φ3200×3100格子型球磨机设计【含7张CAD图纸】
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φ3200×3100格子型球磨机设计【含7张CAD图纸】,含7张CAD图纸,3200,3100,格子,球磨机,设计,CAD,图纸
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第1页PREDICTIVE MODEL FOR BALL MILLWEARAbstract-ball mills, characteristic of the mineral processing industry, are used to reduce orefrom one size distribution to another. Wear is associated with comminution mechanisms foundin the ball charge which in turn affects grinding performance. In this work, ball mill wear, as afunction of mill operating variables, is determined using a mathematical wear model. Thewear model incorporates the energy dissipated in crushing, tumbling and grinding zones ofthe charge profile with adhesive and abrasive wear descriptions. This model has been added toa ball charge motion model allowing the simulation of mill wear rates as well as ball millelement wear and its affect on grinding performance. Simulation results presented show theinteraction between wear and grinding performance. Further work is necessary to validatecharge and wear model results using industrial date.1997 Canadian Institute of Mining andMetallurgy. Published by Elsevier Science Ltd.INTRODUCTIONTo comminute, to reduce to minute particles, to pulverize, are all synonyms of grindingprocesses used in the mineral processing industry. Associated with these processes is metalwear which in Canada and the United States represents an annual consumption of some 300000 tons of iron and steel 1. Wear also affects grinding performance and quality. In such acontext, predictive wear models become a necessity to determine optimal grinding conditionsthat reduce process wear while maintaining grinding performance and quality.Wear and its mechanisms related to grinding has been studied extensively usingexperimental data 2-4, models useful to understanding of wear phenomena 5-9 andtheoretical studies 10-12.The goal of this paper is the presentation of a predictive wearmodel based on a theoretical development for one such grinding process, the ball mill.BACKGROUNDThe ball mill (Fig.1) is a system composed of a number of interrelated and interactiveelements that work together in order to grind a given ore. This comminution process isachieved by the individual balls which constitute the actual ball mill element that brings about第2页ore breakage. Together, these balls form the mill ball charge which, during ball mill operation,typically has a charge profile as found in Fig.2.Note that the charge profile shows three zones that are characterized by the type ofbreakage occurring there. The grinding zone is described by ball layers sliding over oneanother, breaking the material trapped between them; the tumbling zone is described by ballsrolling over one another and breaking the material in low-energy impact; the crushing zone isdescribed by balls in flight re-entering the ball charge and crushing the material inhigh-energy impact.The form of the charge profile is directly dependant on the friction force existing between第3页the charge and the ball mill wall. By the use of different liner profile (Fig.3), the friction forcecan be changed subsequently affecting the form of the mill charge as well.Charge motion modelAs mentioned. Mill wear is a function of the energy transferred between liner and ballcharge as well as between two colliding balls. Therefore, modelling charge motion is a firststep to predicting mill wear and its effect on grinding.Model development starts with defining single ball motion (Fig.4). As described by Mclvorand Powell 15、16, the point of flight of a single ball in a ball mill can be determined as afunction of rotation speed, mill radius, static friction factor and the liner lifer angle:cosarcsin0g(1)However, Hukki 17 mentions that ball charge motion is not entirely dependant on asingle point of flight as assumed with the above equation. It is also dependant on whether theeffective friction factor describing the interrelationship between ball charge and type of linerused is greater or less than I.第4页Therefore, if we describe slippage between two ball layers as a relationship between staticand kinetic friction factors 17;ssskVV110.6112.11(2)Rotational slippage speed becomes:RVssin1(3)Using this result, we can differentiate between ball flight and the point of stable slippage as:1. point of flight (1.0)sosgRarctancosarcsinarctan2(4)2. point of stable slippage (1.0)kokgRarctancosarcsinarctan2(5)Where the effective friction factor is defined as;2arctantans(6)Using these relationships along with those described in 18-20 and applying them to asystem of particles that describe a discretized ball charge, it becomes possible to simulate ballcharge motion (Fig. 5).第5页Having thus defined charge motion, we can further this development by determiningenergy consumed and distributed in the various comminution zones on the charge profile (Fig,2) using the following equations 18, 21: effinciiciconsumedmrE1cos(7)ngiciiikgrindingrNE1(8)第6页tvmEgdmtvmEgdmvmibitumblingbbiibicrushingbbiibi22221:21:21(9)The energy profile (Fig. 6) in a ball mill can now be determined as for the Hardinge mill ofFig. 1. Note that this charge motion model determines how energy is consumed and thendistributed in grinding, crushing and tumbling as a function of mill rotation speed, milldiameter, ball charge and liner representation.Wear rate estimationAs mentioned earlier, there are three comminution zones in the ball charge motion profile.Although other wear mechanisms exist, only adhesive and abrasive wear are associated herewith these comminution zones. Adhesive wear is associated with the tumbling and crushingzone as balls in these zones collide while abrasive wear is associated to the grinding zonewhere balls slide pass one another or over the null liner. These mechanisms can be expressedin terms of energy rate used in wear as 23-24:adhesive wearEHPmrst3(10)abrasive weargrrstEHm)tan(11)Applying these wear models to the ball mill case, we write;grrststjhEHm)tan(12)rumrcrrgrcrstjhEHpEHPEHm33)tan(13)stjwsbjbstjtotmmm(14)Comparing initial and final liner wear profiles, liner wear rate can be estimated using:TnALmmststjw(15)We can determine the abrasion factor by equating eqn (15) with eqn (12), thus getting:第7页grrmwEHTnALP1tan(16)Further, using eqn (13) and eqn (14) with the result of eqn(16)， we can determine the adhesionprobability:grcrststiwatjtottumcrrEHmmEEHP)tan(3(17)With the abrasion factorand adhesion probability P determined for a given mill operatingcontext, we can now determine how changes from this context affect mill wear rates. Keepingand P constant, and varying parameters such as mill rotation speed and charge column, wecan predict the associated changes to mill wear rates 24. However, predicting wear rates isonly of limited use when considering our goal of determining the effect of wear on ball millgrinding performance.Liner wearGrinding performance in a ball mill is determined primarily by how energy is distributedinto the various comminution zone found in the ball charge profile. As mentioned, the form ofthe charge profile, and consequently the importance of each comminution zone, is directlydependant on the friction force existing between the ball charge and the mill wall.Different liner types (Fig.3) affect this friction force between the ball charge and the millwall and the mill grinding performance. For a given grinding context, it is possible to use aliner type that is considered optimal. However, with time, mill wear will modify the initialliner profile and subsequently mill grinding. Modelling the forces acting on the mill linersbecomes the next step to predicting mill wear and its effect on grinding.During mill operation, the hall charge exerts a force field composed of gravitational andcentrifugal components on the mil liner (Fig.7) 23, 25.第8页Using this description, normal force component can be determined as show in Fig.8, giving:(i) centrifugal normal component)cos(cpcpFN(18)(ii) gravitational normal component)cos(21gqgqFN(19)Further, as the ball charge slip over the mill liner, a compression force is created with the第9页local displacement of the mill charge by the liner (Fig.9). This force is defined as:.CKFcom(20)WherexystV.The normal compression component as:)cos(comcomFN(21)The total normal force acting on the liner surface becomes:comgqcptNNNN(22)Liner wear, as a function of the position and intensity of the force field created by the ballcharge as well as the abrasion factor 0, become:surftrstVNHm)tan(23)Where)cos(slsurfVV(24)Note that slippage speed on the liner is defined previously by rearrangement of eqn (2).After liner discretization into differences，and time into, a simulationalgorithm can be developed 23, 25 which allows liner profile wear simulation.As an example, Fig. 10 illustrates a wave liner profile wear simulation which is comparable第10页to the real liner profile wear presented in Fig.11.MILLWEARAND GRINDING PERFORMANCEEven though industrial studies are needed to further validate these wear models, it ispossible envisage the prediction of wear evolution of a given liner type. This, of course,wou1d allow the determination of how wear affects grinding performance here defined asvariations in output granulometry. For the Hardinge case of Fig.1, this translates intosimulating the effect of wear on the bevel liner as shown in Fig.12.Further, simulating how the energy rate profile of Fig.6 changes with this liner wear, it ispossible to predict the changes in mill output granulometry for the same input granulometry.Table 1 shows how, using a breakage model developed in 22,23, it is possible to illustrateoutput variation over the life period of the liner. Here, mill output becomes finer with linerwear.Associated with this phenomenon, mill energy consumption decreases as shown in Fig.13.Both these phenomena illustrate the possibility of optimizing ball mill performance as afunction of the predetermined effect of wear.Table 1. Ball mill output granulometries as a function of worn liner profileParticle size(m)Initial %passing1/2 life %passingFinal %passing741001503008301170165058.0868.2578.5492.1299.4599.96100.0058.2568.4478.6892.1599.4599.96100.0060.1370.3880.2593.9699.6199.97100.00第11页DISCUSSIONBefore concluding this work a few remarks should be made concerning charge motion,liner wear and associated mill output product.As shown, ba11 charge motion is dependant on a number of physical and operating factors;it is also dependant on the rheological characteristics of agiven slurry. These rheologicalcharacteristics are of course a function of percentage solids as well as ore properties. In themodel of charge motion the effect of these factors is included in the relationship (2) forslippage speed as escribed using static and kineticd friction factors. Avariation in the frictionfactors, as caused by a possible change in rheological characteristics of a given slurry, canincrease or decrease the amount of slippage between ball layers and thus increase or decreaseliner wear.第12页In modelling ball mill wear with only two wear mechanisms, it is assumed that a mill isnot run empty or that operating conditions do not send mill balls crashing directly into themill liner. Under such conditions, liner wear increases considerably with added wearmechanisms
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