mill steel charge volume calculation
We can calculate the steelcharge volume of a ball or rod mill and express it as the %of the volume within the liners that is filled with grinding media. While the mill is stopped, the charge volume can begottenby measuring the diameter inside the liners and the distance from the top of the charge to the top of the mill. The %loading or change volume can then be read off the graphbelowor approximated from the equation and calculation:
mill charge - an overview | sciencedirect topics
Rod mill charges usually occupy about 45% of the internal volume of the mill. A closely packed charge of single sized rods will have a porosity of 9.3%. With a mixed charge of small and large diameter rods, the porosity of a static load could be reduced even further. However, close packing of the charge rarely occurs and an operating bed porosity of 40% is common. Overcharging results in poor grinding and losses due to abrasion of rods and liners. Undercharging also promotes more abrasion of the rods. The height (or depth) of charge is measured in the same manner as for ball mill. The size of feed particles to a rod mill is coarser than for a ball mill. The usual feed size ranges from 6 to 25mm.
For the efficient use of rods it is necessary that they operate parallel to the central axis and the body of the mill. This is not always possible as in practice, parallel alignment is usually hampered by the accumulation of ore at the feed end where the charge tends to swell. Abrasion of rods occurs more in this area resulting in rods becoming pointed at one end. With this continuous change in shape of the grinding charge, the grinding characteristics are impaired.
The bulk density of a new rod charge is about 6.25t/m3. With time due to wear the bulk density drops. The larger the mill diameter the greater is the lowering of the bulk density. For example, the bulk density of worn rods after a specific time of grinding would be 5.8t/m3 for a 0.91m diameter mill. Under the same conditions of operation, the bulk density would be 5.4t/m3 for a 4.6m diameter mill.
During normal operation the mill speed tends to vary with mill charge. According to available literature, the operating speeds of AG mills are much higher than conventional tumbling mills and are in the range of 8085% of the critical speed. SAG mills of comparable size but containing say 10% ball charge (in addition to the rocks), normally, operate between 70 and 75% of the critical speed. Dry Aerofall mills are run at about 85% of the critical speed.
The breakage of particles depends on the speed of rotation. Working with a 7.32m diameter and 3.66m long mill, Napier-Munn etal.  observed that the breakage rate for the finer size fractions of ore (say 0.1mm) at lower speeds (e.g., 55% of the critical speed) was higher than that observed at higher speeds (e.g., 70% of the critical speed). For larger sizes of ore (in excess of 10mm), the breakage rate was lower for mills rotating at 55% of the critical speed than for mills running at 70% of the critical speed. For a particular intermediate particle sizerange, indications are that the breakage rate was independent of speed. The breakage ratesize relation at two different speeds is reproduced in Figure9.7.
The blending of different ore types is a common practice to provide a consistent feed to a process in terms of uniform hardness or assay. When several different ore deposits of varying grindabilities are blended prior to closed circuit grinding, the work index of the ore is not an average or even a weighted average of the work indices of the components. The reason for this is that the circulating load will consist predominantly of the harder component and if the circulating load is high then the mill charge will also consist of mostly the harder components. Thus, the work index of the blend will be weighted towards the harder components . Figure3.16 shows the Bond work index of a blend of hard and soft ores as a function of the volume fraction of the softer ore in the blend. The dotted line between the two extremes indicates the weighted average work index based on volume fraction. The work index values of the Magdalinovic method agree with this average Bond work index because the method does not simulate the recycling of harder components into the mill charge. On the other hand, the work index obtained using the standard Bond test shows the weighting of the work index towards the harder component as a result of the circulating load.
Yan and Eaton  also measured the breakage rates and breakage distribution functions of the different ore blends in order to predict the work index of the blend by simulation of the Bond batch grinding test. Qualitative analysis of the breakage properties suggests that there is an interaction between the components of the blend that affect their individual breakage rates. The breakage properties of the harder material appear to have a greater influence on the overall breakage properties and the Bond work index of the blend than the softer material.
Whereas most of the ball-milled systems usually prepared with using ball-to-powder weight ratio (Wb:Wp) in the range between 10:1 and 20:1, the effect Wb:Wp on the amorphization reaction of Al50Ta50 alloy powders in a low-energy ball mill was investigated in 1991 by El-Eskandarany etal. They have used 90, 30, 20, 10, and 3g of powders to obtain Wb:Wp ratios of 12:1, 36:1, 54:1, 108:1, and 324:1, respectively.
The XRD patterns of mechanically alloyed Al50Ta50 powders as ball-milled for 1440ks (400h) as a function of the Wb:Wp ratio is presented in Fig.4.32. Single phase of amorphous alloys is obtained when ratios 36:1 and 108:1 were used. The Bragg peaks of elemental Al and Ta crystals still appear when the Wb:Wp ratio is 12:1, indicating that the amorphization reaction is not completed. In contrast, when the Wb:Wp ratio is 324:1, the amorphous phase coexists with the crystalline phases of AlTa, AlTa2, and AlTaFe.
Based on their results, it is concluded that the rate of amorphization depends strongly on the kinetic energy of the ball mill charge and this depends on the number of opportunities for the powder particles to be reacted and interdiffused. Increasing the Wb:Wp ratio accelerates the rate of amorphization, which is explained by the increase in the kinetic energy of the ball mill charge per unit mass of powders. It has been shown in this study that the volume fraction of the amorphous phase in the mechanically alloyed ball-milled powders increases during the early stage of milling, 86173ks (48h) with increasing Wb:Wp ratio. It is noted that further increasing this weight ratio leads to the formation of crystalline phases and this might be related to the high kinetic energy of the ball mill charge which is transformed into heat. When the Wb:Wp ratio was reduced to 12:1, however, the amorphization reaction was not completed. This indicates that the kinetic energy of the mill charge is insufficient for complete transition from the crystalline to the amorphous phase.
It is worth noting that powder particles reached the minimum of extreme fineness when using a high Wb:Wp ratio. One disadvantage of using such a high weight ratio is being the high concentration of iron contamination which is introduced to the milled powders during the MA process, as presented in Fig.4.33.
Romankova etal. have applied the vibration ball milling for coating of stainless steel balls during milling of TiAl powders. They examined metallographically the development of the TiAl coating structure after milling for 60min as a function of the ball-to-powder weight ratio for 6mm balls (Fig.4.34).
The results showed that the milling energy increased with increasing the number of balls. When the weight ratio was 3:1, the substrate could be covered with a thin Al layer (Fig.4.34A). For this case, only small Ti particles were embedded into the Al matrix. It should be noted that the substrate underwent plastic deformation under the ball impacts and its surface became slightly bent. When the weight ratio was increased to 4:1, the energy was sufficient to embed larger Ti particles in the Al layer than at ratio 3:1 (Fig.4.34B). Al bound these Ti particles to the substrate. They notified that, at the 4:1 ratio, the growth for the TiAl coating across the substrate was clustered; this resulted in a hillock-like morphology and increased the surface roughness. Upon further increasing the ball-to-powder weight ratio from 6:1 to 14:1, the coating roughness gradually decreased. They also reported that the lamellar structure was refined when the ball-to-powder weight ratio was 14:1, as presented in Fig.4.34E.
More recently, Waje etal. have studied the effect of the ball-to-powder weight ratio (BPR) on the crystallite size of ball-milled CoFe2O4 nanoparticles, using XRD (Fig.4.35). From their results it can be seen that the particle size decreases linearly from 15.3 to 11.4nm when used BPR of 8:1 and 30:1, respectively.
The mass-size balance models as written above are in the time-domain. To be more practical they need to be converted to the energy-domain. One way is by arguing that the specific rate of breakage parameter is proportional to the net specific power input to the mill charge (Herbst and Fuerstenau, 1980; King, 2012). For a batch mill this becomes:
where SiE is the energy-specific rate of breakage parameter, P the net power drawn by the mill, and M the mass of charge in the mill excluding grinding media (i.e., just the ore). The energy-specific breakage rate is commonly given in t kWh1. For a continuous mill, the relationship is:
where is the mean retention time, and F the solids mass flow rate through the mill. Assuming plug flow, Eq. (5.17) can be substituted into Eq. (5.15) to apply to a grinding mill in closed circuit (where t=).
The distinctive feature of tumbling mills is the use of loose crushing bodies, which are large, hard, and heavy in relation to the ore particles, but small in relation to the volume of the mill, and which occupy (including voids) slightly less than half the volume of the mill.
Due to the rotation and friction of the mill shell, the grinding medium is lifted along the rising side of the mill until a position of dynamic equilibrium is reached (the shoulder), when the bodies cascade and cataract down the free surface of the other bodies, about a dead zone where little movement occurs, down to the toe of the mill charge (Figure 7.3).
The driving force of the mill is transmitted via the liner to the charge. The speed at which a mill is run and the liner design governs the motion and thus nature of the product and the amount of wear on the shell liners. For instance, a practical knowledge of the trajectories followed by the steel balls in a mill determines the speed at which it must be run in order that the descending balls shall fall on to the toe of the charge, and not on to the liner, which could lead to liner damage. Simulation of charge motion can be used to identify such potential problems (Powell et al., 2011), and acoustic monitoring can give indication of where ball impact is occurring (Pax, 2012).
At relatively low speeds, or with smooth liners, the medium tends to roll down to the toe of the mill and essentially abrasive comminution occurs. This cascading leads to finer grinding and increased liner wear. At higher speeds the medium is projected clear of the charge to describe a series of parabolas before landing on the toe of the charge. This cataracting leads to comminution by impact and a coarser end product with reduced liner wear. At the critical speed of the mill centrifuging occurs and the medium is carried around in an essentially fixed position against the shell.
In traveling around inside the mill, the medium (and the large ore pieces) follows a path which has two parts: the lifting section near to the shell liners, which is circular, and the drop back to the toe of the mill charge, which is parabolic (Figure 7.4(a)).
Consider a ball (or rod) of radius r meters, which is lifted up the shell of a mill of radius R meters, revolving at N rev min1. The ball abandons its circular path for a parabolic path at point P (Figure 7.4(b)), when the weight of the ball is just balanced by the centrifugal force, that is when:
Mills are driven, in practice, at speeds of 5090% of critical speed. The speed of rotation of the mill influences the power draw through two effects: the value of N and the shift in the center of gravity with speed. The center of gravity first starts to shift away from the center of the mill (to the right in Figure 7.4(a)) as the speed of rotation increases, causing the torque exerted by the charge to increase and draw more power (see Section 7.2.2). But, as critical speed is reached, the center of gravity moves toward the center of the mill as more and more of the material is held against the shell throughout the cycle, causing power draw to decrease. Since grinding effort is related to grinding energy, there is little increase in efficiency (i.e., delivered kWh t1) above about 4050% of the critical speed. It is also essential that the cataracting medium should fall well inside the mill charge and not directly onto the liner, thus excessively increasing steel consumption.
At the toe of the load the descending liner continuously underruns the churning mass, and moves some of it into the main mill charge. The medium and ore particles in contact with the liners are held with more firmness than the rest of the charge due to the extra weight bearing down on them. The larger the ore particle, rod, or ball, the less likely it is to be carried to the breakaway point by the liners. The cataracting effect should thus be applied in terms of the medium of largest diameter.
As already discussed, this control loop is provided to maintain the PA header pressure before the mixing of hot and cold PA duly controlled for temperature. FigureVIII/4-2 is also applicable for this type of mill when the PA is common to all the mills. The control loop is of course different for individual PA fan systems, as the above is applicable for the common PA system only. For control loop description, see Section 22.214.171.124 of this chapter. Common PA fans are provided with suction normally from the atmosphere or it may be from the FD discharge header. Header pressure control is performed through various types of final control elements.
As the fuel/load control is solely done by position adjustments to the PA damper near the mill, this control loop assists smooth and bumpless control of the fuel flow transported by the PA flow to the mill as the upstream PA header pressure control takes responsibility for providing an adequate quantity of air at any environmental condition without sacrificing the required downstream pressure,
FigureVIII/5.3-3 later in the chapter depicts the simple control loop. Any of the mill DP transmitters or level (sound-detector) transmitters is selected and the selected signal is connected to the controller as the process or measured variables against a fixed-level set point. Sufficient redundancy in measurement may vary according to the plants operating philosophy. The controller output is utilized for adjustment of feeder speed with the help of a VFD or SCR control for the gravimetric feeder/feeder speed variator.
At the higher load the charge level inside the drum decreases and the feeder speed should increase accordingly to replenish the material. For a decreasing load, the reverse action takes place. To take care of the sudden load change, the deviation between characterized PA flow and DP acrossthe mill is used to modify the controller output to achieve the desired mill charge level.
Mill load or fuel flow control follows the fuel demand from the boiler master demand control signal and is achieved by regulating the quantity of PA that is transporting agent only. Figures VIII/5.2-4 and VIII/5.2-4 depict the functioning of the control loop, which is similar to that of other mill types. For other mills the fuel demand signal from the boiler master demand is first taken care of by the mill-wise PA flow control system if the demand is less than the prevailing air flow control system. The characterized PA flow is then construed as the feeder speed demand. The ball-and-tube mill control system, on the other hand, uses feeder speed control for maintaining mill level control only and so the fuel flow control is achieved through control of the feeder-wise PA flow to mill itself.
However, the feeder-wise PA flow as measured after redundant transmitters voting selection and density compensated through temperature correction is again determined to get equivalent fuel flow. The total fuel flow is then computed by summing all the fuel (PF) flow of the running feeders and the supporting fuel (oil or gas) if any are being utilized at that time with proper weightage, taking consideration of their thermal or calorific value. The higher selection of this total equivalent fuel flow signal and the air flow demand signal from the boiler master demand (FigureVIII/2.1) is then taken as actual air demand just as in other type of mills.
As already discussed in Section 5.2.1, there is another feeder-wise control system associated with fuel flow control known as a bypass damper control. This feeder-wise damper is provided for each mill end for preheating the raw feed, which is an essential requirement during startup. No process measurement signal is utilized in this subloop. The same fuel demand from the boiler master demand (FigureVIII/ 2-1) is taken as the set point for the position demand of the bypass damper after due characterization, as shown (refer to Figures VIII/5.2-4 and VIII/5.2-5) in the control strategy and the graphical representation of approximate positions of the two final control elements. The previously mentioned two-position demands operate in opposite directions. After being in a fully open position for a certain load, ensuring elimination of initial moisture, this bypass damper begins to close gradually as the load increases.
There are two main types of fuel flow controls achieved through the proportionate PA flow only: (1) common PA fans with individual PA dampers and (2) individual PA fans with vane or speed control. There is also one known as a mill-wise PA flow control that is common to both sides.
FigureVIII/5.2-4 may be referred to for this type of control along with FigureVIII/5.2-2. Here the mill PA flow and bypass PA flows are combined to form the total mill-wise PA flow to the furnace. The boiler master demand acts as a set point here, where the mill-wise PA flow is the measured value as this air flow is only responsible for transporting the fuel to the furnace. The controller output is the demand signal for the individual PA damper. For bypass dampers, the boiler master demand generates the set point while the actual position of this damper acts as the measured value for the controller output, which is the demand signal for the bypass damper.
For any load change, the two flows readjust their positions to deliver the required PA flow. For higher load the bypass damper tends to close to allow less flow for preheating of raw feed and the PA damper to the mill opens more to take care of the load demand.
FigureVIII/5.2-5 may be referred to for this type of control along with FigureVIII/5.2-2(a). Here bypass PA flows need to be subtracted from the total mill-wise PA flow for the fuel flow control, and the total mill-wise PA flow to the furnace is required for air flow control. The reason for this is that the final control element and the flow element are both located in the common primary air path to the individual mill. The boiler master demand acts as a set point here, where the PA flow to the mill is the measured value. The controller output is the demand signal for the individual PA vane or variable speed drive as the case may be.
This type of mill design vis--vis operation is somewhat different from other types, as discussed earlier. FigureVIII/5.2-2(b), which is mainly followed by manufacturers, such as the Foster Wheeler Energy AG corporation, may be referred to for information. Here the boiler combustion control signal regulates the output of the mill by PA flow control dampers placed in the common line to both the ends or sides. The predrying of coal feed is done at the entry of each side before it enters the drum, unlike what is done by the bypass PA damper in many types of tube mills.
Another significant difference is the provision of an auxiliary air and purge air supply line taken from the cold PA for each side of the mill drum. The same is designed to the required minimum velocities of the PA/fuel mixture for maintaining proper flow inside the coal duct and to prevent fuel settling during startup or in extreme low-load operation. This feature extends the individual mill load range without encountering drifting or pulsating fuel flow to the burners. The other purpose is to purge the coal air line automatically when burners are taken out of service.
The feed level control in the drum, classifier outlet temperature control, and seal air DP control are very much similar to those in the other type of mills with the exception of the source of the seal air. Here the seal air supply is taken from the cold PA without any provision of a seal air fan.
Selecting dispersion equipment for a specific application is a complex task. Dispersion of the mixture must be complete and the process and equipment must meet economic constraints. But much more is involved. In practice, such simple criteria are complicated by a variety of parameters related to fillers and to the materials in which they are dispersed. These parameters complicate the problem to the degree that it is not easy to formulate general guidelines. In this discussion we will consider the available equipment types most frequently used for filler dispersion and illustrate their applicability with some examples.
A ball mill is an effective means of dispersing solid materials in solids or liquids.8,9 Ball mills have several advantages which include versatility, low cost of labor and maintenance, the possibility of unsupervised running, no loss of volatiles, and a clean process. The disadvantages are related to discharging viscous and thixotropic mixtures, and considerably lower efficiency when compared with other mixing equipment. The millbase viscosity is usually restricted to about 15-20 Poise, and therefore ball mills are most frequently found in production applications such as paints, flexographic, publication gravure, and letterpress news inks, and carbon paper inks which are dispersed at elevated temperatures.
The mill should rotate at 50-65% of the theoretical centrifugal speed in order to allow balls to cascade, since the cascading balls grind most effectively and do not cause an excessive loss of ball material
Viscosity, the order of filler addition, and the quantity of material should be chosen so as not to cause a viscosity increase above the specified range, since the milling efficiency drastically decreases at that point
The degree of dispersion and jetness achieved when grinding carbon black depends on the wetting properties of the dispersing material and to some degree on the filler form. For instance, pelletized carbon black is easier to disperse than a fluffy type
The sandmill has some drawbacks. It is a two stage process (premixing followed by milling). Milling develops high temperatures in the mixture which causes loss of volatiles and requires cooling. If the millbase is high in viscosity or dilatant, the sandmill process may not work at all. Agglomerated or extremely hard pigments are difficult or impossible to disperse
Both ball and sand mills operate based on a viscous shear principle, thus the viscosity of the millbase is a critical factor in achieving dispersion. The size of filler particles is critical, especially in sandmills. It was found that the shearing force is inversely proportional to the square of the linear size of filler agglomerate. An agglomerate of diameter of 7 m attains 100 times the shear stress of an agglomerate of 70 m diameter. The difference between the ball mill and the sand mill is in the size and density of the grinding media, which is reflected in their performance. Sandmilling uses small particles of low density, and therefore, there is no noticeable reduction in the size of the sand particle, whereas the balls in ballmills are very much larger and may have a high density (steel), which results in a more complex mechanism of grinding including shattering and impacting which cause this mill to be more effective in disintegrating hard particles and agglomerates containing sintered particles.
There is another mill type called an attritor, which is similar to both the ball mill and the sandmill. In construction, it is similar to a sandmill. It also has a vertical shaft, but in the attritor the agitator bars replace the milling discs of the sandmill. It is also similar to a ball mill because it uses balls, usually ceramic ones having 5-15 mm in diameter. Because the motion of the balls is independent of gravity, an attritor can handle thixotropic materials and slightly higher viscosity of millbases, but the principle of action and type of forces operating are similar to those of the ball mill. An attritor applied to pigment dispersion gives several advantages. These include rapid dispersion, the possibility of either a continuous or batch process, low power consumption, small floor space, and easy cleaning and maintenance. Their main disadvantage is high heat generation. Attritors are equipped with a cooling water jacket which can control the heat flow to some extent, but conditions are often too severe for some resins, which may degrade during the process.
Three-roll, one-roll, and stone mills constitute a more mature dispersion technology still in use with medium viscosity millbases. A three-roll mill consists of the feed, center, and apron rolls. In roll mill operation:
The speeds of feed and apron rolls are adjustable, and each roll rotates with a different speed in order to induce shear in the material at the nip and facilitate the material transfer from one roll to the other
For mechanical reasons the gap between rolls cannot be less than 10 m and it usually ranges from 40 to 50 m.7 Small particles will not be affected as they pass through the nip, but agglomerates smaller than the distance between rolls will be disintegrated due to the shear stress imposed on the material
The one-roll mill works on a similar principle but the nip is regulated by a pressure bar. Shearing takes place between the roller and the shearing bar. Stone mills have similar principles of operation. The rotor turns on a stator to achieve shearing
With current raw materials, both the primary particles and agglomerates are very small, and if any positive action can be achieved during the milling process, it can only be done by affecting these small particles. It is thus necessary to operate these machines at very tight gaps which causes abrasion of the mechanical elements, rapid deterioration of equipment, and contamination of the product by the abraded material. This affects the properties of the millbase and the color of the product
The high-speed impeller or shear mixer is the most common equipment to prepare dispersions of solids in liquid. High speed shear mills and kinetic shear mills have retained their usefulness because of their ability to deagglomerate material that is not adequately dispersed in the premixing step. A high-speed shear mill is composed of two elements a container and an impeller. These factors are important in the design:
In the first stage, the viscosity changes from low to high as fillers are incorporated; in the second stage, viscosity remains constantly high because of the disintegration of particles which occurs during the application of the highest shear stress
Long mixing increases temperature and decreases viscosity. This does not provide the conditions for the best filler dispersion. By extending mixing over, for example, a 15 min period, the degree of dispersion is not improved, but the resin may actually be degraded
If the quality of dispersion is not satisfactory, the parameters of mixing should be changed. If the expected result cannot be attained, the range of conditions available is not adequate in this particular mill
In the third stage, the viscosity changes from high to low due to the addition of diluent. The viscosity range which can be handled by high speed mixers is similar to the range of a three-roll mill, i.e., up to about 200 Poise
The range of shear rates available in high-speed mixers is not broad. The flow rate of fluid in motion decreases as viscosity increases and is inversely proportional to the width of the flow passage which, in this case, is the distance between the disperser and the container which is very large in a high speed mixer. It is not so much due to an improvement in mixing equipment that high-speed mixers have become so popular, it is mostly because of the high quality raw materials (pigments, fillers) which are available now. High structure carbon blacks can be more easily dispersed. But with the increased structure, the size of the primary particles decreases, inhibiting dispersion. Because of the interrelation between both parameters, only the medium structure, coarser particles of carbon blacks can be dispersed by high-speed mixers. Other carbon black types demand further treatment. It should be noted that this is only true of a few fillers which are known to possess strongly bonded, small sized particles. In most cases, fillers can be successfully dispersed in high-speed mixers. However, care should be taken that the filler is selected with an appropriate particle size.
High-speed mixers have several important advantages over other existing equipment including the possibility of processing a batch in the same vessel, easy cleaning, and flexibility in color changes. The main disadvantage is that the final dispersion depends greatly on the chosen composition and technology, and these are sometimes limiting factors. Frequently, the proper conditions for quality dispersion cannot be achieved at all.
The basic construction of a high-speed mixer can easily be modified to one's special requirements. For example, a change from impeller to turbine rotor changes both the principle of dispersion and the range of application. The tangential velocities of filler particles can be as high as 500 m/sec. Such particles have a very high kinetic energy, sufficient to cause size reduction. Size reduction is due to particle-particle or particle-wall collisions, and this in turn, is related in efficiency to the relative velocities at the moment of collision. Relative velocity can be increased by decreasing the viscosity of the millbase. The upper limit of millbase viscosity is somewhere around 3 to 4 Poise. It is not viscosity alone which is important but the entire rheological character of the millbase. The best results are obtained when the millbase is nearly Newtonian. For this reason, the dispersion process is best performed in a diluted millbase. As is the case with high-speed mixers, a proper dispersion should be achieved in a matter of 10-20 min. If such is not the case, the conditions of processing should be modified. Once dispersion has been achieved, it should be stabilized, with the mixer continuously running, by the addition of more resin to increase the viscosity in order to prevent sedimentation or flocculation of the pigment.
The other possible modification to such a mixer can be achieved by a substantial lowering of the speed and a change in the motion of the mixing element to planetary. This configuration can process material of a much higher viscosity, up to several thousand Poise. The high speed mixer can be modified in various ways to match its capabilities to the process requirements. Stationary baffles may be added to increase the shear rate. The distance between the rotating and stationary elements can be decreased again increasing the shear rate. The mixer may be designed to work under both pressure and vacuum and with inert gas blanketing which permits deaeration and processing of volatile or moisture sensitive materials.
The other group includes heavy-duty mixers, such as the Banbury mixer and double-arm kneading mixers. The Banbury mixer with a power input of up to 6000 kW/m3 is the strongest and the most powerful mixing unit used by industry. Nearly solid materials are mixed by a rotor which is a heavy shaft with stubby blades rotating at up to 40 rpm. The clearance between the walls and rotor is very small, which induces a very high shear in the material. The high shear generates a great amount of heat which melts the polymer rapidly and allows for quick incorporation of filler. After the filler is incorporated, the dispersion process begins, with rapid distributive mixing along and between two rotors and between the chamber walls and rotor tips. Within 2-3 min, mixing is normally completed and the compound discharged into a pelletizing extruder or a two-roll mill which converts it to a sheet form.8 Carbon black, which is most frequently processed in a Banbury mixer, is usually placed between two layers of polymeric material in order to reduce dusting.
Double-arm kneading mixers are very popular in some industries. They consist of two counter-rotating blades in a rectangular trough carved at the bottom to form two longitudinal half cylinders and a saddle section. A variety of blade shapes are used, with a clearance between them and the blades and the side walls of up to 1 mm. The most popular blade shapes include: sigma, dispersion, multiwiping overlapping, single-curve, and double-naben blades. It is important for filler dispersion in this mixer that the viscosity of the millbase be kept high enough to create the required shearing force to disperse the material. The strong construction of the mixer and its high power allow one to work with concentrated compositions of pigments which could not be processed by any other method.
High volume production is done by mixing in an extruder.11 This method offers several advantages such as a continuous process, material uniformity, a clean environment, high output, and low labor. The biggest disadvantage of this method is a high investment cost. The twin-screw extruder is the most flexible type of extruder and most appropriate for compounding. Their screw designs can be varied as can the method of dosing and the output rate. The abrasiveness of the filler may affect the life-span of the equipment, and particle size and its distribution may influence the quality of filler dispersion and material uniformity. But in general, there is adequate machinery available for almost all requirements. For instance, glass-fiber reinforced materials can be produced by this technique with little change to the initial structure and dimensions of the glass fibers, which shows the versatility of the technology. The production rate of this method is comparable to the Banbury mixer, and an additional advantage comes from the fact that the material can be completely processed in one pass through the machinery.
The importance of the proper dispersion of fillers and the complexity of techniques for measuring the degree of dispersion are reflected in numerous publications. Further information on the mixing of fillers is included in Chapter 18.
The renewable power sources are being explored due to possibility of lack in availability of conventional resources in future. The major drawback of Renewable energy resources are dependency on geographical locations and environmental conditions however, the high initial cost, increased maintenance cost, and different rates of depreciation are the main challenges associated with these hybrid systems. The irregular pattern of natural resources necessitates developing a hybrid system which can generate maximum conceivable energy for continuous and reliable operations . The design of hybrid system is influenced by various factors such as condition of sites, energy availability, efficiency of energy sources as well as technical and social limitation In this specific situation, a combination of optimal sizing method is an indispensable factor to accomplish higher reliability quality with least expense [21,79,87,149]. The fundamental parts of the hybrid energy systems are renewable power source, nonrenewable generators, control unit, storage system, load or grid some times, sources and load may be AC/DC .
An arrangement of the renewable power generation with appropriate storage and feasible amalgamation with conventional generation system is considered as hybrid energy system or some time referred as a micro grid . This system may be any probable combination of Photovoltaic, wind, micro turbines, micro hydro, conventional diesel generation, battery storage, hydrogen storage and Fuel Cell in grid-connected or off grid arrangement,
An assembly of interconnected loads, conventional distributed energy resources like distributed generators (DG), renewable resources and energy storage systems in a specified boundary as a controllable single entity referred as micro grid. It may be eternally connected to grid, or isolated by grid. There are worldwide numerous remote communities those are not directly connected to grid, and fulfill electricity demand from distributed generators based on fossil fuel in isolated Microgrids[97,165]. In this paper a assimilated arrangement of solar PV and wind renewable energy resources is discussed which is slightly different from the concept of microgrid.
Solar Photovoltaic /Wind based Hybrid Energy System shows its adequacy to provide the essential electrical demand for off grid utilization. The at most imperative feature of a Solar Photovoltaic (PV) and Wind based Hybrid Energy System is that it uses at least two sustainable power sources which enhances reliability, efficiency and financial restrictions emerges from single energy resources of renewable nature [18,89,133]. Solar Photovoltaic and Wind based Hybrid Energy System is considered as amalgamation of solar PV panel, Wind mills, charge controller, storage system, power conditioning units, diesel based generator set and load . The assessment of performance of Hybrid system can be done by recreating their models at Simulink platform for the accessible insulation, speed of wind, electrical load and various components .
The essential objective for evaluation of Hybrid System are building up the suitable models for various components and their simulation in a sequential manner as firstly availability of speed wind, accessibility of sunlight and the demand of load models are simulated after that model of battery storage and diesel generator can be Simulated. Last strides in the entire procedure of assessment is deciding the coveted criteria and exploring the optimum structure of system. . The optimal hybrid system arrangement should satisfy and compromise the objectives of power reliability and cost of system. The load demand frequently considered as limitation of the optimization issue and ought to be totally satisfied . The solar PV/wind hybrid system is mostly reliant on execution of individual segments. To estimate the performance of solar PV/wind hybrid system, individual components are modeled initially after that entire system evaluated to meet the demand . In general key aspects to analyze a hybrid system are hybrid system configuration with respect to the available resources, the optimization of the available renewable resources exploitation and the optimization of the output power quality .
Solar energy and wind energy are analogous to each other in nature and both are well appropriate to develop a hybrid system . Availability of solar radiations are relatively greater in summer, winds are more accessible in the evening times of winters. This hybrid renewable energy systems give a more reliable output throughout the year can be planned to fulfill craved qualities on more decreased possible cost . The constraints of Photo voltaic system, the assessed energy of wind energy system and the battery storage are the majorly considered parameters for evaluation of solar and wind based hybrid energy system. In addition, the precise angular attitude of Photo voltaic panels and the tower height of wind turbines are considered for achieving the minimum levelised cost of energy. Ribeiro  proposed multi-criteria based analytical decision scheme abbreviated as MCDA which consider several issues like economic, quality of life, technical and environmental issues of local populations.
Metrological data based on technological, economical, socio-political and environmental factors having major impact for estimation and selection of various components of Solar Photovoltaic and Wind based Hybrid Energy System . Hourly climate information as sun oriented radiation, wind speed and temperature are raw information illustrates the inconstancy of the parameter input. Place to place data is hard to obtain for designing purpose at remote location [3,73]. Statistical metrological climatic information can be delivered by the average of month to month meteorological information. The information of climate can be anticipated from an adjacent site or synthetically can be produced . Simulation for performance of Solar PV/Wind Hybrid Energy System required climate data including solar radiation, speed of wind and temperature which can be find from web sources and also from local meteorological station, it is best to find realistic solution preference should be given to the specified location based weather data . To optimize solar photovoltaic and wind based hybrid energy system are hourly or day by day climate information of solar and wind energy are considered as required significant inputs . Meteorological data determined the receptiveness and amount of sunlight based radiation and wind energy sources at a particular region. An investigation of characteristics of sun based emission and availability of wind at a specific location ought to be concluded before starting . Bianchini A et al. gives stress on the metrological data in the form of solar irradiance and wind distribution and considered hybrid renewable energy system as a amalgamation of PV panel of rated power, horizontal axis wind turbine of rated power, a diesel generator of precise nominal power able to manage peak load and a battery bank of specific storage capacity . Hall et al.  proposed the well-known engineered climate information term Typical meteorological year (TMY) utilized in simulation of solar energy model is first time. It is observational technique picking particular months from different years using the Fleckenstein Schafer accurate system .
load demand play a very important role in establishment of solar PV/wind hybrid renewable energy system provides more reliable power for off-grid and standalone applications compared to individual systems  The most of the reviewed studies are about the alone Solar Photovoltaic /Wind based Hybrid Energy System and few studies are available for grid connected system. The unsatisfied load request is procured from the grid. Along this way the hybrid system became noticeably trustworthy. The stand-alone systems with storage infused surplus energy to the grid at a prime cost. Along these lines, the grid connected system becomes more financially acceptable.
how to calculate ball/sag mill charge level? - grinding & classification circuits - metallurgist & mineral processing engineer
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inferential measurement of sag mill parameters iv: inferential model validation - sciencedirect
This paper discusses a case study application of inferential measurement models for semiautogenous grinding (SAG) mills and is the fourth paper in a series of five papers on inferential measurement of SAG mill parameters. The development of the inferential measurement models of SAG mill discharge and feed streams and mill rock and ball charge levels, detailed earlier in the series, is summarised here. The models are then tested on plant data for validation and analysis. Model characteristics are explored to highlight model sensitivity and relative uncertainty. The results are encouraging while limitations are noted and potential avenues for further research are discussed.
inferential measurement of sag mill parameters v: mpc simulation - sciencedirect
This paper discusses a case study application of inferential measurement models for semiautogenous grinding (SAG) mills and is the last in a five-part series on Inferential Measurement of SAG Mill Parameters. Inferential measurements of SAG mill discharge and feed streams and mill rock and ball charge levels, detailed earlier in the series, are utilised in a simulation environment. A multi-variable, model predictive (MPC) controller simulation is developed from plant data and utilised to investigate the potential of utilising the inferential models in a mill charge control strategy. An operating curve is generated and discussed in terms of possible utilisation in conjunction with an MPC controller. The results are encouraging and potential avenues for further research are discussed.