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    AbstractWear in rock crushers causes great costs in the mining and aggregates industry. Change of the geometry of the crusher liners is amajor reason for these costs. Being able to predict the geometry of a worn crusher will help designing the crusher liners for improvedperformance.A model for prediction of sliding wear was suggested by Archard in 1953. Tests have been conducted to determine the wearcoefficient in Archard s model. Using a small jaw crusher, the wear of the crusher liners has been studied for different settings of thecrusher. The experiments have been carried out using quartzite, known for being very abrasive. Crushing forces have been measured,and the motion of the crusher has been tracked along with the wear on the crusher liners. The test results show that the wearmechanisms are different for the fixed and moving liner. If there were no relative sliding distance between rock and liner, Archard smodel would yield no wear. This is not true for rock crushing applications where wear is observed even though there is no mac-roscopic sliding between the rock material and the liners. For this reason, Archard s model has been modified to account for thewear induced by the local sliding of particles being crushed. The predicted worn geometry is similar to the real crusher.A cone crusher is a machine commonly used in the mining and aggregates industry. In a cone crusher, the geometry of thecrushing chamber is crucial for performance. The objective of this work, where wear was studied in a jaw crusher, is to implement amodel to predict the geometry of a worn cone crusher.  2002 Elsevier Science Ltd. All rights reserved.Keywords: Comminution; Crushing; Particle size; Modelling 27931
    Jaw and cone crushers are commonly used in themining and aggregates industry. Today, it is possible topredict the performance of a cone crusher, provided thegeometry, crusher settings and the characteristics of thematerial fed into the crusher are known (Evertsson,2000). The geometry of the crusher will change becauseof wear. Being able to predict the worn geometry willhelp optimising the design of the new crusher for im-proved performance throughout its lifetime.Current research and knowledge in the field of wear isvery extensive. However, much of this research is con-ducted from a material science perspective on a micro-scopic level. The objective is often to gain knowledge inmaterial selection situations, heat and surface treatmentand so forth. In this work, wear on a macroscopic level has been studied, aiming to understand and prevent thedamaging effect of the inevitable wear in cone crushers.
    The operating principles of cone and jaw crushers aredescribed in Fig. 1.In a cone crusher, the shaft of the inner mantle issuspended in two bearings, one eccentric at the bottomand one concentric at the top. When the eccentric at thebottom is turned, a vertical cross section of the innermantle will suffer an oscillating motion. The rock par-ticles between the inner and concave will be squeezed,crushed, and fall down. When the material passesthrough the crusher, it will be subjected to severalcrushing actions. The properties and performance of thecrusher are strongly dependent on the stroke and bedthickness. Because of wear, these geometric quantitieswill change during the life of the liners. In turn, when thegeometry of the liners changes, the performance of thecrusher will change. With very few exceptions, this willbe a detrimental effect.
    In order to design a crushing chamber it is desirableto be able to predict the geometry of the worn chamber.The objective of this study is to develop a model for thispurpose. With such a model, it will be possible to per-form simulations in order to design crusher chambersthat are less sensitive to wear.1.2. Wear mechanismsThe research and literature on abrasive wear andwear mechanisms is very extensive. A lot of differentwear situations have been described, but generally fourtypes of fracture are described as being present inabrasive wear: fatigue, shearing of junctions, microcut-ting and impact (Vingsbo, 1979). There are also sec-ondary effects such as frictional heating and corrosionthat affect the material/wear mechanism. Much of theresearch is done on a microscopic level. In this work, nofurther attention will be paid to such topics.A model for predicting material removal due to wearwas suggested by Archard (1953). In this model, it isassumed that wear is proportional to pressure andsliding distance. Hence, in order to use Archard s wearmodel, the local pressure and motion the crusher need tobe known in. One difficulty in determining the wearresistance coefficient in Archard s model is the fact thatthe abrasive particles are crushed during wear. Someresults have been achieved by (Yao and Page, 2001; Yaoet al. (2000)), who have studied wear during crushing ofsilica sand. They have studied surface damage on amicroscopic level after a single crushing event. To obtainthe wear resistance coefficients needed in Archard smodel, it is necessary to make the measurements after arepeated number of crushing events. Their research in-dicates, however, that a testing device for determining the relationship between wear, pressure and motion willneed to resemble the process in a real crusher, whererock material is crushed, mixed and crushed again. Aftera large number of repeated crushing events, the worngeometry will be measured. In order to predict the worngeometry the components in Archard s wear model, thepressure and relative motion must also be known.1.3. Test equipmentA few schematic testing devices for determining wearcoefficients were suggested by Hutchings (1992). Forcrushing applications, methods such as the ‘‘pin on disc’’test have the drawback that the abrasive properties willchange during crushing. This has also been proven byYao et al. (2000), who have found that by appropriatecontrol of pressure and shear force, a protective layer ofmaterial can be formed near the surface. This meansthat a testing device for determining wear coefficientsneeds to resemble the conditions in a real crusher, wherematerial is crushed, mixed and crushed again. It is alsodesirable to measure the crushing forces during crush-ing, to verify the pressure.2. ExperimentsA small jaw crusher originally designed for testing theproperties of rock material was modified (see Fig. 2).Rock material is fed into the top of the crusher. Therotating eccentric shaft and the link give the right lineran oscillating motion that will crush the material. Theleft, stationary liner has three load cells. Two of themare horizontal, to measure normal forces, and one ver-tical to measure the frictional force. The force cells have been designed to be insensitive to bending and torsion.They only register compressive/tensile forces. The linermaterial is manganese alloy steel, commonly used forcrusher liners, with 1.2% C, 12.5% Mn, 0.6% Si and1.5% Cr. Austenitic manganese steels are common inabrasive wear applications; they are well known for theirexcellent capacity for work hardening. Upon plasticdeformation the austenite in this material transformsinto martensite and becomes harder. There are variousexplanations for this strain-induced hardening; but themajor mechanisms that drive the transformation aretwinning and slipping of dislocations (El Bitar and ElBanna, 2000).The small jaw crusher was used to study the wear as afunction of force (i.e. pressure) and motion. The ex-periments were carried out using quartzite, since thismaterial is known for being very abrasive. The sizedistribution of the feed material was 8–11 mm. Theclosed side setting (the minimum distance across thecrushing chamber) was set to 2, 3and 5 mm. In com-pressive crushing, two modes of breakage were identifiedby Evertsson (1998): inter-particle breakage and singleparticle breakage. The reason for selecting size distri-bution and crusher setting in this study was to ensureinter-particle breakage. Inter-particle breakage occurswhen the size of the particles is smaller than the bedheight i.e. particles will be crushed against each other; asopposed to single particle breakage when a single par-ticle is crushed between the two steel liners.The forces were registered and the motion of thecrusher was measured by recording a signal indicating the eccentric angle of the main shaft. Wear of the linerswas measured on a 13by 8 grid with 10 mm spacing oneach liner. The average wear on each level in thedownward direction was computed.3. Modelling3.1. Modelling flowIn order to predict the wear, the pressure and motionof the crusher need to be determined. Previous work hasbeen carried out by Evertsson (1995, 1998, 1999) on flowand capacity modelling of cone crushers. A particle flowmodel has been implemented for the jaw crusher. In theparticle flow model, three types of motion are defined:free fall, sliding and squeeze. Impact is modelled plas-tically, which means that the normal component of thevelocity is annihilated and the tangential component ispreserved upon impact (Evertsson, 1999).Fig. 3shows the path of a particle through thecrusher. This particle flow model overestimates the ca-pacity of the crusher. Due to dynamic filling effects, theactual capacity will be reduced in comparison with theparticle model (Evertsson, 1999).3.2. Modelling pressureBy crushing a bed of rock material in a cylindricalcontainer (see Fig. 4) it is possible to relate averagepressure p to the compression ratio ðs=bÞ. Rock is crushed in a cylindrical container. By measuring forcealong with compression ðs=bÞ it becomes possible to fit apolynomial to the measured data. This function is de-pendent on grain size distribution. This work has beendone elsewhere (Evertsson, 2002).The nominal compression ratio ðs=bÞnom is deter-mined by the geometry of the crusher (horizontal strokepided by horizontal chamber size). Due to dynamiceffects, the effective compression ratio ðs=bÞeffis less thanthe nominal. In addition, filling effects further reducesthe effective compression. The compression ratio utilizedis denoted ðs=bÞu : ðs=bÞnom > ðs=bÞeff> ðs=bÞu (Everts-son, 1999). By computing the effective compression fromthe particle flow model and using the correlation be-tween pressure and compression obtained in the can test,it is possible to compute the pressure on the crusherliners (see Fig. 5). The pressure is also dependent on sizedistribution. In these simulations, however, an average dependency between ðs=bÞ and pressure has been used,since the change in size distribution before and after thecrusher is not significant in terms of affecting the pres-sure.3.3. Modelling forcesUsing the simulated pressure distribution, it is pos-sible to compute the forces corresponding to the mea-sured forces on the test crusher. It is assumed here thatthe normal force on the moving liner is equal to thenormal force on the stationary liner. In Fig. 6, a prin-ciple image of the crusher is shown.Equilibrium around point A in Fig. 6 yields the fol-lowing equations:
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