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    Optimization of continuous ball mills used for finish-grinding

    of cement by varying the L/D ratio, ball charge filling ratio,

     ball size and residence time

    R. Schnatz

     Polysius AG, Beckum, Germany

    Abstract

    During the last decade, semi-finish-grinding plants have been used more and more for the energy efficient grinding of high-

    quality cement. In 1999, it was found that by decreasing the ball charge filling ratio it was possible to lower the specific energy

    demand for grinding significantly.

    It was obvious, too, that the L/D ratio influences the specific energy demand and the mill throughput as well. Therefore, a

    huge test program was carried with a semi-industrial ball mill, which was operated in closed circuit. The mass-specific surface

    area of the two feed materials (intermediate product) used were quite typical for industrial semi-finish grinding plants. The

    values were 2200 and 3000 cm2

    /g according to Blaine. The product finenesses were 3000 and 3800 cm2

    /g, respectively. The L/ D ratio of the ball mill was varied in four steps of 1.75, 2.1, 2.79 and 3.49, and the ball charge filling ratio was varied in three

    steps of 15%, 20% and 25%. The experiments clearly indicated that the optimal L/D ratio and the optimal ball charge filling

    ratio are different for each feed fineness.

    The influence of the ball charge grading on the specific energy demand, characterised by the average ball diameter, was

    tested by means of a discontinuous laboratory ball mill. The results showed that by using a finer ball grading the specific energy

    demand could be lowered considerably.

    The obtained results can be explained well by theoretical considerations regarding the ruling stress intensity and the number 

    of stress events. The stress intensity expressed as the power input per ball is dependent on the ball diameter to the third power 

    and only slightly dependent on the inner diameter of the mill. The number of stresses can be characterised by the average

    retention time of the ground material inside the mill if the ball charge grading remains unchanged. The optimal retention time

    depends not only on the feed material and the desired comminution result but also on the ball charge filling ratio and particularly

    on the L/D ratio. On the basis of the present results and considerations, a specific optimisation of ball mills in semi-finish-grinding plants can be done.

    D  2004 Elsevier B.V. All rights reserved.

     Keywords:  ball mills; L/D ratio; finish-grinding

    0301-7516/$ - see front matter  D   2004 Elsevier B.V. All rights reserved.

    doi:10.1016/j.minpro.2004.07.024

     E-mail address:  [email protected].

    Int. J. Miner. Process. 74S (2004) S55–S63

    www.elsevier.com/locate/ijminpro

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    1. Introduction

    During the last decade, semi-finish-grinding plants

    have been used more and more for the energy efficient grinding of high-quality cement. Recent research

    work has shown that the operational performance of 

    the ball mill, which is situated downstream of the

    high-pressure grinding roll separator cycle can be

    improved significantly. The results of extensive

    investigations carried out on industrial semi-finish-

    grinding plants indicated that the specific power 

    consumption of the ball mill could be decreased by

    about 20% when lowering the ball charge filling ratio

    from about 30% to about 20%. However, the

    throughput is decreased also by about 20% (Schnatzand Knobloch, 2000).

    Furthermore, it has shown that a L/D ratio of about 

    3.0, which is a quite common value for cement mills,

    might be to high for a ball mill in a Combi-grinding

     plant. This was proven by the fact that there was no

    grinding progress observed in the last third of the total

    grinding path length. This finding was not effected by

    different ball charge filling ratios and different mill

    throughput mass flows. Quite typical are the results

    shown in   Fig. 1   in which the mass-specific surface

    area (Blaine) and the residues on the 32-, 63- and 90-

    Am screens of meter-samples are plotted against the

    grinding path length.

    The ball charge filling ratio and the L/D ratio are

    influencing the specific power consumption and thethroughput simultaneously. Furthermore, the absolute

    fineness of the ball charge and the ball charge

    grading are important factors for the optimal oper-

    ation of a ball mill. Systematic investigations, which

    are necessary for quantifying the different influences,

    cannot be executed in industrial plants. Therefore,

    the test runs were carried out in the R&D facilities of 

    the Polysius AG.

    2. State of the art-L/D ratio and ball charge fillingratio

    The specific power consumption is, as already said,

    influenced by the L/D ratio and the ball charge filling

    ratio of a ball mill. The investigations known from the

    literature were carried out with two compartment 

    c em en t m il ls i n t he 1 98 0s (Kuhlmann, 1985;

    T7 tigkeitsbericht, 1991). This mills produced ordinary

    Portland cement with a Blaine surface area of about 

    3000 cm2/g. The mill discharge had a fineness of 

    about 1800 cm2/g and the material which enters the

    Fig. 1. Sieve residues on 32, 45 and 63  A  and Blaine-specific surface area of meter samples as a function of the grinding path length.

     R. Schnatz / Int. J. Miner. Process. 74S (2004) S55–S63S56

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    second compartment had only a fineness of about 800

    cm2/g. Whereas the material which enters the ball mill

    in a Combi-grinding plant is much finer (~2000 cm2/ 

    g). Therefore, this results canTt be transferred directlyto the one compartment ball mills in Combi-grinding

     plants. But, nevertheless, it gives a good introduction

    into the problems occurring.

    The specific power consumption during this tests

    had a broad optimum in the range of 26% ball charge

    filling ratio.

    The optimal L/D ratio range is quite broad again

    with the minimum in the range of 3.2. For one

    compartment mills, this optimum should be less due

    to the lack of the first compartment used for coarse

    grinding.The optimal ball charge filling ratio for Combi-ball

    mills is supposed to be less too.   Shoji et al. (1982)

    investigated the influence of the ball charge filling

    ratio on the specific power consumption for the

    grinding of quartz sand. They found a flat minimum

    at a ball charge filling ratio of about 15%.

    3. Test runs with the semi-industrial grinding plant

    3.1. Description of the plant 

    The flow-sheet of the semi-industrial plant is

    shown in Fig. 2. Fresh feed and separator grits were

    combined and fed to the mill. The ball mill has an

    inside diameter (inside liners) of 0.72 m. Its length

    can be varied by combining different tube shells with

    a length of 25 or 50 cm in the range of 1.25–3.5 m.

    Fig. 3   shows the mill. The material, which is

    discharged pneumatically by the mill ventilation air,

    is collected in a cyclone and a subsequent bag-filter 

    and fed-combined with the material which is dis-

    charged mechanically-to the high-efficiency separator 

    SEPOLR.

    The ball mill is equipped with a classifying lining

    with a conical undulated shape. The absolute lifting

    height is quite similar to an industrial used liner 

     plate. The discharge diaphragm is of the slotted type.

    The ball charge grading used during most of the test 

    runs was an industrial standard grading with balls

     between 12 and 20 mm. The average ball diameter 

    was 15.8 mm; the average ball weight was 15.3 g/ 

     piece. For the experiments in which a finer ball

    grading was used a bored discharge diaphragm (bore

    hole diameter: 4 mm) was built in. The air velocity

    in the free mill cross-section was adjusted to 0.5 m/ 

    s. The mill speed was kept constant at 37.4 rpm,

    which relates to a relative mill speed of 75%. The

    function of the classifying liners were examined

    several times. The grading was very good in allcases.

    The desired product fineness was adjusted by

    varying the circumferential speed of the rotor cage.

    The circulation factor was limited to 3.0.

    3.2. Test program

    The two feed materials which were used in the test 

    runs were produced with a high-pressure grinding roll

    which was operated in closed circuit with a staticFig. 2. Flow-sheet of the semi-industrial ball mill plant.

    Fig. 3. Semi-industrial ball mill.

     R. Schnatz / Int. J. Miner. Process. 74S (2004) S55–S63   S57

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    separator. The feeds had finenesses of about 2200 and

    3000 cm2/g according to Blaine, respectively. This

    intermediate product finenesses are quite common in

     plants, which are producing Portland cements type

    CEM I 32,5 R and CEM I 42,5 R. The 0.02% grinding

    aid (diethanolamine) was added to the fresh feed.

    The feed were ground to product finenesses of 3000 and 3800 cm2/g, respectively. The system was

    operated near its performance limit during the test 

    runs. In addition, some test regarding the optimisation

    of the ball charge grading were executed.

    4. Test results

    The test results are plotted in Figs. 4 and 5. In bothfigures, the specific power consumption—left ordi-

    nate- and the throughput-right ordinate—is plotted

    Fig. 4. Spec. power consumption and throughput in relation to the L/D ratio for the coarse feed material. Parameter: ball charge filling ratio.

    Fig. 5. Spec. power consumption and throughput in relation to the L/D ratio for the fine feed material. Parameter: ball charge filling ratio.

     R. Schnatz / Int. J. Miner. Process. 74S (2004) S55–S63S58

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    against the L/D ratio. Parameter is the ball charge

    filling ratio. Fig. 4 gives the results for the coarse feed

    material (2200 cm2/g according to Blaine).   Fig. 5

    contains the results for the fine feed. Fig. 4 shows that the throughput is maximal at a L/D ratio of about 2.7– 

    2.9. In the same range, the spec. power consumption

    has a minimum. For the grinding of the coarse feed

    material, a ball charge filling ratio of about 25% or 

    may be more was found to be optimal because the

    throughput was significantly higher (~20%) compared

    to the tests at lower filling ratios and the spec. power 

    consumption was lower (~7%).

    For the fine feed, there is no clear dependence of 

    the L/D ratio and the throughput. The throughput 

    remains nearly constant between L/D=2.1–2.7. A ballcharge filling ratio of 25% increases the throughput 

    only by about 4% compared to a filling ratio of 20%

    and 10% at 15% filling ratio. The optimal L/D ratio

    regarding the spec. power consumption is situated in

    the range of 2.0–2.4. In contradiction to the coarse

    feed, a lower ball charge filling ratio of about 18%

    showed to be advantageous. For an industrial appli-

    cation, one has to decide what should be the

    optimisation target: minimum spec. power consump-

    tion or maximum throughput.

    For determining the comminution progress along

    the grinding path, the mill was crash-stopped during

    several test runs. Samples were taken in distances of 

    40–50 cm along the whole grinding path length. The

     particle size distribution of these samples were

    analyzed by means of a laser diffraction spectrometer.

    The parameters of the RRSB-function ( Rosin  Ramm-

    ler   S  perling and   Bennet equation) were fitted to the

    PSDs.

    The RRSB-slope n of the   bmeter  Q    samples is plotted as a function of the grinding path length in

    Fig. 6. Parameter is the ball charge filling ratio. The

    slope   n   tends towards a constant value along the

    grinding path length. The high values of  n   for low L/ 

    D ratios decrease and the low values of  n  for high L/D

    ratios increase along the grinding path. Furthermore,

    there seems to be no influence of the ball charge

    filling ratio on the RRSB slope n.

    It can be summarised that for ball mills in Combi-

    grinding plants the optimal L/D ratio is clearly below

    3.0. For coarse feed material about 2.7 seems to beappropriate and about 2.3 for finer feed. Recommen-

    dations made by Haubold (2001) who found L/D ratios

    in the range of 4.0–5.0 to be optimal are useful only for 

     ball mills in semi-finish-grinding plants, which are

    operated in open circuit. The importance of open

    circuit ball mills is diminishing because most of the

    cement customers no longer accept coarse particles of 

    about 500  Am in the finished product, which cannot be

    completely avoided with this type of mill.

    5. Stress intensity and number of stress events

    It is useful to analyse the obtained results theoret-

    ically to develop procedures for the target oriented mill

    optimisation.

    Fig. 6. RRSB slope  n  of meter samples for different L/D ratios.

     R. Schnatz / Int. J. Miner. Process. 74S (2004) S55–S63   S59

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    5.1. Theoretical considerations

    The comminution process in ball mills is controlled

     by

    !   how often a particle of the material to be ground is

    stressed (number of stresses) and

    !   with which intensity the particle is stressed (stress

    intensity).

    The comminution progress or result—character-

    ised, e.g., by the newly produced surface area— 

    remains constant if the number of stress events (SN)

    and the stress intensity (SI) are unchanged (Kwade

    and Stender, 1998). Therefore, the mass-specific power consumption   W m   for a defined comminution

    result is proportional to the product of the number of 

    stresses and the stress intensity

    W m~SI d  SN    ð1Þ

    One can calculate   W m   from the power draw of a

    mill measured at shaft   P   and the product throughput 

    ṁ . The throughput itself can be expressed by using

    the definition of the average retention time of the

    material inside the mill.

    W m ¼  P ṁ ¼   P 

    m t ¯ t ¯ ¼  m

    ṁ  ð2Þ

    The stress intensity SI here defined as the average

    energy, which is transferred to the material by each

     ball, should be proportional to the power input per ball

     P / nk   .It is quite clear that the number of stress events

    is directly proportional to the average retention time

    of the material inside the mill. Taking this into

    consideration Eq. (2) can be written as

    W m ¼   P nk 

      nk 

    m t ¯

      ð3Þ

    nk : number of balls.

    The power absorption of industrial ball mills at 

    Polysius has been determined for decades with an

    empirical equation originally developed by Blanc

    (Blanc and Eckhardt, 1928).

     P ¼  p4

     cuk qk   1 eð Þ L

     D D3;5 ð4Þ

    Beside the mill inside diameter  D  and the L/D ratio

    the porosity of the ball charge  e , the true density of the

    grinding media  qk , the ball charge filling ratio  uk  and

    an empirical factor   c   go into the equation.   c   isdependant on the ball charge filling ratio, the used ball

    grading and the mill lining.

    For a constant ball diameter  d , the number of balls

    inside the mill can be calculated as follows

    nk  ¼  32

     D

    3 L

     Duk   1 eð Þ ð5Þ

    The combination of Eqs. (4) and (5) gives an

    expression for the energy input per ball   P / nk , which

    should be proportional to the stress intensity

     BI ~ P 

    nk 

    ¼  p

    6

     ffiffiffiffi D

    p   d 3cqk 

      ð6Þ

    The principal relationships can be seen from Eq.

    (6): The energy per ball is linearly dependent on the

    true density of the balls and the  c-factor. The biggest 

    influencing factor is the ball diameter (to the third

     power). Furthermore, interesting is the fact that more

    energy is transferred per ball in large diameter ball

    mills.The second part of Eq. (3) can be written as Eq. (8)

     by using a relationship for the amount of feed material

    m, which stays inside the mill at a time.

    m ¼  p4

     D3 L

     D quk qe   1 eð Þ ð7Þ

    q: true density of the feed material.

     BH ~

    nk 

    m t ¯

    ¼  6p

    1

    e

    t ¯

    qd 3  ð8Þ

    Eq. (8) shows that the number of stress events is

     proportional to the retention time of the material

    inside the mill and anti-proportional to the true density

    of the material and the ball diameter (to the third

     power).

    5.2. Stress intensity and ball diameter 

    The ball diameter, which is able to comminuting a

     particle of defined size, can be calculated according to

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    Bond (1958)   or   Perow and Brand (1954)   with an

    equation of the following form

    d  ¼ a  ffiffiffi xp    ð9Þa: fitting parameter and  x: particle size.

    For cement clinker   a   can be set to a value of 24

    with sufficient accuracy. A mill feed with a Blaine

    surface area of 1500 cm2/g will not contain particles

    N500  Am. Therefore, the largest balls in a mill should

    have a diameter of about 17 mm. For 50-Am particles,

    a 5-mm ball should be sufficient.

    This well-known but often neglected facts were

    investigated regarding the comminution of intermedi-

    ate product in Combi-grinding plants. For that  purpose, tests were carried out with a discontinuous

    laboratory ball mill. This mill at the Polysius R&D

    centre is used for grindability testing mainly. Seven-

    teen different ball gradings were tested. The lab-mill

    (F   0.750.45 m, ball charge filling ratio 10%,relative mill speed 0.88) were fed with clinker meal

    with a Blaine surface area of 2700 cm2/g. The mass-

    specific power consumption for the grinding to

    finenesses of 3000, 4000 and 5000 cm2/g were

    determined. The results are plotted in  Fig. 7.

    The figure contains the mass-specific power con-

    sumption in relationship to the average ball diameter 

    of the different ball gradings. It can be seen that the

     power consumption decreases with decreasing ball

    diameter. The potential savings are increasing with

    increasing product fineness. It can be concluded that 

    the finer the desired product is the finer the used ballgrading should be. Polydisperse ball gradings showed

    to be slightly more efficient compared to monodis-

     perse gradings with the same average ball diameter. A

    direct transfer of this results to industrial ball mills,

    which are operated continuously, however, is not 

     possible. This is caused by the fact that in continuous

    mills the material to be ground has to be conveyed

    through the ball charge. Very fine balls with diameters

    b8 mm tend to swim up. Furthermore, with finer balls,

    the tendency of the material to form agglomerates,

    which stick to the mill liners increases. Fine balls witha low weight do not have enough energy to clean the

    liners from that agglomerates. This is a limitation for 

    the use of very fine balls. But it is possible to suppress

    the agglomeration by an increased addition of grind-

    ing aid.

    5.3. Number of stress events and retention time

    The results obtained with the semi-industrial ball

    mill (see  Figs. 4 and 5) were analysed regarding the

    number of stress events (calculated according to Eq.

    (6)). For an unchanged ball grading and the same true

    density of the feed material the number of stress

    Fig. 7. Spec. power consumption of a laboratory ball mill as a function of the average diameter of the ball grading. Parameter: fineness of the

    finished product.

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    events can be substituted by the average retention time

    of the feed inside the mill. The calculated values for 

    the coarse and the fine material are plotted in  Figs. 8

    and 9. Both figures show that the spec. power 

    consumption has as significant minimum at a reten-

    tion time of about 7 min. The retention is influenced

     by the ball charge filling ratio and the L/D ratio. The

    fact that this optimal retention time is achieved withdifferent L/D ratios for fine and coarse feed material

    indicates that the transport behaviour of the material is

    an important factor too.

    6. Conclusion and outlook 

    On the basis of the results and considerations

     presented in this paper, a target-oriented optimisation

    of ball mills in Combi-grinding plants is possible. The

    obtained results can be explained well by theoretical

    considerations regarding the ruling stress intensity and

    the number of stress events. The stress intensityexpressed as the power input per ball is dependent on

    the ball diameter to the third power and only slightly

    dependent on the inner diameter of the mill. The

    Fig. 8. Spec. power consumption for the coarse feed materials a function of the retention time of the feed inside the mill. Values of  Fig. 4.

    Fig. 9. Spec. power consumption for the fine feed materials a function of the retention time of the feed inside the mill. Values of  Fig. 5.

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    number of stresses can be characterised by the average

    retention time of the ground material inside the mill if 

    the ball charge grading remains unchanged. The

    optimal retention time depends not only on the feedmaterial and the desired comminution result but also

    on the ball charge filling ratio and particularly on the

    L/D ratio. The influence of the factors ball charge

    filling ratio and L/D ratio on the retention time of the

    material to be ground has to be investigated in detail.

    Furthermore, the extension of the test regarding the

    influence of the mill speed on the retention time is

    necessary.

    References

    Blanc, E.C., Eckhardt, H., 1928. Technologie der Brecher, Mqhlen

    und Siebvorricht ungen. Springer Verlag, Berlin.

    Bond, F.C., 1958. Grinding ball size selection. Mining Engineering

    10 (5), S. 592–S. 595.

    Haubold, S., 2001. Verbesserung des Arbeitsergebnisses von

    Mahlanlagen f qr Zement nach der Technologie der Teilfertig-

    mahlung. ZKG International 54 (10), 556–565.

    Kuhlmann, K., 1985. Verbesserung der Energieausnutzung beim

    Mahlen von Zement. Schriftenreihe der Zementindustrie, Heft,

    vol. 44. Beton Verlag, Dqsseldorf.

    Kwade, A., Stender, H.-H., 1998. Konstantes Zerkleinerungsergeb-

    nis beim Scale-Up von R qhrwerkskugelmqhlen. Aufbereigunts-

    Technik 39 (8), S. 373–S. 382.

    Perow, W.A., Brand, W.J., 1954. Feinmahlen der Erze. VEB Verlag

    Technik, Berlin.

    Schnatz, R., Knobloch, O., 2000. Einfluss des Kugelf qllungsgrades

    auf den Energieverbrauch und den Durchsatz von Ku-

    gelmqhlen in Kombi-Mahlanlagen. ZKG International 53 (8),

    S. 438–S. 447.

    Shoji, K., Austin, L.G., Smaila, F., Brame, K., Luckie, P.T., 1982.Further studies of ball and powder filling effects in ball milling.

    Powder Technology 31, S. 121–S. 126.

    Tätigkeitsbericht, 1991. Verein Deutscher Zementwerke e.V.. Beton

    Verlag, Düsseldorf. 1987-90.

     R. Schnatz / Int. J. Miner. Process. 74S (2004) S55–S63   S63