Grade and Recovery Prediction for Eddy Current Separation Processes

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GRADE

AND

RECOVERY PREDICTION

FOR

EDDY

CURRENT

SEPARATION

PROCESSES

P.C.

REM*,

E.M.

BEUNDER

and

W. KUILMAN

Faculty

_of

AppliedEarth Sciences,

_Delft

University

of

Technology,

Mijnbouwstraat 120, 2628RXDelft, TheNetherlands

(Received 28March1998;Accepted5May 1998)

Grade and recovery of eddycurrentseparationcanbe estimatedonthebasisof trajectory

simulationsfor particlesofsimpleshapes. Inordertodo so,thefeedis characterized in termsofasmallsetof test-particles, each test-particle representingafraction of the feed of

agiven size,shape andmaterial.Inthispaper, the grade and recoverycurvepredicted fora

sample from the6-16 mmnon-ferrousfractionofcarscrapiscomparedwithexperimental data.Theresultsindicatethatitmay be possibletoautomatically control eddycurrent

separatorsonthebasisofsuch predictions.

Keywords: Eddy current; Modelling; Grade and recovery; Non-ferrous

0

INTRODUCTION

Eddycurrent separationis aneffective way of recovering non-ferrous

metals fromstreamsof industrialormunicipalwaste

[1

].

The separation

isbroughtabout by inducingeddycurrents insidetheconductive

par-ticles ofthestream.Thesecurrentslenda transientmagneticmoment to

theparticleswhichisusedtopropelthem inagradient magnetic field

[2].

Among

the many designconcepts for separators that have been tried,

the rotary drumisthemostwidely used type of eddycurrentseparator

today

(see

Fig.

1).

The active part ofthis machine is a fast spinning

drum, with a surface consisting of rows of magnets of alternating

Corresponding author.

non-ferrousmetals

plastics, glass,etc.

FIGURE An eddycurrent separator consisting ofadrum covered withmagnets

that are orientedalternately N-S and S-N. The fluctuatingfieldof the spinning drum

induces eddy currents in electrically conductive particles moving close to the drum. These particlesarethen expelledfromthe feedstream.

polarity.

A

conveyor belt takes the feed over the drum and the

con-ductiveparticlesareejected from themainstream.The trajectory of these

particlesisgenerallydeterminedbyacombination of the electromotive

force, gravity, and the forces of friction with the conveyor belt and theair.

At

present, noneof the published models for eddycurrentprocesses

can claimcompletegenerality.

Most

of thetheorydevelopedbeforethe nineties, inparticularthe workbySchl6mann

[3,4]

andvander Valketal.

[5-7],

is dealing with the limit of smallparticlesorlowfrequencies,and

ignores the effect of particle rotation.

In

the early nineties, work was

done on larger particles by Fletcher et al.

[8-10],

starting from first

principles. The results of this model show a faircorrespondence with

experimental results.

However,

both particle and field geometry were

different from what is common in practical applications. Recently,

Meier Staude and

Mersmann [11]

simulated a rotary drum including

the conveyor belt. Their model ignores the radial component ofthe

magneticforce, however, and has been demonstrated only for special

particleshapes.

Themodel used for thesimulations in thispaperwasdeveloped by

treating the particlesas magneticdipoles

[12-14].

This kind of model

is limited tosmalland medium-sizedparticlesbutit candealwithany kindoffieldgeometry.So far,ithas beenappliedtoratherbasicparticle

shapeslike spheres and cylinders, but thereis nofundamental reason

why it should not be developed formore complex shapes. The basic

theoryof the electromagnetic forces and the model for themechanical interactionsof the particleswiththe beltarebrieflydiscussed inthenext section. Theremainder of the paperdescribes the prediction ofgrade

feedcharacterization isexplained andthe predictedgradeand recovery

curves arecomparedwithexperimental data foranexamplecase.

1

THE

DIPOLE MODEL

The forceFand torque

T

exertedon aparticle byanexternal magnetic

fieldBa

canbeexpressedintermsofthe fieldgradient and theparticle

magnetization

[15].

If thefieldgradient

VB

a

isrelativelyconstant within

the volume of the particle, the expressions become verysimple:

F

M.

VB

a

3:

a.

_(e)

In

these formulas, M is the magnetic (dipole)moment of the particle.

For eddy current separation, the above approximation is sufficiently accurateif particlesaresmaller than aboutonethirdofthewavelength

ofthe magnetic field

(or

equivalently,athirdof the width ofapair of

magneticpoles).This meansthatfor rotary drummachinesthe modelis

limited toparticleswith diametersless than30-50mm.

It was shown in

[14]

that the dynamics of the particle magnetic

moment

M,

asobservedbythe particlein its ownframe ofreference,can

be closely approximatedbyalinear,firstorder differential equation:

d C V d

Ba"

d-M

"M---O"

₍₃₎

oR

#o

In

this formula, Ba

is the magnetic field as observed in the particle’s

frame ofreference, cr is the electricalconductivity ofthe particle and

#0 47r. 10-7

Tm/A

isthe magnetic permeability ofvacuum.

R

defines

the size of the particle and Vis itsvolume. The tensors C and

D

are

dimensionless and depend only on the shape of the particle. For

example,foracylindrical particle, oriented with itslongaxisalong the z-axisofitsframe of reference:

0

0)

C--6 0 0

and

D=g

0 2 0

0 0

In

the absence of other forces,

Eqs. (1)-(3),

in combination with

Newton’s

laws of motion, can be integrated for the trajectory of the particle

[16].

1.1 Contact

Forces

The most important force besides the electromotive force is the

mechanical interaction of the particles with the conveyor belt.

Inter-particle forcesmay alsoplayarole,especiallyathigherthroughputs,but

these forces were not taken into account.

In

order to avoid multiple

points ofcontact between the particle and the belt, the shape of the

particleswas, somewhat arbitrarily,represented bythe largestinternal

ellipsoid. The dynamical states ofthe system were confined to three

modes: roll,slide andfly.

The transitionbetween rollingand slidingwas definedby the stan-dard criterion for the friction force in terms of the support force

F

+/-and the coefficient ofstatic friction

_fs:

[Ffric[

>

fSF+/-.

For the slidemode a modification of Coulomb’s law ofdry friction

wasusedtoguaranteeasmooth transitionbacktorolling:

Ffrie

An

Here,

_fd

isthe dynamic friction factor,

Au

is the differential velocity between the belt and the particleattheirpoint of contact, andeis avery

small velocityconstant.Thetransitionfrom slidingtoflyingwasdefined

by the criterionF

+/-<

0. Occasionalcollisionsof particles withthe belt were simulatedbytherigidbodycollisionmodel of Keller[17,18],with restitution coefficientsof about 0.2.

1.2 AerodynamicForces

Aerodynamic forces ofdrag,and also ofliftand torque

(for

fast

spin-ning particles) are relatively unimportant compared to the

electro-motiveand mechanicalforces.Nevertheless,theireffectscanbe traced

experimentally

[14]. In

the present simulations basic formulas for the

turbulentlimit wereapplied for allcases.

2 PREDICTION OF GRADE

AND

RECOVERY

Suppose

that a mass

F

of feed material isprocessed into amassP of

product and a tailing. Furthermore, suppose that

F,

and

_Pm

are the

mass fractions ofamaterial

_(or

class ofmaterials) m in the feed and

product, respectively. Then the grade

_Gm

and the recovery

_Rm

of the material m intheproductaredefined asusual:

Gm=Pm/P,

m

’m/Fm.

A

grade-recovery diagramcanbe madebyplotting thegradeversusthe

recovery for a number ofoperating conditions of the eddy current

separator. The interestingquestionis whether itis possible to predict

the outer envelop of the points in the grade-recovery diagram: the

grade-recoverycurve.

Thefirststep inmaking the predictionistorepresent the actual feed

by a small set of test-particles, i.e., model particles with properties

similartothe particles ofsomefractionof the feed. Then the trajectories

of these test-particles are computedfor a number of beltspeeds and

drumspeedsof the separator

(cf.

Fig.

2).

Fromthe resultingdata, the

predictedgrade and recoverycan be computed for each combination

of belt speed, drum speed and position of the splitter. Finally, the

grade-recoverycurveis obtainedby rejecting all points from the

grade-recovery diagram thatare inferior to someother point in both grade

and recovery.

2.1 Feed Characterization

The feed ofan eddy current process usually covers a wide range of

FIGURE2 Simulatedtrajectory foracylindricalaluminiumparticle (diameter8mm, length 24mm), processed on a BM 29.701/18 [19] eddy current separator at a belt

speed of m/sanddrumspeed of50rps. Theopencirclesare experimental data for the sameconditions.

trytoaccuratelymodel,alarge number of theseparticlesandcompute

theirtrajectories.Instead,arepresentativesampleofthe feed is splitinto

several fractions, each fraction consisting of particles of the same

materialorclass ofmaterialsandofroughlysimilarshape. Each

frac-tion is then represented by three or four test-particles of the same

materialandidealized shape, but of differentsizes. Finally, amassof

feedisassignedtoeach test-particle that reflects thedistributionofmass

overthe materials, shapesand sizes of the particlesinthesample.

In

our experiment, we selected a sample from the 6-16 mm of the

non-ferrous fraction ofcarscrap

(see

Fig.

3).

Allseparation experiments

were done with this sample, which was carefully reconstructed after each run.

For

the purpose of characterization, the sample was first divided intofourshapecategories:flatparticles,globularparticles and twokindsofrod-shapedparticles

(all-metal

andinsulatedwire).Theflat

particles were represented by circular disks, the globular particles by

spheres and therod-shapedparticlesbycylinders. These categorieswere

FIGURE 3 The6-16mmnon-ferrous source fractionofcarscrap from whichthe sample fortheexperimentswere taken.

steel andfullynon-metallicparticles.Finally,some ofthelargersetsof particlesweresubdividedaccordingtosize.

For

flat particles thelargest

diameterwastakenas abasis forsizeclassification.Thefinal listof test-particlesisshowninTableI.

2.2 Simulations

The list of test-particles was fed to simulation software based on the

dipolemodel discussed in the previous section inorderto compute the

particle trajectories forfivedifferentbelt speeds ranging from to2

m/s

anddrumspeedsof30,40 and 50rpsona

BM

29.701/18

eddy current

separator

[19].

For a given belt speed and drum speed, the splitter

positionwasvariedalonga lineextending radially from thecenterof the

rotor

(see

Fig.

4).

Fivelines of splitter positionswereselected, ranging

from horizontal to almost vertical (q =00,20

,

40

,

60

,

80),

and for

each line, the radii of intersection with the particle trajectories were

computed. The splitter position (x, y) was then stepped up from the

minimum radius to the maximum radius in ten steps and for each

TABLE List of test-particles representing a sample of the 6-16mm non-ferrous fraction ofcarscrap showninFig. 3. Thediameterof the plastics part ofwires given

inthe table referstothe outerdiameter

Shape Material d(mm) orh(mm) Mass(g)

Sphere Aluminium 5.0 0.6 Sphere Aluminium 6.3 2.2 Sphere Aluminium 8.7 4.8 Sphere Aluminium 12.5 11.5 Sphere Non-metal 15.0 222.5 Disk Aluminium 12.5 4.0 7.0 Disk Aluminium 17.5 5.0 17.1 Disk Aluminium 22.5 5.0 10.7 Disk Aluminium 27.5 6.0 12.3 Disk Aluminium 32.5 4.0 10.9 Disk Stainless 17.5 2.0 1.2 Disk Brass 12.5 2.0 1.5 Disk Non-metal 20.0 5.0 35.0 Cylinder Aluminium 5.0 10.0 0.7 Cylinder Aluminium 7.0 15.0 5.5 Cylinder Aluminium 9.0 25.0 6.8 Cylinder Copper 1.5 32.5 0.9 Cylinder Copper 0.7 35.0 0.05 Cylinder Brass 10.0 17.5 4.9 Cylinder Brass 8.0 79.0 29.7 Cylinder Brass 10.0 25.0 9.6 Cylinder Stainless 10.0 21.0 10.3 Cylinder Non-metal 10.0 35.0 29.0 Wire Copper 2.5 35.0 Plastics 3.0 1.5 Wire Copper 1.5 22.0 Plastics 2.0 0.6 Wire Copper 1.7 53.0 Plastics 2.5 0.6

Y

splitter line

FIGURE4 Splitter positionis variedalonglines in thex-yplane.

aluminium and forthenon-ferrousmaterials as awhole. The resulting

grade-recoverycurveforaluminium ispresentedinTable

II.

The table shows that the prediction favors a combination of high

TABLEII Prediction of optimal settingsand grade and recovery foraluminium in

theproduct

Drum(rps) Belt(m/s) x(m) y(m) GAI RA1

50.00 1.75 0.352 0.000 65.81 99.72 50.00 1.75 0.247 0.090 66.51 98.71 50.00 2.00 0.284 0.103 70.34 95.24 50.00 1.75 0.160 0.134 71.49 94.90 50.00 1.75 0.285 0.104 72.46 93.50 50.00 1.75 0.522 0.000 76.51 92.21 50.00 2.00 0.329 0.120 89.04 87.07 50.00 1.50 0.520 0.000 92.23 85.51 50.00 1.75 0.578 0.000 97.10 85.45 50.00 2.00 0.374 0.136 98.99 82.62 50.00 1.75 0.635 0.000 100.00 79.13

TABLEIII Experimental results for the grade and recovery ofaluminiumand total non-ferrousin theproduct. The splitter positionwas fixed at(x, y)=(0.187,0.069)m

Drum(rps) Belt(m/s) GAl

RAI

Gnf Rnf

30 1.68 22.56 100.0 35.34 100.00 30 1.51 24.68 98.65 38.11 97.21 30 1.33 24.74 98.88 80.51 94.13 30 1.16 63.29 93.27 96.19 90.47 40 1.68 22.84 100.0 35.79 100.00 40 1.51 24.43 98.77 38.40 99.07 40 1.33 52.81 99.10 80.20 96.06 40 1.16 62.12 98.09 94.46 95.20 50 1.68 22.47 99.89 35.17 99.79 50 1.51 24.34 99.89 38.10 99.79 50 1.33 53.90 97.76 83.35 96.49 50 1.16 59.53 93.6 91.72 92.05

small size of the material

_[14].

The best splitter position is generally

low, which isalso the experience from thefield.

2.3 Experiments

Thesampleused in thecharacterization wasalso usedasthe feed fora

number of separation experiments on a

BM

_29.701/18

eddy current

separator. Thegrade and recovery both foraluminiumand total

non-ferrousweredetermined atseveraldrumspeeds(30,40 and 50rps)and

beltspeeds

(1.16,

1.33, 1.51 and 1.68

m/s).

The splitter positionwas fixed at(x, y) (0.187,

0.069)

min allruns

(see

Table

III).

2.4 Comparisonof Results

Figure 5 shows the grade-recovery diagram for aluminium, with the

experimental datapoints indicated bydiamonds. The solid line

repre-sents the simulated grade-recovery curve. Note that the simulation

shows a drop in recovery just above 60% grade, in agreement with

experimental data.

As

awhole,the simulationissomewhatmore

opti-misticthanthe experimental datapoints.

In

ordertocheck whether this

wasdue tothe wider range ofsplitterpositions covered by the

simula-tion, the simulation results for splitter positions close to the

experi-mental position were added to the diagram as separate points

(+).

Comparison of thedatashowsthat,indeed, part of the differencecanbe

contributed to this effect, but the simulation remains slightly more

optimistic.

A

similar result is found, comparing the simulated and

experimental results for the non-ferrous product in Fig. 6, with the

exception that for low grades, there are actually a few experimental

datapoints beyond the simulated grade-recovery curve.

In

general,

however,theresults forthiscase show that thecomputedcurvedeviates onlyafewpercentingrade and recovery from the experiments. 2.5

Process

Control

The present technologyfor predicting the gradeand recovery may be

combined with a sensor that automatically characterizes the feed

95-Recovery _[%] 85- 80-20 31"-/

_%

OL+

experiment \ simulation

+

l, 30 40 50 60 70 80 90 Grade[%] 100

FIGURE 5 Simulatedgrade-recovery curveforthe aluminiumproduct versusdata

from experiments. The points marked + are simulated points for splitter positions

100 99 98 97 96-Recovery [%]95 94-93 92 91 90 3O experiment simulation---- 0 simulation

₊

40 50 60 70 80 90 100 Grade[%]

FIGURE6 Simulatedgrade-recovery curve for the non-ferrousproduct versusdata

from experiments. The points marked

+

are simulated points for splitter positions

closest tothat of the experiments.

material inordertoarrive at asystemforcontrolling the eddycurrent

separationprocess.

A

prototypeof suchasensoriscurrentlybeingbuilt

at ourlaboratory. Thesensor estimatesthe size,shapeand material class

of about 10%ofthe particles thatarebeingprocessedby the separator.

Onthebasis of the statistics that aregenerated,the separator settings

canbe adjusted automatically, say, once every few minutes,toimprove

the separation results.

CONCLUSIONS

The first results of simulating grade and recovery for car scrap by

characterizing the feed intermsof model particles and simulatingtheir

trajectories show a fair agreement with experimentalresults.

Simula-tions ofthis kind may help in the selection of process schemes and

the design ofeddycurrentseparators.Another potentialapplicationof

this kind of analysis is on-line process control, given a sensor that

automaticallycharacterizesthefeedmaterial.

References

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SecondInt.SymposiumRecyclingofMetalsandEngineering Materials, TheMinerals, Metals&Materials Society,Pennsylvania, USA(1990).

[2] Edison,T.A.,U.S.Patent400,317(1889).

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[4] Schl6mann, E.,Separation of nonmagnetic metals fromsolid wasteby permanent magnets.II.Experimentson circulardisks, J.Appl. Phys.46(11) (1975)5022.

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266.

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Media,PergamonPress,London(1963)p. 143.

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[19] Theeddycurrentseparator used for theexperimentsismodelBM 29.701/18,from Bakker Magnetics,Son,The Netherlands.