DEM modelling of non-spherical particle breakage and flow in an industrial scale cone
crusher
G.W.Delaney a ,R.D.Morrison b ,M.D.Sinnott a ,S.Cummins a ,P.W.Cleary a ,⇑
a CSIRO Digital Productivity Flagship,Australia b
JKMRC,The University of Queensland,Australia
a r t i c l e i n f o Article history:
Received 8November 2014Accepted 29January 2015幼儿教育的重要性
Available online 2March 2015Keywords:DEM
Cone crusher Breakage Wear
Super-quadric shape Fracture
a b s t r a c t
Predictions of particle flow and compression breakage of non-round rock passing through an industrial scale cone crusher are prented.The DEM (Discrete Element Method)particle breakage model is gener-alid to allow non-round particles to be broken into non-round progeny.Particles are broken in this DEM model when the elastic energy of a contact is sufficiently high to initiate fracture.Progeny size distribu-tion data from JKMRC Drop Weight Test (JKDWT)or JKMRC rotary breakage test (JKRBT)is ud to gen-erate the specific daughter fragments from each breakage event.This DEM model is able to predict the production of both coarr progeny which are resolved in the DEM model and finer progeny which are not.This allows the prediction of product down to very
small sizes,limited only by the fineness of the fragments measured in the breakage characterisation.The predicted flow of material through the crusher,product size distribution and liner wear are discusd.The generalid breakage model demonstrated here is suitable for modelling all forms of crushers.
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1.Introduction
Comminution process reduce raw materials from their initial size to a suitable size for u by the end ur,or for further process-ing.The aim is to take large feed material and to efficiently reduce the size to a target size range.Several methods are ud in this pro-cess,depending on the sizes involved,including crushing,breaking and grinding.Breaking is commonly first employed to reduce the largest sized material (which may often be post extraction from a mine).Crushing is then most suitable for reduction of the mid-size ranges,while grinding can then be applied to the finest sizes,frequently just prior to paration.
A cone crusher is a device that is similar in nature to a gyratory crusher,and is commonly ud for condary or tertiary crushing.The cone crusher breaks rocks by squeezing them between an eccent
rically gyrating cone and a concave.The crushing chamber is less steep than in a gyratory crusher,with more of a parallel zone between the cone and the concave.The cone and the concave are both covered by wear resistant liners.Rocks enter from the top and become wedged between the cone and the concave and are broken from the compressive forces.Larger rocks are first broken once and then their smaller progeny fall to lower positions in the crusher to be broken again until they are sufficiently small to exit from the bottom of the crusher.
The output of a cone crusher is controlled by the clod side t-ting (CSS)which is the minimum approach of the mantle and con-cave at any height.Esntially this determines the maximum strain that can be applied to a particle of a specific size and therefore whether it will break and into what fragments.The open side t-ting (OSS)on the opposite side to the CSS is the maximum con-stricted paration of the mantle and concave and esntially controls the vertical flow of material as the gap opens and particles become mobile and move downwards.The performance of a cone crusher is heavily dependent on the shape of the concave and man-tle,both of which wear as a result of the breakage.The mantle or cone is moved incrementally upward by the operator as the liner wears in order to maintain the CSS.However,the shape of the liner changes as they wear and so the locations where particles become highly stresd and the degree of stressing can vary strongly with changing liner shape.
Measurement of liner wear during operation and direct obr-vation and measurement of breakage are not possible,which limits progress in understanding and optimising crushers.Periodic wear measurements,feed and product size distributions and throughput are the primary data that can be obtained and the are ud to design crusher liners and to manage their operation.The Discrete Element Method (DEM)is a computational method that allows
中国与俄罗斯dx.doi/10.1016/j.mineng.2015.01.013
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⇑Corresponding author at:Private Bag 33,Clayton South 3168,Australia.Tel.:+61395458005;fax:+61395458080.
E-mail address:Paul.Cleary@csiro.au (P.W.Cleary).
prediction of particleflows,including breakage,in comminution devices and which can provide detailed information on what is happening in the machine,both at the individual particle scale and as an overall process.
The earliest model of breakage in DEM simulations consisted of 2D circular discs and simple breaka
ge criteria(Astrom and Hermann,1998)with progeny particles being packed into the space left by a breaking parent particle.This was followed by a model by Cleary(2001a,b)using similar principles but spherical particles and which resolved significantly more of the mass of the fracturing particle.Ben-Nun et al.(2010)also ud a simple replacement model bad on Apollonian packing of discs within a fracturing disc in two dimensions.Lichter et al.(2009)prented a DEM model of breakage in a cone crusher using3D polyhedral particles.The determination of when a particle should break was bad on the energy at a contact and the progeny of the breakage event were determined from a population balance model.Good agreement was found for measured throughputs and product PSD with experimentally obtained data.Li et al.(2012)ud DEM and a bonded spheres approach to model theflow of rocks through a chute that they suggested was reprentative of theflow throw the main chamber of a cone crusher.They compared their results with experimental data,and found that for a constant bite angle, there were two critical CSS values,which depended on the particle sizes.Thefirst allows rocks toflow and the cond results in a minimum clearance time.Li et al.(2014)ud a spherical DEM model and the particle replacement technique to model a cone crusher but only resolved three daughter particles for each break-ing particle.This model ud a very simple packing process to determine the positions of the progeny which allowed initial over-lap of fragments after packing.To allow the artificial large over-laps to relax without generating explosive decompre
ssion of the packed particles,a‘‘freeze state’’was impod where only the frag-ments are initially allowed to move and large dissipation coeffi-cients are ud to remove the excess energy created by the overlap of the fragments.After relaxation the main DEM simula-tion then continued.They obtained behaviour that was qualitative-ly consistent with experimental data when varying the CSS and eccentric speed.Recently,Cleary and Sinnott(2014)and Sinnott and Cleary(2015)prented broad studies of3D DEM modelling of industrial scale compression and impact crushers respectively, using spherical particles,realistic geometries and machine compo-nent motion and a geometric packing replacement model.
Other mathematical models for optimisation of cone crusher performance have also been developed.Atta et al.(2014)consid-ered the problem from a control-oriented perspective,with the crusher being reprented by a ries of cascaded zones.The effect of varying the clod side tting(CSS)and the eccentric speed was studied and clod-loop control of the ratio of the large-size output to the total size output was simulated.Hulthén and Evertsson (2011)has developed a real-time algorithm for cone crusher con-trol and performance optimization,again bad on lection of the eccentric speed with respect to the current CSS.
In this paper,we prent computational simulation results of a new DEM breakage model for an indu
strial cone crusher.The mod-el incorporates non-spherical particles reprented as super-quadrics,which are broken bad on the compressive energy at a contact into non-spherical progeny particles.The prediction of the breakage progeny is bad on an empirical model using data from JKMRC Drop Weight Tests(JKDWT).For each breakage event the packing of the specific daughter fragments is explicitly deter-mined using an advanced packing algorithm.This DEM model is able to predict the production of both coarr progeny which are resolved in the DEM model andfiner progeny which are not. Predictions of the throughput,product PSD,power usage and wear on the crusher liners can all be obtained from this model and are demonstrated for an industrial scale cone crusher.
2.DEM modelling of comminution and breakage
The Discrete Element Method has been demonstrated to be a uful tool for modelling comminution process,providing uful information on the energy utilisation,wear on liners and predic-tions of the product size distribution.Its u wasfirst introduced to predict the motion of media within ball mills by Mishra and Rajamani(1992,1994).Rajamani and Mishra(1996)also applied it in two dimensions to SAG mills.Cleary(1998,2001c),Herbst and Nordell(2001),and Cleary and Sawley(2002)ud DEM to explore mill performance and extended the modelling to three dimensions.Usage was further extend
ed by Cleary(2004), Morrison and Cleary(2004),Djordjevic(2003,2005)and Morrison and Cleary(2008).It has also been ud to study other types of mills,such as the Isamill(Jayasundara et al.,2006,2008, 2009)and tower mill(Sinnott et al.,2006;Cleary et al.,2006; Morrison et al.,2009).
As the DEM models have grown in size(as measured by the number of particles)and complexity(in terms of the level offideli-ty of the physics)they have become sufficiently capable that they can predict charge motion,power draw,energy utilisation and wear.This has led to increasing adoption of this approach to pro-vide detailed information about what is happening in mills, Kalala et al.(2005a,b),Powell et al.(2006,2008,2011),Carvalho and Tavares(2011),Weerakara et al.(2010,2011),Cleary et al. (2008)and conference special issues SAG2006(Mular et al., 2006),DEM2007(Cleary and Morrison,2008)and SAG2011 (Major et al.,2011).The current state of DEM modelling in com-minution is summarized in a recent review paper(Weerakara et al.,2013).
For crushers,DEM modelling is more difficult becau the breakage of the particles needs to be explicitly included in the model.Three basic approaches have been propod
Modelling the fracture process by including internal structure in the form of tetrahedral meshes and allowing the elements to un-bond and parate(Potapov and Campbell,1996).
Treating a fracture event as being instantaneous and replacing a particle by its progeny packed into the original parent space (Cleary,2001a,b).
Using bonded spheres,which is a popular approach particularly using available commercial DEM codes(for example by Potyondy and Cundall,2004).
The original fracture approach of Cleary(2001a,b)was ud for spherical particles.It was ud to qualitatively model impact crushers such as the VSI(vertical shaft impactor)and compressive crushers such as a jaw crusher in Cleary(2009),cone crushers (Cleary et al.,2013)and twin roll crushers(Weerakara et al., 2013)and more generally for compression crushers by Cleary and Sinnott(2014)and impact crushers by Sinnott and Cleary (2015).The bonded sphere approach to breakage in crushers has also been demonstrated in Weerakara et al.(2013).This break-age model was extended to break non-round particles(modelled as super-quadric shapes)into non-round progeny using ore speci-fic breakage data from JKDWT or JKRBT(rotary breakage)testers by Delaney et al.(2010).
Empirical models bad on the amount of damage caud to the particle prior to breakage occurring can be ud to more realistical-ly predict the progeny size distribution for each breakage event than was the ca for the original geometrically driven model of
G.W.Delaney et al./Minerals Engineering74(2015)112–122113
Cleary(2001a,b).Such models allow,in
the full product size distribution
ing both material resolved in the
material that is not reprented
is possible becau a broad progeny size
available from the characterisation
In this DEM breakage model a check is
step for each particle to determine
compression crushers,this is bad on
particle at that time calculated in the form
gy bad on the contact force from the
timestep the elastic strain energy at
the threshold elastic strain energy that is
ture.This criterion can be t to match
being simulated.When this threshold
breaks and is replaced with a t of
品质文化are bad on model predictions from
(typically JKDWT or JKRBT).This DEM
production of both coarr progeny
DEM model andfiner progeny which are
tion of the product particles down to very
by thefineness of the fragments
terisation rather than by the resolution
Each breakage event requires solving
lem for each particle that is being broken.
ter fragment can have any super-quadric
size generated from any progeny size
sary becau no two particle breakage
re-u of pre-computed or simplified
risk of biasing the product size
el.We u a dynamic packing technique
sion of initially small particles.This is
in Delaney and Cleary(2010).It can
inside the bounding parent
structed from the measured progeny size
An example of the packing of such a
progeny is shown in Fig.1(reproduced
The packing method has the following
1.A t of very small daughter particles
ent super-quadric shape.They have
小芋头怎么做好吃and orientations.Their sizes are scaled
by a large factor so that they do not
example of such an initial fragment
Fig.1b.
2.The sizes of the daughter particles
釜山酒店
small steps.A DEM like dynamic simulation is performed on the-
fragments allowing contacts to be resolved and overlaps to be removed by the resulting particle motion and re-orientation as they collide.Fig.1c shows an example of the expansion process part way through.Since the denst possible packing is required,no inter-particle friction is ud and particles can smoothly slide against one another maximising the packing efficiency.
3.When the particles reach full size and jam together then the
process completes and thefinal fragment configuration is obtained(e Fig.1d).The fragments are then ud to create new particles in the DEM crusher simulation(with attributes inherited from the parent)and the parent particle is removed from the simulation.宽广的近义词
Large packing fractions can be achieved for packing of frag-ments with large size ranges.As with all DEM simulation,daughter particles smaller than a chon resolved limit are omitted from the packing process and the subquent simulation in order to main-tain the number of particles within a practical range.For additional details of the rate of expansion of the daughter fragments in the packing process and for examples of the packing,e Delaney et al.(2010).
3.Breakage data measurement
There are many breakage tests ud for crusher design esti-mates.However,more than30years of breakage testing at the JKMRC has demonstrated that veral types of tests map onto one another sufficiently well that any of them can be ud as prox-ies for another.The test in common u is the JK Drop Weight Test or JKDWT(Napier-Munn et al.,1996).The original‘‘pendulum’’test was developed by Narayan and Whiten(1983).
The test breaks single particles at well controlled energy inputs between two rigid platens.The progeny for each energy/parent size combination are sized.The degree of breakage is measured by the t10of the progeny.
t10¼Að1ÀexpðÀbÃE csÞÞð1ÞDiagram showing the stages of the packing process for daughter
packed into the parent particle,(a)parent super-quadric particle, positioning of reduced size ed fragments,(c)part way through the
(d)final denly packed state.
114
where t 10is the fraction of the mass of the original particle which will pass through an aperture of 1/
10of the original particle size –after the impact event.E cs is the specific comminution energy in kW h/t.A is the maximum breakage achievable in a single impact event (percent passing).b is the standard JK ‘‘slope’’parameter.A Âb is often ud as a single value measure of resistance to break-age by impact.
Whiten further normalid the t 10curve against other relative breakage size fractions to generate a relationship which provides a practical way of mapping all of the possible size distribution shapes resulting from impact breakage of brittle materials.As this ‘‘map’’can generate a full size distribution from a specified parent size and energy input,it is very helpful for DEM modelling of breakage.
The link between cone crushing and the t 10relationship was developed by Awachie (1983).He showed that the reduction ratio achieved in an unconstrained piston and die test could be consid-ered in a similar manner and that the reduction ratio and t 10enjoyed a strong degree of correlation.
This relationship has been confirmed in detail for cone crushers (Andern and Napier-Munn,1990)and provides good predictions of progeny size distributions and breakage energy.For accurate modelling of cone crusher power draw,it was necessary to consid-er how particle strength varied with size.Andern and Napier-Munn (1990)also demonstrated that this relationship could als
o be derived from the JKDWT.This relationship was generalid by Shi and Kojovic (2007).The JKRBT (rotary breakage test)provides a more preci test by throwing particles at an anvil at a well con-trolled velocity.
The relationships can be ud to estimate the degree of break-age likely to result from a single compression event and the energy consumed by this event.Hence,they are as good a fit to the DEM approach as to mi-empirical models and provide access to a wide databa of ore breakage properties.Morrison et al.(2007)further extended the t 10model to probabilistic breakage in tumbling mills.
4.Simulation tup and material parameter
Fig.2shows a schematic diagram of the cone crusher ud in this work.The cone diameter is 2.134m and the concave height is 1.538m.The tilt angle for the cone is 1.0°to the vertical which gives an open side tting for the crusher of 58mm,and a clod side tting of 11mm.The side angle of the cone is 50°to the ver-tical.The angular speed of the cone is 255rpm.
A linear spring-dashpot model is ud to calculate the contact forces,(e Thornton et al.,2013for details of this and other con-tact models).The spring stiffness ud in the simulations was k =107N/
m.Considering that the average curvature of the super-quadric particles at the contacts is likely to be around 10À3m,this means that this is broadly equivalent to a Young’s Modulus of around 1010Pa –which is fairly clo to the physical values for real rock materials.In many DEM simulations,the spring stiffness ud is taken to be significantly lower than the real stiffness in order to speed up the simulations.For crushers,as explored by Cleary and Sinnott (2014)this cannot be done due to the very high stress that occur in the system.So a particle stiffness that is clo to tho of the real materials need to be ud.The coefficient of restitution for rock–rock collisions and for rock-liner collisions was chon to be e =0.2reflecting the strong energy loss from small scale local fracture at contact points (as was also done in Cleary and Sinnott,2014)which does not otherwi contribute to body break-age or fracture.The coefficient of friction for rock–rock and rock-liner interactions was l =0.6.The feed had a narrow size range and was reprented as a uniform size distribution from 30to 50mm.
The inclusion of a particle shape reprentation in the DEM simulation is extremely important in realistically modelling the flow and packing properties of the particles (Delaney and Cleary,2010;Delaney et al.,2012).The particles here are reprented as super-quadrics (e Cleary,2004for details)which allows shapes that vary continuously between rounded and blocky and
from equi-axed to platey to needle like.The shape factor controlling the blockiness of the feed was 3.0–6.0,and the aspect ratios of the particles were in the range 0.6–0.9.The are a reasonable rep-rentation of an angular coar crushed rock material with mod-erate aspect ratios.Since the particles are non-round,the relationship between the specified particle size and the indi-vidual shape attributes is not straight forward.The shape of the particle affects its ability to pass through the holes in a sizing screen (Cleary,2009)so it is not clear precily what geometric attribute is actually measured and reported as ‘‘size’’.Here we u the intermediate axis length of the particles to define their size as this is the dimension that most controls the ability of a particle to pass through the holes in a screen.So this is ud becau it matches reasonably with what is actually measured by a sizing screen.
The crusher was operated as choke fed with a continuous stream of material entering the top of the crusher,which gives a steady state throughput of 330tonne/h.The equilibrium mass of rock in the crusher was approximately 825kg,which consisted of 26,500particles.At equilibrium,the compute time on a sixteen core 2.0GHz Xeon E5-2650was 7.5h per cond of simulation time.This gives a Cundall number (defined as the number of par-ticle timesteps performed per wall-clock cond)of around 9Â105.
The breakage parameters for the material were the elastic ener-gy at a contact for breakage to occur of E 0=25J and a breakage intensity (which is input into the progeny model to give the pro-geny size distribution for each fracture event)of 1.15kJ/kg.The parameters are suitable for a range of moderate strength rocks and were chon to create enough breakage that the crusher was able to operate at steady state.The progeny size distribution is tak-en from JKDWT data formulated in accordance with JKMRC t 10practice as outlined in Section 3and detailed in Napier-Munn et al.(1996).
品牌抽油烟机In DEM one cannot resolve all of the particles.In practi a low-er limit needs to be applied which we term the resolved limit.For this paper,the resolved particle size limit is 8mm.The smallest unresolved particle for which the progeny model has a data point (the model interpolates between the points and also has some
Bowl (concave)
Feeder
Cone (mantle)
1.06 °
50 °
Fig.2.Schematic diagram of cone crusher showing the cone (mantle)and bowl (concave).The liners are coloured dark grey.
G.W.Delaney et al./Minerals Engineering 74(2015)112–122115
extrapolation from the last value)is 1/75of the parent size,so this means that 0.66mm is the smallest particle size that can be pre-dicted for breaking the largest particles in the simulation.This means that the DEM model can make predictions of the product size distribution down to 660l m even though particles below 8mm are not explicitly included back into the model.
5.Predicted flow through the crusher
Fig.3shows the flow pattern predicted within the crusher with particles coloured by their size at four times during the cone pre-cession cycle.The cone is tilted to the right in Fig.3a,to the back left in Fig.3b,to the rear in Fig.3c and to the left in Fig.3d.In choke fed operation the upper ction of the crusher is denly filled with feed material.As material lower down in the crusher breaks,the reduction in particle size allows the fragments to migrate deeper into the crusher potentially experi
encing further breakage events.This opens up spaces into which feed material from above can pro-gressively move slowly downwards towards the crushing zone.The feed is preferentially coarr (red)on the left of the view and finer (green)on the right.This is the result of asymmetric feed of a vertically gregated material into the crusher.This asymmetric gregation within the crusher is not uncommon in real operations and can lead to asymmetry in the wear on the liners and potential-ly to under-performance of the crusher.Asymmetric loading of a crusher has been demonstrated using DEM simulation of the filling process by Evertsson et al.(2014).In this ca,it means that the
coarr material on the left will start to break at a higher location inside the crusher.
The edge of the breakage region can be identified as the vertical location where the material shows a dramatic change in colour (particle size)when moving downwards.This is just below the start of the conical lower ction of the concave.On the left,the majority of the red and orange particles are trapped between the mantle and concave,cyclically compresd while incrementally creeping lower leading to significant breakage in a relatively narrow vertical band.By one quarter of the way down the lower conical ction the par-ticles are almost entirely green with some light blue,indicating sizes of the order 20-30mm on average.As the particle move a little lower they are also pinched either directly between concave and mantle or in short chains of smaller particles between the sur-faces.In
龙王台风both cas,particles break and the charge becomes obrvably finer.By half way down the lower ction of the crusher most of the green and a reasonable fraction of the light blue have also broken.By 60%of the way down,the final stage of breakage of single particles trapped directly between the mantle and con-cave occurs and breakage is complete.A very small amount of light blue material escapes by flowing through this region on the open side and exiting the crusher.
The cyclic precession of the breakage region around the perime-ter of the crusher is hard to e with the particle size colouring.Fig.4shows the same situation but with the particles coloured by speed.Particles above the location of the constriction (where the CSS is measured)are not able to move much becau their motion is halted by the compression of material below in
the
flow through the crusher with particles coloured by size (red being 50mm,green being the bottom of the feed size at 30mm and dark blue being progeny of 8mm)at:(a)t =10.1s,(b)12.0s,(c)13.5s and (d)14.9s showing the mantle at different positions.(For interpretation of the references to the reader is referred to the web version of this article.)
