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and their use is restricted to conditions similar to those associated with their

2013 Elsevier Ltd. All rights reserved.

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. . . . . . . . .5. Measurement methodology related to grinding media consumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1. Dropped ball test (DBT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2. Marked ball wear test (MBWT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.3. Other laboratory tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.4. Tests in industrial mills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Address: Department of Metallurgical and Minerals Engineering, WesternAustralian School of Mines, Curtin University, Perth, WA, Australia. Tel.: +61892664349; fax: +61 893584912.

Minerals Engineering 49 (2013) 7791

Contents lists available at SciVerse ScienceDirect

Minerals EngineeringE-mail address: [email protected]. Rotational speed of the mill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.8. Solids and crop load of the mill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.9. pH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0892-6875/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.mineng.2013.04.023. . . . 83

. . . . 83

. . . . 83. . . 84. . . . 844. Characterizing the grinding environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.1. Pulp potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.2. Dissolved oxygen concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.3. Oxyhydroxide species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.4. Slurry viscosity and surface tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.5. Mill feed rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.6. Particle size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Contents

1. Introduction . . . . . . . . . . . . . . . . .2. Properties of grinding media . . . .

2.1. Microstructure . . . . . . . . . .2.2. Effect of carbides in the m2.3. Media shape. . . . . . . . . . . .

3. Grinding wear mechanisms . . . . .3.1. Abrasive wear . . . . . . . . . .3.2. Impact wear. . . . . . . . . . . .3.3. Corrosive wear. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79trix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81calibration. This may not always be possible and alternative modelling methodologies are discussed anddemonstrated by means of a case study on simulated data.Models conditions inside the milleywords:omminutionrinding media

mechanisms, impact, abrasion and corrosion, can simultaneously inuence mass loss in grinding media.Present studies are difcult to compare directly, owing to imprecise information with regard to the com-position of the media or grinding conditions. As a result, most current models do not account for varyingle online 5 June 2013grinding media. Media wear arises as a consequence of complex interaction between a range of variablesrelated to processing conditions, the characteristics of the media, as well as the ores or slurries, and is notwell understood as yet, despite extensive study over the last 50 years and more. The three basic weareceived 29 March 2013ccepted 18 April 2013

minution systems in mineral processing are reviewed, together with models predicting wear losses ini c l e i n f o

history:

a b s t r a c t

In this study, the current understanding of the factors affecting the consumption of steel media in com-r tsumption of steel grinding media in mills A review

Aldrich ent of Metallurgical and Minerals Engineering, Western Australian School of Mines, Curtin University, Perth, WA, Australiaent of Process Engineering, University of Stellenbosch, Private Bag X1, Matieland 7602, Stellenbosch, South Africajournal homepage: www.elsevier .com/locate /mineng

7.8.

ineAcknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 891. Int

Grcant iCommoperaaccou(200945% oof steready1982)ever ia tremment.can reof mi(Long

Aplemsmediaat whwhich1985)therefof the6.3. Mechanistic models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.4. Empirical models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866.5. Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Case study with simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.4.2. Scale-up from laboratory data to industrial environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856. Grinding media wear models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.1. Linear wear theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.2. Nonlinear (general) wear theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.4.1. Wear rate criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Nomenclature

A surface area of grinding media in general, m2

Ab surface area of ball or sphere, m2

Ai abrasion index, Alball surface area of grinding ball in laboratory mill, m2

Arball surface area of grinding ball in industrial mill, m2

C cost of grinding media per unit mass, $/kgCL crop load, %Df nal diameter of grinding ball, mDi initial diameter of grinding ball, mD0 initial diameter of mill, mEabr,i energy dissipated owing to abrasion phenomenon i, JEimp,j energy dissipated owing to impact phenomenon j, Jk0 wear speed or wear constant, m3n s1

kEd energy specic wear rate constant, m J1 kg1

km mass wear rate constant, kg s1

kd linear wear rate constant, m s1

m mass of grinding media, kgmabr,i grinding media mass loss owing to abrasion mechanism

i, kgmcorr grinding media mass loss owing to corrosion, kg

78 C. Aldrich /Minerals Engroduction

inding circuit operators have long been aware of the signi-mpact of grinding media consumption on the cost of grinding.inution accounts for an estimated 3050% of typical miningting costs, and of these, liner wear and media consumptionnt for roughly 50% of the cost. According to Moema et al.), in some instances, media wear can constitute up to 40f the total cost of comminution. An estimated consumptionel grinding media of around 600,000 tons p.a. in the 1980s al-gives an indication of the scale of the problem (Malghan,. Likewise, in the cement industry, as mills are supplied forncreasing capacities, the ball size distribution and wear exactendous effect on the protability of producing nished ce-Improper size distribution or lling level of the ball chargeduce the efciency of grinding by 520%, amounting to lossesllions per annum for a mill with a capacity of 150 tons/hhurst, 2010).art from these cost factors, one of the major unsolved prob-in the optimal design of ball mills concerns the equilibriumsize distribution in the mill, which is determined by the rateich make-up media is added to the mill, as well as the rate atthese grinding media are consumed (Austin and Klimpel,

. Reliable prediction of grinding media consumption canore play an important role in the management and controlse costs, and the overall cost of mining operations.mimp,j grinding media mass loss owing to impact mechanism j,kg

Dm change in the mass of the grinding media, kgN rotational speed of mill, s1

Nc critical rotational speed of mill, s1

n wear rate exponent, R volumetric wear rate of grinding media, m3 s1

T mass of ore milled, kgt time, sv velocity, m s1

W mass loss of grinding media per unit surface area,kg m2

q density of grinding media in general, kg m3

qb density of steel ball, kg m3

XE grinding media consumption based on energy usage,kg J1

XM grinding media consumption based on amount of oreground, kg kg1

Xt grinding media consumption based on operating time,kg s1

ering 49 (2013) 7791The cost associated with grinding media is chiey determinedby two factors, viz. the price and wear performance of the grindingmedia. Different operating conditions can be compared with theeffective grinding cost or the cost-effectiveness of the application(Seplveda, 2004). This is a challenging task, since different operat-ing conditions in comminution circuits arising from changes in oretypes, operational procedures and the properties and size distribu-tions of the grinding media themselves all need to be accounted forwhen the cost of grinding media is calculated (Chenje et al., 2004;Lameck et al., 2006; Jayasundara et al., 2011).

The consumption of grinding media has been studied exten-sively in the mineral process industries, where steel balls and rodsare mostly used to reduce rock fragments and ore particles to thene sizes required for mineral liberation and further downstreamprocessing. Apart from a better understanding of the phenomenainvolved in the wear of grinding media, many of these studies werealso aimed at the development of models capable of predictingmedia consumption based on an understanding of the mechanismsinvolved in the process. In this paper, these studies are reviewed,starting with an overview of the properties of grinding media inSection 2, followed in Section 3 by consideration of the wear mech-anisms onmedia consumption. This is followed by characterizationof the grinding environment in Section 4, and measurement ofgrinding media consumption in Section 5. In Section 6, grindingmedia wear models are reviewed and in Section 7, a simulated casestudy is considered to illustrate the potential of alternative ap-

sista

gineering 49 (2013) 7791 79proaches to modelling wear losses in grinding media. The conclu-sions of the study are presented in Section 8.

2. Properties of grinding media

A wide range of materials is used to resist wear in comminutionprocesses (Durman, 1988; Moema et al., 2009). The abrasiveness ofthe material being processed is of prime importance in determin-ing the absolute wear rate of the grinding media, but conictingcharacteristics of high hardness for maximum wear resistanceand adequate ductility, to avoid catastrophic brittle failure in appli-cation, always has to be balanced cost effectively. A range of mate-rials has been developed for this purpose, which include abrasionresistant steels, non-metallics and alloyed white cast irons, as indi-cated in Fig. 1.

Of these materials, the manganese steels containing additionalalloying elements, such as Cr, Ni and Mo, are considered to be ofthe highest quality. The balls are typically hardened to 6065Rockwell C. The low alloy, low carbon steels are the least expensiveand recommended for rough grinding only, where metallic con-tamination is not a problem. The austenitic stainless steels are typ-ically only used in acid media requiring non-magnetic balls, owing

Fig. 1. Materials used in wear re

C. Aldrich /Minerals Ento their high cost.The NiCr cast irons or nickel-hards are white cast irons alloyed

with Ni and Cr. Two groups are used in grinding media, namelymedium alloyed nickel hards (Ni-hard 1 and 2) and high alloyednickel hards (Ni-hard 4). The last group, the high chromium cast ir-ons represent a wide range of characteristics, owing to their rangeof chemical compositions and heat treatability. Chromium carbidesare harder than iron carbides and therefore more wear resistant,and also play a major role in wear resistance in corrosive environ-ments. Some of these characteristics in grinding media are dis-cussed in more detail below.

2.1. Microstructure

Given the mechanisms of material loss in grinding media (abra-sive, impact and corrosive wear), it is clear that wear resistantmedia should generally be corrosion resistant and have superiormechanical properties. The suitability of specic properties, suchas hardness or toughness, depend on the milling environment.For example, steels with predominantly pearlitic structures pos-sess excellent impact toughness, but inferior hardness. This maymake them more suitable to milling conditions where high impactis required, such as when milling hard gold ores (Moema et al.,2009). As can be expected, the cost of the media, which is ulti-mately consumed in the comminution process, also plays a vitalrole, and in this respect selection again depends on the comminu-tion environment, as superior mechanical properties and corrosionresistance are usually associated with higher cost.

A lesser factor that does not seem to be widely considered in theselection of grinding media at present, is the effect of iron accumu-lating in the mineral slurries or ores, as a result of the consumptionof grinding media. This should be as low as possible, since iron canhave an adverse effect on downstream processing (otation), assuggested by a number of studies on non-sulphide (Kinal et al.,2009) awasakind sulphide ores (Martin et al., 1991; Thornton,1973; Pavlica and Iwasaki, 1982; Yuan et al., 1996).

For example, Chenje et al. (2003a,b, 2004) have conducted com-parative studies with different types of balls, consisting amongother of eutectoid steel, low alloy steel, medium chromium castiron, cast semi-steel and white cast iron. They have used the costeffectiveness (E) as a criterion for grinding media selection, i.e.

E C dmdT

1

where m is the mass of balls in the mill, T is the mass of ore milled

nt applications in comminution.and C is the cost of the grinding media per unit mass. Accounting forthe adverse effect that iron could have on downstream processingof the ores, the criterion proposed by Chenje et al. (2003a, 2004)could be extended to Eq. (2) to constrain the amount of iron re-leased into the ore system over a given period to some upper limit(UL).

E C dmdT

; subject to dmdT < UL 2

Chen et al. (2006) have investigated the consumption of high Cr(2630%) alloy balls in a phosphate mill. Mass loss of the balls in-creased linearly with grinding time or 0.00036 g/h or 247 MPY,1

with all other variables kept constant.Gundewar et al. (1990) have found that high chromium cast

iron had a signicantly higher wear resistance than forged EN 31steel, which in turn exhibited a higher wear resistance than casthypersteel during the wet grinding of Kudremukh iron ore in India.The high resistance of the chrome balls could be attributed to theresistance of the balls to corrosion (passivation), especially in thepresence of oxygen, as discussed before.

1 MPY calculated from MPY = 534Dm/(qbAbt), with density qb (g/cm3), ball surfacearea Ab (inch2), grinding time t (h) and mass loss Dm (mg).

Moroz (1984) has used marked ball wear tests in wet ores toexamine the effect of the microstructure of 0.90% C forged steelballs on their wear resistance. These balls were subjected to differ-ent heat treatment procedures (quenching, quenching and temper-ing, as well as normalization), together with quenched andtempered AISI 4140 steel balls. Wear resistance generally in-creased with the surface hardness of the balls, but carbon contentwas also found to be a key factor.

By grinding quartzite, Jang et al. (1988) and Chandrasekaranet al. (1991) have concluded that the hardness of the worn surfacesof grinding media cannot be used to predict their wear behaviour.Microstructures like pearlite, spheroidite, bainite and martensiteappeared to wear more when their hardness decreased. In contrast,microstructures containing martensite, retained austenite andundissolved carbides showed a minimum wear at a certain levelof austenite. In total, the differences in microstructures could leadto a change of up to 28% in mass losses in the grinding media.

vere conditions, as imposed by quartz in the ball mill test, lead toincreasing wear rates with an increase in the amount of carbides inthe matrix. This can be explained by rapid removal of the metallicmatrix followed by microcracking of the exposed carbides. In lesssevere conditions, such as when grinding hematite or phosphaterock, the carbides protect the metallic matrix from microcuts or -abrasions, and the wear rates decrease as the amount of carbidesincreases, up to the eutectic composition.

Other investigators have observed similar behaviour. For exam-ple, Gates et al. (2008) have used ball mill abrasion tests (BMAT) topredict the relative service lives of wear-resistant alloys for grind-ing media in mineral grinding environments. The results showedthat very hard (above 630 HV) martensitic steels and white cast ir-ons only offer large performance benets when grinding relativelysoft or weak abrasives (Mohs hardness less than about 6) and thatthis may alter the cost-benet balance in favour of simple low-coststeels when grinding hard strong minerals. However, even modestproportions of softer minerals in real ores could favour the use of

grinding media shape on comminution. Shi (2004) has considered

80 C. Aldrich /Minerals Engineering 49 (2013) 77912.2. Effect of carbides in the metal matrix

Albertin and Sinatora (2001) have considered the effect of car-bide volume fractions from 13% to 41% and matrix microstructureon the wear of 50 mm diameter cast iron balls tested in a labora-tory ball mill during wet grinding of hematite, phosphate rockand quartz sand. Martensitic, pearlitic and austenitic matriceswere evaluated. Quartz sand caused the highest wear rates, rang-ing from 6.5 to 8.6 lm/h for the martensitic balls, while the wearrates observed for the phosphate rock ranged from 1.4 to 2.9 lm/h. An increase in carbide volume fractions resulted in lower wearrates for the softer abrasives. The eutectic alloy performed bestagainst the hematite and phosphates, owing to the virtually com-plete protection of the matrix by carbides in the nely divided eu-tectic microstructures.

In contrast, the quartz abrasive rapidly wore out the matrix,continuously exposing and breaking carbide branches in the pro-cess. The martensitic steels performed best against the quartzabrasive. The wear rate of 30% carbide cast irons in contact withphosphate particulates increased from 1.46 to 2.84 and to6.39 lm/h as the matrix changed, respectively, from martensiteto austenite to pearlite. Wear proles of non-martensitic ballsshowed deep subsurface carbide cracking, owing to matrixdeformation.

The effect of the amount of carbides on the wear resistance ofhigh chromium cast irons depends on the severity of the tests. Se-Fig. 2. Impact, abrasion and corrosion wear mechanismsthe effect of tapered cylindrical media (cylpebs) on grinding andobserved that they produced marginally less oversize than steelballs with the same mass and size distribution.

Sinnott et al. (2011) have considered the importance of mediashape on grinding performance in stirred mills. In these mills,the grinding media and charge in a chamber are mobilized by arotating internal agitator. It is generally accepted that highlynon-spherical debris from balls which break or spall due to manu-facturing defects reduce ball mill grinding performance (Sinnottet al., 2011).

More recently, Qian et al. (2013) have investigated the effect ofgrinding media shapes on the grinding kinetics of cement clinkersin balls mills. The specic breakage rates of the clinkers were high-er when the cylinders were used, compared to balls.

3. Grinding wear mechanisms

Mass losses in grinding media can be attributed to three basicmechanisms, viz. abrasion, impact and corrosion. These mecha-nisms can be simultaneously active in a given grinding environ-more sophisticated hard alloys.

2.3. Media shape

Relatively little work has been done to determine the effect ofof grinding media (partly after Radziszewski (2002)).

on c

ence

g ang anon ()on (ajanon (

a anopha

ginee3.1. Abrasive wearment, leading to complex interactions, some which are discussedin more detail below.

Fig. 3. Corrosion models for grinding balls: (a) differential abrasi

Table 1Studies of mineral-grinding media in aqueous sulphide ore slurries.

Grinding media Mineral Refer

Mild steel, Cr-steel (1530%) Arsenopyrite HuanMild steel Pyrite HuanC-steel, Ni-hard cast iron, 22% and 29% Cr white cast iron Sphalerite Isaacs

(1989HCLAa, C-steel, Ni-hard cast iron, 22% and 29% Cr white

cast ironChalcopyrite Isaacs

NatarMild steel, high Cr, C-steel, Ni-hard cast iron, 22% and 29%

Cr white cast ironGalena Isaacs

Mild steel, HCLAa steel, austenitic stainless steels Pyrrhotite PavlicGang

a High carbon (1.7%), low alloy.C. Aldrich /Minerals EnIn mills operating at low cascading speeds, abrasive wear isconsidered to be the dominant wear mechanism (Hukki, 1954).In highly abrasive ores, approximately 12 kg of grinding mediacan be consumed per ton of ore milled (Moema et al., 2009). Inwet milling, this assumes proper pulp coverage of the ball surfaces,i.e. not too thick to cushion the impact between balls and not toodilute to result in insufcient coverage of ball surfaces and exces-sive ball wear. Iwasaki et al. (1988) have concluded that abrasivewear is strongly dependent on slurry rheology, which is in turngoverned by solids loading and viscosity modiers, if present. Inaddition to the effects associated with coating of the grinding med-ia with slurry, the slurry viscosity also affects the movement of thegrinding media in the mill and hence abrasion of the grinding med-ia (Klimpel, 1982, 1983).

Fig. 2 gives a summary of the mechanisms that can affect massloss in grinding media. 2-body abrasive wear assumes grit or hardparticles to remove material from opposite surfaces, while 3-bodywear occurs when the particles are not constrained, and are free toroll and slide down a surface. Likewise, the contact environmentdetermines whether the wear is classied as open or closed. Anopen contact environment occurs when the surfaces are suf-ciently displaced to be independent of one another.

3.2. Impact wear

Abrasive wear is generally less in harder grinding media, wherespalling owing to impact loading can be more pronounced instead.As a phenomenon, spalling has been studied intensively in otherdisciplines, but does not seem to have been covered in much detailin the context of grinding media wear. Essentially, when two ballscollide, the sudden release of energy causes compression waves topropagate through the balls radially from the points of contact.When the compression waves reach areas of acoustic impedancemismatch in the interior of the impacted body, tension waves re-ect back and create spalling at points where these waves exceedthe tensile strength of the material. Mass loss from grinding media

s

d Grano (2006) and Huang et al. (2006)d Grano (2005) and Peng and Grano (2010)1989), Yelloji Rao and Natarajan (1989b, 1990) and Vathsala and Natarajan

1989), Ahn and Gebhardt (1991), Yelloji Rao and Natarajan (1988, 1989a) and(1996)1989), Yelloji Rao and Natarajan (1990) and Peng et al. (2002)

d Iwasaki (1982), Natarajan et al. (1984), Natarajan and Iwasaki (1984) anddhyay and Moore (1985)ell and (b) ball-mineral galvanic cell (after Iwasaki et al. (1988)).

ring 49 (2013) 7791 81can also arise from other mechanical effects, as observed by severalauthors (Moore et al., 1988; Rao et al., 1991), for example, as indi-cated in Fig. 2.

Seplveda (2004) has done calculations on ball breakage basedon impact, showing that the speed (v) in metres per second atwhich a ball could be moving, can be estimated by

v 0:3894pNcD0:5mill 3

where Nc (rad/s) is the critical mill speed, and Dmill the mill diameter(m). In practice, the velocities of grinding media in tumbling millsare in the order of 10 m/s (Gates et al., 2007) and generally impactbreakage of media is more pronounced in larger mills.

3.3. Corrosive wear

Corrosive wear of steel grinding media is strongly associatedwith wet milling environments and has been studied by a numberof investigators by use of electrochemical measurements. Twomodels have been postulated, viz. one based on differential abrad-ing cells and one based on galvanic cells, as indicated in Fig. 3. Inthe differential abrading cell, the unabraded surfaces of the oresact as cathodes, where oxygen is reduced, while the freshlyabraded surfaces act as anodes, where iron is oxidized.

In the galvanic cell system, the mineral particles are cathodicand the steel grinding media anodic, again leading to acceleratedwear through oxidation of the iron in the media. A complicatingfactor in accounting for the effects in these galvanic cells is thatthe effects of galvanic interactions between sulphide mineralsand grinding media need to be considered in conjunction withthe galvanic interactions that can occur between sulphide miner-

estimate that approximately 50% or more of grinding media con-

82 C. Aldrich /Minerals Engineals, as discussed by Rao and Finch (1988), Cheng and Iwasaki(1992), Cheng et al. (1993, 1999), and Li and Iwasaki (1992).

Corrosive wear can be studied by comparison of grinding mediawear losses in wet grinding in corrosive environments with grind-ing in similar environments, where corrosion is suppressed. Sup-pression of corrosion can be accomplished based on dry grinding,grinding in organic liquids and wet grinding in nitrogen atmo-spheres. Of these, the latter is considered to give the best estimateof abrasive wear.

On this basis, the performance of grinding media with differentcompositions has been studied widely in different corrosive envi-ronments. Corrosive wear becomes particularly signicant in thepresence of ore with a high sulphide content in an oxygen-richenvironment, owing to galvanic coupling between the grindingmedia and the minerals. Broadly speaking, corrosion in mineralslurries can be differentiated based on the presence or absence ofsulphide ores, as indicated in Tables 1 and 2, which refer to sul-phide and non-sulphide slurries respectively.

In the sulphide slurries, grinding media with a high chromiumcontent tended to suffer signicantly less wear than their counter-parts containing less chromium. This can be ascribed to the well-known effect of passivation, where initial rapid corrosion of thesteel media leads to the formation of a protective chromium oxidelm tightly adhering to the steel surfaces.

For example, Vathsala (sic) and Natarajan (1989) have studiedthe galvanic interaction between steel balls and sphalerite that re-sulted in the anodic corrosion of the cast steel balls that becamemore severe in the presence of oxygen. Similar studies were con-ducted for pyrite, pyrrhotite and galena by Pavlica and Iwasaki(1982), Adam et al. (1984), and Learmont and Iwasaki (1984). Eventhough oxygen-rich sulphide environments can be seen as aggres-sive, general statements with regard to the effects of corrosion indifferent systems should be treated with care, as indicated by thecontradictory points of view with regard to the importance of cor-rosion in the consumption of grinding media in the literature(Rajagopal and Iwasaki, 1992b). Some researchers suggest that cor-rosion plays a major role in the consumption of grinding mediaduring wet grinding, with the contribution of corrosion to the totalconsumption of grinding media estimated to range from 10% to

Table 2Studies of mineral-grinding media in aqueous non-sulphide ore slurries.

Grinding media

Mild steel, HCLAa steel, austenitic stainless steelsHigh Cr cast Fe, EN31, cast hypersteelHCLAa cast and high Cr cast steel, 1018 C steel

High Cr, forged steelMild steel; HCLA steel; Cast iron balls (0%, 8.5%, 11%, 16%, 21%, 26% and 29% Cr)Low alloy, eutectoid, med Cr cast iron, unalloyed cast iron, cast semi-steelAISI 1020, HCLA, SS 304

a High carbon (1.7%), low alloy.90%.In contrast, other researchers suggest that corrosion is respon-

sible for only a small part of the total wear. For example, Tolleyet al. (1984) have investigated corrosion rates of alloys commonlyused in media in synthetic mill water using an ultrasonic grindingdevice especially designed for this work. The grinding media alloysconsisted of forged and cast steel (carbon content from 0.61% to0.79%, as well as so-called nickel hard and high chromium steels(discussed in more detail in Section 3). Electrochemical measure-ments showed variations in corrosion rates for these alloys be-tween 9.8 MPY2 for medium-carbon steels and 0.14 MPY for whiteirons. The authors concluded that based on Bureau data, along with

2 1 MPY = 0.0254 mm/y (SI units).sumption can be attributed to corrosion. They have found the solu-tion pH to have the most signicant effect on grinding mediaconsumption. For 1018 carbon steels, minimum wear was associ-ated with a grinding environment characterized by a solution pHof 7.36, rotation speed at 70.31 rpm, solids percentage at 75.50,and crop load (%total volume of grinding media, ore, and water rel-ative to volume of the mill) at 71.94%. For high chromium media,minimum wear was observed at a solution pH of 8.69, rotationspeed at 61.13 rpm, solid percentage at 64.86, and crop load at57.63%.

If anything, this underscores the complexity of corrosion phe-nomena in milling environments, as further illustrated by a US Bu-reau of Mines study. In this study, Isaacson (1989) has determinedthe effect of common sulphide minerals on various types of ferrousalloy grinding media. The minerals included chalcopyrite, galenaand sphalerite. In the presence of oxygen, chalcopyrite was foundto increase the corrosion rate through galvanic coupling, galenawas found to decrease the corrosion rate through an oxygen scav-enger mechanism, and the effect of sphalerite was dependent uponthe type of grinding media.

Many of the studies outlined above are difcult to compare sys-tematically, as the materials they refer to, although roughly simi-lar, are not the same and in many cases not described insufcient detail for comparative purposes. The same goes for theconditions in which these experiments were conducted. This isnot helpful as far as continuous process improvement and a betterunderstanding of wear mechanisms are concerned, as was also ob-served by Albertin and Sinatora (2001).

4. Characterizing the grinding environment

Changing conditions inside the mill that can have an effect ongrinding media consumption include pulp potential, dissolved oxy-data from the literature, corrosion causes less than 10% of the wearof grinding media in commercial mills.

This is in contrast with the observations of Lui and Hoey (1973),Hoey et al. (1977) and Tao and Parekh (2004), for example, who

Mineral References

Magnetite Natarajan and Iwasaki (1984)Hematite Gundewar et al. (1990)Phosphates Deshpande and Natarajan (1999), Tao and Parekh (2004)

and Tao et al. (2005)PGMs (low S) Miettunen et al. (in press)Quartz Pitt et al. (1988) and Rajagopal and Iwasaki (1992b)Granite Chenje et al. (2004)Taconite Iwasaki et al. (1985)

ering 49 (2013) 7791gen concentrations, pH, particle size and other, as discussed inmore detail below.

4.1. Pulp potential

During grinding with iron-based media or in iron mills, the pulppotential can change, the extent of which is naturally related to thetype of media used. For example, Leppinen et al. (1998) found, thatdepending on ore type, the potential difference (after milling) forcomplex sulphide ores between grinding in normal steel and stain-less steel mills was about 100250 mV, while Kelebek et al. (1995)have reported differences of 500600 mV for pyrrhotite-rich cop-per-nickel sulphide ores in the initial stages of grinding. In princi-ple, these changes could affect the corrosion rate of the grindingmedia, but little has been done to show this.

ginee4.2. Dissolved oxygen concentrations

Interaction between sulphide minerals and mild steel grindingmedia leads to a reduction in the amount of dissolved oxygen pres-ent in the pulp during the course of grinding (Martin et al., 1991).Reduction in oxygen level can also occur by other means and maybe strongly inuenced by ore type. Dissolved oxygen levels ofpulps following laboratory grinding with mild steel mill/mediahave been reported to be as low as 1 ppm (Kelebek, 1993), owingto corrosion of the grinding media and in conventional full-scaleiron mill discharge pulps, dissolved oxygen levels of less than0.1 ppm have been measured (Grano et al., 1994). This changesthe environment experienced by the grinding media and couldhave a signicant effect on mass loss attributable to corrosion.

4.3. Oxyhydroxide species

At regions of higher alkaline pulp pH, the iron can dissolve fromthe grinding media during milling as ferrous ions and subsequentlyoxidize to the ferric form (Bruckard et al., 2011). Ultimately it canprecipitate at the cathodic sulphide mineral sites as oxy-hydrox-ides species, such as Fe(OH)2, FeOOH, and Fe(OH)3. These ironhydroxides, which may be hydrophilic, can coat completely or par-tially the sulphide mineral surfaces, which can in turn affect theinteraction between the grinding media and the mineral speciesin the pulp.

4.4. Slurry viscosity and surface tension

Although the effect of slurry rheology has already been dis-cussed in general terms in Section 3.1, the mechanisms are stillnot well understood. Klimpel (1982, 1983) has drawn attentionto the importance of rheological properties in ball mill grindingon the specic rates of breakages of minerals in the presence andabsence of chemical additives. Meloy and Crabtree (1967) havestudied the effect of viscosity and surface tension of various liquidson grinding efciency. Abrasion of grinding media is further inu-enced by the coefcient of friction that depends on the type of me-tal (media material), the hardness and concentration of minerals inslurries and by solution properties such as viscosity and pH.

4.5. Mill feed rate

Mill feed rate is thought to inuence consumption of grindingmedia in that it inuences the wear mechanisms acting on themedia. At low feed rates, impact forces are considered to dominateover abrasion (Gates et al., 2007) and Howat and Vermeulen (1988)have observed that at low feed rates, when the residence time ofparticles within the mill is long, the consumption of grinding med-ia is high and the grind is ne.

4.6. Particle size

The effect of particle size on the wear rates of grinding media isnot yet fully understood. Chandrasekaran and Kishore (1993) haveshown that wear rates during dry sand-quartz grinding increaserelatively rapidly with mean particle size up to some critical size,beyond which the wear rate increases at a lower rate. They attrib-uted the observed behaviour to accumulation of ne particles onthe ball surface. Pintaude et al. (2001) have considered the effectof particle size on the abrasive wear of high-chromium white castiron mill balls. They have concluded that the ratio of steel ball toparticle size is the critical factor. The highest ball wear rates oc-

C. Aldrich /Minerals Encurred during grinding of ne granite under dry (120 mg/cycle)and wet (129 mg/cycle) conditions. The lowest wear rate (approx-imately 50 mg/cycle) was observed during the wet and dry grind-ing of coarse granite. In addition, they have observed that duringwet grinding of raw granite, the mineral constituents present inthe ground material may have a signicant inuence on the wearbehaviour of the media. For granite grinding, feldspar can act asa bonding agent, gluing ne quartz particles to the coarse graniteand to the surfaces of the balls. This can alter the wear behaviourof the media, resulting in a weaker correlation between relativesize of the particles and media consumption rates.

4.7. Rotational speed of the mill

Effect of speed variation on ball wear is confounded by severalcontradictory trends and factors. As an example, by use of highspeed photography, Kumar et al. (1989) have observed that at70 rpm in a 2D mill setup used to wet grind quartz, all the ballsin the mill interact with each other and with the ore through mu-tual sliding, rolling and colliding. At 86 rpm approximately 50% ofthe balls went out of circulation, reducing the probable number ofinteractions in one revolution of the mill, decreasing efciency, aswell as ball wear. In addition, as the speed increased from 50 to70 rpm, the ball distribution pattern in the mill and the numberof revolutions did not change substantially, but the coating thick-ness of the balls decreased. This increased the prospect of metal-to-metal contact and increased wear of the balls. Increasing thespeed from 70 to 86 rpm reduced the number of interactions perrevolution and led to an increase in the coating thickness of theballs. The net effect of this is was reduced wear.

Rajagopal and Iwasaki (1992b) have observed that an increasein the rotational speed of a mill resulted in an increase in the highchromium steel balls (austenitic stainless steel, 26% and 29% Crcast iron) materials exhibited low corrosion. However, increasingrotation speed, had a comparatively small effect on the corrosionrates of low Cr balls (containing less than 21% Cr), which wasmarkedly higher than those of the high Cr balls.

4.8. Solids and crop load of the mill

With regard to the effect of solids loading, Iwasaki (1985) hasused mild steel and high carbon low alloy (HCLA) steel balls towet grind a taconite ore and observed that ball wear decreasedas the solids loading and hence pulp density increased. This couldbe attributed to the pulp viscosity controlling the thickness of thepulp layer on the balls, thereby affecting grinding efciency andball wear.

In another study comprising pH, rotational speed of the mill,crop loading and solids concentration in the slurry, Chen et al.(2006) have proposed a multilinear regression model as a goodt for their experimental data. Of these variables, pH had the larg-est effect on wear rate, and the variables could be ranked as fol-lows: pH > rotational speed > solids loading > crop load.

4.9. pH

In sulphide minerals in particular, pH is a critical variable thatinuences the effect the galvanic interaction between grindingmedia and minerals (Peng, 2002), but this can also be the case inother minerals. For example, Chen et al. (2006) have observed a de-crease in wear rate of high Cr balls with increasing solution pH, in aphosphate mill, e.g. a wear rate of approximately 224 MPY atpH = 3.1, which was approximately twice the wear rate of115 MPY at pH = 10.0. Corrosion was observed to increase at lowpH values as a result of the increased availability of H+ for reduc-tion by the cathodic half-cell reaction (Davis, 2000).

ring 49 (2013) 7791 83These observations could be explained by the fact that no pas-sive lm was formed in a strong acidic solution and the chromiumalloy corroded by active dissolution and enhanced access of dis-

Likewise, Hebbar (2011) has studied the grinding wear behav-

point metal alloy. Upon recovery, the plug is melted and the ball

ineering 49 (2013) 77915.1. Dropped ball test (DBT)

The dropped ball test (DBT) was originally developed by the USBureau of Mines (Blickenderfer and Tylczak, 1983, 1985) and lateradapted by the international MolyCop Grinding Systems organi-zation to assess the resistance of any given sample or lot of ballsto repeated severe ball-to-ball impacts. The DBT facility consistsof a J-shaped tube, 10 m high.

The curved, bottom part of the tube is lled with a known num-ber of balls (e.g. 24, when testing 129 mm balls). When anotherball is dropped through the tube the top ball retained below inthe tube suffers the direct impact of the falling ball, which is rep-licated through the whole line of balls retained in the curve atthe bottom of the J-tube.

This also results in the removal of the rst ball in the linethrough the lower tip of the tube, which is replaced by the last balldropped. The balls removed from the tube are continuously liftedwith a bucket elevator back to the top of the tube to be droppeddown once again. The DBT is run until a certain maximum numberof balls are broken (say, ve balls) or a reasonable number of totalcycles have been completed (e.g. 20,000 drops).

5.2. Marked ball wear test (MBWT)

The marked ball wear test (MBWT) is a reliable approach tocompare the wear rates of different materials under identical con-5. Measurement methodology related to grinding mediaconsumption

In a recent review paper, Seplveda (2004) gave an overview ofthe test methodology for grinding media consumption, coveringthe dropped ball test, marked ball wear test and testing in indus-trial mills, as discussed in more detail below.iour of austempered ductile iron as media material in the commi-nution of Kudremukh haematite iron ore in a ball mill. The grindingexperiments were conducted under different pH conditions, i.e.pH = 7.0 and pH = 8.5, while keeping other parameters xed, at amill speed of 74 rpm for 1 hr. The ore samples were crushed tothe size of10 and +30 mesh size using the laboratory jaw crusher.The mill charge consisted of a set of 200 balls including 25 markedones. After each grinding experiment the 25 marked balls werewashed, dried and weighed. Similar grinding experiments werecarried using 200 forged EN 31 steel balls as media material. Thevolumetric wear rate (R) of the grinding media per revolution ofthe mill was calculated using following equation:

R DmNq

4

Hebbar (2011) concluded among other that the austemperedductile iron balls offered better wear resistance than the forgedEN 31 steel balls, and that the wear loss of the media was lowerin the slurry with higher pH values. Raghavendra et al. (2010) havereported similar ndings with austempered ductile iron balls com-pared to EN 31 steel balls.solved oxygen to the alloy, which further increased the corrosionrate. The formation of a passive lm in the presence of dissolvedoxygen at a pH > 10 slowed down the rate of corrosionsignicantly.

84 C. Aldrich /Minerals Engditions. Different approaches can be used to identify grinding med-ia. One of these is to drill a hole in each ball to me identied, put anidentication tag in the hole and seal it up with some low meltingidentied.Another approach is to use different congurations of holes

(number of holes, hole diameters and orientations) in each. Thishas to be done with care, so as not to change the microstructureand mechanical properties of the balls as a result of localized heat-ing during drilling.

Regardless of the method used to identify the balls, they are allweighed individually before placing them into an operating mill.With periodic recovery of the balls, for example when the mill isdown for scheduled maintenance, they can be retrieved, identiedand weighed to determine the rate of mass loss.

5.3. Other laboratory tests

Although the MBWT and DBT have found wide acceptance asstandard tests of the performance of grinding media, other testapparatus have also been proposed, of which one such is discussedhere. Fiset et al. (1998) have proposed a three-body laboratory im-pact-abrasion pin test. In this test, samples were subject to impac-tion and rotation in a cup containing the abrasive (ore), underconditions that closely simulated the forces inside a mill. The re-sults correlated well with those obtained by a marked ball weartest, at a signicantly lower cost. Other such tribological systemsare reviewed by Spero et al. (1991), many of which were developedfor the coal industry. Pons et al. (2004) have made use of multivar-iate image analysis to compare the degree of abrasion of grindingmedia, but it is not clear how these data should be interpreted.

5.4. Tests in industrial mills

5.4.1. Wear rate criteriaIn laboratory experiments, media wear is typically determined

by measuring the mass of the media before and after sequentialgrinding experiments (Hebbar, 2011), but wear rates of breakageconstants according to Eqs. (7), (8) are not commonly used inindustry to analyze results. Instead, the following consumptionindicators are used (Seplveda, 2004; Seplveda et al., 2006):

Consumption based on energy consumed, XE (g/kW h). Consumption based on operating time, Xt (g/h). Consumption based on amount of ore ground, XM (g/ton).

The last indicator (XM) is used most commonly, but is also theleast reliable (Seplveda, 2004), since it does not account for theenergy required to grind the ore.

On industrial plants, advantage can be taken of parallel lines ofmills, as reported by Banisi and Farzaneh (2004) for example,where they have made use of four identical parallel lines at the Sar-cheshmeh copper mine to test three different ball charges and onecombined charge simultaneously.

Plant trials can be based on sequential, concurrent or cross-ref-erenced evaluation. In sequential evaluation, historical rates ofconsumption in the same mill are compared before and after purg-ing.3 In concurrent evaluation, two or more mills are operated inparallel over exactly the same time interval, once purging has beencompleted. During cross-reference evaluation, the difference in con-sumption rate of mill 1 is subtracted from the difference in con-sumption rate of mill 2, and this is normalized with respect to thewear constant of the rst mill (discussed in more detail in the nextsection), e.g.3 Lapse of time required for complete consumption of media A before beginning oftest with media B, or time required for complete consumption of rst new ballcharged at beginning of test with media B, whichever takes the longest.

dD 2k =q k 7

gineedt m b d

In Eq. (7), D (m) is the diameter of the ball, qb (kg m3) is thedensity of the ball and kd (m/s) is the linear wear constant. Assum-kEd

mill1;before kEd

mill1;after

kEd

mill2;before

kEdmill2;after

kEd

mill1;before

5

5.4.2. Scale-up from laboratory data to industrial environmentsData obtained from laboratory studies are not directly applica-

ble to industrial systems. One obvious reason is that impact ener-gies in laboratory mills are negligible compared to those inindustrial mills. For example, Dodd et al. (1985) have estimatedthat an increase in ball kinetic energy from 1.4 J for a 0.025 m ballin a 0.20 m ball mill to 350 J for a 0.127 m ball in an 8.5 m ball mill.

A studybyAlbright andDunn (1983) have conducted a study thatyielded wear rate data for 22 different alloys (including pearlitic,martensitic and bainitic steels and white cast irons) in contact withmolybdenite orewith gangue comprisingquartz, granite and a smallproportionofMoS2) in two2.9 mdiameterballmills. The same22al-loyswere subjected to a pin-on-plate version of the pin abrasion test(PAT). Some signicant differences were seen between themill trialresults and thePAT results,which indicate some fundamental differ-encesbetween the laboratory test and the industrial serviceenviron-ment. Similar relatively disappointing service performance of whitecast irons has been reported inmany anecdotal accounts ofmineralsindustry experience (Gates et al., 2007). In fact, this disappointingperformance of white irons in the plant compared to predictions oflaboratory tests became the dening characteristic underlyinghypotheses of impact-abrasion wear mechanisms.

Spero et al. (1991) highlighted the need for improved correla-tion between laboratory test results and productionmill wear ratesbased on a more fundamental understanding of the wear processesinvolved was identied. They have cited several examples givingreasonable indications that wear rates in full-scale mills can be ob-tained empirically from the many results of laboratory test meth-ods (based on some moderate correlation rates ofR2 = approximately 60%). They have concluded that further workis required to obtain more reliable simulation of the wear condi-tions in production mills, and to set the limits of predictability ofthree-body laboratory wear tests. In addition, they have identiedscope for further work based on the application of statistical distri-butions such as the log-normaI, Gaussian, and Weibull functions tocharacterize wear rates.

6. Grinding media wear models

6.1. Linear wear theory

The linear wear theory originally developed by Prentice (1943)and Norquest and Miller (1950) to characterize the slow sustainedconsumption of grinding bosies in rotating mills is the most widelyaccepted approach in current use (Seplveda, 2004). According tothis theory, the rate of mass loss of a body being ground in a millis directly proportional to its exposed surface area, i.e.

dmdt

kmAb 6In Eq. (6), m (kg) is the mass of the body at time t (s), while km

(kg s1 m2) is the mass wear rate constant and Ab (m2) is the sur-face area of the body exposed to wear.

If the geometry of the body (assumed to be a sphere) is takeninto account, then

C. Aldrich /Minerals Ening kd to be time invariant, integration of Eq. (7) gives

D D0 kdt 8This means that the kinetics is linear and that kd is not depen-dent on the ball diameter at any given time, i.e. a ball will lose1 mm of its diameter over a given period, regardless of whetherit is large or small. The mill is therefore continuously or at leastat regular intervals recharged with monosized media of diameterD0.

6.2. Nonlinear (general) wear theory

When the assumptions of linear wear theory do not hold, thekinetics become more complex, but can still be accounted for withappropriate models (Seplveda, 2004). For spherical media, themass wear rate can be generalized as follows:

dmdt

kqpD2DD 9

where k is again a linear wear rate constant. If D = 0, the wear lawreduces to the linear model, i.e. mass loss is proportional to the ex-posed surface area of the sphere and the rate of decrease of the ballradius (dD/dt) is constant. This is known as Bonds wear law (Bond,1943). If D = 1, the rate of mass loss is proportional to the volume ofthe sphere, which is known as Daviss wear law (Davis, 1919). Inmost tests, Bonds wear law is observed (linear wear theory).

An alternative (simpler) form of the above wear law for steelballs was given by other authors (Lorenzetti et al., 1977; Meulen-dyke and Purdue, 1989; Moroz and Goller, 1986). In these papers,they present the basic wear law as

dmdt

kDn 10

In Eq. (10), m is the mass of the ball, t is time, D is the diameterof the grinding ball, k is a proportionality constant and n is anexponential constant, that is the wear rate of the ball is propor-tional to the ball diameter. Different exponential constants rangingfrom 2 to 3 have been proposed by different authors (Davis, 1919;Norquest and Miller, 1950; Bond, 1943; Austin and Klimpel, 1985;Vermeulen and Howat, 1986; Azzaroni, 1987), depending on therelative importance of surface dependent abrasion and corrosion(n = 2) or volume (mass) dependent impact forces (n = 3).

The solution of Eq. (10) gives (Meulendyke and Purdue, 1989)

k0 D3ni D3nft3 n 11

where k0 (m3n s1) is the wear constant or wear speed, t (s) is thegrinding time, Di and Df (m) are the initial and nal grinding balldiameters and n is the wear rate exponent. Vermeulen and Howat(1986) postulated the theory of combined wear, where the wearrate constant may vary during the course of grinding, dependingon the prevalence of abrasion or impact phenomena and changesin the grinding environment. For example, as the mill diameterand charge diameter increases and the mill volume decreases, theintensity of impact forces will be larger than that of abrasive forces(Azzaroni, 1987). Corrosion may also play a part in the apparenttime variance of the exponent.

Yildirim and Austin (1998) have extended Eq. (9) to the con-sumption of cylinders, the geometry of which is specied by twoparameters (length and radius). This yielded a radial and axial wearmodel, the details of which is beyond the scope of this document.

6.3. Mechanistic models

More recent attempts have been made to construct models

ring 49 (2013) 7791 85based on an understanding of the mechanistic principles of wearof the grinding media. Radziszewski (2002) have proposed asemi-empirical total media wear model on the assumption that

the effect of each wear mechanism can be determined indepen-

they depend on other variables that may change during the grind-

of the mill, such as the mill load or power consumption. According

86 C. Aldrich /Minerals Enginedently to give an additive model of the form

dmdt

X3i1

dmidt

12

Eq. (12) has three terms to account for abrasion, impact and cor-rosion, as presented in an expanded form in Eq. (13).

dmdt

Xnabri1

dmabr;idt

Eabr;i dmcorrAlballdt Arball Xnimpj1

dmimp;jdt

Eimp;j 13

The abrasion and impact terms make provision for differentphenomena and are expressed as functions of the abrasion and im-pact energies (Eabr;i; Eimp;j) associated with the specic phenomena.However, the parameters of the model have to be determinedexperimentally, which may not be feasible in practice. Moreover,the assumption of additivity of the different mechanisms maynot hold, as abrasion and corrosion may work together to enhancegrinding media consumption. Radziszewski (1997) has proposed amathematical model describing ball mill wear as a function of milloperating variables. The wear model incorporated the energy dissi-pated in crushing, tumbling and grinding zones of the charge pro-le with adhesive and abrasive wear descriptions.

Radziszewski (2000) has given and overview of abrasive andcorrosive wear mechanisms and has proposed an experimentalprocedure to facilitate prediction of the effect of changes in chargemedia composition. In addition, he has presented experimental re-sults for four cases and used these to predict changes in mediawear.

He has used a simple rule-of-thumb procedure based on theobservations that (i) in laboratory tests, corrosion can representanywhere from 25% to 75% of metal loss depending on the oreme-tal-environmental factors involved (Rajagopal and Iwasaki,1992a,b), while (ii) corrosion represents less than 10% of total me-tal loss in typical large diameter balls mills.

Radziszewski (2000) further assumed that regarding the batchmill corrosion test procedures: (i) the stainless steel mill has a neg-ligible effect on real corrosion wear rates, (ii) no constant temper-ature, (iii) no air circulation in the test mill, (iv) lack of control ofthe grain size of the slurry has a negligible effect on real corrosionwear rates, and (v) similar charge volume/geometry exists be-tween test mills and real mills. Based on these observations andassumptions, he has used a few simple rules to predict grindingmedia wear.

6.4. Empirical models

One of the earliest models was that of Bond (1943), who pro-posed a specic consumption rate for balls XE (kg/kW h) in wetmills of

XE 0:16Ai 0:0151:3 14and for dry balls

XE 0:023Ai0:5 15where Ai is an abrasion index that depends on the ball material,which could range from Ai = 0.016 for dolomite to Ai = 0.891 foralumina.

More recently, Kor et al. (2010) have developed a fuzzy logicmodel4 to predict the wear rate of a high chromium alloy. The model

4 Fuzzy systems essentially consist of compact sets of fuzzy IF-THEN rules and a

mechanism to interpret these rules (e.g. IF the Cr content of the steel ball is high, andmilling is dry, THEN consumption is low, with some means to interpret or quantify thelabels high, dry and low).to the theorem of Takens, these variables could be unfolded in astate or phase space to account for the behaviour of unseen statevariables, which could potentially be used as predictor variablesfor grinding media consumption.

Grinding wear models may also benet from better instrumen-tation, including online analyzers of iron in the ore slurry thatcould potentially give an indication of the corrosive wear of theing process.Since these models are primarily used in the selection of grind-

ing media, it also implies that models have to be used under thesame conditions for which they had been calibrated. It wouldclearly be futile to attempt prediction of wear losses in the mediain a wet mill, based on a model calibrated under dry mill condi-tions. However, even if the same nominal systems are observed,the variation in the ore and internal conditions in the mill may stillbe affect the reliability of the models.

In principle, this can be accounted for by including additionalvariables in the model, as was done by Chen et al. (2006) for a lab-oratory system. In practice it may be more difcult to measurevariables representative of the environment of grinding mediaand very little work has been done in this context. For example,conditions in the mill should be embedded in other state variablescould explain 96% of the variance in the mass loss of the alloy as afunction of solution pH, solids loading, crop load and rotationalspeed of the mill, whereas a linear model could explain only 80%.

Although the modelling methodology is sound, in this particularcase it is not clear whether the model would be able to generalizewell, as it consisted of 25 IF-THEN rules tted to 29 measurementsobtained from a study by Chen et al. (2006).

6.5. Numerical simulation

Ashrazadeh and Ashrazadeh (2012) have used numerical(discrete element) simulation to predict the wear caused by solidparticle impact. More specically, the discrete element method(DEM) was used to simulate the behaviour of a jet of particles thatexit a nozzle and hit a at plate for various impact angles, particlevelocities and particle concentrations. The main idea was to evalu-ate DEM as a reliable method for predicting wear rate and erosionmechanism in problems associated with solid particle interactions.Comparing the simulation results with reported experimental data,it was conrmed that there is a correlation between shear impactenergy and the wear rate. In future this may become a useful ap-proach to predicting the performance of grinding media.

7. Case study with simulated data

Although the basic phenomena underlying the wear mecha-nisms of these media, viz. impact, abrasion and corrosion, havebeen studied extensively, the interaction between grinding mediaand ore particles or mineral slurries is too complex to generally al-low modelling from rst principles that can account explicitly forthese phenomena.

As a consequence, in practice, predictive wear models for grind-ing media (mostly steel balls) are empirical in nature and dependon grinding media mass loss data to parameterize. These modelsgenerally predict wear from a single variable, typically the diame-ter or surface area of the grinding media (usually assumed to bespherical), i.e. dmdt kD

n. In effect the model parameters (k and n)are assumed to be constant, but this is not generally the case, as

ering 49 (2013) 7791media in ore systems. This could also inferential models basedon wear of other components, such as special coupons with mate-rial properties similar to the media placed in the mill, the state of

gineeC. Aldrich /Minerals Enwhich could be easier to monitor online. These ideas are diagram-matically portrayed in Fig. 4.

In this gure, modelling can be quantitative or qualitative. Thequantitative models are expressed as simple deterministic modelswear the mass loss rate of grinding media depend on the dimen-sions (ball diameter) of the media only. This assumes constantcomminution conditions that are represented by the two parame-ters, k and n, of the model. This linear model that is widely used in

Fig. 4. Grinding med

Fig. 5. Prediction of wear wit

Fig. 6. Variable importance analysiring 49 (2013) 7791 87industry, can be generalized to include additional variables x1,x2, . . . ,xm. The functional relationship can be determined explicitly,e.g. by multiple linear regression, or otherwise, e.g. by means offuzzy models, neural networks, etc.

Qualitative modelling is also possible, especially where corro-sion could be an important factor in media losses. For example,in this instance, knowledge-based systems (expert systems, case-based reasoning, etc.) could be used to capture some of the knowl-

ia wear models.

h neural network model.

s with neural network model.

edge with regards to the effect of different ores on corrosive wearof the grinding media.

To illustrate these points, the data of Chen et al. (2006) wereused to simulate the specic mass loss of grinding media (W, g/m2) as a function of time t, (h), pH, rotational speed of the millRS, (rpm), mill crop load CL (%) and solids concentration SC (%).150 data points of the form [t, pH, RS, CL, SC, W] were simulatedand a multilayer perceptron with a single sigmoidal hidden layerwas trained with the LevenbergMarquardt algorithm to t thedata. Fivefold cross-validation was used to ensure that the modelcould generalize on data not used during training. The model couldexplain 86.4% of the variance of the data, as indicated in Fig. 5.

By permuting the variables one at a time in the model, theimportance of each variable on the response (specic mass lossof the media) could be determined, as explained in more detailby Auret and Aldrich (2011, 2012). The results of this variableimportance analysis are shown graphically in Fig. 6. By comparingthe results with those of a random variable, the signicance of the

variables could be determined as well. As indicated in Fig. 6, timeplayed the most important role in the consumption of the media,while pH was less important, but also signicant. The other vari-ables had a negligible impact on the response variable.

In addition, partial dependence analysis (Auret and Aldrich,2011, 2012) could be used to assess the inuence of each variableon the response. This inuence could depend on the values of theother variables in the model, and could potentially be positive ornegative. The effect of time is indicated in Fig. 7. Note that all vari-ables were scaled to the range [1;1]. As expected, time had amonotonously increasing effect of mass loss, i.e. more mass waslost the longer the media were used. Owing to the effect of theother variables in this case, the relationship was not linear overthe entire duration of mill operation.

The problem could also be treated as a classication problem,by discretising the response variable into Low (W 6 3.9 g/m2),Med (3.9 8.7 g/m2) values. In thiscase, for illustrative purposes, a classication tree was tted to the

Fig. 7. Relationship between wear and time.

88 C. Aldrich /Minerals Engineering 49 (2013) 7791Fig. 8. Structure of a classication tree tted to the wear loss data.

egre

gineedata, recast as 300 samples of the form [t, pH, RS, CL, SC|CLAS-S = {Low, Medium, High}]. The Gini information criterion wasused to recursively split the variable space based on an exhaustiveunivariate search, class probabilities estimated from the data andequal misclassication costs. This yielded a tree model with 7 ter-minal nodes as shown in Fig. 8.

The tree could predict the correct class 88.7% of the time. Theseven terminal nodes are equivalent to seven IF-THEN rules, viz.

IF t 6 1.26 THEN Class = LowIF t > 1.26 AND t 6 1.73 AND pH 6 6.9 THEN Class = MedIF t > 1.73 AND t 6 2.88 AND pH 6 6.9 THEN Class = HighIF t > 1.26 AND t 6 2.88 AND pH > 6.9 THEN Class = MedIF t > 2.88 AND pH 6 8 THEN Class = HighIF t > 2.88 AND pH > 8 AND RS 6 65 THEN Class = MedIF t > 2.88 AND pH > 8 AND RS > 65 THEN Class = High

The response surface (variables t and pH only) of the classica-tion tree is a coarser approximation of that of the regression modelderived with the neural network, as shown in Fig. 9. Even coarserapproximations are possible when the predictor variables are alsodiscretized. Rules such as these could be used in conjunction withan inference engine as part of an expert system. It would also bepossible to fuzzify the rules to form the basis of a fuzzy rule-based

Scaled Time

Sca

led

pH

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

7f2

4

6

8

10

12

Fig. 9. Response surface generated by the neural network r

C. Aldrich /Minerals Ensystem or alternatively, fuzzy rules could be derived directly fromthe data, as was done by Kor et al. (2010) in this case. Such modelscould be used as expert systems to guide the selection of grindingmedia for different grinding systems, or at least in principle, toguide the addition of grinding media to the mill.

8. Conclusions

The consumption of grinding media plays an important role inthe economics of grinding and as a consequence also in the overallprocessing of a large variety of ores. Although the effects of individ-ual variables on the mass loss of grinding media may be wellunderstood in principle, the large number of variables and theirinteraction, coupled with the difculty in directly observing thesevariables, makes quantitative estimates of the wear of grindingmedia a formidable challenge. Despite steady progress over severaldecades of research, a number of areas could still benet consider-ably from further investigation. These include the following:

Characterization of the grinding environment is difcult, andlittle progress has been made to date to systematically identify-ing potential state variables that could be used to represent theeffect of the environment on the consumption of grindingmedia, e.g. pH or electrochemical noise in corrosive slurry sys-tems, mill load or power consumption, etc.

Direct or inferential measurement of the variables representingthe interior of mills also remains to be further investigated.When steel media are used, it could possibly include onlinemeasurement of the iron in the mill product, or measurementof particle size distributions in the feed and mill product byuse of machine vision systems.

Scale-up from laboratory test data to industrial systemsremains an issue, as some of the wear mechanisms change fun-damentally during scale-up, although studies in large labora-tory ball mills are probably a good compromise.

A number of studies relating the properties of media to theirwear resistance in different systems have been done, but thesehave been mostly system specic and more work can be done todevelop models of a more generic nature, even if these are qual-itative only. Generally, studies on the relationship between thegrinding media composition and microstructures are difcult tocompare.

Linear models are well-established and reliable, but have lim-ited application, as they require grinding conditions to be sim-ilar to those they had been calibrated on. As was indicated inthis paper, in principle at least, it would be possible to construct

ssion model (left) and the classication tree model (right).ring 49 (2013) 7791 89more general models with wider applicability by using a fewadditional measurements currently available on many grindingcircuits.

Acknowledgement

Donhads support of this study is gratefully acknowledged.

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