Review of test methods for abrasive wear in ore grinding

Wear,

146 (1991)

389-408

389

Review of test methods for abrasive wear in ore grinding C. Spero’, D. J. Hargreavesb, R. K. KirkcaIdieb and H. J. FlitP “Queensland Electricity Commission, Chemical Technology Section, Paringa Murarrie, Queensland 4172 [Australia) bQueensland University of Technology, GPO Box 2434, Brisbane, Queensland [Australia)

Road, 4001

(Received November 7, 1990; revised and accepted January 9, 1991)

Abstract Maintenance costs associated with wear in coal grinding mills operating in Queensland pulverised coal-fired power stations are in excess of $lOm per year. In other fuel-ore and mineral-ore processing industries metal wastage through wear and corrosion is also a major component of maintenance cost. The aim of this paper is (1) to define the relevant terminology applicable to abrasive wear and wet-grinding, and (2) to review the more commonly used test methods for examining wear associated with ore grinding. The test methods considered simulate open three-body abrasive wear and were compared in terms of their tribo-mechanical characteristics, general wear theory concepts such as wear coefficient and wear susceptibility, and the correlation of wear rate with pilot-scale and full-scale mill wear rates. The paper also reviews the application of statistical distributions as a means of interpreting wear rate data from laboratory test mills and production mills. A need for improved correlation between laboratory test results and production mill wear rates based on a more fundamental understanding of the wear processes involved was identified. This review outlines a basis for detailed work leading to this end.

1. Introduction Several studies [l-5] have indicated that abrasion and corrosion in the coal and mineral processing industries are areas for research priority owing to their significant impact on metal wastage and maintenance costs. The present authors have estimated that maintenance costs associated with mill grinding parts in Queensland (Australia) pulverised coal-fired power stations are in excess of $1 Om per annum. There are signifkant incentives therefore to reduce wear rates and maintenance costs in ore-grinding operations on the basis of a more fundamental understanding of the processes involved and through the selection and development of cost-effective wear-resistant materials. The aim of this paper is two-fold: to define the terminology applicable to wet-ore grinding and the mechanistic processes involved, and to review the methodology and validation of test methods for examining ore grinding, elucidating the mechanisms involved, and predicting full-scale mill wear rates. 0043-1648/91/$3.50

0 Elsevier Sequoia/Printed in The Netherlands

390

Ore grinding can be broadly subdivided into two general types on the basis of differences in the physical properties of the ores and differences in the grinding process involved [5, 61. (i) Mineral ores, involving grinding of mineral slurries in low-speed tubeball mills where water is added to a pre-sized feed at levels normally exceeding 50%. (ii) Fuel ores, involving the grinding of coal and peat where moisture is present as an impurity at levels ranging from a few percent to 20% in bituminous (higher rank) coals, 20%60% in sub-bituminous, lignite and brown coals (lower rank coals), and greater than 60% in peat. A review of mill types applicable in each case is given by Sligar [2 ] and Hiorns and Parish [ 7 1. In the case of mineral ores, the addition of water to produce slurries whilst yielding significant improvements in grinding efficiency and mill capacity, generally results in significant increases in grinding element wear rate [6, 8, 91. In coal and peat mills, several investigators [2, 5, 7, 10, 111 suggest that increasing moisture content in a given fuel ore also results in increased grinding element wear rate. The only quantitative data reported in the case of fuel ores, however, is that concerned with brown coal milling in beater mills given by Coldham [ 111. Several possible mechanisms are ascribed to mill wear behaviour in chemically active environments. These relate to: (i) the conjoint and synergistic action of abrasion and corrosion, traditionally referred to as abrasive-corrosive wear [ 12-161; (ii) surface-adsorption (Rebinder) effects of the chemical environment on the physico-mechanical properties of both the ore [ 17, 181 and wear surface [19-211; and (iii) the effect of the chemical environment on bulk properties of the ore such as slurry rheology [ 141, particle cohesion and inter-granular friction [22, 231. Collectively, these mechanistic effects are referred to as physico-chemical effects, and of these only abrasion-corrosion has received any detailed attention in the literature [ 1, 241. The literature review presented here considers bench-scale testing used to model open, three-body, high-stress wear conditions, i.e. ore-grinding processes. In most cases, however, these test methods have not been standardised, the wear mechanisms and related physico-chemical effects involved are poorly understood, and the correlation of these tests with full-scale mill wear is not well established.

2. Definitions

and terminology

2.1. General

When discussing abrasive wear it is usual to refer to either two- or three-body abrasion [25, 261. Two-body abrasive wear results when a rough

391 Two-body

Abrasive

wear -

closed Three-

body

Goug? ng High

Open

1Low

stress stress

Fig. 1. Classiflcationof abrasive wear types [27-301. surface or fixed abrasive particles slide across another to remove material. According to Misra and Finnie f34] “two-body abrasive wear is similar to

small angle erosion where material is mostly removed by a Mets-cuing process”. In three-body abrasive wear, particles are loose and mobile during their interaction with the wearing surfaces. In this case, Misra and F’innie [34] report that “three-body abrasion is similar to large angle erosion where more material deformation takes place”. Three-body abrasion can be further divided into “open” and “closed” three-body abrasion (Fig. 1). Closed three-body abrasive wear occurs when loose abrasive particles are trapped between two sliding or rolling surfaces which are close to one another [27, 281. An example of this form of abrasion is that which occurs when solid particles intrude into bearings. Open threebody abrasive wear occurs when the two surfaces are far apart or when only one surface is involved in the wear process [26]. Open three-body abrasive wear normally involves one or more of the following forms. (i) Gouging, involving a combination of abrasion and impact forces f29-321. (ii) High-stress abrasion or abr~ive-~~d~g involving the removal of relatively fine particles (having diameters of tens of microns) from the wearing surfaces, is commonly associated with operations involving breakage (comminution) of the abrasive particles 11, 24, 261. (iii) Low-stress abrasion involving either a low impact angle of the abrasive onto the wear surface (scratching abrasion) [ 7, 331 or a high angle of incidence of the abrasive onto the wear surface (erosion) 1341. 2.2. Corrosive wear processes The general term “corrosive wear” is defined in ASTM G40-88 [35] as “wear in which chemical or electrochemical reaction with the environment is significant”. As noted by Dorinson and Ludema [36], however, when chemical reaction processes occur during abrasion, a distinction between the purely chemical and the tribo-chemical aspects of the chemical reaction is necessary. In the purely chemical case, the material of the wearing surface is capable of direct reaction with the en~onment under the prevailing ambient conditions. For tribo-chemical action, the surface must be activated by rubbing for reaction to occur.

392

The mechanisms relating to abrasion-corrosion, i.e. surface adsorption effects and bulk property effects including intergranular friction and particle cohesion, are only significant during the abrasion process. These effects can therefore be regarded essentially as tribo-chemical in nature.

3. General

concepts

The most widely accepted quantitative description of abrasive wear is the constant wear rate model, eqn. (l), in which the volume wear rate (volume wear per unit of sliding distance, dV/ds) is unaffected by progressive change in the apparent area of contact. Dorinson and Ludema [36] derived the constant wear rate model from a purely geometric analysis of asperity, or third-body encounter, by the application of the plastic deformation postulate A =F/H,, where A is the real area of contact, F the fixed load and H, the yield pressure or hardness of the wear surface. Archard [37] earlier derived an equivalent expression from a physical analysis of sliding wear, given by V= F

S

(1)

where k is the dimensionless wear coefficient, which is affected by the modulus of elasticity and microstructure of the wear surface as well as the size and hardness of the abrasive particles [ 271. A more detailed application of the plastic deformation postulate is described by Hailing [38], who gives a rigorous description of k on the basis of assumptions about the statistical distribution of asperity heights, or thirdbody size, and the stress-strain characteristics of the material. Another useful approach is that described by Blickensderfer [ 391, in which the two concepts of wear intensity, and wear susceptibility are described. Wear intensity w is the instantaneous potential to produce wear at a given point on a wear surface by a counter-body such that w=gY,

(21

where g represents the wear parameters of the counter-body, and p is the applied pressure at the point of wear. The wear parameter g is dependent upon the properties of the counter-body, and upon environmental factors such as temperature, moisture content and pH. The tendency for a material to wear at the wear surface is referred to as the wear susceptibility B, and is defined as the volume of material removed per unit of energy applied E

Wear susceptibility is dependent upon the physico-mechanical properties of the material as well as environmental factors. The reciprocal of wear susceptibility is referred to as wear resistivity.

393

Blickensderfer [39] reported that when a material with a susceptibility to wear of B is exposed to a wear intensity w, the total wear volume is obtained by the integral V=(jBw

dA ds=jJBgp

dA ds

(4)

which can be simplified to the Archard wear equation given in eqn. (1). The basic wear equations and wear concepts outlined above provide a basis for: (i) design and comparison of laboratory wear tests; (ii) interpretation of field wear data; and (iii) correlation of laboratory and field wear test results.

4. Test methods 4.1. Comparison of wear characteristics A number of wear tests have been used to evaluate the abrasiveness and abrasive-corrosiveness of ores and/or the wear resistance of ferrous alloys in three-body high-stress grinding applications. A general summary of these tests is given in Table 1. For comparison, the characteristics of a fullscale Babcock 1OElO ring-ball mill is also presented. An historical overview of the development and application of these test methods is reported by Sligar [2] and Raask [5] in the case of fuel ores, and by Lowrison [6] and Jones [49] for mineral ores. Wear tests utilising predominantly an attrition grinding mechanism [8] include the YGP [Z, 24, 40-421, GE-hammer mill [2], tribotester [22] and BCURA-roll mill abrasion tests [ 7, 441. The grinding action in each case is characterised principally by rolling and sliding of particles over other particles and wear surfaces, and to a lesser extent the compression and shear of particles between wear surfaces. In each case the wear coefficient k estimated for a typical set of conditions using eqn. (1) is less than 100 E-06, and the wear susceptibility B, from eqn. (3), is less than 0.5 mm3 W-l. The marked-ball [12, 46, 471, jaw crusher [43, 631, rotating electrode [ 15, 161 and dry-sand rubber wheel [ 48, 631 abrasion tests have significantly higher values of wear coefficient (Ic> 1000 E-06), and correspondingly higher wear susceptibly values (B> 1 mm3 W-l). In these tests the crushing loads are applied over much smaller areas of contact than in the previous examples, and involve predominantly compression, shear and impact forces, and attrition less so. The remaining tests described in Table 1, namely the Babcock radiochemical [ 2,451 and loaded column [ 341 wear tests, exhibit wear characteristics intermediate between the extremes of the other categories of test just described. In this case, estimated k: values range between 100 E-06 and 1000 E-06, and estimated wear susceptibly, for the reference material used, ranges from 0.5 to 1 mm3 kJ- ‘. In these tests a combination of attrition, compression and shear forces is involved.

(typical)

Test precision

Sliding distance Test duration Ref. wear material Wear surface macrohardness (HV) Wear volume, typical Load X slid. distance Wear coefficient Energy input Wear susceptibility

Crushing load

Wear conditions

Feed conditions Type Wet or dsy Size Mass/feed rate

Dimensions

Blade

Test

L

Coef. var. 5%

V=4 mm3 Fs= 100 kNm k = 7OE-06 ICI=35 kJ S= l.lE-01 mm3 k.-*

V=5 mm3 Fsa370 kNm k = 7OE-06 El=360 W B= 1.4IC02 mm3 kJ-’

V=8 mm3 Fs=2150 kNm k = 6E-06 EI=4700 kJ B= 1.7E-03 mm’ kJ-’

Coef. var. 5%

F= 1960 N s=50 m td= 400 rev Mild steel H,= 160

Fuel ores Wet and dry 1.18-0.60 mm 0.050 kg

R=0.025 n=lOO rev min-’ z= 1 test blade

i’+

I

F

_ 14!

Tribo-tester Scieszka mill [22]

F=53 N s=6780 m t, = 14000 rev Ni-hard 2 H,= 500

1.18-0.60 mm 0.10 kg min-’

Dry

Fuel ores

R=0.077 m n = 2800 rev min-’ a=2 test blades

Product

C&hammer mill abrasion test [Z]

F,=F,=295 N s=7163 m t, = 12000 rev Mild steel H,= 165* 15

Fuel and mineral ores Wet and dry 6.7-O mm 2 kg

R=0.095 m n=(1470*30) rev min-’ z = 4 test blades

Yancey, Geer and Price (YGP) abrasion test [Z, 24, 40-421

Comparison of the tribe-mechanical and related wear characteristics of three-body abrasive wear test methods

TABLE 1

kNm

Coef. var. 5%

k = 298OE-06 El=590 k-J B=: 1.1 mm3 W-’

Fs=60

V==650 mm3

F=12500 N s=47 m t&=60 min Low alloy steel H,=275

Mineral ores Dry 50-38 mm 4x27 kg

Crush. stroke = 0.003 m n =260 cycles min- ’ z= 1 movable jaw

Jaw crusher gouging wear test 143, 631

conditions

mill

m

td = 2000 rev Ni-hard 2 H, = 500 v==3 mm3 Fs=45 kNm k = 32OE-06 El= 10 k.J B=3.OE-01 mm3 W-’

vzo.4 mm3 Fs = 300 kNm k = 7E-06 EI= 10800 kJ B=3.7E-02 mm3 kJ_’

Coef. var. 4%

Test precision

Fuel and mineral ores Wet and dry 1.18-0.60 mm 0.050 kg

R, =0.0127 m RZ=0.0190 m n = 40 rev min-’ 2=8 balls

F=176 N s=1734 m &=720 s Tool steel H,=550

Fuel ores Wet and dry 6.7-O mm 3 kg at 15 kg h-’

n=460 rev min-’ 2=2 rolls

R=0.050

Babcock radiochemical abrasion test [2, 451

Wear conditions (typical) Crushing load Sliding distance Test duration Ref. wear material Wear surface macrohardness (BV) Wear volume, typical Load X slid. distance Wear coefficient Energy input Wear susceptibility

Mass/feed rate

Wet or dry Size .

?Srpe

Feed

Dim.ensions

ConJigumtion

BCURA-roll

abrasion test 17, 441

kJ mm3 kJ-’

EI=124 Bz2.2

Coef. var. 2~5%

mm3

V=276

*

td=1200 s Low alloy steel H,=500

Mineral ores Wet and dry 2.0-O mm 1.15 kg

R,=O.lO m Rz=0.0127 m n= 70 rev min-’ z= 14 marked balls of 126 total

Marked-ball wear test (12, 46, 471

m

s 165

(continued)

Coef. var. 5%

V= 120 mm3 Fs=190 kNm k = 102OE-06

H.=

Mild steel

t,=685

F=132 N s=1436 m

Dry 0.3-0.2 mm 0.13 kg min-’

Sand abrasive

n=200 rev min-’ z= 1 test specimen

R=O.lO

Dry-sand rubber wheel abrasion test 148, 631

g

Test precision

Wear conditions (typical) crushing load Sliding distance Test duration Ref. wear material Wear surface macrohardness (Hv) Wear volume, typical Load x slid. distance Wear coefficient Energy input Wear susceptibility

Feed condtiions Type wet or dry Size Mass/feed rate

DimvnsionS

VxO.06 m3 Fs=7.2ElO kNm k = 4E-06 EZ=2.16E9 k.J B = 2.8Z.G02 mm3 kJ_ ’ Coef. var. = 10%

V=3 mm3 Fsm4.3 kNm k - 98OE-06

Coef. var. 4%

Coef. var. 2-A%

F=666400 N s = 1.06EOS m td= 6000 h Low ahoy cast steel H, = 500

V=20 mm3 Fsz2.9 kNm k = 33OOOE-06

m

Fuel ores Moisture content < 25% 63-O mm Max feed rate, 12-12.5 kg s-’

F=20 N s=220 m td= 1000 rev Mild steel H.= 165

SiC Wet and dry O-Cl.25 mm Column height 0.04-0.075

rev min-’

F=2.4 N s=1200 m td=60 min High C, low-afloy steel Hs = 500

Mineral ores Wet 2.0-O mm 1.150 kg

n=250 rev min-’ z=3 steel balls

n=20

R=0.768 m R’=0.698 m (fill-in ball dia.) n=37 rev min-’ z= 10 balls (plus 1 fill-in ball)

R = 0.036 m

R=0.0127

m

1OEl 0 ring-and-ball mill (full-scale) [23j

Loaded abrasive column wear test [34]

Rotating electrode ball wear test 115, 161

397

Typical wear surface morphology reported for each test described in Table 1 tends to support the general arguments presented above relating the wear characteristics of the test employed to the nature of the grinding process involved in each case. 4.2. YGP-abrasion test The YGP-abrasion test (Table 1) was originally developed by Yancey, Geer and Price [40] as a rapid method for comparing the abrasiveness of different coals. The method, now in its standardised form [41], involves the measurement of total loss in mass from four carbon steel blades (each fixed to a spindle arm) after rotation in a 2 kg mass of air-dry coal (6.7 mm topsize) under specified conditions. The Abrasion Index of the air-dry coal (AI;,_,) is calculated from the total weight of metal loss (in mg) over the weight of coal used in the test (in kg). The measured value of AZ is dependent on the nature and distribution of minerals in the coal [24, 50-521, and the moisture, grindability and bulk density of the coal [ 10, 23, 401. For several Australian coals, A&, adhas been empirically related to the parameters just described by the following equation ]23, 241

AI y,ad=

K103 2 WjHj j- 1

(5)

PCYBY

where K is an empirical constant; Wj and Hj are the concentration and relative hardness (ratio of the natural logarithm of mineral hardness to quartz hardness, Vickers units) of mineral component j, respectively; PC, is the mass fraction of pulverised coal (minus 75 pm) produced during the test, and is empirically related to the Hardgrove Grindability Index [53] of the coal; and By (kg rnm3) is the bulk density of the test material (at 6.7 mm top-size). In addition, utilisation of the test to determine the relative abrasion resistance of several ferrous alloys against a reference coal is reported by Spero [23] and Browne [42]. Tests conducted over a range of moisture contents for several coals have shown that the value of the Abrasion Index (My, Bswhere the subscript “as” denotes as-analysed condition) and the temperature of the sample as it is being pulverised, typically increase in an exponential and logarithmic manner, respectively, with an increase in moisture content for a given coal [ 10,23,40,42]. Several possible causes of this behaviour have been postulated including abrasion-corrosion, Rebinder effects, and coal bulk mechanical property influences, but the question still remains largely unresolved. In 1970, Parish [54] reported very similar behaviour for wet coals in the BCURAroll mill abrasion test. The observations. concerning the moisture effects in the test methods applicable to coals, as well as in other laboratory tests used for testing mineral ores [ 11, can be related somewhat to similar effects in full-scale mills [ 7-111, although according to Dodd [l] the effects are

398

much less pronounced in the latter case. On the basis of the literature cited, however, it is difhcult to make meaningful comparisons of the relative wear rates in wet us. dry grinding in laboratory ‘us. production mills. Typically, in both cases wear rates under wet grinding conditions range from 1.5 to 5 times those observed under dry grinding conditions. Sligar [2] compared the abrasion indices for several coals in the YGP mill with those obtained in the CE-hammer mill and Babcock radiochemical abrasion tests (Figs. 2 and 3, respectively), and reported that the correlation was relatively poor, particularly in the latter case. Scieszka (221 on the other hand reported good agreement between the results obtained in the YGP mill and the tribotester (Fig. 4). Compared with other laboratory tests, the YGP-abrasion test appears to be the most widely used and accepted test for fuel ores in Australia, the United Kingdom, South Africa and India. The marked-baa wear test involving a bench-scale tube-ball mill, although not formally standardised, appears to be an industry standard for evaluating wear associated with mineral-ore grinding, and also appears to be favoured in the United States for fuel ores as well. 4.3. Precision of test method resutts An historical overview and general discussion of the precision of a number of wear tests is reported by Avery [55]. The repeatability of results for the test methods described in this review is summarised in Table 1, expressed as a “coefficient of variation” v (o/o>given by the expression 100 SD ‘u= ~ mean

(6)

60 y” B E i D

50

”

30

8 I

20

7

10

40

0

0

:o

20 Ai

-

30 YGP

40 (ad).

mQ/kQ

50

60

0

10

20 Al

-

30 YGP

40 (ad).

50

60

mgikg

Fig. 2. Comparison of Abrasion Index of air-dry coal from CE and YGP abrasion tests [Z]. Regression output: constant, - 0.18; standard error of Y, estimated, 8.3; R2, 0.61; number of observations, 14; degrees of freedom, 12; X coefficient, 0.85; standard error of coefiicient, 0.20. Pig. 3. Comparison of Abrasion Index of air-dry coal from Babcock radiochemical and YGP abrasion tests [2]. Regression output: constsnt, 12.8; standard error of Y, estimated, 6.5; R’, 0.24; number of observations, 14; degrees of freedom, 12; X coefficient, 0.30; standard error of coefficient, 0.15.

399

4

0

100 Al

-

YGP

(ad),

200

mQ/kQ

Fig. 4. Relationship between Abrasion Factor from the tribotester and YGP Abrasion Index for air-dry coal [22]. Regression output: constant, - 130; standard error of Y, estimated, 355; R2, 0.80; number of observations, 19; degrees of freedom, 17; X coefficient, 23; standard error of coeflkient, 2.4.

where SD is the standard deviation of the test results. In every case the maximum coefficient is 5% or less, which contrasts with an estimated value of approximately 10% for the lOEl0 ring-ball full-scale mill. Although not evident in Table 1, the coefficient of variation actually observed for the wear volume test results decreased with increasing wear volume for each test. Two principal assumptions are made in establishing repeatability data for any test method. The first is that the test material, which is normally a sub-sample of the parent “lot”, is a representative portion of that lot, and the second is that the test results are “normally” distributed about the mean. In 1987, Wallbridge and Dowson [56] raised some doubt about the validity of the second assumption in the case of the pin-on-disk wear test, since a log-normal distribution ‘was observed for a large number of test results reported by the same laboratory for several materials. F’urther work would be required however to establish if a log-normal distribution would be obtained for results from another laboratory, and whether this distribution was applicable to other types of wear test. Reproducibility values for wear test results are seldom quoted since results reported by different laboratories can be markedly influenced by the condition of the test materials and the laboratory ambient conditions [ 41, 571. 4.4. Gmaparison of laboratory and full-scale mill wear rates Mill types used for ore-grinding fall into three categories [5-7, 581: low speed tube-ball and rod mills suitable for hard and highly abrasive fuel ores and mineral ores; vertical spindle, medium-speed mills, used for coals (containing less than 25% moisture) and mineral ores, of average hardness in each case; and high-speed hammer mills and beater mills for softer mineral ores and coals, and brown coal and peat, respectively. The normal operation of a tube-ball mill is at a speed of rotation such that the ball charge is lifted and thrown back to the base of the mill [5-71.

400

At this point there are considerable impact forces that play an important part in both the size reduction of the feed and the wear of the charge and mill liners. In vertical spindle mills, recirculation rates of the ore, previously dried on the mill table, are much higher compared with tube-ball mills, humidity is less, and the corrosion component is correspondingly less [2, 7, 581. Grinding in this type of mill occurs predominantly by attrition and, to a lesser extent, as a result of compressive and shear forces. High-speed mills employ the principles of impaction and attrition to crush the ore [2, 71. These mills normally consist of a hammer section for coarse grinding through which the product passes into the attrition zone comprised of a rotating rim of pegs for fine grinding of the coal. In the case of brown coals and peat, which contain very high moisture contents (> 259/o), high-speed mills consisting of a rotating rim of beater blades are used to pulverise the fuel by impact, shear and attrition forces [ 111. Drying of the fuel in the beater mill is normally assisted by the recirculation of hot flue gas from the associated boiler plant. For high-speed mills, Sligar [2] reported a linear correlation between the coal Abrasion Index (as-sampled) and the hammer wear rate (WRnsH, mg kg-‘), as given by the following equation W&n

= 0.50 +0.0&U,, W (r=0.97,

for 4 observations)

(7)

For low-speed tube-ball mills, Sligar reported no significant dependence of ball wear rate on the coal Abrasion Index. Observations relating (a) the wear of roll segments in a pilot-scale (500 kg h- ’ capacity) bowl mill [591 to A.&,ad, and (b) the wear of roll segments in full-scale bowl mills [2] to A& ,_, are presented in Fig. 5. In the case of the full-scale bowl mills, Sligar [2] found that the correlation of roll wear with AI,, ad was very poor (r= - 0.41), in contrast to the Abrasion Index determined on the as-sampled (wet) coal. In addition, a comparison of the observations reported for the pilot-scale and full-scale bowl mills also shows

Al

-

YGP.

mglkg

Fig. 5. Influence of coal Abrasion Index (YGP mill) on roll wear rate in medium-speed type bowl mills. IJ Pilot-scale bowl mlll 1591; A full-scale bowl mills [2].

401 a marked difference in the magnitude of the dependence

of roll wear rate on the Abrasion Index in each case. Observations relating the wear rate of grinding balls in Babcock ringball mills with fuel-ore and mineral-ore Abrasion Index (A&, ad) collated for a number of mills are given in Fig. 6. Wear rates (in mg kg-’ or the equivalent g t- ‘) are of the same order of ma~tude in each case, which is consistent with the relative values of the wear coefficient k and the wear susceptibility B (mm3 kJ-‘) estimated in Table 1. It should be noted, however, that the observations presented in Fig. 6 are generalisations only, since different Ring-ball mills have different mechanical characteristics, in addition to differences in applied load, grinding element material properties, product fineness, and feed moisture contents, which have not been taken into consideration. Similar ~~rnen~ are applicable to field correlations reported by Scieszka 1621 in relation to the wear life of bottom rings in Babcock ring-ball mills utilised for grinding South African coals. On the basis of the coal Abrasion Factor AF, (mg kg-‘) determined in the laboratory tribotester (Table l), the following correlation was reported MSL -27

287 - 95.6 AF,

(r= - 0.83, for 5 observations)

(3)

where MSL (h) is the maximum service (wear) life of bottom rings. Dodd et a&. [9] made a comp~son of ball wear rates from wet grinding of several mineral ores in laboratory marked-ball wear tests and production tube-ball mills (Table 2). These observations indicate a significant underestimate of wear rate from the laboratory tests. It was noted that the corrosion component of the wet-grinding action is a significant component in the laboratory marked-ball wear tests. By contrast, in production tube-ball mills the mechanical forces involved appear to be much larger, and surface wear by direct me~h~cal removal rather than abr~ion~o~osion probably predominates. Dodd et al. [ 1, 91 estimated an increase in ball kinetic energy from 1.4 J for a 0.025 m ball in a 0.20 m ball mill to 350 J for a 0.127

Al

-

YGP

(ad).

m&a

Fig. 6. Influence of coal Abrasion Index (YGP mill) on ball wear rate in Babcock ring-ball mills [23,58,60,61, and unpublisheddatafrom SouthAfricanand Hong Kong power stationsf. 0 lOEl0 and lO.SElO mIl& A 6E11, 6E9 and 6.2E9 mills; +EL?6 mUf; 0 8.5ElO mills; V other types of ring-ball mill.

402 TABLE 2

Comparisonof ball wear rates in wet grinding of mineral ores in laboratory marked-ball wear tests and production tube-ball mills [9] Rate of ball metal loss (pm h-l)

Description of mill conditions (mm yr-‘)

Laboratory marked-ball wear tests 1.35 11.9

3.07

0.97

1.50

26.9

8.46

13.1

Production mill field tests 9.22 80.8

38.8

340

51 mm alloy steel balls in a 0.2 m dia. mill grinding 10 mol/‘L taconite (iron ore)-water slurry 76 mm alloy steel balls in a 0.2 m dia. mill grinding 10 mol/L MO& ore-water slurry 25 mm alloy steel balls in a 0.2 m dia. mill grinding 10 mol/L NiCu-sulfide ore-water slurry 25 mm alloy steel balls in a 0.2 m dia. mill grinding 10 mol/L taconite-glycol methanol slurry 76 mm alloy steel balls in a 2.9 m dia. mill grinding 9.5 mm top-size MoSz ore-water slurry of pH 8 127 mm alloy steel balls in an 8.5 m dia. mill grinding 178 mm top-size MO& ore-water slurry of pH 8

m ball in an 8.5 m ball mill. Fiset et al. [64] recently demonstrated that an improved ranking of wear performance of selected alloys in a production ball miIl could be achieved by incorporating a cyclic impact component to alloy pins used in the pin-on-disc (two-body) wear test. These observations again highlight the importance of closer simulation, in laboratory test mills, of the magnitude of the mechanical forces observed in production mills. It appears from the several examples given in Figs. 5 and 6 and Table 2 that reasonable indications of wear rates in full-scale mills can be obtained empirically from the many results of laboratory test methods. Further work is required, however, to obtain more reliable simulation of the wear conditions in production mills, and to set the limits of predictability of three-body laboratory wear tests. 5. Statistical

simulation

A number of statistical distributions have been utilised in the engineering analysis of component wear-out failure [65, 661, the most common of which are the gaussian (normal), exponential, log-normal and Weibull distributions. The utilisation of statistical distributions is reviewed in this paper in the

403

context of their applicability to the interpretation of laboratory and production mill wear data. Goh et al. (671 used an inverse gaussian distribution to model the failure of sliding components owing to wear-out. The boundary condition a representing time to failure was expressed in terms of the Archard wear law as follows V*H,

(9)

a= xi-

where V* is the critical wear volume beyond which failure results, and V, is the sliding velocity. The failure rate of the sliding component is then determined after substitution of eqn. (9) into the inverse gaussian distribution given by

where t is the time to wear-out failure, and CLand a2 are the mean and variance, respectively, of the logarithm of the times to wear-out failure. Goh et al. [ 671 verified by means of Monte Carlo simulation that the conventionally assumed normally distributed failure models are asymptotic limits of the inverse gaussian distribution when the boundary condition a is very large relative to the mean time to failure I_L.Hence, the inverse gaussian distribution is regarded as being more generally applicable to failure prediction since it can be applied in the case of intermediate values of a. As noted earlier, laboratory results for pin-on-disc wear tests reported by Wallbridge and Dowson [56] yielded a log-normal frequency of wear coefficient k values for a number of materials. From a mechanistic point of view, the log-normal distribution varies from the normal distribution in that the normal distribution arises from the summation of a number of independent variables, whereas the log-normal distribution is generally attributed to the product of these variables. The log-normal distribution of wear coefficients was therefore regarded as being consistent with the generalisation that the amount of wear debris produced during a sliding interaction is the product of the number of wear-producing events and the magnitude or duration of those events (both these variables being assumed to be normally distributed themselves). The Weibull distribution [ 661, formerly known to statisticians as the Fisher-Tippett Type III distribution of smallest values, is given by the equation F(z)=l-exp[( where

- zr]

x>6

(11)

404

F(X) = cumulative probability of failure 6= location parameter or minimum life, which in the general case is zero 8 = scale parameter or characteristic life given by the value of x at F(s) = 1 - e- 1 p= shape parameter or Weibull slope. The theoretical justification of the Weibull distribution is generally on the basis of extreme value theory, but many processes that are phenomenological in nature also have been described empirically by the Weibull distribution [ 681. Recently, Spero [69] demonstrated the application of a two-parameter Weibull distribution (6= 0) to the analysis of the wear rate of grinding elements in coal-grinding ring-ball mills. A shape parameter p of 1.2 +0.2 was observed in the examples considered, indicating an approximately constant instantaneous wear rate h(x) given by the equation when /3= 1

(12)

The results presented in ref. 69 were consistent with the constant wear rate model of Archard (given in eqn. (1)). In addition, it is reported that the Weibull shape parameter p is a mechanistic parameter dependent on the nature of the wear involved, and that the characteristic wear life 8 is a system parameter dependent on such variables as the fixed load, sliding velocity, and the physical characteristics of the wear components and third bodies. Another application of statistical distributions was reported by Beerbower (70) in ex amining the size distribution of wear debris. In this case the slope parameters of the log-normal c and Weibull p distributions were related to the wear regimes (spalling, scoring, fatigue, abrasion and scufllng) and hence provided a diagnostic tool for establishing the dominant wear mechanism in the process of interest. Beerbower [70] also noted that the Weibull distribution can be used to character&e the size distribution of feed and product in ore grinding. The application of statistical distributions to interpret wear rates in laboratory and production mills recognises the probabilistic nature of wear. In addition, statistical evaluation techniques, used in conjunction with field data, laboratory testing and production mill studies, provide an additional tool for describing and understanding the underlying wear processes involved. 6. Conclusion This paper considered the tribo-mechanical and related wear characteristics of a number of commonly used three-body laboratory test methods for assessing abrasive wear in ore-grinding applications. The relationship between laboratory wear rates and production mill wear rates, and the applicability of statistical distributions in the study of wear associated with these processes, was also discussed. The specific conclusions drawn from this review are as follows.

405

(i) The wear coefficient k and wear susceptibility B parameters give an indication of the severity of wear and grinding conditions in both test mills and production mills. (ii) A reasonable correlation (R2 > 60%) is observed between laboratory and production mills having similar values of the parameters k and 23. A more fundamen~l ~de~~~g of the mechanistic processes involved in each case is required to establish more definitive correlations. Some of the factors that require further study include the effects of abrasion-corrosion interactions, surface adsorption (Rebinder) effects, and the effect of the chemical environment on the bulk physical properties of the ore. Scope for further work lies in the application of statistical distributions such as the log-normaI, gaussian, and Weibull functions to character&e (a) wear rates, (b) ore breakage characteristics, and (c) wear debris size distribution. Scope also exists for refinement of existing laboratory test methods to obtain more information about the wear and grinding processes involved, to extend the value of existing laboratory and production mill wear rate correlations, and to establish the limits of predictability of existing laboratory tests.

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Eng.

408

Appendix

a A

MC

4 B

BY E F

F(x, t) g

h(x) Hj HS k MSL n ;c, ii S

SD t td

V V,

V V* W wj z

A: Nomenclature

boundary condition denoting time to failure real area of contact (mm’) abrasion factor in the tribotester laboratory mill (mg kg- ‘) abrasion index, where subscript y denotes Yancey, Geer and Price (YGP) mill (mg kg-‘) wear susceptibility (mm3 kJ- ‘) bulk density of ore used in abrasion index determination (kg rne3) energy input (kJ) fixed load (kg) probability of failure wear constant instantaneous wear rate relative Vickers hardness (In HVmineralAn HV,,,,,) of mineral component j surface hardness or yield pressure (kg mm-‘) wear coefficient maximum service or wear life (h) speed of rotation (rev min-‘) applied pressure (kg mmw2) mass fraction of pulverised coal (- 75 Fm) least squares, linear correlation coefficient radius (m) sliding distance (mm) standard deviation time test duration coefficient of variation (%) sliding velocity (mm s- ‘) wear volume (mm3) critical wear volume at time to failure (mm3) wear intensity (kg mme2) concentration of mineral component j wear rate (mg kg-‘) number of grinding elements

Greek symboLs P

6 8 CL,u2

Weibull shape parameter Weibull location parameter Weibull scale parameter or characteristic mean and variance, respectively

life

Subscripts

ad as HSH

air-dry condition of an ore as-received or as-sampled condition of an ore high-speed mill hammers