122.2翻译—锥式破碎机的发展.pdf

Wear xxx (2006) xxxxxx Development of wear model for cone crushers M. Lindqvist, C.M. Evertsson Department of Applied Mechanics, Chalmers University of Technology, SE 412 96 G oteborg, Sweden Received 30 March 2005; received in revised form 2 November 2005; accepted 12 December 2005 Abstract Conecrushersareusedintheaggregatesandminingindustriestocrushrockmaterial.Amodeltopredicttheworngeometryofconecrusherswas previouslydeveloped.Inthatmodeltherewassomedisagreementsbetweenpredictedandmeasuredgeometryandseveraleffectsweresuggestedto explainthediscrepancyinthemodel.Inthisstudytheeffectofshearforcesalongthecrushingsurfaceswasimplementedinthemodel.Simulations were compared to measurements on two different crushing chambers. The results show a signifi cant improvement with respect to the discrepancy between measured and simulated geometry. Measurements were made on a coarse crushing chamber where the operating parameters hydroset pressure, power draw and capacity were tracked during the lifetime of the set of liners. The simulated operating parameters show some agreement with measured data, but the crusher was not run under ideal conditions at all times. 2005 Elsevier B.V. All rights reserved. Keywords: Comminution; Crushing; Modelling; Abrasive wear; Cone crusher 1. Introduction Cone crushers are widely used in the mining and aggregates industry to crush blasted rock material. The two main crushing parts are the mantle and the concave. The main shaft of the mantle is suspended on a spherical radial bearing at the top and in an eccentric at the bottom. A hydraulic cylinder supports the thrust bearing that carries the thrust force of the main shaft. The hydraulicsystemcanraisethemainshaftinordertocompensate for the wear of the mantle and concave. The hydraulic pressure in the cylinder that supports the thrust force from the main shaft is called the hydroset pressure. As the eccentric is turned the rock material will be squeezed and crushed between the liners (see Figs. 14). Along its path through the crushing chamber, a rock parti- cle will be subjected to several crushing events. The shortest distance across the crushing chamber is called the closed side setting,CSS,andisanimportantvariablefortheperformanceof the crusher. The control system is calibrated regularly to main- tainaconstantCSS.Previousresearch1,2hasmadeitpossible to model the behaviour of a given cone crusher. Evertsson 1 Corresponding author. Tel.: +46 31 772 13 76; fax: +46 31 772 3872. E-mail addresses: mats.lindqvistme.chalmers.se (M. Lindqvist), cmemvs.chalmers.se (C.M. Evertsson). developed a fl ow model, a size reduction model and a pressure response model. The geometry of the crushing chamber is crucial for the per- formance. Due to wear the geometry of the liners will change, and hence the crusher performance will also change and some- times suffer. Therefore it is desirable to simulate the change of geometry and performance as the liners wear. A model for this purpose was previously developed 3,4. That model was based on the results of Evertsson 1. In the model for wear prediction there was some discrepancy between the simulated geometry and measured geometry in the upper part of the crushing cham- ber3.Severalexplanationsofthisdiscrepancyweresuggested. It was fi rst assumed that the work hardening behaviour of the liner material might depend on the applied pressure. In a study by the author 5 it was concluded that it was not a variation in work hardening in the chamber that caused the discrepancy in the wear model. Among the other explanations for the discrepancy, that were proposed by Lindqvist and Evertsson 3, the prediction of pressure on the liners was assumed to be an important fac- tor. To address this, an improved fl ow- and pressure model was presented by Lindqvist and Evertsson 6. That model showed a signifi cant improvement in prediction of the oper- ating parameters CSS, power draw and capacity, but only a slight improvement of wear prediction for a fi ne crushing chamber. 0043-1648/$ see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2005.12.010 WEA-97899;No. of Pages 8 2M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxx Fig. 1. Cone crusher, schematic image. Fig. 2. Operating principle of cone crusher. Fig. 3. An H8800 hydrocone crusher. This particular model is nearly 5m high. Fig. 4. A new set of crusher liners, mantle and concave. Other suggested explanations are non-linear dependency between pressure and wear, shear stress at the interface between rock and liner, dependency between particle size and wear rate. ChenjeandRadziszewski7showedthattherewasanon-linear relationship between applied force and wear rate in a sliding wear experiment. If Chenjes 7 results were also applicable for the case of non-sliding wear in cone crushers, they would, at least in part, explain the discrepancy. The technique used in the presentstudy,tomeasurethegeometryoftheliners,issimilarto the technique used by Rosario 8. He has made measurements of liner wear on gyratory crushers. Among the possible explanations of the disagreement in the model, shear forces in the contact between rock and liner is the one that is addressed in this paper. 2. Method 2.1. Wear model The wear model presented by Archard 9 suggests that wear is proportional to sliding distance and applied pressure. In the previous work carried out by the author 10 it was found that wear occurs even if there is no macroscopic sliding motion betweenrockmaterialandliner.Thisisthecaseinaconecrusher where there is no macroscopic sliding motion between liner and rock. The mantle is free to roll against the bed of rock mate- rial. On at least one point, the point of moment equilibrium for the mantle, there is pure rolling between the mantle and bed of material. At other points the relative sliding motion is very small,sincetheconcaveisdesignednearlyasanidealconewith the generatrix of the mantle intersecting the pivot point of the main shaft (see Fig. 5). The wear model presented by Archard 9 suggests that the wear rate is proportional to sliding velocity. If a worn crusher liner is inspected, no ploughing grooves can be observed. The wearmechanismissqueezingwearwithoutmacroscopicrelative motion between the bed of rock particles and the steel surface. On a small scale there is of course some relative motion since M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxx3 Fig. 5. Mantles are designed nearly as an ideal cone whose generatrix intersects the pivot point of the main shaft. particles are rearranged as they are crushed, but the direction of this motion is random. A wear model like Archards 9 that is dependentofslidingvelocitywouldinthecaseofconecrushers, yield no wear. Therefore, Lindqvist and Evertsson 3 adapted the wear model used for cone crushers. In the model for wear prediction, described by Lindqvist and Evertsson 3 it is proposed that the amount of wear in a single crushing action is proportional to the maximum average pres- sure p that occurs during the crushing event (see Eq. (1). In this constitutive equation W is the wear resistance coeffi cient, a materialparameteruniqueforeachcombinationofrockmaterial and steel. Wear w is here expressed in mm, pressure in N/mm2, and hence the unit for the wear resistance will have the unit N/mm3. ?w = pmax W (1) The “average pressure” expressed in Eq. (1), consists of a large number of contact loads of different magnitude acting on the steel surface. The wear that occurs is a function of the mechanical properties of the steel, the number and magnitude of the contact loads, and the shape and mechanical properties of the rock particles. The wear resistance coeffi cient W is deter- mined by the mechanical properties of the steel and rock, and is verifi ed in experiments or in full-scale measurements. The wear resistance parameter W in Eq. (1) was found to be 94kN/mm3in a previous study 3. The material was highly abrasive quartzite in combination with austenitic manganese steel. It was shown in that study that the wear model in com- bination with the crusher model yielded an under-prediction of wear in the upper part of the crushing chamber. The objective here is to present a model that will address this discrepancy. If a particle squeezed between oblique surfaces, as in Fig. 6, the shear force increases as the nip angle increases. Among sev- eralmentionedandpartlyinvestigatedreasons,ashearforceina Fig. 6. The nip angle between the liners is larger for a coarse crushing chamber (left) than for a fi ne chamber (right). contactishereassumedtochangethestressstatearoundthecon- tact and increase the wear rate. As mentioned, it is not possible to observe any ploughing grooves on a worn liner surface. This indicates that there is no macroscopic sliding motion between the rock particles and the steel surface and that friction is not fully developed. If a particle is squeezed between oblique surfaces, the shear force in the contact can be computed. Consider the particle squeezed between two oblique surfaces in Fig. 7. Since the par- ticle does not slip, the friction is not fully developed. The tangential frictional force Ftcan be decomposed as the product of a frictional factor f times the normal force N. Since friction is not fully developed f where is the coeffi cient of friction. With reference to Fig. 7, equilibrium require that N = F cos 2 (2) fN = F sin 2 (3) Fig. 7. Shear forces are present when a particle is squeezed between oblique surfaces. 4M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxx Fig. 8. Simulated pressure distribution on a mantle used with an H6800 EC concave. : fN cos 2 = N sin 2 (4) f = tan 2 (5) If the computed factor f exceeds the coeffi cient of friction, the particle will slide. In the crusher model, the pressure is computed according to the pressure response model presented by Evertsson and Lindqvist 4. The pressure response model relates compres- sion ratio (i.e. the compressive engineering strain of the particle bed: deformation/original thickness), and variational coeffi cient of the particle size distribution to crushing pressure. A second- degreepolynomialintwovariables(compressionandvariational coeffi cientofsizedistribution)wasfi ttedtotestresults.Thetotal pressureptotiscomputedusingthepressureresponsemodel(see Fig. 8). So the shearstress pshearand normal pressure pnormalat the surface is hence computed according to Eqs. (6) and (7). pnormal= 1 ? 1 + f2 ptot(6) pshear= f ? 1 + f2 ptot(7) where ptotis the total pressure computed from the pressure response model. The proposed wear model hence looks as: ?w = 1 W (pnormal+ Kpshear)(8) Here K is a new model parameter that scales the effect of the shear force when there is no slip. Sliding wear in a jaw crusher hasbeenfoundtobethreetosixtimesfasterthansqueezing-only wear, at the same crushing load 10. Fig. 9. Measurement rig. 2.2. Wear measurements A measurement rig that was previously developed for mea- suring the worn geometry of cone crushers was used. The method resembles the one used by Rosario (2004). The crusher is stopped and a probe detects the location of the surfaces of the mantle and concave. The device is made of a frame that is attached to the main shaft of the crusher (see Fig. 9). A step motor moves a carrier by turning a threaded rod. Small stepping motors send out probes. The number of pulses sent to the step motor corresponds to a certain position relatively to the measur- ing frame. When a probe contacts the liner the controller stops the motor and the number of pulses is registered. The number of pulses is then converted into geometric coordinates. The measurements were carried out at the NCC quarry located approximately 70km:s east from G oteborg, Sweden. The crusher was a secondary SANDVIK H6800 crusher, with a coarse crushing chamber. The material fed to the crusher was 32250mm granite that had previously been crushed in a pri- mary jaw crusher. 3. Results 3.1. Measurements The coordinates from the measurements were transformed, andthemeasuredgeometrywasenteredintoaCAD-tool.Fig.10 Fig. 10. Measured geometry compared with a 3D-CAD model of mantle and concave. M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxx5 Fig. 11. Simulated geometry of a worn mantle profi le at different times, using two different wear models. showsthemeasuredworngeometry,comparedtoacrosssection of the nominal CAD-geometry. 3.2. Simulation versus measurement of wear The worn liner profi les were computed using the crusher model. Fig. 11 shows worn mantle profi les at different times, using the two different wear models. The left profi le shows the worn geometry obtained using the previous wear model that is independent of shear forces. The right profi le shows the worn geometry from the new shear-dependent wear model. There is an obvious difference between the two models in prediction of wear in the upper part of the chamber. The effect of non-sliding shear force is scaled so that simulations fi t measured data. The wear model parameter K in Eq. (8) was selected so that the wear was correctly predicted at two points on the liner: where the maximum wear occurs, near the bottom of the mantle, and on onepointlocatednearthetopoftheliner,one-thirdofthecham- berheightfromthetop.K=50givesthebestagreement.Ashear wear factor of 50 may seem high, but the shear force factor f in Eq. (5) is small, since the angle between the liners is small. Fig.12showsthemeasuredandsimulatedwearonanH6800 mantle.Theweariscomputedasthedifferencebetweennominal new and worn geometry, measured in the normal direction of the surface. As can be seen in Fig. 12, the new wear model signifi cantlyimprovesthewearpredictionintheupperpartofthe crushing chamber compared to the old model. The fl ow model used here was presented by Lindqvist 6. Fig. 13 shows simulated and measured wear on the concave of a worn SANDVIK H3000 MF chamber. The measurement in Fig. 13 was made by Lindqvist and Evertsson 3. Highly abrasive quartzite was crushed. The simulation in reference 3 Fig. 12. Simulated and measured amount of wear on the mantle of an H6800 EC liner set. The geometry was measured in the normal direction of the surface after 385h of operation. was made with the fl ow model presented by Evertsson 1. That modelisslightlydifferentfromtheoneusedhere.Fig.12shows the wear on the mantle of a Sandvik, H6800 crusher, Fig. 13 shows the wear on a Sandvik H3000 MF concave. The mantle and the concave have different local coordinate systems in the simulator, hence the difference in y-coordinate. 3.3. Simulation versus measurement of operating parameters Hydroset pressure and power draw were read off the control panel of the crusher once every day. When the inlet bin of the crusher is entirely fi lled with rock material, the crusher is said to be choke fed, and this is the preferred way to operate a cone crusher. Readings were taken during normal operation of the crusher, i.e. choke fed conditions. The feed was between 32 and 250mm and came from the primary crusher. Fig.13. SimulatedandmeasuredwearonaconcaveofaSANDVIKH3000MF chamber. Measurements were made by Lindqvist and Evertsson 3. 6M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxx Fig. 14. Correlation between power draw and hydroset pressure. The wear model is indifferent to how time is scaled, and the wear rate is exaggerated in the simulations, to save computa- tion time. The wear was accelerated by a factor of 4700 times, as compared to the wear rate found by Lindqvist and Everts- son 3. If the wear rate is accelerated too much, the simulated worn geometry will deteriorate as compared to the measured geometry. Fig. 14 shows the correlation between power draw and hydroset pressure. The model for fl ow and crushing pressure require a validation of some model parameters 7. In the sim- ulations made here, the model parameters were selected so that power draw and hydroset pressure were predicted as accurately as possible with respect to average measured data. Power draw and hydroset pressure cannot be predicted accurately without takinglossesintoaccount.Lossesinaconecrusherarisemainly in the electric motor, the belt drive, the roller bearings support- ing the driveshaft. Frictional losses occur in the top bearing, the eccentric bushings and the spherical thrust bearing who are all boundary lubricated plain bearings. According to the machine manufacturer, this particular crusher usually has an idle power draw of 3035kW. The mass of the main shaft corresponds to a hydraulic pressure of 0.28MPa. To adjust for losses, load dependent and load independent losses were simply added to the nominal data to make simulations match measured data. A constantloadindependentlossof35kWwasaddedtothepower draw and the load dependent loss was computed by dividing the nominal power draw by the total effi ciency. The effi ciency used here was 59%. If the losses are subdivided onto electric motor, beltdrive,driveshaft,bevelgearandeccentricbushing,theaver- age effi ciency of each of these power-transmitting components willbeabout90%.ThetwomodelparametersforanH3000MC chamber that were found by Lindqvist 6 were K1=0.312 and K2=1.01. For this crusher, which is much larger, K1=0.3590 and K2=1.2387. Readings of power draw and hydroset pressure were taken during normal choke fed conditions once every day (see Figs. 15 and 16). The time of these readings were only specifi ed by date. The number of hours per day each crusher was in oper- ation was recorded, and was below 8h every day. This means Fig. 15. Power draw, simulation and measurement. there is an inaccuracy of less than 8h as for when each read- ing was made. Simulated time has here been expressed as dates. Simulated time corresponds to the time it takes for the model to produce the same amount of maximum wear on the mantle as is measured. In other words, maxi