ball mill design/power calculation
The basic parameters used in ball mill design (power calculations), rod mill or anytumbling millsizing are; material to be ground, characteristics, Bond Work Index, bulk density, specific density, desired mill tonnage capacity DTPH, operating % solids or pulp density, feed size as F80 and maximum chunk size, productsize as P80 and maximum and finally the type of circuit open/closed you are designing for.
In extracting fromNordberg Process Machinery Reference ManualI will also provide 2 Ball Mill Sizing (Design) example done by-hand from tables and charts. Today, much of this mill designing is done by computers, power models and others. These are a good back-to-basics exercises for those wanting to understand what is behind or inside the machines.
W = power consumption expressed in kWh/short to (HPhr/short ton = 1.34 kWh/short ton)
Wi = work index, which is a factor relative to the kwh/short ton required to reduce a given material from theoretically infinite size to 80% passing 100 microns
P = size in microns of the screen opening which 80% of the product will pass
F = size in microns of the screen opening which 80% of the feed will pass
Open circuit grinding to a given surface area requires no more power than closed circuit grinding to the same surface area provided there is no objection to the natural top-size. If top-size must be limited in open circuit, power requirements rise drastically as allowable top-size is reduced and particle size distribution tends toward the finer sizes.
A wet grinding ball mill in closed circuit is to be fed 100 TPH of a material with a work index of 15 and a size distribution of 80% passing inch (6350 microns). The required product size distribution is to be 80% passing 100 mesh (149 microns). In order to determine the power requirement, the steps are as follows:
The ball mill motorpower requirement calculated above as 1400 HP is the power that must be applied at the mill drive in order to grind the tonnage of feed from one size distribution. The following shows how the size or select thematching mill required to draw this power is calculated from known tables the old fashion way.
The value of the angle a varies with the type of discharge, percent of critical speed, and grinding condition. In order to use the preceding equation, it is necessary to have considerable data on existing installations. Therefore, this approach has been simplified as follows:
A = factor for diameter inside shell lining
B = factor which includes effect of % loading and mill type
C = factor for speed of mill
L = length in feet of grinding chamber measured between head liners at shell- to-head junction
Many grinding mill manufacturers specify diameter inside the liners whereas othersare specified per inside shell diameter. (Subtract 6 to obtain diameter inside liners.) Likewise, a similar confusion surrounds the length of a mill. Therefore, when comparing the size of a mill between competitive manufacturers, one should be aware that mill manufacturers do not observe a size convention.
In Example No.1 it was determined that a 1400 HP wet grinding ball mill was required to grind 100 TPH of material with a Bond Work Index of 15 (guess what mineral type it is) from 80% passing inch to 80% passing 100 mesh in closed circuit. What is the size of an overflow discharge ball mill for this application?
ball mill parameter selection & calculation - power, critical speed | jxsc
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The production capacity of the ball mill is determined by the amount of material required to be ground, and it must have a certain margin when designing and selecting. There are many factors affecting the production capacity of the ball mill, in addition to the nature of the material (grain size, hardness, density, temperature and humidity), the degree of grinding (product size), the uniformity of the feeding material, and the portion of loaded, , and the mill structure (the mill barrel length, diameter ratio, the number of bins, the shape of the partition plate and the lining plate). It is difficult to theoretically determine the productivity of the mill. The grinding mills production capacity is generally calculated based on the newly generated powder ore of less than 0.074 mm (-200 mesh). V Effective volume of ball mill, m3; G2 Material less than 0.074mm in product accounts for the percentage of total material, %; G1 Material less than 0.074mm in ore feeding accounts for 0.074mm in the percentage of the total material, %; qm Unit productivity calculated according to the new generation grade (0.074mm), t/(m3.h). The values of qm are determined by experiments or are calibrated in production with similar ore physical properties and the same equipment and working conditions. When there is no test data and production calibration value, it can be calculated by formula (1-3). Di1- Standard mill diameter, m; K4 feed size and product size coefficient of mill. G3 G4 The production capacity of existing or experimental mills with newly designed and parameters (feed size or product size calculated according to the new generation 0.074mm level) is shown in Table 1-6. The values of G1 and G2 above should be calculated according to actual data. If there is no actual data, they can be selected according to tables 1-7 and 1-8.
When the filling rate of grinding medium is less than 35% in dry grinding operation, the power can be calculated by formula (1-7). n - mill speed, r/min; G - Total grinding medium, T; - Mechanical efficiency, when the center drive, = 0.92-0.94; when the edge drive, = 0.86-0.90.
\ Critical Speed_ When the ball mill cylinder is rotated, there is no relative slip between the grinding medium and the cylinder wall, and it just starts to run in a state of rotation with the cylinder of the mill. This instantaneous speed of the mill is as follows: N0 - mill working speed, r/min; Kb speed ratio, %. There are many layers of grinding media in the mill barrel. It is assumed that the media will be concentrated in one layer, called the polycondensation layer, so that the grinding media of this layer will be in the maximum drop, i.e. the calculating speed of the mill when the total impact energy is the largest nj. Therefore, it is theoretically deduced that the reasonable working speed is The working speeds of various mills are shown in Table 1-10. Table 1-10 Working speeds of various mills
In production practice, there are many factors affecting the motion state of grinding media. Therefore, the appropriate working speed should be selected according to the actual situation. In determining the actual working speed of the mill, the influences of the mill specifications, production methods, liner forms, grinding media types, filling rate, physical and chemical properties of the ground materials, particle size of the grinding materials and grinding fineness of the products should be taken into account. The actual working speed of the mill should be determined by scientific experiments, which can reflect the influence of these factors more comprehensively.
Ball loading capacity The volume of the grinding medium is the percentage of the effective volume of the mill, which is called the filling rate of the grinding medium. The size of filling directly affects the number of shocks, the area of grinding and the load of grinding medium in the grinding process. At the same time, it also affects the height of the grinding medium itself, the impact on the material and the power consumption. A kind of The ball loading capacity of the mill can be calculated according to the formula (1-14). Gra Quantity of Grinding Medium, T. Rho s loose density of grinding medium, t/m3. Forged steel balls; P=s=4.5-4.8t/m3 cast steel balls P=4.3-4.6t/m3; rolling steel balls P=6.0-6.8t/m3; steel segments P=4.3-4.6t/m3_-filling ratio of grinding medium, When wet grinding: lattice ball mill pi = 40% 45%; overflow ball mill phi = 40%; rod mill phi = 35%. Dry grinding: When material is mixed between grinding media, the grinding medium expands, and when dry grinding is adopted, the material fluidity is relatively poor, material flow is hindered by abrasive medium, so filling rate is low, and the filling rate is between 28% and 35%. The pipe mill is 25%-35%. The void fraction of grinding medium_k=0.38-0.42 and the quality of crushed material accounts for about 14% of the quality of grinding medium.
Size and Proportion of Grinding Medium In the ball mill, the size and proportion of steel balls have a great influence on the productivity and working efficiency of the mill. For coarse and hard materials, larger steel balls should be selected, for fine and brittle materials, with smaller diameter steel balls, the impact times of steel balls in the mill increase with the decrease of ball diameter, and the grinding between balls increases. The clearance is dense with a decrease of spherical diameter. Therefore, it is better to choose the ball with a larger mass and smaller diameter (loose density) as the grinding medium. The size of the ball mainly depends on the particle size of the material to be ground, and the diameter and speed of the mill can be considered appropriately. Formula (1-15) is an empirical formula for spherical diameter and feed size. dmax The maximum diameter of steel ball, mm; amax the maximum size of feeding granularity, mm. After calculating the maximum steel ball diameter, the steel ball ratio in the mill can be calculated with reference to Fig. 2-1 (suitable for cement mill, other mills can refer to). After choosing the maximum diameter and minimum diameter of steel balls according to technological requirements, material properties, mill specifications and various parameters, and then matching grade, using curves, the accumulative percentage of the mass of each corresponding steel balls loaded into the mill can be found, the actual percentage of the mass can be calculated, and the loading quality of steel balls at all levels can be obtained. According to the production practice of production enterprises, the relationship between ball diameter and material size is shown in Table 1-11. A kind of Steel balls are gradually worn out in the process of grinding materials. The wear of drop steel ball is related to its impact force. The wear of grinding steel balls is related to the surface area of steel balls. In general, the steel ball in the grinder has both impact and abrasion effects, so the wear is proportional to the n power of the diameter of the steel ball, and the value of n is between 2 and 3. Table 1-11 The Relation between Steel Ball Diameter and Material Size
The quality and surface area of forged steel balls of various sizes are shown in Table 1-12. A kind of Because of the wear of steel balls in the mill production process, in order to keep the mill stable. Steel balls need to be added regularly. The maximum diameter of additional steel balls is still determined by the method mentioned above. In addition to the addition of additional steel balls, several smaller diameter steel balls should be added according to production experience.
effect of ball and feed particle size distribution on the milling efficiency of a ball mill: an attainable region approach - sciencedirect
In this article, alternative forms of optimizing the milling efficiency of a laboratory scale ball mill by varying the grinding media size distribution and the feed material particle size distribution were investigated. Silica ore was used as the test material. The experimental parameters that were kept constant in this investigation was the grinding media filling, powder filling and the mill rotational speed. The data obtained from these batch tests was then analyzed using a model free technique called the Attainable Region method. This analysis technique showed that the required product fineness is a function of grinding media and feed material size distributions. It was also observed from the experimental results that in order to increase the milling efficiency of a ball mill, towards optimum production of material in the desired size class, there is a need to correlate the ball size and the feed size distributions.