φ3200×3100格子型球磨机设计【含CAD图纸】
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第13页PREDICTIVE MODEL FOR BALL MILL WEARAbstract-ball mills, characteristic of the mineral processing industry, are used to reduce ore from one size distribution to another. Wear is associated with comminution mechanisms found in the ball charge which in turn affects grinding performance. In this work, ball mill wear, as a function of mill operating variables, is determined using a mathematical wear model. The wear model incorporates the energy dissipated in crushing, tumbling and grinding zones of the charge profile with adhesive and abrasive wear descriptions. This model has been added to a ball charge motion model allowing the simulation of mill wear rates as well as ball mill element wear and its affect on grinding performance. Simulation results presented show the interaction between wear and grinding performance. Further work is necessary to validate charge and wear model results using industrial date.1997 Canadian Institute of Mining and Metallurgy. Published by Elsevier Science Ltd.INTRODUCTIONTo comminute, to reduce to minute particles, to pulverize, are all synonyms of grinding processes used in the mineral processing industry. Associated with these processes is metal wear which in Canada and the United States represents an annual consumption of some 300 000 tons of iron and steel 1. Wear also affects grinding performance and quality. In such a context, predictive wear models become a necessity to determine optimal grinding conditions that reduce process wear while maintaining grinding performance and quality. Wear and its mechanisms related to grinding has been studied extensively using experimental data 2-4, models useful to understanding of wear phenomena 5-9 and theoretical studies 10-12.The goal of this paper is the presentation of a predictive wear model based on a theoretical development for one such grinding process, the ball mill.BACKGROUND The ball mill (Fig.1) is a system composed of a number of interrelated and interactive elements that work together in order to grind a given ore. This comminution process is achieved by the individual balls which constitute the actual ball mill element that brings about 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 of breakage occurring there. The grinding zone is described by ball layers sliding over one another, breaking the material trapped between them; the tumbling zone is described by balls rolling over one another and breaking the material in low-energy impact; the crushing zone is described by balls in flight re-entering the ball charge and crushing the material in high-energy impact. The form of the charge profile is directly dependant on the friction force existing between the charge and the ball mill wall. By the use of different liner profile (Fig.3), the friction force can be changed subsequently affecting the form of the mill charge as well.Charge motion model As mentioned. Mill wear is a function of the energy transferred between liner and ball charge as well as between two colliding balls. Therefore, modelling charge motion is a first step to predicting mill wear and its effect on grinding. Model development starts with defining single ball motion (Fig.4). As described by Mclvor and Powell 15、16, the point of flight of a single ball in a ball mill can be determined as a function of rotation speed, mill radius, static friction factor and the liner lifer angle: (1) However, Hukki 17 mentions that ball charge motion is not entirely dependant on a single point of flight as assumed with the above equation. It is also dependant on whether the effective friction factor describing the interrelationship between ball charge and type of liner used is greater or less than I. Therefore, if we describe slippage between two ball layers as a relationship between static and kinetic friction factors 17; (2) Rotational slippage speed becomes: (3)Using this result, we can differentiate between ball flight and the point of stable slippage as:1. point of flight (1.0) (4)2. point of stable slippage (1.0) (5)Where the effective friction factor is defined as; (6) Using these relationships along with those described in 18-20 and applying them to a system of particles that describe a discretized ball charge, it becomes possible to simulate ball charge motion (Fig. 5). Having thus defined charge motion, we can further this development by determining energy consumed and distributed in the various comminution zones on the charge profile (Fig, 2) using the following equations 18, 21: (7) (8) (9) The energy profile (Fig. 6) in a ball mill can now be determined as for the Hardinge mill of Fig. 1. Note that this charge motion model determines how energy is consumed and then distributed in grinding, crushing and tumbling as a function of mill rotation speed, mill diameter, ball charge and liner representation.Wear rate estimation As 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 here with these comminution zones. Adhesive wear is associated with the tumbling and crushing zone as balls in these zones collide while abrasive wear is associated to the grinding zone where balls slide pass one another or over the null liner. These mechanisms can be expressed in terms of energy rate used in wear as 23-24:adhesive wear (10)abrasive wear (11)Applying these wear models to the ball mill case, we write; (12) (13) (14)Comparing initial and final liner wear profiles, liner wear rate can be estimated using: (15)We can determine the abrasion factor by equating eqn (15) with eqn (12), thus getting: (16)Further, using eqn (13) and eqn (14) with the result of eqn(16)，we can determine the adhesion probability: (17)With the abrasion factor and adhesion probability P determined for a given mill operating context, we can now determine how changes from this context affect mill wear rates. Keeping and P constant, and varying parameters such as mill rotation speed and charge column, we can predict the associated changes to mill wear rates 24. However, predicting wear rates is only of limited use when considering our goal of determining the effect of wear on ball mill grinding performance.Liner wear Grinding performance in a ball mill is determined primarily by how energy is distributed into the various comminution zone found in the ball charge profile. As mentioned, the form of the charge profile, and consequently the importance of each comminution zone, is directly dependant 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 mill wall and the mill grinding performance. For a given grinding context, it is possible to use a liner type that is considered optimal. However, with time, mill wear will modify the initial liner profile and subsequently mill grinding. Modelling the forces acting on the mill liners becomes 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 and centrifugal components on the mil liner (Fig.7) 23, 25.Using this description, normal force component can be determined as show in Fig.8, giving: (i) centrifugal normal component (18)(ii) gravitational normal component (19)Further, as the ball charge slip over the mill liner, a compression force is created with the local displacement of the mill charge by the liner (Fig.9). This force is defined as: (20)Where The normal compression component as: (21)The total normal force acting on the liner surface becomes: (22)Liner wear, as a function of the position and intensity of the force field created by the ball charge as well as the abrasion factor 0, become: (23)Where (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 simulation algorithm 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 to the real liner profile wear presented in Fig.11.MILL WEAR AND GRINDING PERFORMANCEEven though industrial studies are needed to further validate these wear models, it is possible 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 as variations in output granulometry. For the Hardinge case of Fig.1, this translates into simulating 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 is possible 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 illustrate output variation over the life period of the liner. Here, mill output becomes finer with liner wear.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 a function 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 %passing741001503008301170165058.0868.2578.5492.1299.4599.96100.0058.2568.4478.6892.1599.4599.96100.0060.1370.3880.2593.9699.6199.97100.00DISCUSSIONBefore 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 a given slurry. These rheological characteristics are of course a function of percentage solids as well as ore properties. In the model of charge motion the effect of these factors is included in the relationship (2) for slippage speed as escribed using static and kineticd friction factors. A variation in the friction factors, as caused by a possible change in rheological characteristics of a given slurry, can increase or decrease the amount of slippage between ball layers and thus increase or decrease liner wear. In modelling ball mill wear with only two wear mechanisms, it is assumed that a mill is not run empty or that operating conditions do not send mill balls crashing directly into the mill liner. Under such conditions, liner wear increases considerably with added wear mechanisms (surface fatigue, fracture, cratering) g
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