maciejewski and Jarzebowski 12. The aim of their research was optimization of the digging process and buckettrajectories.Itisshownthatthemostenergyecient bucket is the one where the pushing eect of the back wall is minimized.Owenetal.21modelled3Ddraglinebucketfill- ing. In there approach, the bucket was modelled with the finite 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 filling behaviour of scaled dragline buckets experimentally with the focus on rigging configuration, 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 fill a bucket. The bucket with the 218 C.J. Coetzee, D.N.J. Els/Journal of shortest fill distance was found to produce the highest peak drag force. Two parallel glass panels were fixed 200 mm apart to form the soil bin. The bucket profile was fixed to a trolley which was driven by a ball screw and stepper motor. The Friction k n k s Fig. 1. DEM contact model. complete rig could be set at an angle h to the horizontal as shown in Fig. 2a. The first arm was then rotated and fixed 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 profile and the second arm assembly. This resulted in a weightless” bucket. Counterweights were then added at position B to set the eective” bucket weight. Since arm 2 was always vertical even for rig angles other then zero, the eective 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 eective 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 Teflon wipers were used to seal the small opening between the bucket profile and the glass panels. A forcetransducerwasdesignedandbuilt tomeasurethedrag 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 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- suredwithalinearvariabledierentialtransformer(LVDT) andusedasinputtotheDEMsimulation.Inboththeexper- imentsandtheDEMsimulationsthebucketwasgivenadrag velocity of 10 mm s C01 . The dimensions of the bucket profile 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 flow into dragline buckets. C.J. Coetzee, D.N.J. Els/Journal of Terramechanics 46 (2009) 217227 219 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 A Direction of drag Direction of vertical motion 2 nd Arm 1 st Arm B Force transducer 100 mm 200 mm 150 mm Max volume 35 mm 45 W b cosW b Counter weights a bc Fig. 2. Experimental setup. 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 fixed 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 forcohesionlessmaterial. Theparticle size,shape and density were determined from physical measurements. Thelaboratorysheartestsandcompressionstestswereused todeterminethematerialinternalfrictionangleandstiness respectively. These tests were repeated numerically using DEM models with dierent sets of particle friction coe- cientsandparticlestinessvalues.Thecombinationofshear testandcompressiontestresultscouldbeusedtodeterminea unique set of particle friction and particle stiness values, Table 1. 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). In the software used, PFC 2D , 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 influence the motion of the wall. During the experiments a constant drag velocity of 10 mm s C01 was applied while the vertical displacement was measured. The vertical displacement was influenced by 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 given setup, and increased with an increase in bucket weight. In the DEM model, the drag velocity was set to 10 mm s C01 end of the drag the error was 20%. The frictional force between 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 forces between the grains and the side panels would also have an influence 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 defined as the area under the drag forcedisplacement curve. Making use of dierent rig angles h and eective bucket weights W b , the drag energy E 700 up to a displacement of 700 mm is compared in Fig. 8. The first observation that could me made was that with an increase in eective 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 220 C.J. Coetzee, D.N.J. Els/Journal of Terramechan and the measured vertical displacement was read from a data file and applied to the bucket. Standard functions build into PFC 2D were 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 dicult to make quantitative comparisons regard- ing flow patterns. When comparing the material free surface, some comparisons could however be made. Figs. 5 and 6 show how the material flowed into the bucket for rig 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 the initial stages of filling. The simulations however failed to accurately predict the material free surface during the final stages of filling. Curves were fitted to the experimental free surface and overlaid on the numerical results in Figs. 5 and 6. The max- imum dierence 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. Table 1 Summary of corn properties and DEM parameters used. Macro property Measured DEM Internal friction angle 23C176 24C176 Angle of repose 25 2C176 24 1C176 Bulk density 778 kg m C03 778 kg m C03 Confined bulk modulus 1.60 MPa 1.52 MPa Material-steel friction 14C176 14C176 Calibrated DEM properties Particle stiness, k n = k s 450 kN/m Particle density, q p 855 kg/m 3 Particle friction coecient, l 0.12 Other properties Damping, C 0.2 Model width 0.2 m The values and the positions where they were measured are indicated in the figures. 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 0 100 200 300 400 500 Drag displacement mm 600 700 20 40 60 80 100 Vertical displacement mm 120 W b = 202.1 N 138.3 N 93.2 N 49.1 N Fig. 4. Measured vertical displacement of the bucket with h =10C176 and four values of eective bucket weight W b . ics 46 (2009) 217227 increase in the rig angle, there is a decrease in drag energy. The eective bucket weight W b always acted vertically TerramechanC.J. Coetzee, D.N.J. Els/Journal of downward (Fig. 2c) so that the normal force pushing the bucket into the material is given by W b C1 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 lower rig angle. The DEM simulations were able to capture the gen- eral trends, but it predicted drag energies lower than the measured. The reason for this is that the predicted drag forces were too low due to the exclusion of the friction forces between the grains and the glass panels. It would, however, still be possible to use the simulation results for qualitative optimization of bucket filling. Fig. 5. Bucket filling results ics 46 (2009) 217227 221 Using the simulation results it was possible to identify how much of the total force was exerted on each of the bucket sections. In Fig. 9 the bucket was divided into six sections. The graphs show, as a ratio of the total drag force, the force on each of the sections. From the start up 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 curve and finally the front section. Less than 5% of the force acted on the top section. This was far less than the bottom section (30%). The reason for this is that the material inside the bucket showed little movement relative to the bucket with rig angle h =0C176. Terramechan222 C.J. Coetzee, D.N.J. Els/Journal of and the pressure on the top section was only due to the weight of the material inside the bucket. On the bottom section, the pressure was due to the combined weight of the material inside the bucket and the weight of the bucket itself. During the complete filling process, 2030% of the drag force acted on the lip. This shows that the design of the lip and teeth is important. It is well known that the length of the lip/teeth and the angle of attack are important factors influencing bucket filling 2 . Rowlands 2 made use of mixtures of millet, peas and corn in his 2D test rig. The observation of the filling behav- iour led to the development of a theory that describes the flow characteristics and patterns of material entering the bucket. Rowlands 2 named this concept the Shear Zone Fig. 6. Bucket filling results ics 46 (2009) 217227 Theory. He observed that de