型砂處理機(jī)破碎機(jī)構(gòu)的設(shè)計圖紙,型砂,處理機(jī),破碎,機(jī)構(gòu),設(shè)計,圖紙 Original Research PaperA new size distribution model by t-family curves for comminution of limestonesin an impact crusherVedat DenizDepartment of Chemical Engineering, Hitit University, orum, Turkeya r t i c l ei n f oArticle history:Received 11 July 2010Received in revised form 20 October 2010Accepted 31 October 2010Available online 13 November 2010Keywords:LimestoneBreakageImpact crusherBond work indexSize distributiont-Familya b s t r a c tIn the evaluation of crushers, t-family curves obtained from single particle test methods are frequentlyused. It is known that there are many difficulties and problems in these tests. In this study the breakagebehaviour of three different limestones in an impact crusher was investigated. A new size distributionmodel was developed by t-family value evaluation and Bond work index approach. As a result, the validityof the equation was proved by a high regression value (r2= 0.88).? 2010 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of PowderTechnology Japan. All rights reserved.1. IntroductionImpact-induced rock fragmentation is relevant for many fieldsof science and technology. Impact mills have been applied inmineral, coal, cement and chemical industries for a long time.The literature shows that substantial effort has been expended inunderstanding the impact mill performance in relation to machineconfiguration and operational conditions through experimentalwork and mathematical modelling. However, due to lack of de-tailed knowledge on velocity and energy distributions of collisioninside a milling chamber, the mechanisms are still not clear 1.Bond testing has been in use since the late 1920s; laboratoriesand operations around world used the procedure as a componentof comminution circuit design as well as evaluation of plant perfor-mance. In spite of such long-standing use, the topic of accuracy andprecision of Bond work index determinations recurs with great fre-quency 2.Single particle tests to determine the comminution behaviour ofore can be separated into twin pendulum device (Fig. 1) and dropweight apparatus (Fig. 2) based tests 37.Schuhmann 8 reported that the size reduction events couldthemselves involve varying energy input, varying feed particle sizeand varying size distribution. Flavel and Rimmer 9 have reviewedsingle-particle breakage on the pendulum device, and stated thatthe pendulum device can be suitable for obtaining the relation be-tween the breakage product distribution and comminution energy.Twin pendulum test relies on the particle being broken betweenan input pendulum released from a known height and a reboundpendulum. Twin pendulum, however, has some important limita-tions, particularly regarding its low flexibility and reproducibility,long test duration, and the poor accuracy in estimating the commi-nution energy as a result of secondary motion of the rebound pen-dulum 47.The drop weight test differs, in that the particles are placed on ahard surface and struck by a falling weight. Both tests have beenextensively used in the field of comminution. In recent years, how-ever, the drop weight apparatus are being replaced by the twinpendulum. The standard drop weight device is fitted with a 20 kgmass, which can be extended to 50 kg. The effective range of dropheights is from 0.05 to 1.0 m, which represents a wide energyrange from 0.01 to 50 kW h/t (based 1050 mm particles). Follow-ing sample preparation the mean mass of each set of particles to bebroken is calculated. The results from the drop weight testsprovide an energy/input size/product size relationship. This rela-tionship is analysed using a set of curves to describe the size distri-bution produced from breakage events of increasing size reductionor energy input 35,1011.In the drop weight test, a known mass falls through a givenheight onto a single particle providing an event that allows charac-terisation of the ore under impact breakage. Although, the dropweight test has advantages in terms of statistical reliability andthe potential use of the data from the analysis, it has a number0921-8831/$ - see front matter ? 2010 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.doi:10.1016/j.apt.2010.10.020Tel.: +90 364 2274533; fax: +90 364 2274535.E-mail address: vedatdenizhitit.edu.trAdvanced Powder Technology 22 (2011) 761765Contents lists available at ScienceDirectAdvanced Powder Technologyjournal homepage: disadvantages, including necessity a special apparatus, tiringand particularly the length of time taken to carry out a test. Foreach drop weight test, 15 samples are tested in five size fractionsat three levels of energy input 1013.Narayanan 14 was used a novel procedure for estimation ofbreakage distribution functions of ores from t-family of curves. Inthis method, the product size distribution can be represented bya family of curves using marker points on the size distribution de-fined as the percentage passing (t) at a fraction of the parent par-ticle size. Thus, t2is the percentage passing an aperture of halfthe size of the parent particle size, t4is one quarter and t10isone-tenth of parent particle size. Narayanan and Whiten 15 haveproposed empirical equations for relating the reference curve datat10with the impact energy.The t10value is related to the specific comminution energy bythe Eq. (1):t10 A1 ? e?bEcs1The tnversus t10relationships can then be used to predict theproduct size distributions at different grind times 16.It is known that there are many difficulties and problems indrop weight and twin pendulum test methods such as beinglaborious, requiring long test time and requiring a special appara-tus. In this study, breakage behaviours of three different lime-stones in a laboratory impact crusher were investigated. A newsize distribution model equation was developed by t-family valueevaluation and Bond work index approach, and this model equa-tion was tested.2. Materials and method2.1. MaterialThree different limestone samples taken from different regionof Turkey were used as the experimental materials. The chemicalproperties of the limestone samples were presented in Table 1.2.2. The test of standard Bond grindabilityThe Bond grindability tests were conducted less than 3.35 mmof dry feed materials in a standard ball mill (30.5 ? 30.5 cm) fol-lowing a standard procedural outline described in the literature1724. The work indices were determined at a test sieve size of106lm. It has no lifters and all the inside corners are rounded.The Bond ball mill (Fig. 3) is operated at 70 rpm and is equippedwith a revolution counter. The grinding charge consists of 285 ironballs weighing 20.125 g. The standard Bond grindability test is aclosed-cycle dry grinding and screening process, which is carriedout until steady state condition is obtained. This test was describedas follow 1724.The material is packed to 700 cc volume using a vibrating table.This is the volumetric weight of the material to be used forgrinding tests. For the first grinding cycle, the mill is started withan arbitrarily chosen number of mill revolutions. At the end of eachgrinding cycle, the entire product is discharged from the mill and isscreened on a test sieve size (Pi). Standard choice for Piis 106l.The oversize fraction is returned to the mill for the second runtogether with fresh feed to make up the original weight corre-sponding to 700 cc. The weight of product per unit of mill revolu-tion, called the ore grindability of the cycle, is then calculated andis used to estimate the number of revolutions required for thesecond run to be equivalent to a circulating load of 250%. Theprocess is continued until a constant value of the grindability isachieved, which is the equilibrium condition. This equilibriumcondition may be reached in 612 grinding cycles. After reachingequilibrium, the grindabilities for the last three cycles are aver-aged. The average value is taken as the standard Bond grindability(Gbg).The products of the total final three cycles are combined to formthe equilibrium rest product. Sieve analysis is carried out on thematerial and the results are plotted, to find the 80% passing sizeof the product (P80). The Bond work index values (Wi) are calcu-lated from the Eq. (2) .Nomenclaturet10the cumulative percentage passing 1/10th of the initialmean size (%)tnthe cumulative percentage passing 1/nth of the meanparticle size (%)nratio dividing to a characteristic size of the mean parti-cle sizeEcsspecific comminution energy (kW h/t)A,bore impact breakage parametersWiBond work index (kW h/t)Pitest sieve size at which the test is performed (106lm)Gbgstandard Bond grindability, net weight of ball mill prod-uct passing sieve size Piproduced per mill revolution (g/rev)F80sieve opening which 80% of the feed (lm)P80sieve opening which 80% of the product (lm)Xmean particle size (mm)Fig. 1. Twin pendulum device.762V. Deniz/Advanced Powder Technology 22 (2011) 761765Wi 1:1 ?44:5P0:23i? G0:82bg? 10=ffiffiffiffiffiffiffiP80p ? 10=ffiffiffiffiffiffiffiF80p?23. ExperimentsFirstly, standard Bond grindability tests were performed forthree limestone samples. From the result of tests, Bond work indexvalues were calculated 4.44, 10.10 and 13.53 kW h/t, respectively.Then, 1 kg sample of six mono-size fractions (?6.7 + 4.75, ?4.75 +2.8, ?2.8 + 1.7, ?1.7 + 1.18, ?1.18 + 0.600, ?0.600 + 0.355 mm)were prepared by screens for determination of the t-family curves.The laboratory impact crusher (Fig. 4), used in the experiments,works with driven by a 1.1 kW motor, rotating at 2840 rpm, carrythree rows of hammers. Each sample was taken out of the labora-tory impact crusher, and then samples were sieved for product sizeanalysis.Results of t-family curves versus mean particle size fraction fordifferent limestones were shown in Figs. 57.Fig. 3. Bond mill.Fig. 4. Impact crusher using in experiments.Fig. 5. tnversus mean size fraction for limestone-I.Fig. 6. tnversus mean size fraction for limestone-II.Fig. 2. Drop-weight test apparatus.Table 1Chemical composition of limestone samples using in experiments.Oxides (%)Limestone-ILimestone-IILimestone-IIICaO31.0346.8548.99SiO20.058.4510.60Al2O30.901.021.07Fe2O30.000.350.59MgO22.420.921.11SO30.020.070.09Na2O0.070.020.04K2O0.100.060.08Loss on ignition45.2436.5038.72V. Deniz/Advanced Powder Technology 22 (2011) 7617657634. Proposed size distribution model equationKing 25 described a method of presenting the product sizedistributions obtained from drop weight tests. It is based on theobservations made by Narayanan and Whiten 26, that the cumu-lative fraction of products passing 1/nth of the mean size was de-noted by tn, is related to that passing one-tenth of the parent sizedenoted by t10. It was also reported that this relationship wasapplicable to different ore types tested under different impactloading conditions.In this study, a different size distribution relationship has beenexposed tnvalues for crushing products in the direct laboratoryimpact crusher. As a result of this study, the relationship betweenthe cumulative percentage passing (tn) with Bond work index (Wi)and mean particle size (X) was empirically described by Eq. (3).tn406:35W0:921i? n1:1X0:108W0:668i?n2:47W?1:184i3The experimental values and the calculated results obtained byEq. (3) were compared in Fig. 8.Eq. (3) mostly satisfies the experimental values in a wide rangeof feed size, and Eq. (3) is useful especially when evaluating the par-ticle size distribution in the actual operation by a high regressionvalue (r2= 0.88). Thus, the relationship between the cumulativepercentage passing (tn) with Bond work index (Wi) and mean parti-cle size (X) was empirically described by Eq. (3).5. Results and discussionThe results showed that limestone-I sample was more friablethan limestone-II sample while limestone-II sample was more fri-able than limestone-III sample. A set of t-curves were calculatedfrom the direct a laboratory impact mill and a new size distributionequation was developed.The product size distribution from the breakage by impactcrusher of particle can be described as all-parameter (tn) familyof curves. The product size distributions were found to be normal-izable with respect to particle sizes. Cumulative percentages ofpassing material belong to (tn) the experimental data was com-pared with the proposed equation given a better results with dataand has a potential use in industrial applications.In this study, the type of limestone has emerged very clearlyplayed an important role in comminution. In addition, in crusherselection was played an important role of the standard the Bondgrindability and work index values.The t-curves are the family of size distribution curves which canbe used to describe the product size distribution of the breakageparticles during single-particle breakage tests. The cumulative per-centages passing of the parameters t2, t4, t10, t25, t50and t75aredetermined by linear interpolation from the breakage productspassing against the different range of sieve sizes. However, thereare many difficulties and problems in drop weight and twin pendu-lum test methods such as being laborious, requiring long test timeand requiring a special apparatus.This paper presents the results of an investigation into the ef-fects of the Bond work index and the mean particle size on particlesize distribution in a pilot scale impact mill. The results denote thatparticle size distribution is strongly related to mean particle size(X) and Bond work index (Wi). The relationship with data fromexperimental and proposed equation for determination of particlesizedistributionshasemergedbyahighregressionvalue(r2= 0.88).6. ConclusionsIn this study, laboratory crushing tests of three different lime-stones with an impact crusher were carried out. The effects ofmean particle size and Bond work index of limestones on productsize distribution were investigated.The proposed model equation which incorporates the self-similar breakage behaviour in laboratory comminution could beused an alternative to the drop weight and twin pendulum tests,as its particle size distributions could evaluated more readily andreliably.There are no studies in the literature which have been madeabout the effect of the amount of feed, effect of rotor speed, liningdesign and design of the hammer on the impact crushers, verycommonly used in quarries. Therefore, crusher and grinder manu-factures will be possible to make appropriate choices of such stud-ies with different designs for different material to be developingsimilar models.This study showed that product size distribution could be dif-ferent for different material properties. Therefore, it appears thatthe particle size distributions of each material in crushing processmust be evaluated in order to lower the energy costs.References1 N. Djordjevic, F.N. Shi, R.D. Morrison, Applying discrete element modelling tovertical and horizontal shaft impact crushers, Miner. Eng. 16 (2003) 983991.Fig. 7. tnversus mean size fraction for limestone-III.Fig. 8. Comparison of experimental and calculated tnvalue for limestone.764V. Deniz/Advanced Powder Technology 22 (2011) 7617652 J.B. Mosher, C.B. Tague, Conduct and precision of Bond grindability testing,Miner. Eng. 14 (2001) 11871197.3 R.A. Bearman, C.A. Briggs, T. 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