Some investigations of Vezin sampler performance · SOME INVESTIGATIONS OF VEZIN SAMPLER PERFORMANCE 221 One measure of sizing is the mass weighted mean particle size score. For the

SOME INVESTIGATIONS OF VEZIN SAMPLER PERFORMANCE 219

IntroductionSampling is an important activity in industries whichhandle particulate materials such as mineral ores, coal,alumina, sugar and wood chips. Sampling is necessary forobtaining information about raw materials being used inprocesses and about products produced. It is particularlyimportant that samples be unbiased when they are part ofthe evaluation of the economic value of material beingbought and sold. Vezin samplers are commonly used assecondary and tertiary sampling devices, reducing the massof sample from that taken by primary cutters, sometimesafter the particle size has been reduced by crushing orshredding.

Computational testing of sampler performance hasbecome well developed over the last decade. Robinson andCleary (1999) introduced the use of discrete elementmodelling (DEM) for evaluating sampler bias with a twodimensional model of a falling or cross stream sampler.This was extended to three dimensional modelling of crossstream, cross-belt and Vezin samplers by Cleary et al.(2005). Robinson et al. (2007) used the computationalsample evaluation method to explain the dominant biasgeneration mechanisms of cross belt samplers andparticularly to explore the difference in performancebetween square and skew samplers.

More recently, Cleary and Robinson (2008a), extendedthe sample testing methodology to use precisely matchedactual and reference samples allowing significantreductions in the variability. The variability arising fromcomputational sampling arises almost entirely from thesampling process and is much smaller than that which ispossible with physical sample bias testing. This was used tounderstand the basic mechanisms that generate bias forcross stream samplers and to quantitatively evaluate sampleextraction ratios and bias for varying cutter apertures andspeeds. Cleary and Robinson (2008b) investigated the effectof particle shape on sample accuracy and used anunderstanding of the bias generating particle congestionzone that forms at the opening of the cutter to establish thatthe fall height and bed depth were also importantconsiderations for sample performance.

Francis Pitard (2005) has suggested that Vezinssometimes need to be run at 30 cm/s or 45 cm/s rather thanat the 60 cm/s specified by Gy’s rules (1982, page 198).Pitard (2008) indicated that this was partly based on anexperiment in which the extraction ratio was about 90%when the cutter speed was about 60 cm/s in the regionwhere the blades of the cutter intersected the stream offalling particles, but the extraction ratio was near to 100%when the cutter speed was reduced to 30 cm/s. The materialtop size was 2 mm. The cutter aperture was at least 20 mm,or 10 times the nominal top size. The vertical drop from theexit of the vibro-conveyor to the cutter blades was at least 2cm.

The purpose of this paper is to investigate the factorswhich influence extraction ratio for Vezins, in the light ofthe knowledge that extraction ratios can be poor underconditions like those reported by Pitard. We use DEMsimulation to help understand the mechanisms that mightpossibly lead to sample bias. Computer experimentsinvestigate the effects of several factors on extraction ratioand sample bias. The factors considered are:

• Top size (D) of material (2 mm, 6 mm),• Drop from end of feeder to top of cutter (1 cm, 3.1 cm,

16 cm)• Speed of cutter (0.6 m/s, 1.2 m/s)• Feed rate or bed depth on feeder• Material properties (such as friction and restitution

coefficients)• Particle shape.Details of the DEM method that we use for the modelling

can be found in Cleary (2004, 2009) and the referencestherein.

Simulation configurationThe sampler consists of a vertical cylindrical shell in whicha sample cutter rotates about its center at constant angularspeed. The sampler consists of two angled planar bladesthat meet at an angle θ at the center of the sampler. Theleading edges of these blades are almost perfectly radial, sothat the cutter opening is a constant time at all distancesfrom the centre. Material falls from a feeder located above

CLEARY, P.W. and ROBINSON, G.K. Some investigations of Vezin sampler performance. Fourth World Conference on Sampling & Blending, TheSouthern African Institute of Mining and Metallurgy, 2009.

Some investigations of Vezin sampler performance

P.W. CLEARY, and G.K. ROBINSONCSIRO Mathematical and Information Sciences, Australia

Francis Pitard has suggested that Vezins sometimes need to be run at 30 cm/s or 45 cm/s ratherthan at the 60 cm/s specified by Gy’s rules. Discrete element modelling (DEM) is used toinvestigate the effects of several factors on extraction ratio and sample bias and to understand themechanisms that can lead to sample bias on sampling using a Vezin. This modelling suggests thatthey have a good extraction ratio and negligible sample bias over a wide range of operatingconditions. Having investigated other possible bias mechanisms, we conjecture that the biasobserved by Pitard could be due to the effects of air motion generated by the Vezin rotation onvery fine particles.

Key word: Sampling, granular material, particle, DEM simulation, sample bias

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FOURTH WORLD CONFERENCE ON SAMPLING & BLENDING220

the sampler and forms a stream falling into the samplershell. The revolving sampler, periodically intersects thefalling stream separating the particles that pass between thecutter blades to form the sample. The large majority ofmaterial falls far from the leading edges of the cutter bladesand does not contribute to the sample. The Vezin samplingconfiguration is illustrated in Figure 1. This sampler issubstantially similar to that described by Pitard (2005).Features of the base simulation sampler configuration weregenerally as follows:

• Particles were spherical with a uniform size distributionfrom 0.5 mm to 2 mm

• The coefficient of restitution was 0.3.• The friction coefficient for both particle-particle and

particle-cutter interactions was 0.5• The density of all particles was taken to be 3000 kg/m3

• The vibrating feeder transporting particles to the Vezinsampler was 5 cm wide and delivered particles with ahorizontal velocity of 0.05 m/s. The vertical componentof the feeder motion is not important here so wasomitted from the model. The flow rate produced was0.03 kg/s

• Material falls 3.125 cm vertically from the end of thefeeder to the top of the cutter blades

• The outer cylindrical shell of the Vezin had a radius of15 cm.

• The radius of the top of the Vezin cutter blades was 1mm

• The Vezin sampler rotation rate was 44 rpm. Hence thespeed of the Vezin where it contacts the falling stream(about 13 cm from the axis of rotation) wasapproximately 0.6 m/s and, therefore, satisfies theconventional standards for sampler operation

• The angle θ between the pairs of blades of the Vezinwas about 17.7 degrees. In the later cases, two pairs ofblades were used, so that two cuts are taken on eachrotation of the Vezin. The spacing of the blades aresufficiently separated that there is no interaction of theflow from the different cuts

• The cutter blades have slopes φ = 15 or 30 degreesfrom vertical, sloping away from the opening.Therefore the gap between the blades becomes widerwith distance travelled down into the cutter. This angleis referred to as the ‘sampler face angle’.

Evaluating sampler performanceBias testing, whether physical or computational, requirescomparison against an alternative sampling method whichis more reliably unbiased than the sampling method to betested. This more reliable method may be referred to as a‘benchmark’ method. Samples taken by the more reliablemethod are often referred to as ‘reference samples’, and thesamples taken by the sampling method to be tested arereferred to as ‘routine samples’. For example, for physicalbias testing of falling stream sample cutters, the mostcommon benchmark sampling method consists of stoppinga conveyor belt, manually removing all material from aportion of the belt, and doing careful sample preparationand chemical and physical analyses.

Cleary and Robinson (2008a) showed that a majoradvantage of DEM computational bias testing over physicalbias testing is that the matching of the positions of thereference and routine samples within the stream of materialis very much more accurate. Computational bias testingtakes a reference sample from the same position in thestream as the routine sample without affecting the simulated

flow. It is, therefore, capable of much more accurateestimation of biases for a given number of replicates than isphysical bias testing.

As in previous computational sampling work, we define a‘reference sampling plane’ which is located just after theend of the vibrating feeder. As a particle passes through thisplane, a computation is performed to determine whether thecentre of the particle would pass between the blades of thesample cutter if it continued on its current trajectory.Particles expected to pass between the blades of the samplecutter constitute the reference sample. The routine sample isthe set of particles which actually end up in the cutter,possibly after complex interactions with the cutter and withother particles. It is generally different from the referencesample because particles are deflected by hitting a cutterblade or by colliding with other particles after passingthrough the reference sampling plane.

The measures used to summarize the results of simulationruns were generally the same as used in previous DEMbased computational bias tests. Particles are classified as‘missed’ if they are in the reference sample but not in thephysical sample. They are classified as ‘extra’ if they are inthe physical sample but not in the reference sample. Themasses of missed and extra particles are expressed aspercentages of the mass of the reference sample. Thedifference between these percentages is the extraction ratio(i.e. the mass of the physical sample relative to the mass ofthe reference sample.)

The construction of the sample cutter and the sampleplanes were not quite perfect. Small precision errors in themesh geometry of the rounded cutter lips and the exactlocation of the highest point of the cutter at each radiusmeant that very small variations between the sample planewidth and the cutter aperture existed. In the region of 13 cmfrom the axis of rotation where the cutter meets the fallingparticles stream this difference ranged up to about 0.4 mmwith the sample plane being slightly wider. These verysmall mis-matches cause the extraction ratio to be about 1%smaller than it should be. They are consistent between allthe DEM runs so they do not affect the main conclusions.

Figure 1. Illustration of the Vezin sampler set up



One measure of sizing is the mass weighted mean particlesize score. For the majority of cases with 2 mm top sizeparticles, the particle score is 1 to 10 according to whethertheir size in mm is in the range 0.5 to 0.65, 0.65 to 0.8, 0.8to 0.95, …, 1.85 to 2.0, respectively. Size bias is computedas the average size score of the physical sample minus theaverage size score of the reference sample. This measure iseasy to calculate using data from computer models.

An alternative measure of sizing translates the firstmeasure into percent of the inter quartile range deviationfrom the average size. When the particle scores are 1 to 10,the median size score is 5.5, the quartiles of size score are 3and 8, and the inter quartile range of size scores is 5, so thefirst measure will be multiplied by 100/5 = 20. Thismeasure can be interpreted without considering the sizescores used in the computer models. For instance, a sizebias of minus 3 means that the physical sample wascomposed of particles which were, on average, smaller thanthe particles in the reference sample by an amount which is3% of the inter quartile particle size range.

For many commodities size is not itself important, butproperties such as chemical composition which areimportant, are correlated with particle size. A size bias of10% of the inter-quartile particle size range may beacceptable if small and large particles have similar averagechemical compositions but is unlikely to be acceptable ifthey do not.

Mechanisms for bias generation in Vezinsamplers

Congestion at cutter apertureFor falling stream samplers, one mechanism which oftencauses extraction ratios to be less than 100% and, therefore,causes sample bias, is the formation of a particle congestionzone at the cutter aperture. The mass of particles competingto enter the cutter are slowed by the frictional interactionswith the cutter surfaces leading to the formation of adensely packed zone. The congested zone pushes particlesthat are in the reference sample to the sides leading toreduced extraction ratios. Coarse particles are preferentiallypushed to the sides in this region leading to under samplingof these large particles. This mechanism is governed by thebalance of momentum in the incoming stream to theresistance of congestion zone material flowing. One of themain factors affecting this is the size of the cutter aperturerelative to the maximum particle size, D. If the cutteraperture is as small as 2D, then congestion is usually amajor problem; if the cutter aperture is at least 3D thencongestion is often a minor problem.

Gy (1982) gives the impression that an importantmechanism causing bias for falling stream cutters isparticles bouncing off cutter blades completely over thecutter aperture. He refers to the ‘rebounding rule’ on page189. If this were the major mechanism, then the minimumacceptable cutter aperture would have little dependence onD, because the size of particle bounces is not stronglyrelated to particle size.

In Cleary and Robinson (2008b), recognition thatcongestion was the most important physical mechanism forfalling stream cutters suggested that belt speed, fall height andbed depth would be relevant to sample bias and cutter designsince they all affect either the momentum of the flow at thecutter or the resistance to flow generated by the sample cutter.

Understanding the physical mechanisms behind samplebias is also important because it can provide guidance as to

whether the ‘rules’ used for each type of cutter areappropriate to the flow behaviour actually occurring. Forexample, the 3D rule is applied to cross-belt samplers eventhough the congestion mechanism on which the 3D rule isbased is not observed leading to unnecessary restrictions onthe sampler design (Robinson, Sinnott and Cleary, 2007).The uncritical adoption of rules based on the congestionmechanism dominant for falling-stream samplers also leadsto the neglect of other possible mechanisms.

For Vezin samplers, there is a falling stream of particlesso this mechanism might generate bias. However, for thestandard Vezin configuration used in this paper the cutteraperture is 10 times the 2 mm top size. Even for the largesttop size investigated, 6 mm, the aperture is larger than 3D.Therefore the cutter aperture is generally large enough forbias caused by congestion at the cutter aperture to benegligible.

Bouncing off blades completely over the cutter apertureAnother mechanism that can cause sample bias in a Vezinis particles bouncing off the cutter blades with enoughspeed to bounce completely over the cutter aperture. Gy(1982) called this the ‘rebounding rule’. This mechanismtends to result in under-sampling of larger particles. It isaffected by the:

• Coefficient of restitution of the particles• Fall height • Speed of motion of the cutter blades• Separation of the cutter blades.Particle shape might conceivably also influence this

mechanism, but is not expected to have a major effect.This mechanism may sometimes be the most important

bias mechanism. However, for Pitard’s scenario, presentedin the introduction, we can be confident that it will notexplain how an extraction ratio can be as low as 90%.

Consider particles of 2 mm diameter when they first fallto vertical positions 1 mm above the tips of the cutterblades. Figure 2 shows five such particles. If the particletrajectory is more than a particle radius from the centre ofthe leading edge of a cutter blade then that particle will nothit a leading edge, so will not bounce upwards. If thetrajectory is between half a particle radius and one particleradius from being in line with a leading edge then theparticle will be deflected through an angle of less than 90degrees. The range of the trajectories over which this logictells us that particles are sure to enter the cutter aperture isshown by the range of the five particles in Figure 2 and is19 mm. The size of the reference sample is equivalent to arange of 20 mm, so the extraction ratio must be at least19/20 = 95%.

Particles rolling up the sampler surfaces and intosamplerThis mechanism involves particles rolling upwards along

Figure 2. Five 2 mm diameter spherical particles atpositions just above the level of the cutter blades.

All will enter the cutter aperture



the surface of the leading cutter blade and over the samplerlip and into the sampler aperture. For instance, particle A inFigure 3 might end up with a component of velocityupwards and towards the leading edge of the cutter bladeafter it and the smaller particle have collided with the cutterblade and with each other. The maximum speed upwardsfrom such collisions is constrained by the energy from therelative motion in the horizontal plane between the cutterblade and a particle. For a relative velocity of 0.6 m/s, thisenergy is equivalent to a vertical drop of 18 mm, using theformula 1⁄2mv2 = mgh. Collisions are being assumed to havea coefficient of restitution of 0.3, so approximately = 91%of relative kinetic energy will be lost in each collision,leaving energy equivalent to a vertical drop of 2 mm. Thisenergy could cause a variety of rotational and gross motionsof particles, but given the steepness of the cutter blades it isdifficult to imagine that many particles will end up usingthis energy to make their way even as much as a millimetreup the cutter blade.

Figure 3 shows two similar particles arriving at each ofthe cutter blades of a Vezin. Particle A might make its wayup the cutter blade a small distance after collisions with thesmaller particle and with the cutter blade. It is impossiblefor Particle B to make its way up the other cutter blade.

This mechanism would appear to be a relatively weakone. It also cannot explain the experimental results reportedby Pitard as it would tend to increase the extraction ratio,whereas Pitard reported an extraction ratio much less than100%.

Air effectsA fourth mechanism results from the effect of air drag onthe particle trajectories. Air drag is strongly size dependentwith larger particles being relatively uninfluenced by the airbut smaller particles significantly affected. This providessignificant opportunity for different size particles to bedifferently sampled. It should be noted that the rotation ofthe sample cutter will generate air, a potentially strong airflow within the Vezin sampler which will be swirling innature. The air drag will make smaller particles want tofollow these air motions and will tend to disperse them (asdust in wind). The air drag will also tend to slow the finerparticles so that they will be delayed in reaching the cutterwhich will have moved onto a new position. This delaymeans that the finer particles actually sampled will havebeen from earlier in the falling stream. Therefore, thecoarse and fine material actually sampled will be fromdifferent sections of the feed stream. This increases the riskof bias from compositional variations along the feed stream.Particles that are nearer the edges of the falling feed streamare more likely to be affected in this way, whereas, ones inthe middle of the stream are more protected by thesurrounding larger particles.

Figure 4 shows some particles arriving at each of the two

blades of a Vezin. One of the large particles, A and B, islikely to end up in the cutter aperture. The air flow mightmove the small particles so that none or one of them end upin the cutter aperture.

The extent of these air related effects is controlled by theparticle Reynolds number (Re) which is defined by:

Re = ρ d(v – vair)/μ [1]where � is the density of air and μ is its viscosity, d is theparticle diameter, v is the velocity of the particle and vair isthe velocity of the air at the particle location.

For a 1 mm particle moving in air Re = 100, which meansair has only a small effect. For 100 micron particles though,Re = 10 and the air effect is significant. For 10 micronparticles, Re = 1 and the motions of particles are dominatedby the air and there will be little slip between the air and thevery fine particles.

Air effects introduce two distinct, possible biasmechanisms. The first relates from the air drag induceddelay of finer particles reaching the sampler meaning thatcoarse and fine particles are sampled from slightly differentparts of the feed stream. This is most likely a weak effectunless there are significant short term variations in the feedstream. The second mechanism results from the preferentialloss of finer particles which are entrained by the air flowand transported away from the sample cutter. This is likelyto be a significant effect for finer particles.

For our feed here, with a bottom size of 500 micron, theair influence is still quite mild and may reasonably beneglected. For finer particles such as reported by Pitard(2005), the air drag will become increasingly dominant.However, a large fraction of the fine particles could easilybe carried away from the cutter aperture by air currents, sothis mechanism would tend to reduce the extraction ratio.This will be explored in future work.

Comparison of two sampler face anglesFigure 5 shows the simulated particle behaviour as theVezin sampler passes through the falling stream. In the leftcolumn, is a sample being taken by a Vezin with a 15°inclination on the blades, and in the right column is asample taken by one with a 30° blade angle. The top rowshows the system as the left side blade is pushing into thestream just prior to the cut being made. The middle rowshows the stream falling freely into the space between theblades. This material will form the actual sample. Thebottom row shows the particles as the trailing blade haspushed through the falling stream and the sampling processis complete for this cutter pass. Many particles not sampledroll down the outside of the sample cutter and arediscarded. The reference sample is predicted using a sampleplane just offset from the end of the vibratory feeder.Reference sample particles, which are predicted to passthrough the sampler opening, are changed in colour to lightgreen for colour visualizations and light grey for greyscale.

Figure 3. Particles arriving at cutter blades. The arrows show thedirection of motion of the particles relative to the cutter blades

Figure 4. Particles arriving at cutter blades. The arrows indicatepossible directions of air flow which might deflect fine particles



This leads to a contiguous band of material across thefalling stream being identified as the reference sample. Asmall amount of reference material can be seen slidingdown the outside cutter blade and not being sampled. Oncethe feed stream has reached a steady state, successivesamples are taken. Here, 14 passes of the Vezin weretreated as repeats for the purpose of statistical analysis ofdata.

The results of these sampling operations for the twocutter blade angles are given in Figure 6. Figures 6a and 6bshow the size specific extraction ratios for these two cases.Size category 1 is particles having diameters from 0.5 to0.65 mm; size category 2 is particles having diameters from0.65 to 0.8 mm, and so on with size category 10 beingparticles from 1.85 to 2 mm. Figures 6c and 6d show thesize-specific percentages of particles missed and Figures 6eand 6f show the size specific percentages of extra particles.Here we see that for the larger size categories it is commonfor the particles in the sample to correspond precisely to theparticles in the reference sample.

Tables I and II give summaries of some statisticalanalyses of the results of these and later DEM tests in termsof extraction ratios and biases for the overall sample and forthe extra and missing components. In both these cases, theaverage extraction ratio is slightly less than 100% because

slightly more material is missed than there is extra. Theamount missed is only around 2 % and the partiallycompensating extra is only around 1 %. The average sizebiases of both missed and extra material do not differsignificantly from zero (the average sizing of the materialbeing sampled), so it is not surprising that the size bias ofthe samples does not differ significantly from zero in eithercase. Therefore, both Vezins are predicted to operate verywell with very high extraction ratios, very small amounts ofmissed and extra and no observable size bias. This indicatesthat the basic Vezin design operated with standardconditions appears to be unbiased and that the sampler faceangle is not an important factor.

Effects of material properties and operatingconditions

Base conditions–‘standard’ caseA series of DEM tests were used to investigate severalaspects of material properties and operating conditions toexplore if these influenced Vezin sampling performance.The conditions were varied around the standard conditionsdescribed earlier, with the intention of finding out whichaspects are more important. The Vezin with the face angle

Table IISize biases (as scores on range 1 to 10) of samples and of missed and extra material. The three numbers in each column are the lower 95%

confidence limit, the best estimate, and the upper 95% confidence limit

Size bias of sample Size bias of missed Size bias of extraLower limit Upper limit Lower limit Upper limit Lower limit Upper limit

15 degree face angle −0.006 0.005 0.015 −1.31 −0.72 −0.14 −1.77 −1.06 −0.3430 degree face angle −0.025 −0.008 0.010 −0.38 0.10 0.59 −1.47 −0.57 0.33Standard −0.014 0.000 0.013 −0.40 0.05 0.50 −0.44 0.05 0.53ε = 0.8 0.001 0.010 0.020 −1.29 −0.92 −0.54 −1.36 −0.86 −0.3616 cm drop, ε = 0.8 −0.010 0.017 0.044 −1.14 −0.75 −0.36 −1.39 −0.93 −0.47μ = 0.2 −0.013 0.007 0.026 −1.24 −0.51 0.22 −1.08 −0.33 0.42Extreme shapes −0.047 −0.015 0.017 −0.68 −0.25 0.17 −1.24 −0.77 −0.31Moderate shapes −0.024 −0.006 0.012 −0.92 −0.44 0.03 −1.51 −0.93 −0.366 mm top size −0.025 −0.005 0.015 −0.33 0.05 0.44 −0.98 −0.54 −0.111 cm drop −0.021 −0.002 0.016 −0.48 0.07 0.62 −0.64 0.00 0.64Feed rate of 60 g/s −0.028 −0.009 0.010 −0.37 0.09 0.55 −0.65 −0.30 0.05Moved at 1.2 m/s −0.023 −0.001 0.022 −0.45 −0.04 0.38 −0.51 −0.09 0.34

Table IExtraction ratios and percentages of missed and extra material. The three numbers in each column are the lower 95% confidence limit, the

best estimate, and the upper 95% confidence limit

Extraction ratio Percent missed Percent extraLower limit Upper limit Lower limit Upper limit Lower limit Upper limit

15 degree face angle 98.46 98.86 99.26 1.70 2.04 2.39 0.66 0.90 1.1530 degree face angle 98.36 98.72 99.09 2.08 2.37 2.67 0.90 1.10 1.29Standard 98.33 98.80 99.26 2.36 2.86 3.35 1.36 1.65 1.95ε = 0.8 98.54 99.01 99.47 2.38 2.82 3.26 1.58 1.83 2.0816 cm drop, ε = 0.8 96.45 97.05 97.65 5.30 5.97 6.65 2.70 3.02 3.35μ = 0.2 98.61 99.33 100.05 1.81 2.38 2.95 1.29 1.71 2.13Extreme shapes 96.66 97.53 98.40 5.48 6.51 7.54 3.38 4.04 4.71Moderate shapes 98.41 98.98 99.55 2.67 3.25 3.83 2.00 2.23 2.466 mm top size 98.32 98.89 99.45 1.90 2.37 2.84 0.92 1.25 1.591 cm drop 98.85 99.26 99.66 2.61 3.08 3.55 1.95 2.33 2.71Feed rate of 60 g/s 98.11 98.74 99.37 3.14 3.59 4.04 1.97 2.33 2.70Moved at 1.2 m/s 98.10 98.79 99.48 4.11 4.73 5.35 3.06 3.52 3.98



of 15 degrees was used for this series of tests. Thesimulations were typically run for 13 seconds. The earlycuts (taken in the first 5 seconds) were ignored as the feedersystem came to a steady state, so 11 useful cuts wereobtained for each.

The most important results are given in Table I and II.Table III is an alternative version of Table 2 in which theunit of sizing bias is one percent of the inter-quartile range,as explained near the end of section 3. This base case islabelled ‘standard’. The average extraction ratio for the

samples was 98.8%, with 2.86% by mass of material in thereference samples being missed and 1.65% by mass ofparticles which were not in the reference samples somehowfinding their way into the sample cuts. The overall size biaswas not statistically significant and the missed and extramaterial did not separately show a statistically significantsize bias.

Figure 7 shows the amounts of missed and extra materialfor each cut and for each size class. The points show datafor single cuts and the lines show averages over all cuts. We

Figure 5. Particle flow during sampling by Vezin cutters. The rows show three times during the passage of the Vezins through the fallingparticle stream: (left) the Vezin has a blade angle of 15°, and (right) the Vezin has a blade angle of 30°



can see from these figures (noting that a single particle insize class 10 has a mass of approximately 0.012 g) that thenumbers of missed and extra particles are generally quitesmall. For size class 10 there were two particles from thereference sample missed for one cut, but, otherwise, thenumbers of particles of this size class missed were one orzero. The number of particles extra in size class 10 wasalways either zero or one. The smallness of the numbers ofparticles missed and extra is highly desirable from the pointof view of Vezin cutters being very near to perfectlyunbiased. However, the total numbers of particles missedand extra in the replicate samples are likely to followPoisson distributions. Therefore, the variances of thesenumbers will be approximately equal to the averages and so

the fractional uncertainty in the bias estimates will be poor.

Coefficient of restitutionThe first material property that affects flow behaviour is thecoefficient of restitution, denoted by ε. This essentiallycontrols how bouncy a material is, and measures the ratio ofthe outgoing to incoming velocity of a collision. The ratioof the height of a bounce for a single particle collision to itsoriginal fall height is ε2. In this test, the coefficient ofrestitution was increased from the standard value of 0.3 to0.8. We do not know of any mineral commodity which hassuch a high coefficient of restitution, so this represents anextreme case. This produces a dramatic change in flowbehaviour with many particles bouncing back significantly

Figure 6. Statistical results for 15° and 30° blade angle Vezin cutters

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rather than just being deflected downward by the cutter.Despite this, the masses of missed and extra material werenot significantly different from the corresponding massesfor the standard case and the extraction ratio was 99%.However, both missed and extra material now had averagesize scores significantly below average (i.e. the materialwas finer than average) and, with more material beingmissed than extra, the samples were slightly coarser thanaverage for the flow being sampled.

The bouncing effect will increase in magnitude withincreasing speed of the particles. The factor determining thespeed of the particles at the point where they contact thecutter, is the fall height from the feeder to the cutter bladelips. In order to explore the worst case scenario, weincreased the drop height to 16 cm, from the standard dropheight of 3.1 cm, while keeping the coefficient of restitutionat 0.8. The extraction ratio for this case (see Table I) is still

very good at 97%, but the amount missed increased toaround 6% with a balancing increase in the extra to 3%.Tables II and III show that the size biases of the missed andextra are similar to what they were for the standard dropheight. The overall size bias is larger than for the standarddrop height but is not statistically significant due to thegreater variability in the results. From a practical point ofview, the bias as reported in Table III is 0.35% of the interquartile range, even though this is an extreme case of verybouncy material with a large drop height.

Friction coefficientAnother important material parameter is the frictioncoefficient. The value used for the standard case was 0.5which is a reasonably high value. The value of the frictioncoefficient, μ, was therefore reduced to 0.2 to test thesensitivity of the sampler performance to the friction level.The extraction ratio was slightly higher than for thestandard case, but none of the differences from the standardcase were statistically significant. This suggests that theVezin performance is not sensitive to the frictionalproperties of the material being sampled. This result is notsurprising given that the mechanism thought likely to behaving the most effect on sample bias, is particles bouncingcompletely over the cutter aperture. In circumstances wherecongestion at the cutter aperture was an importantmechanism, we would expect cutter performance to besensitive to particle friction.

Particle shapeParticle shape can sometimes be important to the flow ofparticulates. Previously, we have shown (Cleary andRobinson, 2008b) that particle shape can have a moderateeffect on falling stream cutter performance. Therefore herewe use super quadric rather than spherical particles toexplore whether the shape of the particles, which affects thedetails of the particle trajectories after they collide with thesample cutter blades, affects the sampling performance.Two cases, one with an extreme particle shape and the otherwith a moderate particle shape range, are tested to see ifthey affect sampler performance. For more details on theimportance of particle shape and on the super quadricshape, see Cleary (2004, 2009). The details of the particleshape ranges used are given in Table IV.

For the extreme shape distribution, (the extraction ratio

Table IIISize biases of samples and of missed and extra material as % of inter quartile range. The three numbers in each column are the lower 95%

confidence limit, the best estimate, and the upper 95% confidence limit

Size bias of sample Size bias of missed Size bias of extraLower limit Upper limit Lower limit Upper limit Lower limit Upper limit

15 degree face angle −0.11 0.10 0.31 −26.24 −14.48 −2.72 −35.35 −21.11 −6.8730 degree face angle −0.50 −0.15 0.19 −7.60 2.06 11.71 −29.48 −11.48 6.52Standard −0.27 −0.01 0.26 −7.96 0.99 9.94 −8.71 0.95 10.61ε = 0.8 0.02 0.21 0.40 −25.87 −18.31 −10.74 −27.24 −17.19 −7.1416 cm drop, ε = 0.8 −0.19 0.35 0.89 −22.84 −15.04 −7.24 −27.80 −18.59 −9.39μ = 0.2 −0.26 0.13 0.53 −24.79 −10.17 4.45 −21.59 −6.62 8.35Extreme shapes −0.94 −0.30 0.34 −13.54 −5.08 3.38 −24.81 −15.50 −6.19Moderate shapes −0.49 −0.13 0.23 −18.35 −8.88 0.59 −30.18 −18.66 −7.136 mm top size −0.49 −0.10 0.30 −6.66 1.08 8.82 −19.58 −10.86 −2.141 cm drop −0.42 −0.05 0.33 −9.51 1.47 12.44 −12.86 0.00 12.8760 g/s −0.57 −0.19 0.19 −7.49 1.71 10.92 −12.98 −5.99 1.01Moved at 1.2 m/s −0.46 −0.01 0.43 −9.04 −0.76 7.53 −10.25 −1.75 6.74

Figure 7: Masses of a) missed material, and b) extra material forall cuts for each size fraction for the ‘standard’ configuration.



was smaller), the amounts of missed and extra materialwere larger than for the standard case. All three of thesedifferences were statistically significant. The correspondingresults for the moderate particle shapes, showed a smallincrease in extraction ratio and increased amounts of missedand extra material, but none of these differences from thestandard case were statistically significant.

Tables II and III show no statistically significant size biases,though the extra material has a statistically significantnegative bias (i.e. the material is finer than average) for bothparticle shape variants. These results are consistent with thehypothesis that the mechanism having most effect on bias, isparticles bouncing completely over the cutter aperture. Whenparticles have less regular shapes they bounce moreirregularly, so more particles are missed or extra. However,few particles bounce as far as the distance over the cutteraperture. Therefore, the Vezin performance appears to beinsensitive to the shape of the particles, even when they havehigh aspect ratios and are blocky.

Particle top sizeThe final attribute of the feed material that mightpotentially influence the Vezin sampler performance, is thetop size of the feed. To explore this, a broader sizedistribution from 0.5 to 6 mm was used. This simulationwas run for 100 seconds of simulated time and 139 samplecuts were included in the data analysis.

The average extraction ratio and sample size are notsignificantly different from those for the standard DEM runwith 2 mm top size. The overall percentages of missed andextra are slightly smaller than for the standard case. Themissing material has close to the same average size as thefeed, but the extra material is finer than the average for allmaterial in the stream by an amount which is statisticallysignificant. The overall sizing of the samples is veryslightly finer than average but the difference is notstatistically significant. A plausible explanation for this isthat coarse particles are less likely to be deflected by otherparticles.

Figure 8a shows the masses of missed material in thevarious size classes. Very few large particles were missedin any of the 139 sample cuts. Figure 8b shows the massesof extra material in the various size classes. The numbers oflarge particles extra are smaller than the numbers ofparticles missed. Owing to the numbers of large particlesbeing very small for this case, the confidence intervals forthe quantities being estimated are of similar width to thosefor the standard case, despite the larger number of samplecuts.

For the range of conditions modelled, the extraction ratioand size bias of the Vezin cutter are not sensitive to feed topsize. The fact that the masses and sizings of cuts are morevariable when the top size is larger is not a novelobservation. It is well known that the component ofsampling variance which Gy (1982) calls the FundamentalError variance increases with top size.

Fall heightEarlier, we examined the effect of an increase in dropheight in conjunction with the bounciness of the particles. Ifthe drop height is instead reduced, then the vertical velocityof falling particles is much smaller than the velocity of thecutter. To see if this can lead to any performance issues, thefall height was reduced to 1 cm. This produced a smallincrease in extraction ratio compared to the standard case,with a tiny increase in missed and a slightly larger increasein the extra. The increase in the mass of extra material wasstatistically significant. This suggests that the biasmechanism of particles rolling up the surface of the leadingcutter blade and into sampler does occur when the dropheight is small. However, the increase in the amount ofextra material is about 0.7% of the sample mass and is notof practical importance. The changes to size bias and to theaverage size of the missed and extra material, were notstatistically significant.

Overall, the sampler performance is not sensitive to thefall height from the feeder. Since this case is the one that isbest suited for the rolling particle bias mechanism to occurand no size bias was found, we can conclude that this biasmechanism is not important for such a laboratory scaleVezin sampler.

Feed bed depthThe bed depth on the vibratory feeder is controlled by themass flow rate. For falling stream samplers (Cleary andRobinson, 2008b) we have found that the depth of the bedcan influence bias generation. To explore if the thickness ofthe bed and, therefore, of the falling stream is important fora Vezin sampler, we performed a test with a doubled feedrate of 60 g/s. The percentages of material missed and extraboth increased slightly, but by the same amount leading tothe same extraction ratio as found for the standard case beddepth. The average sizing of the missed material was

Table IVDetails of particle shape variations

Blockiness Intermediate axis Short axis range aspect ratio range aspect ratio range

Extreme shapes 4.0 1.0 0.5Moderate shapes 2.5-6.0 0.85-1.0 0.7-0.85

Figure 8. Masses of a) missed material, and b) extra material forall cuts for each size fraction for the feed with 6 mm top size



unchanged, but decreased modestly for the extra materialleading to a very slightly finer sample being taken. Thisslight bias towards finer material was not statisticallysignificant. We conclude that the Vezin performance is notinfluenced by changes in feed rate within the practicallimits of what can be delivered by the feeder.

Sampler speedSampler speed is generally considered to be critical forsampler performance based on the work of Gy (1982, 1992)for small scale falling stream sampler tests. A maximumoperating speed of 0.6 m/s for the sampler is oftenautomatically adopted based on experiences with fallingstream cutters. It is possible that the sampler speed could beimportant for Vezins since the mechanisms relating toparticles bouncing over the cutter aperture and rolling up theblade would both be influenced by the sampler speed.Therefore, to evaluate the importance of the sampler speed,we doubled the rotation rate of the cutter. This gives a speedof the sample cutter of 1.2 m/s at the point where the cuttermeets the particles. A total of 23 cuts were taken when thesampler speed was increased. The individual sample masseswere halved, so the total mass of sample was almost the sameas for the standard case.

The percentages of material missed and extra bothincreased moderately by about 1.9%. This doubles theamount of extra material compared to the standard case. Thenet result is that the extraction ratio is unchanged at around98.8%. The sizing of the missed and extra material is veryclose to the feed average and very close to the values foundfor the standard case. The size bias was not statisticallysignificant for either the standard case or for the double speedcutter. For the conditions investigated, the sampling bias ofthe Vezin was not influenced by its speed of operation.

These results are consistent with the hypothesis that themain mechanism causing bias is particles bouncing off cutterblades completely over the cutter aperture. A faster movingcutter causes the bounces of particles off the cutter blade tobe slightly more energetic, but it remains true that very fewparticles bounce as far as the distance between the cutterblades.

Note about statistical analyses presented in tablesStudent’s t-test is satisfactory for finding 95% confidencelimits like those given in Table I–III when the masses ofmaterial are reasonably consistent between. However, whenthe masses are very variable this technique is not satisfactory.This is particularly true for the sizing of extra material whenthe particle top size is 6 mm. For most cuts, most of the extraparticles are small so the mass-weighted average sizing issmall. However, there are a small number of cuts for whichthere are a small number (usually one) of large particles. Forthese cuts, the mass-weighted average sizing is large and themass of extra material is generally larger than for the cutswith small mass-weighted average sizing.

The alternative statistical analysis technique used, was tofind confidence limits based on weighted linear regression.For instance, for the average sizing of extra material themass of extra material was used as a weight. This ensuredthat larger masses of material were given appropriateimportance in the data analysis.

ConclusionWe have investigated the sampling performance of Vezinsamplers using DEM modelling. The ability of DEM topredict closely correlated reference and actual samples

allows the detection of very small biases and changes inextraction ratios and the linking of these to basicmechanisms of bias generation. Vezin samplers operatingon particles with minimum bottom size of 500 micronsappear to be very reliable and robust devices. Theyconsistently produce extraction ratios very close to 100%and with negligible bias. Their performance is insensitive tothe material properties, particularly the particle shape,friction coefficient and restitution coefficient. Sample biasdoes not appear to increase with increasing top size of thefeed material provided that this is much smaller than thecutter aperture.

Vezin samplers operate satisfactorily at peripheral speedswell in excess of the 0.6 m/s speed normally considered theupper limit for unbiased sampling. Over the range ofconditions investigated, there is little evidence that highcutter speed produces any problems. Analysis of thepossible bias generating mechanisms does not identify anyphysical process that could lead to a cutter speed dependentsampling error. Other operational settings such as the fallheight and the depth of the feed or the feed rate havesimilarly little effect on the sampler performance. Cutterdesign variations such as different face angles for the cutterblades also do not affect performance.

The worst case investigated was a very bouncy, angularmaterial sampled in a Vezin operating at high speed andwith a very large fall height. Even in this very extreme casethe amount of sample bias is likely to be acceptable from apractical point of view.

Analysis of the possible physical bias generatingmechanisms identified four potential candidates. Three ofthese are relevant to the Vezin used in this study with theparticle size distribution considered. Our investigationindicates that the effect of all three mechanisms is veryweak and that they are unable to generate any significantbias. We were not able to reproduce any substantialdeparture from 100% extraction ratio such as that reportedby Pitard (2005) from physical experiments using a widerange of possible parameters.

The fourth mechanism is that of air drag whichpreferentially affects finer particles. This was not includedin the DEM models used in this paper. For the feed sizeused in this study, which had a minimum particle size of500 microns, this mechanism is expected to have negligibleeffect because the particle Reynolds numbers are largeenough to indicate that the fluid motions are unimportant. Ifthere are particles in the feed that are significantly smallerthan 500 microns, then the air drag mechanism will createbias via at least two different avenues. It should be notedthat the rotation of the Vezin sample cutter will generatesignificant air motions in the device which will significantlyaffect the trajectories of fine particles and slow down theirmotion. This combination can strongly reduce the amountof fine material sampled. There would appear to be a clearcase that the mechanism of air drag is likely to be themechanism responsible for that departure from 100%extraction ratio reported by Pitard. The reported solution ofreducing the Vezin speed would reduce the speed of the airflow and therefore the consequent loss of fine material dueto air flow so is consistent with the observed behaviour.This will be investigated in future work.

ReferencesCLEARY, P.W. Discrete Element Modelling of Industrial

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CLEARY, P.W., ROBINSON, G.K. and SINNOTT, M.D.(2005). Use of granular flow modelling to investigatepossible bias of sample cutters. Second WorldConference on Sampling and Blending 2005, pp.69–81. The Australasian Institute of Mining andMetallurgy.

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Geoffrey Keith Robinson Industrial Statistician, CSIRO Mathematical and Information Sciences

He has had a continuing interest in mineral sampling and mineral stockpiles since becominginvolved with a review of Hamersley Iron's grade control system in 1987-8. He has used a general-purpose three-dimensional stockpile model called CHASM for investigating the relative merits ofstockpiling options for a variety of proposed mine developments for iron ore, coal, copper, nickeland phosphate rock. He has completed several research projects studying sampling procedures andsampling devices, and has served on International Standards Organization subcommittee ISO/TC102/SC 1 and a few Standards Australia Subcommittees.




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