Transcript
Discrete Element Modelling of a Bucket Elevator Head Pulley Transition Zone W.McBride1, M.Sinnott2, P.W.Cleary2 1 School of Engineering, University of Newcastle University Drive Callaghan NSW 2308 Email –
[email protected] 2 CSIRO – Mathematical and Information Sciences Private Bag 33, Clayton South, VIC 3169 ABSTRACT Bucket elevators are common industrial devices used to elevate bulk materials, and outwardly they appear to be simple devices. However having a rigid bucket bolted to a flexible belt creates difficulties at the interface of the belt, bucket and head pulley. At the point where a bucket’s connection line to the belt contacts the pulley, the tip of the bucket must undergo an theoretically infinite acceleration. In reality, as the point of tangency is reached, the tip of the bucket lags behind its theoretical position before accelerating and overshooting its nominally correct position. This motion is complicated with the bulk material contained within the bucket being able to decouple and re-engage with the bucket during the transition phase. This paper presents results of a discrete element modelling (DEM) investigation to better understand the bucket motion at the transition point, and its effect on the discharge pattern from a typical bucket. KEYWORDS bucket elevator, bulk materials, mechanical handling, DEM
Introduction Bucket elevators are common industrial devices used throughout bulk materials handling industries. They offer a compact footprint for the vertical elevation of a wide variety of bulk materials. There is little restriction on the elevation height, and throughputs are broadly scalable. The mechanical construction of a bucket elevator is relatively simple with most elevators using conventional style fabric reinforced conveyor belt material for power transmission and bucket attachment, large elevators may utilise steel core belts, hybrid belts or chain. For the purpose of this paper a flexible belt is assumed in the construction. Typically, buckets are bolted onto the belt using a purpose designed bucket elevator bolt with a large diameter head that embeds into the belt cover to provide a flush finish on the underside of the belt. The buckets generally have a flat inner/back wall through which the fasteners pass and these determine the effective pivot of the bucket on the belt. Figures 1 illustrate a typical steel bucket and the mounting of these buckets onto a typical belt.
Figure 1 - Pressed steel bucket illustrating shape, the retaining holes, and indicative fitment [1] In operation, the buckets within a bucket elevator pass through the lowermost section of the elevator called ‘the boot’. The material to be elevated is supplied by chutes on either the downward, or upwards strands of the elevator located close to the boot end. A percentage of material elevated will return to the boot through spillage at the head pulley end. Irrespective of the mode of feeding, at some point soon after the boot area, the buckets are filled to a level commensurate with the nominal tonnage rate. 1
During the traverses between the top and bottom pulley, the bucket, its contents, and the belt must travel at the same velocity. As the bucket passes around either pulley, the tip speed of the bucket must increase by the ratio of bucket tip radius divided by pulley radius. As it is clearly impossible for this increase in speed to occur instantaneously, it is evident that the belt deforms over a finite time period to facilitate the acceleration phase. Mechanics dictate that the motion is a rapid acceleration leading to a corresponding overshoot of the desired position, followed by a damped oscillatory motion until the global angular velocity stabilises. During any bucket decelerations during the oscillations, the material carried in the bucket will have a greater propensity to move due to a reduction in the contact force between material and bucket. Table 1 – Basic simulation data. Bucket style
Starco Jumbo 370/4 (approximate)
Belt Speed
1.35 m/s
Pulley Diameter
550 mm
Particle solids density
1100 kg/m3
Particle size
2-10 mm
Belt deforms to buffer acceleration level
a
b Head Pulley Profile
α Force on Bucket
Deformed belt position
At rest belt position β
V=Vbelt
Reality
Material in bucket can be 'kicked' out and fall down the carry strand.
To Tail Nominal Belt Tension 'T'
Figure 2 – a) Illustration of belt deformation leading to bucket velocity change as it transitions to the head pulley. b) Restorative force diagram.
Restoration force There are two restoring forces resulting from the deformation of the belt at the tangency point. The first, illustrated in Figure 2b, is geometrically defined by the displacement of the belt. It can be shown that there is negligible increase in the local belt fibre tension due to the deflection imposed by the buckets motions and, accepting this, it can be shown that the force exerted to the bucket causing it to accelerate it is defined by the length of belt between the head and tail pulley centres, and the distance between the buckets attachment bolts and the lowest point of contact between belt and bucket. As the bottom of the bucket pushes onto the belt an angle α will be formed from the attachment point to the lowest point of bucket contact and a corresponding smaller angle β will form towards the tail pulley. Considering Figure 2b, the magnitude of the force F can be determined from (eq 1) 2
It should be noted that the tension at the head will be greater than the tension at the tail due to the mass of the belt and buckets. The second restoring force is a Hertzian contact force generated as the bucket compresses the belt carcass against the pulley face. Rubber lagging on the pulley will facilitate a larger deflection due to the overall increase in compliance at the contact point. The rate of generation and the centre of pressure associated with that contact, is dependent on the transverse modulus of elasticity of the belt and the compliance of the lagging material on the head pulley. In the simulation work to date, these two contributing restorative forces have not been decoupled and this is a point for further research.
Discrete Element Analysis The Discrete Element Method (DEM) is a numerical tool for modelling granular flows at the grain level. It is showing great promise as an optimisation tool for a variety of industries dealing with granular materials [2]. At each computation timestep, the DEM tracks all unit particles in the system, and calculates the forces between particles and between particles and boundaries. For each collision, a contact force model is applied. A variety of different contact models of varying complexity are available [3-4] but it is not a priori obvious that a more complex (and more computationally expensive) force model is necessary at the particulate level in order to correctly predict flows of very large assemblies of particles. We use a DEM solver developed by CSIRO that has been applied successfully to granular flows in mining [5-6], bulk solids handling [7-8], geophysical [9] and pharmaceuticals [10] applications. A linear spring is used to model elastic loading of the particles, and a dashpot models the energy dissipated in inelastic collisions. This contact model simplifies the computation allowing for large numbers of particles (107) to be realistically modelled. To facilitate the simulations presented, a path equivalent to an infinitely stiff system was created in the DEM software. Attached to this path was a ‘bucket’ object constrained to rotate about a horizontal axis parallel to the axis of the head pulley. The buckets rotation is controlled by a pair of spring contacts. The springs are positioned 10 mm above and 10 mm below the buckets pivot point. The CYS indication in Figure 3 designates the centreline of the retaining bolts of the bucket. This enables us to simulate the deformation of the supporting belt as these springs adjust to varying load states. For the simulations we define a “soft” case as having a spring constant of 5.0x106 N/m for the joint to the belt (verified with laboratory measurements of bucket tip deflection for a given loading) and a “stiff” case for a joint spring constant of 5.0x108 N/m.
Vb
a
b
CYS Z CYS
Y Springs
Figure 3 – a) An ‘infinitely stiff’ coordinate system path around a head pulley and b), bucket geometry indicating the hinge point (CYS) and spring location. The two CYS points are ‘pinned’ together in the model as a hinge joint. The springs are used in the simulation to model the restoring forces as the bucket deforms the belt. For DEM simulations reported here, spherical grains with diameters in the range 2 – 10 mm with an equal mass distribution in each size class were used. The material parameters applied to the particles include a solid density of 1100 kg/m3, a coefficient of friction of 0.5 for particle-particle
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and particle-boundary collisions, and a coefficient of restitution of 0.5 for particle-particle and particle-boundary collisions.
RESULTS Bucket Discharge Observations Figures 4a, b, c present images taken at different times during the discharge cycle for the soft/low spring stiffness condition and Figures 4d, e, f show equivalently timed images for the high/stiff spring stiffness case. The bucket’s contents are initially coloured in vertical bands to indicate the original location of the particles during the discharge cycle. These particle colours are maintained throughout the simulation. Evident from visual comparison is that with the lower spring stiffness more material is discharged from the bucket in the early phase, Figures 4b and 4e. The horizontal velocity for many of the particles first discharged is insufficient to ensure that they can discharge from the elevator without interactions with other particles or buckets. This is illustrated in images 4c and 4f. In this case the material impacting on the headpulley will be returned to the boot of the elevator. In the simulations we predict 4% of the initial load returned to the boot for the stiff spring case, and 8% returned with the softer spring scenario. This is consistent with experimental data for a single bucket systems. a
Soft
d
Stiff
b
c
f
e
Figure 4 - Comparison of discharge for a low ‘bucket to belt’ spring stiffness of 5x106 N/m (a, b, c) and a high ‘bucket to belt’ spring stiffness of 5x108 N/m (d, e, f) Images presented as Figures 5a and 5b provide insight into the interaction of the discharged material with the ‘splitter plate’ with divides the stream either to the discharge outlet, or back to the boot of the elevator. This simulation indicates that a lowering of the splitter plate would likely improve the elevators efficiency as the particles are impacting and being physically split by this plate. a
b
Splitter Figure 5 – Particle interactions with the splitter plate.
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Bucket motion studies Figure 6 presents the results obtained from monitoring the rotation rate of the bucket during a simulation. For clarity Figure 6 has been labelled in two zones (α and β). The α zone is where the bucket accelerates (start of the head pulley) and β is the empty bucket exiting the head pulley. In the α zone, heavily damped oscillations are observed with significant damping by the bulk material. Given that the belt is moderately constrained at the entry tangency point by the proximity of the pulley, and the direction of travel, we expect the results presented to be reflected in experimental evaluations. In the β zone the bucket decelerates back to the nominal belt velocity and the absence of bulk material to dampen the oscillations provides a much longer period of oscillation. This long period of oscillation is unlikely to be witnessed in laboratory studies as the belt becomes free to vibrate in sympathy with the forcing functions provided by all the buckets fitted to the downward strand. The ability of the belt to vibrate with little constraint will most likely cancel a significant portion of the vibration presented in the β zone of Figure 6. α
β
Figure 6 - Bucket angular velocity of the bucket as it traverses the head pulley. Belt to bucket spring stiffness 5.0x106N/m
a - Soft
b - Stiff
Figure 7 - Influence of spring stiffness on bucket oscillations presented as angular acceleration. Simulation’s with ‘bucket to belt’ spring stiffness of; a) 5.0x106 N/m, and b) 5.0x108 N/m Figure 7a and 7b illustrate the impact of the simulations ‘bucket to belt’ spring constant on the motion of the bucket at entry and exit to the head pulley. The ‘motion’ at time =1.8 seconds is the buckets entry to the head pulley and at 2.5 seconds, the exit from the pulley. In Figure 7a there is some evidence of the buckets mass, and the contained bulk material, acting independently at the entry to the headpulley resulting in the unusual appearance of the oscillations particularly when compared to the exit trace at T=2.5 seconds. With the higher spring constant (Fig 7b) the decay in the oscillations are much faster and the peak acceleration is much higher. These motions occur over a correspondingly shorter time frame. These very high accelerations are not anticipated to be realised in physical testing due to the mass and damping of the belt material, and its additional freedom which was unable to be captured in this current simulation.
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Conclusions A DEM study was conducted into the headpulley transition effects of bucket elevators. From the work completed it is apparent that the effective stiffness of the belt/bucket interface has a noteworthy impact on the buckets bulk material discharge pattern. We have illustrated a capacity for modelling multi-body systems coupled with DEM to provide insights that cannot be achieved using alternate methods. We have shown the value of DEM in helping to understand bucket discharge patterns which will be expanded upon in future work by considering a range of common bucket profiles in both physical experiments and numerical simulations. We have shown a capacity to account for ‘carry back’ during operation. This is the material returned to the boot of the elevator by virtue of premature discharge and incorrect positioning of the splitter or head box arrangement. Overall this paper illustrates that DEM techniques can be realistically applied to mechanical handling devices such as bucket elevators to provide insight into the complex interactions that occur during operation.
References 1.
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