ball mill design/power calculation

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 mills

ball mills

In all ore dressing and milling Operations, including flotation, cyanidation, gravity concentration, and amalgamation, the Working Principle is to crush and grind, often with rob mill & ball mills, the ore in order to liberate the minerals. In the chemical and process industries, grinding is an important step in preparing raw materials for subsequent treatment.In present day practice, ore is reduced to a size many times finer than can be obtained with crushers. Over a period of many years various fine grinding machines have been developed and used, but the ball mill has become standard due to its simplicity and low operating cost.

A ball millefficiently operated performs a wide variety of services. In small milling plants, where simplicity is most essential, it is not economical to use more than single stage crushing, because the Steel-Head Ball or Rod Mill will take up to 2 feed and grind it to the desired fineness. In larger plants where several stages of coarse and fine crushing are used, it is customary to crush from 1/2 to as fine as 8 mesh.

Many grinding circuits necessitate regrinding of concentrates or middling products to extremely fine sizes to liberate the closely associated minerals from each other. In these cases, the feed to the ball mill may be from 10 to 100 mesh or even finer.

Where the finished product does not have to be uniform, a ball mill may be operated in open circuit, but where the finished product must be uniform it is essential that the grinding mill be used in closed circuit with a screen, if a coarse product is desired, and with a classifier if a fine product is required. In most cases it is desirable to operate the grinding mill in closed circuit with a screen or classifier as higher efficiency and capacity are obtained. Often a mill using steel rods as the grinding medium is recommended, where the product must have the minimum amount of fines (rods give a more nearly uniform product).

Often a problem requires some study to determine the economic fineness to which a product can or should be ground. In this case the 911Equipment Company offers its complete testing service so that accurate grinding mill size may be determined.

Until recently many operators have believed that one particular type of grinding mill had greater efficiency and resulting capacity than some other type. However, it is now commonly agreed and accepted that the work done by any ballmill depends directly upon the power input; the maximum power input into any ball or rod mill depends upon weight of grinding charge, mill speed, and liner design.

The apparent difference in capacities between grinding mills (listed as being the same size) is due to the fact that there is no uniform method of designating the size of a mill, for example: a 5 x 5 Ball Mill has a working diameter of 5 inside the liners and has 20 per cent more capacity than all other ball mills designated as 5 x 5 where the shell is 5 inside diameter and the working diameter is only 48 with the liners in place.

Ball-Rod Mills, based on 4 liners and capacity varying as 2.6 power of mill diameter, on the 5 size give 20 per cent increased capacity; on the 4 size, 25 per cent; and on the 3 size, 28 per cent. This fact should be carefully kept in mind when determining the capacity of a Steel- Head Ball-Rod Mill, as this unit can carry a greater ball or rod charge and has potentially higher capacity in a given size when the full ball or rod charge is carried.

A mill shorter in length may be used if the grinding problem indicates a definite power input. This allows the alternative of greater capacity at a later date or a considerable saving in first cost with a shorter mill, if reserve capacity is not desired. The capacities of Ball-Rod Mills are considerably higher than many other types because the diameters are measured inside the liners.

The correct grinding mill depends so much upon the particular ore being treated and the product desired, that a mill must have maximum flexibility in length, type of grinding medium, type of discharge, and speed.With the Ball-Rod Mill it is possible to build this unit in exact accordance with your requirements, as illustrated.

To best serve your needs, the Trunnion can be furnished with small (standard), medium, or large diameter opening for each type of discharge. The sketch shows diagrammatic arrangements of the four different types of discharge for each size of trunnion opening, and peripheral discharge is described later.

Ball-Rod Mills of the grate discharge type are made by adding the improved type of grates to a standard Ball-Rod Mill. These grates are bolted to the discharge head in much the same manner as the standard headliners.

The grates are of alloy steel and are cast integral with the lifter bars which are essential to the efficient operation of this type of ball or rod mill. These lifter bars have a similar action to a pump:i. e., in lifting the product so as to discharge quickly through the mill trunnion.

These Discharge Grates also incorporate as an integral part, a liner between the lifters and steel head of the ball mill to prevent wear of the mill head. By combining these parts into a single casting, repairs and maintenance are greatly simplified. The center of the grate discharge end of this mill is open to permit adding of balls or for adding water to the mill through the discharge end.

Instead of being constructed of bars cast into a frame, Grates are cast entire and have cored holes which widen toward the outside of the mill similar to the taper in grizzly bars. The grate type discharge is illustrated.

The peripheral discharge type of Ball-Rod Mill is a modification of the grate type, and is recommended where a free gravity discharge is desired. It is particularly applicable when production of too many fine particles is detrimental and a quick pass through the mill is desired, and for dry grinding.

The drawings show the arrangement of the peripheral discharge. The discharge consists of openings in the shell into which bushings with holes of the desired size are inserted. On the outside of the mill, flanges are used to attach a stationary discharge hopper to prevent pulp splash or too much dust.

The mill may be operated either as a peripheral discharge or a combination or peripheral and trunnion discharge unit, depending on the desired operating conditions. If at any time the peripheral discharge is undesirable, plugs inserted into the bushings will convert the mill to a trunnion discharge type mill.

Unless otherwise specified, a hard iron liner is furnished. This liner is made of the best grade white iron and is most serviceable for the smaller size mills where large balls are not used. Hard iron liners have a much lower first cost.

Electric steel, although more expensive than hard iron, has advantage of minimum breakage and allows final wear to thinner section. Steel liners are recommended when the mills are for export or where the source of liner replacement is at a considerable distance.

Molychrome steel has longer wearing qualities and greater strength than hard iron. Breakage is not so apt to occur during shipment, and any size ball can be charged into a mill equipped with molychrome liners.

Manganese liners for Ball-Rod Mills are the world famous AMSCO Brand, and are the best obtainable. The first cost is the highest, but in most cases the cost per ton of ore ground is the lowest. These liners contain 12 to 14% manganese.

The feed and discharge trunnions are provided with cast iron or white iron throat liners. As these parts are not subjected to impact and must only withstand abrasion, alloys are not commonly used but can be supplied.

Gears for Ball-Rod Mills drives are furnished as standard on the discharge end of the mill where they are out of the way of the classifier return, scoop feeder, or original feed. Due to convertible type construction the mills can be furnished with gears on the feed end. Gear drives are available in two alternative combinations, which are:

All pinions are properly bored, key-seated, and pressed onto the steel countershaft, which is oversize and properly keyseated for the pinion and drive pulleys or sheaves. The countershaft operates on high grade, heavy duty, nickel babbitt bearings.

Any type of drive can be furnished for Ball-Rod Mills in accordance with your requirements. Belt drives are available with pulleys either plain or equipped with friction clutch. Various V- Rope combinations can also be supplied.

The most economical drive to use up to 50 H. P., is a high starting torque motor connected to the pinion shaft by means of a flat or V-Rope drive. For larger size motors the wound rotor (slip ring) is recommended due to its low current requirement in starting up the ball mill.

Should you be operating your own power plant or have D. C. current, please specify so that there will be no confusion as to motor characteristics. If switches are to be supplied, exact voltage to be used should be given.

Even though many ores require fine grinding for maximum recovery, most ores liberate a large percentage of the minerals during the first pass through the grinding unit. Thus, if the free minerals can be immediately removed from the ball mill classifier circuit, there is little chance for overgrinding.

This is actually what has happened wherever Mineral Jigs or Unit Flotation Cells have been installed in the ball mill classifier circuit. With the installation of one or both of these machines between the ball mill and classifier, as high as 70 per cent of the free gold and sulphide minerals can be immediately removed, thus reducing grinding costs and improving over-all recovery. The advantage of this method lies in the fact that heavy and usually valuable minerals, which otherwise would be ground finer because of their faster settling in the classifier and consequent return to the grinding mill, are removed from the circuit as soon as freed. This applies particularly to gold and lead ores.

Ball-Rod Mills have heavy rolled steel plate shells which are arc welded inside and outside to the steel heads or to rolled steel flanges, depending upon the type of mill. The double welding not only gives increased structural strength, but eliminates any possibility of leakage.

Where a single or double flanged shell is used, the faces are accurately machined and drilled to template to insure perfect fit and alignment with the holes in the head. These flanges are machined with male and female joints which take the shearing stresses off the bolts.

The Ball-Rod Mill Heads are oversize in section, heavily ribbed and are cast from electric furnace steel which has a strength of approximately four times that of cast iron. The head and trunnion bearings are designed to support a mill with length double its diameter. This extra strength, besides eliminating the possibility of head breakage or other structural failure (either while in transit or while in service), imparts to Ball-Rod Mills a flexibility heretofore lacking in grinding mills. Also, for instance, if you have a 5 x 5 mill, you can add another 5 shell length and thus get double the original capacity; or any length required up to a maximum of 12 total length.

On Type A mills the steel heads are double welded to the rolled steel shell. On type B and other flanged type mills the heads are machined with male and female joints to match the shell flanges, thus taking the shearing stresses from the heavy machine bolts which connect the shell flanges to the heads.

The manhole cover is protected from wear by heavy liners. An extended lip is provided for loosening the door with a crow-bar, and lifting handles are also provided. The manhole door is furnished with suitable gaskets to prevent leakage.

The mill trunnions are carried on heavy babbitt bearings which provide ample surface to insure low bearing pressure. If at any time the normal length is doubled to obtain increased capacity, these large trunnion bearings will easily support the additional load. Trunnion bearings are of the rigid type, as the perfect alignment of the trunnion surface on Ball-Rod Mills eliminates any need for the more expensive self-aligning type of bearing.

The cap on the upper half of the trunnion bearing is provided with a shroud which extends over the drip flange of the trunnion and effectively prevents the entrance of dirt or grit. The bearing has a large space for wool waste and lubricant and this is easily accessible through a large opening which is covered to prevent dirt from getting into the bearing.Ball and socket bearings can be furnished.

Scoop Feeders for Ball-Rod Mills are made in various radius sizes. Standard scoops are made of cast iron and for the 3 size a 13 or 19 feeder is supplied, for the 4 size a 30 or 36, for the 5 a 36 or 42, and for the 6 a 42 or 48 feeder. Welded steel scoop feeders can, however, be supplied in any radius.

The correct size of feeder depends upon the size of the classifier, and the smallest feeder should be used which will permit gravity flow for closed circuit grinding between classifier and the ball or rod mill. All feeders are built with a removable wearing lip which can be easily replaced and are designed to give minimum scoop wear.

A combination drum and scoop feeder can be supplied if necessary. This feeder is made of heavy steel plate and strongly welded. These drum-scoop feeders are available in the same sizes as the cast iron feeders but can be built in any radius. Scoop liners can be furnished.

The trunnions on Ball-Rod Mills are flanged and carefully machined so that scoops are held in place by large machine bolts and not cap screws or stud bolts. The feed trunnion flange is machined with a shoulder for insuring a proper fit for the feed scoop, and the weight of the scoop is carried on this shoulder so that all strain is removed from the bolts which hold the scoop.

High carbon steel rods are recommended, hot rolled, hot sawed or sheared, to a length of 2 less than actual length of mill taken inside the liners. The initial rod charge is generally a mixture ranging from 1.5 to 3 in diameter. During operation, rod make-up is generally the maximum size. The weights per lineal foot of rods of various diameters are approximately: 1.5 to 6 lbs.; 2-10.7 lbs.; 2.5-16.7 lbs.; and 3-24 lbs.

Forged from the best high carbon manganese steel, they are of the finest quality which can be produced and give long, satisfactory service. Data on ball charges for Ball-Rod Mills are listed in Table 5. Further information regarding grinding balls is included in Table 6.

Rod Mills has a very define and narrow discharge product size range. Feeding a Rod Mill finer rocks will greatly impact its tonnage while not significantly affect its discharge product sizes. The 3.5 diameter rod of a mill, can only grind so fine.

Crushers are well understood by most. Rod and Ball Mills not so much however as their size reduction actions are hidden in the tube (mill). As for Rod Mills, the image above best expresses what is going on inside. As rocks is feed into the mill, they are crushed (pinched) by the weight of its 3.5 x 16 rods at one end while the smaller particles migrate towards the discharge end and get slightly abraded (as in a Ball Mill) on the way there.

We haveSmall Ball Mills for sale coming in at very good prices. These ball mills are relatively small, bearing mounted on a steel frame. All ball mills are sold with motor, gears, steel liners and optional grinding media charge/load.

Ball Mills or Rod Mills in a complete range of sizes up to 10 diameter x20 long, offer features of operation and convertibility to meet your exactneeds. They may be used for pulverizing and either wet or dry grindingsystems. Mills are available in both light-duty and heavy-duty constructionto meet your specific requirements.

All Mills feature electric cast steel heads and heavy rolled steelplate shells. Self-aligning main trunnion bearings on large mills are sealedand internally flood-lubricated. Replaceable mill trunnions. Pinion shaftbearings are self-aligning, roller bearing type, enclosed in dust-tightcarrier. Adjustable, single-unit soleplate under trunnion and drive pinionsfor perfect, permanent gear alignment.

Ball Mills can be supplied with either ceramic or rubber linings for wet or dry grinding, for continuous or batch type operation, in sizes from 15 x 21 to 8 x 12. High density ceramic linings of uniform hardness male possible thinner linings and greater and more effective grinding volume. Mills are shipped with liners installed.

Complete laboratory testing service, mill and air classifier engineering and proven equipment make possible a single source for your complete dry-grinding mill installation. Units available with air swept design and centrifugal classifiers or with elevators and mechanical type air classifiers. All sizes and capacities of units. Laboratory-size air classifier also available.

A special purpose batch mill designed especially for grinding and mixing involving acids and corrosive materials. No corners mean easy cleaning and choice of rubber or ceramic linings make it corrosion resistant. Shape of mill and ball segregation gives preferential grinding action for grinding and mixing of pigments and catalysts. Made in 2, 3 and 4 diameter grinding drums.

Nowadays grinding mills are almost extensively used for comminution of materials ranging from 5 mm to 40 mm (3/161 5/8) down to varying product sizes. They have vast applications within different branches of industry such as for example the ore dressing, cement, lime, porcelain and chemical industries and can be designed for continuous as well as batch grinding.

Ball mills can be used for coarse grinding as described for the rod mill. They will, however, in that application produce more fines and tramp oversize and will in any case necessitate installation of effective classification.If finer grinding is wanted two or three stage grinding is advisable as for instant primary rod mill with 75100 mm (34) rods, secondary ball mill with 2540 mm(11) balls and possibly tertiary ball mill with 20 mm () balls or cylpebs.To obtain a close size distribution in the fine range the specific surface of the grinding media should be as high as possible. Thus as small balls as possible should be used in each stage.

The principal field of rod mill usage is the preparation of products in the 5 mm0.4 mm (4 mesh to 35 mesh) range. It may sometimes be recommended also for finer grinding. Within these limits a rod mill is usually superior to and more efficient than a ball mill. The basic principle for rod grinding is reduction by line contact between rods extending the full length of the mill, resulting in selective grinding carried out on the largest particle sizes. This results in a minimum production of extreme fines or slimes and more effective grinding work as compared with a ball mill. One stage rod mill grinding is therefore suitable for preparation of feed to gravimetric ore dressing methods, certain flotation processes with slime problems and magnetic cobbing. Rod mills are frequently used as primary mills to produce suitable feed to the second grinding stage. Rod mills have usually a length/diameter ratio of at least 1.4.

Tube mills are in principle to be considered as ball mills, the basic difference being that the length/diameter ratio is greater (35). They are commonly used for surface cleaning or scrubbing action and fine grinding in open circuit.

In some cases it is suitable to use screened fractions of the material as grinding media. Such mills are usually called pebble mills, but the working principle is the same as for ball mills. As the power input is approximately directly proportional to the volume weight of the grinding media, the power input for pebble mills is correspondingly smaller than for a ball mill.

A dry process requires usually dry grinding. If the feed is wet and sticky, it is often necessary to lower the moisture content below 1 %. Grinding in front of wet processes can be done wet or dry. In dry grinding the energy consumption is higher, but the wear of linings and charge is less than for wet grinding, especially when treating highly abrasive and corrosive material. When comparing the economy of wet and dry grinding, the different costs for the entire process must be considered.

An increase in the mill speed will give a directly proportional increase in mill power but there seems to be a square proportional increase in the wear. Rod mills generally operate within the range of 6075 % of critical speed in order to avoid excessive wear and tangled rods. Ball and pebble mills are usually operated at 7085 % of critical speed. For dry grinding the speed is usually somewhat lower.

The mill lining can be made of rubber or different types of steel (manganese or Ni-hard) with liner types according to the customers requirements. For special applications we can also supply porcelain, basalt and other linings.

The mill power is approximately directly proportional to the charge volume within the normal range. When calculating a mill 40 % charge volume is generally used. In pebble and ball mills quite often charge volumes close to 50 % are used. In a pebble mill the pebble consumption ranges from 315 % and the charge has to be controlled automatically to maintain uniform power consumption.

In all cases the net energy consumption per ton (kWh/ton) must be known either from previous experience or laboratory tests before mill size can be determined. The required mill net power P kW ( = ton/hX kWh/ton) is obtained from

Trunnions of S.G. iron or steel castings with machined flange and bearing seat incl. device for dismantling the bearings. For smaller mills the heads and trunnions are sometimes made in grey cast iron.

The mills can be used either for dry or wet, rod or ball grinding. By using a separate attachment the discharge end can be changed so that the mills can be used for peripheral instead of overflow discharge.

mesh | size, micron comparison chart | kramer industries inc | nj, nh

mesh | size, micron comparison chart | kramer industries inc | nj, nh

The term Mesh is used to describe the size of an abrasive particle. In some instances, such as withAluminum Oxide GritorSilicon Carbide Grit, a single number is used. This does not mean every particle in that product is exactly that size but rather than mesh size indicator is approximately the mean or average size of the range of particles in that grade. In other instances, such as withWalnut Shell GritorGlass Beads, two numbers are used. This indicates that all of the particles in that grade of product are within that range of mesh sizes.

U.S. Mesh Size (or U.S. Sieve Size) is defined as the number of openings in one square inch of a screen. For example, a 36 mesh screen will have 36 openings while a 150 mesh screen will have 150 openings. Since the size of screen (one square inch) is constant, the higher the mesh number the smaller the screen opening and the smaller the particle that will pass through. Generally US Mesh is measured using screens down to a 325 mesh (325 openings in one square inch).

Sometimes the mesh size of a product in noted with either a minus (-) or plus (+) sign. These signs indicate that the particles are either all smaller than (-) or all larger than (+) the mesh size. For example, a product identified as -100 mesh would contain only particles that passed through a 100 mesh screen. A +100 grade would contain particles that did not pass through a 100 mesh screen. When a grade of product is noted with a dash or a slash is indicates that the product has particle contained within the two mesh sizes. For example, a 30/70 or 30-70 grade would only have particles that are smaller than 30 mesh and larger than 70 mesh.

The terms Mesh and Grit are often confused. The terms can be used interchangeably when referring to abrasive grit. A 60 mesh Aluminum Oxide can also correctly be termed a 60 grit Aluminum Oxide. In practical terms, identifying a specific abrasive product with the term 60 Mesh would normally indicate that the product has a median size of the openings on a 60 mesh screen. The term 60 Grit more accurately identifies the particle size distribution of the product but the difference in terminology is insignificant for industry purposes. See our blog post Mesh vs. Grit for more detail.

The chart below shows the approximate size in inches and microns for various mesh sizes. These values are generally accepted as accurate but are approximates because the thickness of the wire used to make a specific screen will vary the number of openings in the one square inch. A micron is one-millionth of a meter or one-twenty-five thousandths of an inch. Most grades below 325 mesh are indicated by the micron size as these sizes are not manufactured using screens.

grinding cylpebs

grinding cylpebs

Our automatic production line for the grinding cylpebs is the unique. With stable quality, high production efficiency, high hardness, wear-resistant, the volumetric hardness of the grinding cylpebs is between 60-63HRC,the breakage is less than 0.5%. The organization of the grinding cylpebs is compact, the hardness is constant from the inner to the surface. Now has extensively used in the cement industry, the wear rate is about 30g-60g per Ton cement.

Grinding Cylpebs are made from low-alloy chilled cast iron. The molten metal leaves the furnace at approximately 1500 C and is transferred to a continuous casting machine where the selected size Cylpebs are created; by changing the moulds the full range of cylindrical media can be manufactured via one simple process. The Cylpebs are demoulded while still red hot and placed in a cooling section for several hours to relieve internal stress. Solidification takes place in seconds and is formed from the external surface inward to the centre of the media. It has been claimed that this manufacturing process contributes to the cost effectiveness of the media, by being more efficient and requiring less energy than the conventional forging method.

Because of their cylindrical geometry, Cylpebs have greater surface area and higher bulk density compared with balls of similar mass and size. Cylpebs of equal diameter and length have 14.5% greater surface area than balls of the same mass, and 9% higher bulk density than steel balls, or 12% higher than cast balls. As a result, for a given charge volume, about 25% more grinding media surface area is available for size reduction when charged with Cylpebs, but the mill would also draw more power.

why use different size balls in a mill

why use different size balls in a mill

Several years ago, Davis assumed that the rate of wear of the different sizes of balls in a ball mill was directly proportional to the weight of each ball, and he evolved a formula for calculating a balanced charge. Operators have used this formula when purchasing balls for a new mill or when reloading an old one that had been emptied for repair. The formula required that the largest ball size and the size to be rejected should be determined, and after that the other sizes were set. Stress was laid on the coarsest size, and to facilitate the use of the formula many writers have made their contribution by reporting ratio of coarsest particle size to the optimum ball size. Close adherence to this ratio has prevented giving attention to sizes and amounts of particles not falling in the category of the coarsest size.

The inadequacy of the formula and the futility of extensive experimentation for ratio determinations involving the coarsest particle size only is at once obvious when it is seen that the formula did not take into account the slow grinding rate of the finer sizes of ore and the amount present. To be sure, operators who were doing very fine grinding have sometimes altered the make-up load by using some additional small balls with the big ones, but this practice has been somewhat haphazard. Too much of the work has followed the old idea that there should be no ball present that is incapable of crushing the largest particle in the feed.

Today operators have a keener sense of the relatively large amount of work required to finish the finest sizes, so that the insufficiency of the formula is readily seen. It would have been fortunate had the formula been devised to attract more attention to the large amount of finer but unfinished particles. The formula is excellent from the basis of balance with respect to ball wear, but the literature has contained very little about the rationing of ball sizes for the best grinding of all sizes and amounts of particles extending throughout the length of the mill. Research has submitted in this matter.

It is not denied that the coarse particles have to be crushed else no fine material would accrue, but here the fact is emphasized that when crushing to 200-mesh stress should be on the selection of balls of the right size and amount to crush, say, from 100- to 200-mesh; or, when crushing to 65-mesh, the operator should judiciously load the mill for crushing from 48- to 65-mesh. If this were done, the circulating load would be relieved of the large amount of nearly finished size, and in its stead there would be some coarser material from which the classifier could more easily remove the finished size. Opposing this idea is the fact that a coarse circulating load would be undesirable in some of the recent supplementary recovery processes. However, this objection might be met by introducing a bypassing screen at the end of the ball mill.

Tests of other experimenters have been supplemented with detailed information on the optimum size of balls for grinding sized ore. Figures have been obtained that show what particular size of ball is the most efficient in crushing certain sizes of chert and dolomite. It is fortunate that this work has been done,

because it has brought out facts that would have been unsuspected otherwise. The method used here for showing what particular size of ball is best for a particular particle size of ore is to some degree unique. The reason for this is that usually such tests have been run to finish the grinding at a fine size. Those tests were as much a criterion of the work on the particle size in the finished product as of the feed, but they were not so interpreted. The tests reported in this paper are different because the first step in reduction is given the main emphasis.

As a guide in laying out this work, a mill was visualized as divided into sections. The first section had the largest media and performed the first step in grinding by reducing the particles for the second section; the second section, in turn, used smaller media to reduce the articles for the third section; and so on. This line of thought was the basis for the distribution of sizes in the ball loads already mentioned.

The ball sizes were 2.75-to 0.62-inch and the ore sizes plus 65- to plus 10-mesh. The results for chert are shown in four series in table 27 and for dolomite in five series in table 28. The ore (feed) sizes are in quotation marks because they are only nominal; their meaning is set forth in the sizing analyses under feed.

Any plan adopted would give but litle more than an approximation of the facts sought, owing to the difficulty in timing the grinding correctly. If it is desired to find the effect of balls grinding 20-mesh ore and the mill is loaded with 20-mesh material, the grinding time should be infinitely short, because fine particles are made as soon as the mill starts and if the run continues the test is of the comminuted products of the 20-mesh sample rather than that which was supplied for the test.

Extrapolation back to zero time would be desirable if it were possible. However, a very short period is unsatisfactory because the flaky particles, being the first to yield, would give a wrong impression of the sample as a whole. Long grinding periods would be useless because the particle size at the end of the run would be too far removed from the original particle size under investigation. A mean procedure had to be adopted.

The surface calculations that are given must be used guardedly, else they will be misleading. The fine particle sizes are likely to be weighted too much; when the ball size for crushing 10-mesh sizes through 14-mesh is sought, the very fine sizes should be weighted with caution.

A casual examination of each series for minimum of cumulative weights in the coarse sizes of the screen analyses probably would be a fair guide to the best ball size. But this minimum, though important of consideration, is not final, because the amount, power, and time have to be taken into account. These three quantities are resolved into tons per horsepower-hour and will be applied in table 29. Before going to that table, however, the present tables may be used to bring out a fact not commonly knownballs that were too large as well as balls that were too small failed in selective grinding. In any of the series except the last one of each table, where the largest ball sizes were not large enough, the low cumulative percentage weight of the coarse sizes is in a mean position and rises with the use of larger as well as smaller balls. Hence, it is shown that balls that were too large did nonselective grinding.

mesh size in table 27 and are shown in sizing diagrams. The percentage weights of the products from the largest, and the smallest balls are shown by broken lines. They are high in the upper part of the diagram. Their position shows that much of the coarse material was not reduced through 35-mesh. The solid line shows good selective work of the balls of optimum size.

In the study of these diagrams, it must be remembered that the main variables in the tests were ball size and that the tests were timed to give the same amount of subsieve size. The conditions imposed on the tests were entirely different from closed-circuit grinding, in which the composite feeds would have been unlike, although the new feeds might have been the same.

The nonselective grinding of the off-size balls may be explained as follows: The largest balls failed on the coarsest sizes because they did not offer a sufficient number of points of contact for the number of grains present; hence, some of the particles remained at the end of the test. Furthermore, due to the small number of points of contact of such large balls, the crushing impulse was so great that the grains that did meet it received excessive comminution and much of the subsieve size resulted.

The smallest balls had so many points of contact that the impulse at a given point was too much reduced to exert sufficient stress on the coarsest particles; hence, some of them remained without the desired reduction. However, a few that were reduced yielded grains readily comminuted by the smallest balls, and much subsieve size again resulted; hence, there was an intermediate ball size for the best work.

Table 29 will now be discussed: It is made by using the two preceding tables. It gives the amount of the coarsest size per unit of power crushed through a stated coarse but finer size. To illustrate the method of calculation, take the first test in table 27: The amount of plus 65-mesh crushed through 100-mesh is 89.563.3=26.2 parts per hundred, and by the table the ton per horsepower-hour was 0.16; hence, the tons per horsepower-hour crushed through 100-mesh was 26.2/1000.16=0.042. Similarly, in the first test in the second series 97.352.0=45.3, and 45.3/1000.186=0.084 ton per horsepower-hour through 48-mesh. Thus, table 29 has four series of tests or chert and five series for dolomite. The preferred value in each series is underscored to show what seems to be the preferable ball size. The optimum ball size for grinding closely sized particles through the limiting screen, as determined by these experiments, may be expressed in the following equation

where D is diameter of ball, d is diameter of particle to be ground, and K is a constant depending on the grindability of the ore. When D and d are expressed in inches, the value of K for chert is 55 and for dolomite is 35. This formula is of the same type as that developed by Starke. He evaluated the grind through a broader range and his dimensions are in microns.

Having selected the best ball size, it will be seen by referring to tables 27 and 28 that the preferable ball size usually gave the best capacity and efficiency. Also, the preferable ball size coincides closely with the best selective grinding, the main exception being the plus 10-mesh series in table 28. There the preferable ball size is smaller than the size for the best selective grinding. Probably the exception is due to an error in planning the plus 10-mesh series; the time periods were too long and too much grinding resulted. The spread in reduction in this series was greater than in any other series. It was intended to avoid such a broad spread in reduction. In the study of the exception and the study of the sizing analyses in the other tests an attempt has been made to gain additional information by using the Gaudin log-log method for plotting sizinganalyses, but the results were not satisfactory. It is believed, however, that the method was not expected to apply to the moderate reduction of a sized product.

Tables 27 and 28 cannot be dismissed without consideration of the variation of power throughout a test. Figure 5 is submitted for that purpose. In it the time extends from 0 to 3.5 minutes. The change in power through the grinding periods was watched in all the tests. This change is illustrated in figure 5, which deals with the plus 20-mesh size in table 28. In the discussion of this figure, what will be said about the relation of power to other factors is premised by the belief that the degree to which the balls nip the particles influences the power, and that when nipping is best the power will be the highest. The curve at the bottom of the figure shows that the 2.75-inch balls required less power than the other loads. The balls were too big for good nipping, and as the grinding continued they became relatively bigger and further power reduction resulted. Correlated with this is the fact that the grinding was poor in selection and unsatisfactory in capacity and efficiency. (It is not consistent to compare the numerical-values of capacities and efficiencies of one series in tables 27 and 28 with those of another series. The principles underlying the reason were mentioned under Sillimanite balls.)

Turning next to the deportment of the 0.62-inch balls, which were the smallest in the group, the change in power from beginning to end of the run is in a reverse order from that with the largest balls. The balls were too small for good nipping, but as comminution proceeded they became relatively larger so that nipping and power increased but did not reach the high power indicating good nipping. The selective grinding, capacity, and efficiency were again poor.

The record of the 1-inch balls is more favorable. The power was high throughout the test, indicating that a desirable mean size had been reached. The selective grinding, capacities, and efficiencies were good. This all indicates that when nipping is best the mill (when not run too fast) will do its best work. This statement is not new; the evidence is given for those who wish to weigh it.

A comprehensive examination of mills that segregate the ball sizes shows that they require mixtures containing a greater number of small balls than is supplied by the Davis ball load. This deficiency was met by using the rationed ball load, in which small balls predominated. Before going ahead, the mills will be considered.

Conical mills and cylindrical mills with grids were contemplated in introducing the new loads. Hence, these mills must be discussed before showing the tests, and they must be compared with the standard cylindrical mill.

Should the ball sizes be segregated, or should they be mixed as in the standard cylindrical mill? In the metallics industry the most effective method of segregating is to place the mills in series and use succeedingly smaller balls from first to last mill in the series. In the cement industry, dividers or grids are used to divide the long mills into sections, each of which has the appropriate size of medium. Finished material is removed at the end of each section.

With the knowledge that the cone of a conical mill functions like a grid in segregating the balls with respect to size, conical mills were built and tested. The first one was only 3 feet long. A taper of 2 inches to the foot was ample to segregate the largest balls in the big end and the smallest balls in the small end. Grinding tests in this mill with a rationed ball load were compared with the old cylindrical mill loaded with the old style ball load. A decided advantage was gained by the newer practice.

A larger conical mill was built and is shown in figure 6. It was 6 feet long and had the same taper as the smaller one. The big end was 2 feet in diameter and the small end 1 foot. The ability of the mill to segregate the balls was demonstrated by tests.

Grinding tests with several types of mills and ball loads led to the conclusion that advantages that had been gained were due more to the appropriate average size of balls than to the new design of mill. It was difficult to show that the conical mills had an outstanding advantage over the cylindrical mill. The 6-foot conical mill had a disadvantage; it induced the media to drift to the big end and pile up there so much that the balls passed through the feed entrance into the scoop. For a simple remedy a grid was placed on the feed opening to retain the load. A change was made to a cylindrical mill lined with a series of identical truncated cones. The idea was suggested by C. L. Carman, of Independence, Kans.

Although the efficiency of the long cone was good, the loss in capacity induced by the taper was marked. This may be shown by the following analysis: If the last unit section with diameter D2 = 1 foot could be speeded up to the same percent critical as the first unit section with diameter D1 = 2 feet, it would have a relatively low capacity

A 2- by 3-foot cylindrical mill was lined to employ the conical effect, but instead of having one cone it had three identical truncated cones, end to end, and apexing in the same direction. (See fig. 7.) Any cylindrical mill may be lined in this fashion by using liners tapered in thickness. If the liners are 2 feet long, a 12-foot mill would have six truncated cones, end to end. The mill would have the same capacity at the discharge end as at the feed end. In some way, at least, this would be an advantage over the long cone. The mill with truncated cones proved to be as good a sizing device as the long single cone, but when compared with the old cylindrical mill its advantage as a grinder was not marked.

Finally, a cylindrical mill with a grid was used. The grid was 1 foot from the feed end of a 2- by 3-foot cylindrical mill. Balls of 2.5 inches to 1 inch were placed in the feed-end sections and 0.75-inch balls in the discharge end. The grinding was moderately better than without the grid. Possibly the grid would have appeared to have more advantage if the feed had been coarser and the finishing finer. The

In table 30, grinding to a fine size was stressed to give the extra amount of small media in the new load a chance to work advantageously. Grinding was continuous and about 74 percent of the product passed through 200-mesh. The Davis ball load in the cylindrical mill was used first; next, the rationed ball load was used in the same mill; and finally, the rationed ball load was used in a mill having a lining of truncated cones. In selecting the Davis ball load the no. 1 load was used instead of no. 2 in accordance with the old idea that all of the balls should be of a size to crush any of the particles of ore. The free migration of the ore induced by the large, interstices would be compatible with a heavy circulating load. In the cylindrical mill the work of the rationed ball load was about 60 percent better than the Davis ball load, and when the mill which was lined with truncated cones was used there was a further gain of about 5 percent. The rationed ball load left more of the coarse sizes unfinished.

In table 31 the results of five tests with different ball loads in cylindrical, grid, and conical mills are shown. The feed was coarser than was used in table 30. The grinding in test 2 with the rationed ball load, which contained 64 percent of 0.75-inch balls, was about 44 percent more efficient than with the Davis load. The power was about 11 percent higher. If Davis ball load no. 2 instead of no. 1 had been used, the divergence in grinding results would have been reduced. In test 3, in which the grid was used to segregate the different sizes of balls, a further advantage of about 4 percent in efficiency is shown. The conical mill in test 4 increased the efficiency to 58 percent more than in test 1. The efficiency with the long (6-foot) conical mill was about the same as with the short (3-foot) one.

The validity of having graded sizes of balls to grind the ore in steps with ample provisions for a circulating load and removal of fines in each step cannot be denied, but without this quick removal of finished material the advantage was not great.

In the conical mills or in the grid mill, as used in these tests, it was difficult to set a correct feed rate. If the feed were too fast some of the coarse particles would pass the zone intended to grind them. Having passed that zone, they were likely to continue without being ground. Again, if the feed were too slow, energy would be wasted by making the fine particles remain too long with the coarse medium. Nonselective grinding and inefficiency would result.

Thus far the evidence of the efficacy of a rationed load in plant operation may be questioned because, as is shown by tables 30 and 31, the coarse sizes were not reduced as much as with the Davis load. Fear was entertained lest a circulating load might develop trouble- some characteristics. Hence, closed-circuit grinding was tried.

Rationed ball sizes were of advantage in batch and open-circuit grinding. The degree depended on the particle size of feed and product. Examination will now be made to see if the deportment of rationed sizes is satisfactory in closed-circuit grinding.

The tests were performed as shown in tables 32 and 33. In the first table dolomite B was used, and in the second the feed was chert rejects from earlier grinding tests. The procedures in the two tables have one fundamental difference; in table 32 the feed to the rationed ball load was increased on account of the extra efficiency of the rationed sizes, whereas in table 33 the feed was maintained at the same rate but the mill speed was reduced. That is, in the first table the advantage is shown by the increased amount of ore ground, and in the second the advantage is shown by the power saved. If preference is given to one of the two methods it should apply to the latter, because in it the two ball loads being compared deal with the same amount of feed, and the drag is worked under almost identical conditions. The pulp consistencies of the drag overflows were maintained at 17 percent solids.

In table 32 the drag classifier finished at a finer size when rationed sizes of balls were used. This variation is on the right side for safe conclusions about the advantage of the new ball load. With the Davis ball load, 2.95 pounds per minute were finished, and with the rationed ball load the amount was increased to 4.06 pounds perminute an increase of 37 percent. The surface tons per hour show, an increase of 45 percent in favor of the rationed ball sizes, and the surface tons per horsepower-hour show a more moderate advantage37 percent. The reason the advantage in capacity was greater than in efficiency is because of the difference in power in the two tests; the smaller balls required more power than the larger ones. The surface calculations are made from the part of the table marked section 3. There a composite feed has been calculated, so that surface calculation can be based on feed and product. However, the ultimate values would have been the same if the sizing analyses of new feed and over- flow in sections 1 and 2 had been used.

It will be seen that the circulating loads in each table are about the same, respectively. Due precaution was taken to make sure that the circulating load was balanced, about 2 hours being required after the last adjustment.

The closed-circuit set-ups are shown in figures 8 and 9. They do not include the inclined belt and weightometer formerly used. A better plan was to permit the drag sand to fall into buckets and at set intervals to pass the sand back to the new-ore belt feeder after a hurried weighing. The record of the weights obtained after decanting

superfluous water indicated the trend of the circulating load, but a more accurate estimate was made at frequent intervals by catching the ball-mill discharge in a graduate and weighing it. The weight of solids minus new feed gave the circulating load with exactness. The test was continued for a goodly period after the amount of discharge became constant.

In the two tests shown in Table 33, the overflows are nearly identical. The innovation in the manner of conducting the tests, as stated before, was to keep the new feed constant and reduce the speed of the mill containing the new ball load until the circulating load in section 2 was the same as in section 1. When the new ball load was used, the speed was reduced from 70 to 55 percent critical and the capacity was maintained. The increase in efficiency was 28 percent. The Davis ball load took 22.6 percent more power than the rationed ball load.

The comparison of different sizes of media when the mill speeds are not the same might not have been justified by the old literature, but it is justified by table 13, which shows that for speeds from 40 to 70 percent critical, inclusive, the efficiencies were almost identical when the amount of ore in the mill was the same; of course, capacity increased with speed. It is readily seen from table 33 that the capacity with the rationed ball load at 55 percent speed was about the same as with the Davis load at 70 percent speed. If the finishing could have been at 200-mesh in all the closed-circuit tests, the load of large balls would have been greatly handicapped and the load of small balls would have had a greater relative advantage. Then the difference in efficiency might have been as much as 75 percent. The grinding seems to have been a little more selective with the larger media.

By table 2 the diameter of the ball of average weight in the rationed load no. 2 was 1 inch. A load of 1-inch balls would have given about the same results but would not have permitted the study of the effect of segregation in the grid and conical mills. Furthermore, the practical application would have been doubtful. A Davis ball load with sizes from 1 to 1 inch would have done good work, but it would not have been representative of the old standard because some of the balls would have been too small to crush the largest particles.

The quantities obtained in these tests enable the mill man to get a vision of the amount of power required to do his grinding. Take, for example, the tests represented by section 1 in table 33, in which grinding was to flotation size by what may be called the ordinary ball load and the ore feed was almost 100-percent Tri-State chert through 8-mesh. Calculations show that the net energy input was 21 horsepower-hours per ton. One-third should be added for friction and motor losses, which would bring the motor input up to 28 horsepower-hours per ton of ore. An ore would have to be rich to justify the expenditure of so much additional power for grinding.

bond work index formula-equation

bond work index formula-equation

You can read all the details of this now Biblical grinding power requirement calculation formula in Fred Bonds original paper. You can also review the step-by-step Bond Work Index Test Procedure I posted here.

For any circuit, whether a crushing circuit, a rod mill, or a closed ball mill circuit, the Work Index always means the equivalent amount of energy to reduce one ton of the ore from a very large size to 100 um.

The sample was received crushed appropriately for the ball mill test. Ball Mill Grindability Testwas conducted by standard practice using 100-mesh (150 pm) closingscreens.The ball mill work index is shown below.

Any improvement in the accuracy of commercial comminution calculations under the Third Theory must be accomplished either by increased precision in energy input measurements, or by a better evaluation of the total new crack length produced, as indicated by the feed and product size distributions. Since at the present time feed and product sizes are approximated solely by the microns 80% passes, the most promising opportunity for increased accuracy lies in consideration of their plotted size distribution characteristics. This paper shows how more accuracy can be obtained over an increased range of feed and product sizes from size distribution studies.

where W is the work input required in kilowatt hours per short ton to grind from 80% passing F microns to 80% passing P microns, and Wi is the work index, or the grinding resistance parameter. It represents the energy input required in kilowatt hours to reduce a short ton from theoretically infinite feed size to 80% passing 100 microns. This simple equation has been extremely useful in analyzing and grinding operations, and in predicting the performance of new installations.It can be written in the following form:

The work index Wi can be determined from plant operations and from laboratory ball mill grindability, rod mill grindability, and impact crushing tests. The laboratory test results are used to check the efficiency of commercial operations and to compute the proper machine sizes for new installations.

where Pi is the opening in microns of the sieve mesh tested, and Gbp is the net grams of mesh undersize produced per revolution of the 12 x 12 test ball mill. The closed circuit 80% passing size P averages P1/log 20 for all sizes larger than 150 mesh. For 150 mesh the average P value is 76 microns, for 200 mesh it is 50, for 270 mesh it is 32.3, and for 325 mesh it is 26.7. These average values can be used when P cannot be determined from screen analyses.

where Sg is the specific gravity and C is the impact crushing strength of the twin pendulum weights in foot-pounds per inch of rock thickness. No size distribution measurements are made in the impact test.

The trend of the particle size distribution line is shown by plotting its screen analysis in, such a manner that a complete homogeneous crushed or ground product will form a straight line; any curvature then indicates a natural or induced grain size. Semi-log paper is used with the percent cumulative retained plotted on the vertical logarithmic scale Y. Straight lines which each represent one mesh sieve size of P1 microns are drawn radiating from the upper left hand corner of the plot; each crosses the 20% retained, or 80% passing, line at w = 10/P1 where w is the horizontal lineal X value at Y = 20. The total work input to the sample in KWH/ton divided by the work index Wi is w. The straight plotted distribution line follows the exponential equation:

The exposure ratio Er is the quantity that expresses the line trend, or the fine size distribution. Er equals X2/W where X2 is the value of x at the top of the chart with Y = 100%. It has the following relationship to b.

When the exposure ratio Er is zero only one particle size is present and there has been no exposure of fines to the grinding media. The fines present increase as Er increases, and when Er is unity b is infinite.

When natural or induced grain sizes cause the plotted distribution line to curve in the region of 80% passing, the straight line determining Er is drawn through w at the average slope from Y = 10 to Y = 40, or is estimated to avoid the curvature. The exposure, ratio of the feed is Erf and that of the product is Erp.

It is apparent that the specific work input required, as represented by the new crack length Cr produced in centimeters per cc of solid (Crp Crf), will be decreased at large product sizes and will increase at fine product sizes when Crf and Erf are increased. In this case the work index Wi will increase as the product size P becomes smaller. Conversely, when the feed contains little fines and Erf and Crf are small, the work index will increase as P increases. These conditions are largely responsible for the observed work index variations at different product sizes which were formerly thought to require an exponent different from .

In a recent publication fifteen different ores each had grindability tests made at 28, 35, 48, 65 and 100 mesh, with many work index variations at the different product sizes. These tests are used here to develop empirical equations from which the work index at different product sizes can be computed from a grindability test at one size. In each of the 15 ores the data from the grindability test at 48 mesh alone were used to calculate the Wi values at 28, 35, 65, and 100 mesh, and these were compared with the actual values obtained by testing. In the calculation the exposure ratio Erp of each mesh product size was considered to be that determined by testing at 48 mesh, and Crp was determined from that value and the average P for each mesh size.

However, an equation is desired which uses the exposure ratios and does not require calculation of the crack lengths, Eq. (8) was derived to give the work index Wi at any 80% passing product size P from the work index Wio found from a single grindability test with a product size Po and exposure ratios Erf and Erp. It is

The work index values calculated from Eq. (7) and Eq. (8) are listed in Table I. Comparison with the actual Wi values shows that Eq. (8) is slightly more accurate than Eq. (7), and it is much simpler to use. Eq. (8) is suitable for determining the work index at various product sizes from one ball mill grindability test made at product size Po. It can be checked by grindability tests made at other product sizes.

The exposure ratio of the prepared minus 6 mesh feed Erf is regularly somewhat larger than that of the closed circuit product Erp, and Eq. (8) indicates that when Erf/Erp equals 1.29 the work index continues constant at all product sizes. When Erf/Erp is greater than 1.29, the work index increases as the product size decreases, and when Erf/Erp is less than 1.29 the work index decreases.

When Wi100 is calculated by Eq. (9) from the data at 48 mesh for each of the 15 ores listed, then Wip found by Eq. (10) for each of these ores at 28, 35, 65, and 100 mesh is essentially the same as the Wi value found from Eq. (8).

Comparison of the Wi100 values from Eq. (9) for different ores furnishes a measure of the relative grindability unaffected by size distribution differences; and comparison of the Wi100 values for the same ore calculated from the data at different mesh sizes gives a measure of the actual experimental errors involved in testing, plus any error in measuring the plotted Er values, and any error resulting from natural grain sizes causing curved plotted lines.

The standard work index Wi100 values calculated from Eq. (9) for each ore at each mesh size are included in Table I. Comparison for each ore shows a reasonable agreement among the tests made at various mesh sizes, and indicates that Eq. (9) and Eq. (10) can be used with confidence. The data show that the ball mill grindability tests at 28 mesh are somewhat less accurate than the others; this is expected because of the low ratio of reduction and the short retention time in the mill, when grinding prepared minus 6 mesh feed.

The total crack length Cr in centimeters per cubic centimeter of solids is most conveniently found from log-log charts prepared from a previously published table. However, in the absence of these chart the crack length of a crushed or ground product can be calculated for any 80% passing size P in microns and any exposure ratio Er by the following equation:

In the standard ball mill and rod mill grindability tests the specific crack lengths of the product Crp and of the feed Crf are found from their Erp, P, Erf, and F values. Where Y is the cumulative fraction of the feed retained on the mesh size tested the centimeters of new crack length produced per mill revolution are found from:

The average useful work input to the standard ball mill is 65 joules/Rev. with 115 joules/Rev. to the rod mill. The crack energy Ce of the sample tested is found by dividing joules/Rev. by Cm/Rev. The standard work index can then be found by transposing Eq. (16) and solving for Wi100.

In commercial grinding mills the operating work index is found by Eq. (19). However, when exposure ratios of the feed and product are obtained by plotting the screen analyses, their specific crack lengths Crf and Crp can be found. This furnishes the crack energy Ce in joules/Cm from:

The standard work index Wi100 can then be found from transposed Eq. (16). Comparison with the plant operating work index at product size P may show that the coefficients .018 and .014 in the last term of Eq. (9) should be altered slightly for the commercial grind. With the proper coefficients Eq. (9) can be used to evaluate the plant grinding operation at different product sizes with considerable accuracy.

ball mills - mt baker mining and metals

ball mills - mt baker mining and metals

Ball mills have been the primary piece of machinery in traditional hard rock grinding circuits for 100+ years. They are proven workhorses, with discharge mesh sizes from ~40M to <200M. Use of a ball mill is the best choice when long term, stationary milling is justified by an operation. Sold individually or as part of our turn-key ore processing system.

Our ball mills are industrial grade and designed for continuous operation, equipped with oversize roller bearings and a complete drive system. All wear parts are highly abrasion resistant and replaceable.

The capacity, or throughput, of a ball mill is directly linked to particle size of the ball mill discharge. For example, it takes approximately 3 times as long to achieve 200 mesh grind as it does to achieve 65 mesh grind. Establishing a commercial liberation size is critical when designing and engineering your grinding circuit.

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bond work index procedure and method

bond work index procedure and method

This Grindability Test orBond Ball Mill Work Index Procedure is used to determine the Bond Work Index of minus six mesh or finer feed ore samples. These equation application methods are used to process <1/2 ore samples in a Ball Mill using a standard ball charge.

Below describes in general terms the Bond Work Index Procedure used by a Professional Metallurgical Testing Laboratory. If you think the equation is complicated, wait until you try using that famous Bond Work Index equation Mr. Fred worked so hard at.

9. Enter the combined sizing data from Feed No. 1 and No. 2 (or No. 2 and No. 3) into a new Bond Feed Screen Analysis sheet and calculate the K80 and the average percent of less than 150 mesh product. 10. Record the K80 in um as factor, F, on yourBond Mill Grindability Test-sheet. 11. Record the percent of the under-size, i.e. less than 150 mesh product.

The sample was crushed to 100% passing 6 mesh (3.35mm), from this a 700 cc volume was measured and weighed to be used as feed for the Bond Mill. A feed particle size analysis was performed to determine feed P80 and % -106 micron. The sample was milled for 100 revolutions and passed over a 150 mesh (106m) sieve, the undersize was removed from the samples, weighed, and new sample was added to the feed to maintain the initial sample weights. The number of rotations for the next milling was calculated based on the undersize sample weights. This was repeated until the milling produced stable results for three consecutive cycles.

The Bond grindability was calculated to be 1.21 g net undersize/revolution by averaging the results from the last 3 runs on the Bond Mill. The grindability is defined as the ease at which a mineral particle is reduced to a predetermined size and used to calculate the Work Index. The feed and final undersize particle size analysis as well as the grindability test data sheet are found in the appendix.

bond tests | sgs

bond tests | sgs

The grinding circuit is among your largest capital investments and greatest operating costs. SGS can reduce your risk by combining different test procedures and design methodologies to ensure that you optimize this critical part of your plant.

Our philosophy is to first determine the variability of your ore using rigorous comminution testing, including Bond tests for ball and rod mills. We conduct a small number of expensive tests that require a larger sample size, such as the Bond Ball Mill Grindability Test. The results are used to calibrate a large number of less expensive tests that require only a small sample, such as the Modbond Grindability Test.

Similar to a Comparative Work Index, this test is an open circuit dry batch grindability test run in the standard Bond Ball Mill for a set time. It can be used at mesh sizes from 65 to 200 mesh (normally 100 mesh). The test requires calibration against the standard Bond Ball Mill Work Index test to estimate the Work Index. It is used to show the orebody hardness profile and to predict throughput in a ball mill circuit.

SGS created the Modbond grindability test and has a large proprietary database. The small sample size enables many tests to be conducted, resulting in extensive variability information that our experts use to efficiently design your grinding circuit.

Where W = Net power consumption in kWh/t Wi = Bond work index (either Imperial or Metric units) P= The 80% passing size of the ground product in m F = The 80% passing size of the feed in m

The test determines the Bond Impact Work Index which is used with Bonds Third Theory of Comminution to calculate net power requirements when sizing crushers*. It is also used to determine the required open-side settings (jaw crushers and gyratory crushers) or closed-side settings (cone crushers) for a given product size.

WhereOss = Open-side setting in inches Css = Closed-side settings in inches Ecc = Eccentric throw in inches P80 = Aperture through which 80% of the product will pass. Wi = Work Index

The impact apparatus consists of two pendulum-mounted hammers, mounted on two bicycle wheels so as to strike equal blows simultaneously on opposite sides of each rock specimen. The height that the pendulum is raised is increased until the energy is sufficient to break the specimen.

The test determines the Bond Rod Mill Work Index which is used with Bonds Third Theory of Comminution to calculate net power requirements when sizing ball mills*. Various correction factors may have to be applied.

ball mill for sale | grinding machine - jxsc mining

ball mill for sale | grinding machine - jxsc mining

Ball mill is the key equipment for grinding materials. those grinding mills are widely used in the mining process, and it has a wide range of usage in grinding mineral or material into fine powder, such as gold, ironzinc ore, copper, etc.

JXSC Mining produce reliable effective ball mill for long life and minimum maintenance, incorporate many of the qualities which have made us being professional in the mineral processing industry since 1985. Various types of ball mill designs are available to suit different applications. These could include but not be restricted to coal mining grate discharge, dry type grinding, wet mineral grinding, high-temperature milling operations, stone & pebble milling.

A ball mill grinds ores to an end product size of thirty-five mesh or finer. The feeding material to a ball mill is treated by: Single or multistage crushing and screening Crushing, screening, and/or rod milling Primary crushing and autogenous/semi-autogenous grinding.

Normal feed sizes: eighty percent of six millimeters or finer for hard rocker eighty percent of twenty-five millimeters or finer for fragile rocks (Larger feed sizes can be tolerated depending on the requirements).

The ratio of machine length to the cylinder diameter of cylindrical type ball mills range from one to three through three to one. When the length to diameter ratio is two to one or even bigger, we should better choose the mill of a Tube Mill.

Grinding circuit design Grinding circuit design is available, we experienced engineers expect the chance to help you with ore material grinding mill plant of grinding circuit design, installation, operation, and optimization. The automatic operation has the advantage of saving energy consumption, grinding media, and reducing body liner wear while increasing grinding capacity. In addition, by using a software system to control the ore grinding process meet the requirements of different ore milling task.

The ball mill is a typical material grinder machine which widely used in the mineral processing plant, ball mill performs well in different material conditions either wet type grinding or dry type, and to grind the ores to a fine size.

Main ball mill components: cylinder, motor drive, grinding medium, shaft. The cylinder cavity is partial filling with the material to be ground and the metal grinding balls. When the large cylinder rotating and creating centrifugal force, the inner metal grinding mediums will be lifted to the predetermined height and then fall, the rock material will be ground under the gravity force and squeeze force of moving mediums. Feed material to be ground enters the cylinder through a hopper feeder on one end and after being crushed by the grinding medium is discharged at the other end.

Mining Equipment Manufacturers, Our Main Products: Gold Trommel, Gold Wash Plant, Dense Media Separation System, CIP, CIL, Ball Mill, Trommel Scrubber, Shaker Table, Jig Concentrator, Spiral Separator, Slurry Pump, Trommel Screen.

ball mill, ball grinding mill - all industrial manufacturers - videos

ball mill, ball grinding mill - all industrial manufacturers - videos

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... LN2 feeding systems, jar and ball sizes, adapter racks, materials low LN2-consumption clearly structured user interface, memory for 9 SOPs programmable cooling and grinding cycles (10 ...

The XRD-Mill McCrone was specially developed for the preparation of samples for subsequent X-ray diffraction (XRD). The mill is used for applications in geology, chemistry, mineralogy and materials science, ...

The Planetary Ball Mill PM 200, engineered by Retsch, is a milling device best suited for mixing and size reduction processes and is also capable of meeting the necessary requirements for colloidal grinding ...

... Micro Mill PULVERISETTE 0 is the ideal laboratory mill for fine comminution of medium-hard, brittle, moist or temperature-sensitive samples dry or in suspension as well as for homogenising of emulsions ...

... , fast, effective. WORKING PRINCIPLE Impact and friction The FRITSCH Mini-Mill PULVERISETTE 23 grinds the sample through impact and friction between grinding balls and the inside wall of the grinding ...

... grinding mills includes being safe throughout. When the mills are quoted we make sure to include any and all safety components needed. Long life and minimum maintenance To help you get the most of your ...

Annular gap and agitator bead mills are used for processing suspensions and highly viscous products in chemicals and cosmetics as well as in the food sector. Studies have shown that annular gap bead ...

... Pneumatic extraction from the surface of the agitated media bed Wet grinding: Separation of suspension from the agitated media by ball retaining device Flexibility Through careful selection of the size and quantity ...

... details; Agitating power: 0,37 kW Total Power Consumption : 1.44 kW Total Weight : 100 kg Metal Ball Size : 6.35 mm Metal Ball Amount : 7 kg Cold water consumption : 10 liters / hour ...

Cement Ball Mill Processing ability: - 200 t/h Max feeding size: - 25 mm Product Fineness: - 0.074-0.89mm Range of application: - limestone, calcium carbonate, clay, dolomite and other minerals ...

... grinds and classifies a product. Vilitek MBL-NK-80 mill is specially designed for grinding valuable materials, which, when grinding, the re-milled fractions are not a commodity product. In particular, this mill ...

Dimensions: Height: 1530 mm Width: 650 mm Length : 1025 mm Description: Ball mills are capable of rapidly producing chocolate, nut pastes (for gianduia), and spreadable creams. It has been ...

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