Influence of Particle Size on Wear Rate in Compressive Crushing, Lindqvist, M. (2006)

7/27/2019 Influence of Particle Size on Wear Rate in Compressive Crushing, Lindqvist, M. (2006)

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Influence of particle size on wear rate in compressive crushing

Mats Lindqvist a,*, Magnus Evertsson a, Tapiwa Chenje b, Peter Radziszewski b

a Department of Applied Mechanics, Chalmers University of Technology, S412 96 Goteborg, Swedenb Department of Mechanical Engineering, McGill University, 817 Sherbrooke Str. West, Montreal, Que., Canada H3A 2K6

Received 6 September 2005; accepted 1 December 2005Available online 19 January 2006

Abstract

The influence of particle size on wear rate in compressive crushing of rock was investigated experimentally. A test apparatus wasdeveloped to replicate the squeezing wear that is present in many rock crushers. Silica sand of different size classes between 0.725and 2.03 mm was used. The crushing load was varied. The results show a strong relationship between particle size and wear rate.The wear rate increases as particle size increases. Not only mean particle size, but also size distribution width also has an influenceon wear rate. From some theoretical considerations, an alternative wear model was derived, that matches experimental data well. Inthe new model, the wear is proportional to particle size and to the square root of the pressure. 2005 Elsevier Ltd. All rights reserved.

Keywords: Crushing; Comminution; Simulation; Modeling; Particle size

1. Introduction

In a series of papers by the author, a model to predictthe worn geometry of a cone crusher has been presented(Lindqvist and Evertsson, 2003a, 2004). Even though themodel predicts the worn geometry fairly well, many vari-ables that change as the material passes through the crush-ing chamber are neglected. One of those variables is theinfluence of the particle size distribution on wear rate.According to Hutchings (1992), the wear rate in erosivewear, two body, and three body abrasion, increases as par-ticle size increases.

In compressive crushing rock particles of various sizes

are squeezed and crushed against a steel surface. The wearmechanism is pure squeezing wear without macroscopicrelative motion between the rock particles and the steel sur-face. Many wear models described in the literature, see forexample Hutchings (1992), assume that wear is propor-tional to sliding distance. However, in a cone crusher thereis no or very little relative sliding motion between rock and

liner. If a worn crusher liner is inspected, no ploughinggrooves can be observed. Therefore, the wear model imple-mented for cone crushers was adapted to this fact. In themodel for wear prediction, described by Lindqvist andEvertsson (2003b), it is assumed that the amount of wearin a crushing action is proportional to the maximum aver-age pressure that occurs during the crushing event, Eq. (1).In this constitutive equation W is the wear resistance coef-ficient. The average pressure is here the sum of contactloads exerted by the particles within a certain area enclos-ing those contacts, divided by that area. Wear w is hereexpressed in mm, pressure in N/mm2, and hence the wearresistance will have the unit N/mm3.

Dw pmaxW

1

This is a material parameter unique for each combinationof liner material and rock (Hutchings, 1992). The averagepressure expressed in Eq. (1), is in reality a number ofcontact loads of different magnitude acting on the steel sur-face. The wear that occurs is a function of the number andmagnitude of those contact loads, and by the shape andstrength of the particles pressed against the surface. Therelationship between particle size, average pressure and

0892-6875/$ - see front matter 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mineng.2005.12.002

* Corresponding author. Tel.: +46 704 955 663.E-mail address: [email protected] (M. Lindqvist).

This article is also available online at:

www.elsevier.com/locate/mineng

Minerals Engineering 19 (2006) 13281335
mailto:[email protected]:[email protected]


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wear rate is not known. The aim of this study is to investi-gate whether or not particle size has any influence on wearrate in squeezing wear.

Successful efforts have been made to theoretically derivethe statistical distribution of contact loads in particulatematerials. See for example Ngan (2004). Those theories

are typically based on assumptions of frictionless, equallysized, linearly elastic spheres in contact, and they have suc-cessfully been verified in experiments (Ngan, 2004).

In rock crushing applications, however, where the parti-cle shape and size varies considerably, and especially whenparticle breakage occurs, theoretical solutions for the con-tact load distribution are not available. Some experimentalresults have been achieved by Hansson (2002), who studiedfatigue of aggregate beds in roads. Hansson (2002) resultsindicate that particle size does influence the distributionof contact loads, but he does not discuss the contact loaddistributions influence on wear.

Yao and Page (2000, 2001) and Yao et al. (2000) pre-

sented thorough work where sliding wear was investigatedon microscopic scale for a single crushing event. They con-cluded that a layer of fine particles near the metal surfacewill yield less wear as compared to coarser particles, andthat higher crushing pressure will produce more fines nearthe surface, and hence less wear in relation to the appliedpressure. Yao and Page (2001) used average pressuresmuch higher than what is present in cone crushers, up to300 MPa, as opposed to typically 7 MPa in a cone crusher.

Chenje and Radziszewski (2004) found a linear relation-ship between crushing load and wear rate up to a certainlevel of load, above which the wear rate levels off. This

result is in agreement with Yao and Page (2000), eventhough the pressure levels in Chenje and Radziszewski(2004) study are likely to be much lower than in Yao andPage (2000).

2. Experimental setup

As a consequence of the complexity of wear, a largevariety of devices for wear testing exist. See for exampleOsara (2001), who has made a thorough evaluation of dif-ferent wear testing methods. Each of these methods has the

objective of investigating some specific aspect of wear.None of the test devices described by Osara (2001), aresuitable for investigating squeezing wear while having con-trol of the variables particle size and crushing pressure.

An abrasive wear tester was previously used by Rad-ziszewski (2002) with a steel wheel and subsequently mod-ified to allow the measurement of friction as well as testingat higher applied forces (Radziszewski et al., 2005). Thatwear tester was developed from the standardized rubberwheel abrasion test described by Misra and Finnie (1980).Radziszewski (2002) modified the rubber wheel abrasiontester and replaced the rubber wheel with one made ofsteel, mainly in order to make it possible to increase the

crushing load to levels commonly found in grinding. Thetests carried out by Chenje and Radziszewski (2004) weremade with a fixed specimen and a moving wheel. The wearmechanism was hence sliding wear.

In order to study the compressive wear found in conecrushers, the wear tester was further modified. The fixedspecimen was replaced with a roller, see Figs. 13. The pur-pose of the roller is to ensure that we get the pure squeezingwear mechanism that is present in cone crushers.

The rock material was silica sand, well known for itsstrongly abrasive properties. The silica sand was thor-oughly sieved into four different size classes: 0.6

0.85 mm, 0.851.18 mm, 1.181.7 mm and 1.72.36 mm.Two tests were made with material that was not sieved tostudy the effect of size distribution width. Weights wereput on the pivoted beam so that a well defined crushing

Fig. 1. Modified abrasive wear tester.

M. Lindqvist et al. / Minerals Engineering 19 (2006) 13281335 1329


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force on the roller was obtained. The flow of material was

controlled by adjusted the nozzle at the end of the hosefrom the hopper. The wheel of the wear tester was run at20 rpm. The nozzle was adjusted to obtain a slightly exces-sive flow of material. Unfortunately it was not possible toadjust the flow of material so that it exactly matched thecapacity of the tester. An excessive amount of materialwas used and some of the material passed on the sides ofthe crushing zone without being crushed. It would havebeen desirable to see the particle size distribution beforeand after crushing. But it was not meaningful to screenthe crushed material since it was mixed with material thatpassed on the sides without being crushed.

The valve of the abrasive hopper was opened and theroller was released onto the rotating wheel of the abrasivetester. The wear on the roller was measured with a verniercalliper. Since the abrasive tester consumes large amountsof material, the wear tests were made as short as possible.Each test was made long enough so that a diameter changeof at least 10 times the resolution of the vernier calliper(0.02 mm) was obtained.

3. Results

In the first few tests many measurements were madewith short intervals. It was noted that the wear rate wasvery low or even negative when starting from a new speci-men. The explanation for this is that when a measurementis made, it is the peaks of the rough surface that are mea-sured. This means that the smooth surface of a new speci-men needs to be used for a certain time before takingmeasurements of wear. For this reason the first 5 min ofeach particle size tested were not included in the measure-ment of wear. Doing this, Fig. 4 shows that the wearincreases linearly with the number of crushing events, asexpected. One crushing event corresponds to one revolu-tion of the specimen. The number of revolutions of thespecimen is computed as the ratio between the average

diameter of the wheel and the specimen multiplied with

the test time and wheel rotational speed. The wear mecha-nism is squeezing wear. No ploughing grooves can beobserved, see Fig. 3. Note that the new specimen hasflanges to ensure that material is not squeezed to the sidesof the crusher.

For each revolution of the specimen, each point on theroller will be subject to one crushing event. The wearexpressed as wear per crushing event, for the different par-ticle sizes is shown in Fig. 5.

The wear resistance coefficient described by Eq. (1), canbe computed only if the crushing pressure is known.Evertsson and Lindqvist (2002) presented a pressureresponse model for compressive crushing. The compressionratio (s/b) is the squeezed distance s divided by initial bed

thickness b. The pressure response model is a polynomialfit that relates compression ratio, (s/b) and size distributionwidth, denoted, to pressure. Evertsson and Lindqvist(2002) used the variational coefficient (standard devia-tion/mean particle size) of the size distribution to charac-terize size distribution width. See Eq. (2). The pressure pis returned in MPa.

ps;r a1s=b2r2 a2s=b2r a3s=b2

a4s=br2 a5s=br a6s=b 2Approximate values for coefficients a1a6 are here pre-sented for quartzite.

a1 957; a2 512; a3 119; a4 184;a5 120; a6 1:07To estimate the crushing pressure on the roller, the equilib-rium equation between the applied force and the pressuredistribution needs to be established. But in order to do this,the pressure distribution area must be computed.

The position where squeeze starts in a roll crusher isgoverned by the coefficient of friction l. See Fig. 6. A par-ticle, or a bed of particles, squeezed between oblique sur-faces as the particle in Fig. 6 will slide against the rollerunless the angle (a + b) < arctanl and the particle, or

bed of particles is nipped (Magi and Gerbert, 1993). Eq.

Fig. 2. Wear test in progress.

Fig. 3. Worn specimen. The initial diameter of the specimen was44.45 mm.

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(3) shows the relationships that can be derived from geom-etry and equilibrium, assuming that the bed of particles willbe nipped when (a + b)/2 = arctanl. The angle arctanl is

often called the frictional angle (Magi and Gerbert, 1993).

a b=2 arctan lD R1 R3 cos a R2 R3 cos bR1 R3 sin a R2 R3 sin b

9>=>; 3

By making an initial guess of the distance D, the angles aand b can be computed iteratively. The pressure distribu-tion on the roller is shown in Fig. 7.

The pressure distribution in Fig. 7 corresponds to acrushing force according to Eq. (4).

F

B Z

a

0

pcos a0Rda0

4

B is the width of the wheel. The tangential shear force ishere neglected. To estimate the maximum crushing pres-sure, an initial guess of the distance D was made. The angle

a was computed according to Eq. (3) and the pressure dis-tribution was computed using Eq. (2). The compression ra-tio is 2R3/(D R1 R2). The integral in Eq. (4) wassolved. This was done in an iterative procedure until theknown crushing load F is in equilibrium with the pressuredistribution.

Several studies (Chenje and Radziszewski, 2004; Yaoand Page, 2000; Lindqvist and Evertsson, 2003a), haveshown that the coefficient of friction between crushed rockand steel is between 0.3 and 0.5. Here a coefficient of fric-tion of 0.4 was used. The wear was measured, and the num-ber of revolutions of the roller was computed. Ideal rolling

(no gross slip) between the specimen roller and wheel was

0

0.05

0.1

0.15

0.2

0.25

0.3

0 200 400 600 800 1000 1200 1400 1600 1800

Number of crushing events

Radialwear

[mm]

Load: 938 N, Part . Size: 2.03 mm

Load 633 N, P.S. 2.03

Load 1141 N, PS: 1.44

Load 633 N, PS: 1.44

Load 1548 N, PS: 2.03

Load 1141 N, PS: 0.725

Load 633 N, PS: 1.015

Load 1141 N, PS: 1.015

Load 1548 N. PS: 1.015

Fig. 4. Radial wear on specimen as a function of the number of crushing events.

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

1.4E-04

1.6E-04

1.8E-04

2.0E-04

0 200 400 600 800 1000 1200 1400 1600

Crushing load [N]

Radialwear rate

[mm/crushing event]

d50=0.725 mm

d50=1.015 mm

d50=1.44 mm

d50=2.03 mm

d50=1.63, Wide size distr.

Fig. 5. Wear rate per crushing event as a function of crushing load, for different particle sizes.



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assumed, and the average diameter of wheel and specimenduring each test was used to compute the number of revo-lutions. A point on the roller is subject to a crushing eventfor each revolution of the roller. Now that we have an esti-mate of the pressure on the roller, Eq. (1) is used to com-

pute to corresponding wear resistance W for each test.

Crushing load and particle sizes were varied. Fig. 8 showsthe wear resistance for each test.

Fig. 8 clearly shows that the wear resistance is lower forlarger particles. As mentioned, two tests were made withmaterial with a wider size distribution width, in order to

investigate if this affects wear rate, see Fig. 8. The size dis-

Fig. 6. Geometry of roll crusher.

Fig. 7. Pressure distribution on roller.

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tribution width was computed as (d80 d20)/d50, and wasbetween 0.20 and 0.22 for all tests except the two withwider size distribution where (d80 d20)/d50 = 0.65.

4. Discussion

The results show a clear relationship between particlesize and wear rate, see Fig. 8. Two of the tests were per-formed with material that was not screened before crush-ing, i.e. with a wider size distribution. Fig. 8 shows thatthe wear resistance lies outside the trend for the other

tests. This indicates not only mean particles size, butalso size distribution width affects wear rate. The resultsimply that a particle size dependent wear model wouldbe more appropriate when modeling squeezing wear. Sucha model is here derived through some theoreticalconsiderations.

Assume that a bed of roughly equally sized particles aresqueezed against a steel surface of a certain area. Smallerparticles, compared to larger ones, will cause a larger num-ber of contact loads within that area, since the number ofparticles increase as the particle size decreases. Each con-tact load will be lower as the number of particles and con-tacts increase. With knowledge of the wear or damage

caused by each contact load, a wear model can be derived.Consider a number N of particles squeezed against a sur-face of area A. The crushing pressure p is the total load Ftotdivided by the area A. The contact load from each particleis f and the sum of all individual contact loads is Ftot, seeEqs. (5) and (6).

Ftot Nf 5p Ftot=A 6The linear size of each particle is d. As the particle sizedecreases there will be more contact points. The numberof particles N, squeezed against the surface is given by

Eq. (7).

N a1A 1d2

7

a1 is a proportionality constant dependent on particleshape. It is reasonable to assume that the damage, orwear caused to the surface by each contact load is amonotonous function of the applied load f. Several differ-ent functions that relate contact load f to local wear wcan be conceived. A first, simple assumption would be thatwear is proportional to contact load, Eq. (8).

w1 a2f 8

A rock particle pressed against a steel surface will, by plas-tic deformation, make an indent of size h. A linearly elasticand perfectly plastic material will exert the same pressureon the entire indenting body, namely a pressure that equalsthe yield stress. This means that the area of the indent markis proportional to the load. So if the steel is assumed to belinearly elastic and ideally plastic, then the size h of the in-dent is proportional to the square root of the contact load fsince f krh2 () h f1=2=rk. r is the yield stress ofthe material, and k is a constant depending on particleshape.

If the indent size h is used as a direct measure of thedamage or wear w inflicted on the steel surface, Eq.(9) would be an alternative function to describe the surfacedamage or wear caused by a single contact load.

w2 a3ffiffiffif

p9

In Eqs. (8) and (9), a2 and a3 are constants, dependent onthe mechanical properties of rock and steel, and on particleshape. Combining Eqs. (5)(7) with Eq. (8) or (9) hencegives the wear equations expressed in Eqs. (10) and (11).

w1 1W1

d2p 10

w2

1

W2d ffiffiffipp

11

0.0E+00

2.0E+04

4.0E+04

6.0E+04

8.0E+04

1.0E+05

1.2E+05

1.4E+05

1.6E+05

1.8E+05

0 0.5 1 1.5 2 2.5

Particle sized 50 [mm]

Wearresistancecoefficient[N/mm

3]

Wider size distribution

(d80-d20)/d50=0.65

Fig. 8. Wear resistance as a function of mean particle size, d50.



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the rock and liner, leading to a significant improvement inprediction of worn geometry.

The alternative wear model of Eq. (11) is also likely toimprove the results with respect to that deviation. The rea-son for this is that particles are smaller, and that the pres-sure is higher further down in the chamber. This indicates

that the predicted wear rate will relatively increase in theupper part of the crushing chamber as compared to thelower part.

5. Conclusions, future work

In compressive crushing of rock material, a difference inparticle size in the range 0.752.03 mm has here beenshown to have an impact on wear rate. The results inFig. 10 show that not only mean particle size, but also sizedistribution width affects the wear resistance. This needs tobe investigated further before the wear model of Eq. (11)can be implemented in a cone crusher model.

In a cone crusher, the level where the cross sectional areais at a minimum is called the choke level. Below the chokelevel, the cross sectional area increases, and there is moreand more space between particles as they move furtherdown. In the flow model for cone crushers presented byEvertsson (1999) and Lindqvist and Evertsson (2004), allparticles are assumed to move in the same way. Duringsqueeze, it is possible that smaller particles trickle downbetween larger ones, and has a different residence time inthe crusher. To what extent finer particles participate inthe pressure build up and wear in a cone crusher is notknown.

We now have a cone crusher model that predicts theoperating conditions with some accuracy (Lindqvist andEvertsson, 2006). Introducing more complex model behav-iour to take more phenomena into account, might makethe problem of finding optimal model parameters poorlyconditioned, i.e. several different combinations of modelparameters will make simulations match measurements.Possibly, the new wear model of Eq. (9), just as the previ-ously implemented shear force dependent wear model, willalso solve the issue with poor wear prediction. More workwill be necessary to fully understand the relative impor-tance of these different wear models.

Acknowledgement

Professor Emeritus Goran Gerbert, Chalmers Univer-sity of Technology is gratefully acknowledged for valuablediscussions regarding wear models.

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Influence of Particle Size on Wear Rate in Compressive Crushing, Lindqvist, M. (2006)