Power draw estimations in experimental tumbling mills using PEPT

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    2010 Elsevier Ltd. All rights reserved.

    The power draw of a tumbling mill is known to be an importantmeasure in determining its efciency. M

    a functSchnocto calobserv(Gove

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    method it has been shown that the bulk properties of a particularsize class can be ascertained from tracking the motion of singleparticles within that size class at steady state (Conway-Baker

    given distribution including power draw.

    the medium in which it travels. Fig. 1 shows a picture of an exper-imental mill in a parallel plate PEPT camera system (Positron Imag-ing Centre, University of Birmingham), along with a schematicdescribing the method used to detect and triangulate particlepositions.

    3. Experimental methodology

    Single particle tracking experiments using PEPT were conductedfor this study at the Positron Imaging Centre, University of

    Corresponding author at: Centre for Minerals Research, Department of Chem-ical Engineering, University of Cape Town, South Africa. Tel.: +27 21 650 5554; fax:+27 21 021 650 5554.

    E-mail addresses: lawrence.bbosa@uct.ac.za (L.S. Bbosa), indresan.govender@uct.ac.za (I. Govender).

    Minerals Engineering 24 (2011) 319324

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    Minerals En

    journal homepage: www.els1 Tel.: +27 21 650 5520; fax: +27 21 650 5501.describe the distribution of power draw into the charge. Thus,the charge has often been simplied to a single bulk body over adened region of the mill. It has been noted that in order to intro-duce more informative power draw functions, greater understand-ing of the fundamental mechanisms associated with charge motionis necessary (Govender et al., 2001b).

    Positron Emission Particle Tracking (PEPT) offers a way ofstudying the internal environment of tumbling mills. PEPT is atechnique by which trajectory information of single particles intumbling mills can be obtained (Parker et al., 1997). With this

    et al., 2004). The premise of the method is the positron annihilationof a tracer, a particle taggedwith a radionuclide. Positron-emittingtracers are normally labelled using radionuclides such as 18F, 64Cuand 68Ga. These radionuclides decay by emission of back to backgamma rays of 511 keV. Simultaneous detection of the two gammarays in an array of detectors (a PET camera) denes a straight linealongwhich the particle position lies. At a frequency of up to 250 Hz,the position of the particle can be triangulated in three dimensions.

    The accuracy of the method depends on factors such as thespeed and activity of the particle, as well as the attenuation ofderived to predict the power drawaslated to charge motion (Harris andWhile these models have been showntions of mill power, they have beenscope under which they were dened

    As in situ characterisation of chardue to the aggressive internal envmany models have focused on usi0892-6875/$ - see front matter 2010 Elsevier Ltd. Adoi:10.1016/j.mineng.2010.10.005any models have beenion of characteristics re-k, 1985; Morell, 1992).culate good approxima-ed to be limited to thender et al., 2001a).ion has proved difcultent of tumbling mills,pirical relationships to

    2. Positron Emission Particle Tracking (PEPT)

    Positron Emission Particle Tracking (PEPT) is a technique formeasuring the ow trajectory of a radioactive particle in a granularoruid systemsuchas a tumblingmill. This techniquewasoriginallyintroduced in the medical eld as positron emission tomography(PET), andhasbeenmodied to suit engineeringapplications (Barley1. Introduction et al., 2002). The unique value of this aspect is that data from PEPTcan be used to calculate charge properties for every size within aPower draw estimations in experimental

    L.S. Bbosa a,1, I. Govender a,b,, A.N. Mainza a, M.S. PoaCentre for Minerals Research, Department of Chemical Engineering, University of CapebDepartment of Physics, University of Cape Town, South Africac Julius Kruttschnitt Mineral Research Centre, University of Queensland, Australia

    a r t i c l e i n f o

    Article history:Available online 15 December 2010

    Keywords:Positron Emission Particle Tracking (PEPT)Power drawResidence time

    a b s t r a c t

    Positron Emission Particlebeads in an experimental trepresentative tracer partiTwo approaches for calcuthe mill centre, and the timof the mill. Results were cpower.ll rights reserved.mbling mills using PEPT

    ll c

    n, South Africa

    king (PEPT) was employed to reconstruct the motion of mono-sized glassbling mill run in batch mode. In each case, the derived trajectory eld of awas used to determine the charge power draw at steady state operation.g power draw were considered: the torque of the centre of mass abouteraged torque contribution per discrete grid cell summed over the volumeared across different operating conditions and particle sizes to measured

    evier .com/locate /minengle at ScienceDirect

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  • ngin320 L.S. Bbosa et al. /Minerals EBirmingham. A 300 mm diameter mill with a variable speed drivewas designed for this purpose, whose picture and schematic is pro-vided in Fig. 2. A torque transducer was coupled to the drive shaftto measure the power draw of the mills. Spherical glass beads wereused as the dry charge. Tests were conducted using either 3 mm or5 mm charge. To determine the mass requirements for 31.25%

    Fig. 1. PEPT camera in parallel plate cong

    Fig. 2. Picture and schematic of 300 mm tumeering 24 (2011) 319324volumetric lling of the mill, the bulk density of the glass beadswas determined by assuming a packing ratio of 0.6.

    Glass beads for either size were subjected to direct activationusing a 33 MeV 3He beam to produce the radioactive tracer parti-cles. The resulting positron emitter was 18F (which has a half lifeof 109 min). Experiments with each tracer particle were conducted

    uration and schematic of its operation.

    bling mill used for PEPT experiments.

  • The velocity was calculated using a central difference approxi-

    5.2. Centre of mass approach

    For the rst approach, the power draw was calculated using avariation of the torque arm principle commonly used for tum-bling mills in comminution literature; for example Harris and Sch-nock, 1985. The centre of mass was based on the previously

    i__

    Fig. 4. Diagram illustrating power draw calculation using torque per bin approach.

    Fig. 3. Diagram illustrating power draw calculation using centre of mass approach.

    ngineering 24 (2011) 319324 321mation scheme. The mass distribution was calculated using the to-tal charge mass, M, weighted by the normalized residence timefraction (RTF) in each bin; see Sichalwe et al. (2010) for a detailedexplanation.

    5. Power draw formulation

    5.1. Measurement of power draw

    A torque transducer coupled to the drive shaft provided voltagereadings directly proportional to the dynamic torque applied onthe shaft. Therefore, for each PEPT experiment the mean measuredpower draw (PM) was calculated by:

    PM K V x; 1where K = 2.1 was the calibration factor, V the average voltage atsteady state operation, and x was the angular velocity of the millin radians per second. The voltage readings from the torquein 1 h durations. Table 1 summarises the experiments that wereconducted in this work.

    4. Treatment of data

    The Cartesian coordinates and logged time of the tracer particlewere imported into MATLAB (Mathworks, 2009a), which was usedto perform all the analyses required for this work. In order toexamine charge behaviour in the azimuthal plane of the mill, themill face was divided into a 50 50 set of discrete squares. Allaverage quantities per rectangular bin excluded data near the feedand discharge grate. Consequently, the charge was assumed to beaxially symmetric.

    Table 1Summary of PEPT experiments investigated in this study.

    PEPT mill

    Internal diameter (m) 0.3Internal length (m) 0.27% Filling by volume 31.25No. of lifters 20Speeds investigated (% mill critical speed) 50, 60, 75

    Glass bead size (mm) Charge mass (kg)

    Mono-size dry3 9.6625 9.662

    L.S. Bbosa et al. /Minerals Esensor were observed to uctuate in a sinusoidal motion with therotation of the mill. The amplitude of these uctuations was0.1 V (voltage ranged between 2 V and 4 V). Combining thisuncertainty with that of the angular velocity, the resulting propa-gated error in the measured power draw was determined usingthe following equation:

    DPM DV

    V

    2 Dx

    x

    2s; 2

    where DV was the standard deviation of the measured voltage,while Dx was 0.02 radians per second.

    Two methods were investigated to calculate power draw fromPEPT data. These were named as follows:

    Centre of mass approach (PCOM). Summed torque per bin method (PBIN).-0.1 -0.05 0 0.05 0.1 0.15

    -0.1

    -0.05

    0

    0.05

    0.1

    0.15

    calculated residence time fraction distribution and not necessarilyequal to the mean position of the PEPT tracer coordinates.1 Theeffective power draw of the entire charge body (PCOM) approxi-mated as a continuum was thus the moment due to the centreof mass about the mill centre multiplied by the rotational speed ofthe mill,

    PCOM M g R cosh x; 3where M was the total mass of the charge, R the torque arm radiusfrom the mill centre to the centre of mass, g the acceleration due togravity (9.81 m/s2), and h the angle between the x-axis and the ra-dial arm R, as shown in Fig. 3.

    Noting that R cos(h) was simply the x-coordinate of the centreof mass in meters, the centre of mass power draw was recon-

    1 The mean tracer position would only equal the centre of mass position if the PEPTsampling rate were very high (>1 104 s1).

  • ngin322 L.S. Bbosa et al. /Minerals Estructed to incorp