## ball agitator mill - all industrial manufacturers - videos

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... high-performance bead mill adds easy handling and local configuration to the higher production capacities, better energy efficiency and improved product quality you expect from our MicroMedia solution.
Maximum ...

... volume agitated bead mill with innovative combination of functional elements. Ideal for pass operation, in many cases highly suitable for economic recirculation mode. Conveying EcoMizerTM-discs guarantee ...

- Minimized specific energy requirement
- Higher productivity from smaller mill volume
- High flow capacity
- Entire machine family from 10 to 1000 l available
Leading companies have been relying on Bhler Cenomic ...

... main agitator and chocolate pump. Just that easy. When it comes to other remarkable features of chocolate ball mill BSCM200-HL;
All the outer surfaces are isolated for energy efficiency.
...

## 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 ...

## small ball mills for sale

Our small-scale miners Ball Mills use horizontal rotating cylinders that contain the grinding media and the particles to be broken. The mass moves up the wall of the cylinder as it rotates and falls back into the toe of the mill when the force of gravity exceeds friction and centrifugal forces. Particles are broken in the toe of the mill when caught in the collisions between the grinding media themselves and the grinding media and the mill wall. In ball mills, the grinding media and particles acquire potential energy that becomes kinetic energy as the mass falls from the rotating shell. Ball mills are customarily divided into categories that are mainly defined by the size of the feed particles and the type of grinding media.

Intermediate and fine size reduction by grinding is frequently achieved in a ball mill in which the length of the cylindrical shell is usually 1 to 1.5 times the shell diameter. Ball mills of greater length are termed tube mills, and when hard pebbles rather than steel balls are used for the grinding media, the mills are known as pebble mills. In general, ball mills can be operated either wet or dry and are capable of producing products on the order of 100 um. This duty represents reduction ratios as great as 100.

The ball mill, an intermediate and fine-grinding device, is a tumbling drum with a 40% to 50% filling of balls. The material that is to be ground fills the voids between the balls. The tumbling balls capture the particles in ball/ball or ball/liner events and load them to the point of fracture. Very large tonnages can be ground with these devices because they are very effective material handling devices. The feed can be dry, with less than 3% moisture to minimize ball coating, or a slurry can be used containing 20% to 40% water by weight. Ball mills are employed in either primary or secondary grinding applications. In primary applications, they receive their feed from crushers, and in secondary applications, they receive their feed from rod mills, autogenous mills, or semi-autogenous mills. Regrind mills in mineral processing operations are usually ball mills, because the feed for these applications is typically quite fine. Ball mills are sometimes used in single-stage grinding, receiving crusher product. The circuits of these mills are often closed with classifiers at high-circulating loads.

All ball mills operate on the same principles. One of these principles is that the total weight of the charge in the mill-the sum of the weight of the grinding media, the weight of the material to be ground, and any water in the millis a function of the percentage of the volume of the mill it occupies.

The power the mill draws is a function of the weight of the charge in the mill, the %of volumetric loading of the mill, the %of critical speed, which is the speed in RPM at which the outer layer of the charge in the mill will centrifuge.

For closed grinding circuits producing typical ball mill products, indirect and direct on-line measurements of the product size are available. The indirect means are those which assume that the product size is relatively constant when the feed condition to the classifying unit and the operating conditions in the classifying unit are constant. One example is maintaining a constant mass flow, pulp density and pressure in the feed to the cyclone classifier.

By using math modeling, it is possible to calculate the product size from measured cyclone classifier feed conditions and circuit operating data, thus establishing the effect on the particle size distribution in the product for changes in the variables.

Direct on-line means to measure either particle size or surface area are available for typical ball mill circuit products. These require the means to obtain representative or at least consistent samples from the grinding circuit product stream. These direct means and the calculated product particle size distributions can be used to:

Small variations in the feed size to ball mill circuits generally is not critical to the calculation of operating work index because they make a very small change in the 10F factor. Thus, a computer program can be developed to calculate operating work indices from on-line data with the feed size a constant and with the program designed to permit manually changing this value, as required to take into account changes in feed size resulting from such things as drawing down feed bins, crusher maintenance, work screen surfaces in the crushing plant, etc. which are generally known in advance, or can be established quickly. Developments underway for on-line measurement of particle size in coarser material which when completed will permit measuring the feed size used to calculate operating work indices.

recorded by a data logger, gives continuous means to report comminution circuit performance and evaluate in-plant testing. Changes in Wio indicated on data loggers alert operating and supervisory personnel that a change has occurred in either the ore or in circuit performance. If sufficient instrumentation is available, the cause for a problem can often be located from other recorded or logged data covering circuit and equipment operation, however, generally the problem calls for operator attention to be corrected.

Wio can be used to determine the efficiency of power utilization for the entire comminution section of a mill, and for the individual circuits making up the comminution section. The efficiency of a comminution circuit is determined by the following equation.

Wi is obtained by running the appropriate laboratory tests on a composite sample of circuit feed. Wio is calculated from plant operating data covering the period when the feed sample was taken. Since Wi from laboratory tests refers to specific conditions for accurate efficiency determinations, it is necessary to apply correction factors as discussed in The Tools of Power Power to Wio to put the laboratory and operating data on the same basis.

To-date, there is no known way to obtain standard work index data from on-line tests. Continuous measurement of comminution circuit efficiency is not possible and thus efficiency is not available for circuit control. Using laboratory data and operating data, efficiency can be determined for overall section and individual circuit for evaluation and reporting. Just monitoring Wio and correcting operating problems as they occur will improve the utilization of the power delivered to the comminution circuits.

Samples taken from the chips around blast hole drillings and from broken ore in the pit or mine for laboratory work index and other ore characteristic determinations before the ore is delivered to the mill, can be used to predict in advance comminution circuit performance. Test results can also be used for ore blending to obtain a more uniform feed, particularly to primary autogenous and semi-autogenous circuits.

We sell Small Ball Mills from 2 to 6 (600 mm X 1800 mm) in diameter and as long as 10 (3000 mm) in length. The mills are manufactured using a flanged mild steel shell, cast heads, overflow discharge, removable man door, spur type ring gear, pinion gear assembly with spherical roller bearings, replaceable roller bronze trunnion bearings, oil lubrication, replaceable trunnion liners with internal spirals, rubber liners and lifters, feed spout with wash port, discharge trommel with internal spiral, motor and gear reducer drive, direct coupled to pinion gear, gear guard and modular steel support frame. All ball mills always come withOSHA-type gear guard.

A PULP level sufficiently high to interpose a bed of pulp, partly to cushion the impact of the balls, permits a maximum crushing effect with a minimum wear of steel. The pulp level of theseSmall Ball Millscan be varied from discharging at the periphery to discharging at a point about halfway between the trunnion and the periphery.The mill shell is of welded plate steel with integral end flanges turned for perfect alignment, and the heads are semi-steel, with hand holes in the discharge end through which the diaphragm regulation is arranged with plugs.The trunnion bearings are babbitted, spherical, cast iron, and of ample size to insure low bearing pressure; while the shell and saddle are machined to gauge so that the shells are interchangeable.

Data based on:Wet grinding, single stage, closed circuit operation: feed:( one way dimension); Class III ore. All mills:free discharge, grated type, rapid pulp flow. N. B.for overflow type mills: capacity 80%power 83%. Dimensions :diameters inside shell without linerslengths working length shell between end liners.

The CIW is a Small Ball Mill thats belt driven, rigid bearing, wet grinding, trunnion or grate discharge type mill with friction clutch pulley and welded steel shell. The 7 and 8 foot diameter mills are of flange ring construction with cut gears while all other sizes have cast tooth gears. All these mills are standard with white iron bar wave type shell liners except the 8 foot diameter mill which is equipped with manganese steel liners. The horsepowers shown in the table are under running conditions so that high torque or wound rotor (slip ring) motors must be used. Manganese or alloy steel shell or head liners and grates can be supplied with all sizes of mills if required. Alloy steel shell liners are recommended where 4 or larger balls are used and particularly for the larger sized mills.

Small (Muleback Type) Ball Mill is built for muleback transportation in 30 and 3 diameters (inside liners). A 4 (Muleback Type) Ball Mill is of special design and will be carefully considered upon request. Mankinds search for valuable minerals often leads him far away from modern transportation facilities. The potential sources of gold, silver and strategic minerals are often found by the prospector, not close by our modern highways, but far back in the mountains and deserts all over the world. The Equipment Company has realized this fact, and therefore has designed a Ball Mill that can be transported to these faraway and relatively inaccessible properties, either by the age old muleback transportation system, or by the modern airplane. As a result these properties may now obtain a well-designed ball mill with the heaviest individual piece weighing only 350 pounds.

The prime factor considered in this design was to furnish equipment having a maximum strength with a minimum weight. For this reason, these mills are made of steel, giving a high tensile strength and light weight to the mills. The muleback design consists of the sturdy cast iron head construction on the 30 size and cast steel head construction on the larger sizes. The flanges on the heads are arranged to bolt to the rolled steel shell provided with flanged rings. When required, the total length of the shell may consist of several shell lengths flanged together to provide the desired mill length. Liners, bearings, gears and drives are similar to those standard on all Ball Mills.

This (Convertible) and Small Ball Mill is unique in design and is particularly adapted to small milling plants. The shell is cast in one piece with a flange for bolting to the head. In converting the mill from a 30x 18 to a 30x 36 unit with double the capacity, it is only necessary to secure a second cast shell (a duplicate of the first) and bolt it to the original section.

30 Convertible Ball Mills are furnished with scoop feeders with replaceable lips. Standard mills are furnished with liners to avoid replacement of the shell; however, themill can be obtained less liners. This ball mill is oftendriven by belts placed around the center, although gear drive units with cast gears can be furnished. A Spiral Screen can be attached to the discharge.

This mill may be used for batch or intermittent grinding, or mixing of dry or wet materials in the ore dressing industry, metallurgical, chemical, ceramic, or paint industries. The material is ground and mixed in one operation by rotating it together with balls, or pebbles in a hermetically sealed cylinder.

The cast iron shell which is bolted to the heads is made with an extra thick wall to give long wearing life. Two grate cleanout doors are provided on opposite sides of the shell by means of which the mill can be either gradually discharged and washed, while running, or easily and rapidly emptied and flushedout while shut down. Wash-water is introduced into the interior of the mill through a tapped opening in the trunnion. The mill may be lined with rubber, silex (buhrstone) or wood if desired.

The Hardinge Conical Ball Mill has been widely used with outstanding success in grinding many materials in a wide variety of fields. The conical mill operates on the principle of an ordinary ball mill with a certain amount of classification within the mill itself, due to its shape.

Sizes of conical mills are given in diameter of the cylindrical section in feet and the length of the cylindrical section in inches. Liners can be had of hard iron, manganese steel or Belgian Silex. Forged steel balls or Danish Flint Pebbles are used for the grinding media, depending upon the material being milled.

The Steel Head Ball-Rod Mill gives the ore dressing engineer a wide choice in grinding design so that he can easily secure a Ball-Rod Mill suited to his particular problem. The successful operation of any grinding unit is largely dependent on the method of removing the ground pulp. The Ball-Rod Mill is available with five types of discharge trunnions, each type obtainable in small, medium or large diameters. The types of discharge trunnions are:

The superiority of the Steel Head Ball-Rod Mill is due to the all steel construction. The trunnions are an integral part of the cast steel heads and are machined with the axis of the mill. The mill heads are assured against breakage due to the high tensile strength of cast steel as compared to that of the cast iron head found on the ordinary ball mill. Trunnion Bearings are made of high- grade nickel babbitt.

Steel Head Ball-Rod Mills can be converted intolarger capacity mills by bolting an additional shell lengthonto the flange of the original shell. This is possible because all Steel Head Ball or Rod Mills have bearings suitable for mills with length twice the diameter.

Head and shell liners for Steel Head Ball-Rod Mills are available in Decolloy (a chrome-nickel alloy), hard iron, electric steel, molychrome steel, and manganese steel. Drive gears are furnished either in cast tooth spur gear and pinion or cut tooth spur gear and pinion. The gears are furnished as standard on the discharge end of the mill, out of the way of the classifier return feed, but can be furnished at the mill feed end by request. Drives may be obtained according to the customers specifications.

Thats one characteristic of Traylor Ball Millsliked by ownersthey are built not only to do a first class job at low cost but to keep on doing it, year after year. Of course, that means we do not build as many mills as if they wore out quicklyor would we? but much as welike order, we value more the fine reputationTraylor Ball Mills have had for nearly threedecades.

Thats one characteristic of Traylor Ball Mills We dont aim to write specifications into thisliked by ownersthey are built not only to do advertisementlet it suffice to say that theresa first class job at low cost but to keep on do- a Traylor Ball Mills that will exactly fit anyanything it, year after year. Of course, that means requirement that anyone may have.

If this is true, there is significance in the factthat international Nicked and Climax Molybdenum, theworlds largest producers of two important steel alloys, areboth users of MARCY Mills exclusively. With international interest centered on increasingproduction of gold, it is even more significant that MARCYMills are the predominant choice of operators in everyimportants gold mining camp in the world.

Ball Mill. Intermediate and fine size reduction by grinding is frequently achieved in a ball mill in which the length of the cylindrical shell is usually 1 to 1.5 times the shell diameter. Ball mills of greater length are termed tube mills, and when hard pebbles rather than steel balls are used for the grinding media, the mills are known as pebble mills. In general, ball mills can be operated either wet or dry and are capable of producing products on the order of 100 pm. This duty represents reduction ratios as great as 100.

The ball mill, an intermediate and fine-grinding device, is a tumbling drum with a 40% to 50% filling of balls (usually steel or steel alloys). The material that is to be ground fills the voids between the balls. The tumbling balls capture the particles in ball/ball or ball/liner events and load them to the point of fracture. Very large tonnages can be ground with these devices because they are very effective material handling devices. The feed can be dry, with less than 3% moisture to minimize ball coating, or a slurry can be used containing 20% to 40% water by weight. Ball mills are employed in either primary or secondary grinding applications. In primary applications, they receive their feed from crushers, and in secondary applications, they receive their feed from rod mills, autogenous mills, or semiautogenous mills. Regrind mills in mineral processing operations are usually ball mills, because the feed for these applications is typically quite fine. Ball mills are sometimes used in single-stage grinding, receiving crusher product. The circuits of these mills are often closed with classifiers at high-circulating loads.

These loads maximize throughput at a desired product size. The characteristics of ball mills are summarized in the Table, which lists typical feed and product sizes. The size of the mill required to achieve a given task-that is, the diameter (D) inside the liners-can be calculated from the design relationships given. The design parameters must be specified.

The liner- and ball-wear equations are typically written in terms of an abrasion index (Bond 1963). The calculated liner and ball wear is expressed in kilograms per kilowatt-hour (kg/kWh), and when multiplied by the specific power (kWh/t), the wear rates are given in kilograms per ton of feed. The wear in dry ball mills is approximately one-tenth of that in wet ball mills because of the inhibition of corrosion. The efficiency of ball mills as measured relative to single-particle slow-compression loading is about 5%. Abrasion indices for five materials are also listed in the Table.

The L/D ratios of ball mills range from slightly less than 1:1 to something greater than 2:1. The tube and compartment ball mills commonly used in the cement industry have L/D ratios 2.75:1 or more. The fraction of critical speed that the mill turns depends on the application, and most mills operate at around 75% of critical speed. Increased speed generally means increased power, but as the simulations presented in Figure 3.26 show, it can also produce more wasted ball impacts on the liners above the toe. causing more wear and less breakage.

There are three principal forms of discharge mechanism. In the overflow ball mill, the ground product overflows through the discharge end trunnion. A diaphragm ball mill has a grate at thedischarge end. The product flows through the slots in the grate. Pulp lifters may be used to discharge the product through the trunnion, or peripheral ports may be used to discharge the product.

The majority of grinding balls are forged carbon or alloy steels. Generally, they are spherical, but other shapes have been used. The choice of the top (or recharge) ball size can be made using empirical equations developed by Bond or Azzaroni or by using special batch-grinding tests interpreted in the content of population balance models. The effect of changes in ball size on specific selection functions has been found to be different for different materials. A ball size-correction method can be used along with the specific selection function scale-up method to determine the best ball size. To do this, a set of ball size tests are performed in a batch mill from which the specific selection function dependence on ball size can be determined. Then, the mill capacities used to produce desired product size can be predicted by simulation using the kinetic parameter corresponding to the different ball sizes.

The mill liners used are constructed from cast alloy steels, wear-resistant cast irons, or polymer (rubber) and polymer metal combinations. The mill liner shapes often recommended in new mills are double-wave liners when balls less than 2.5 in. are used and single-wave liners when larger balls are used. Replaceable metal lifter bars are sometimes used. End liners are usually ribbed or employ replaceable lifters.

The typical mill-motor coupling is a pinion and gear. On larger mills two motors may be used, and in that arrangement two pinions drive one gear on the mill. Synchronous motors are well suited to the ball mill, because the power draw is almost constant. Induction, squirrel cage, and slip ring motors are also used. A high-speed motor running 600 to 1,000 rpm requires a speed reducer between the motor and pinion shaft. The gearless drive has been installed at a number of locations around the world.

## castings, wear resistant and heat resistant parts for cement plant of flsmidth, khd, sinoma and polysius

We supply all major castings, wear and heat resistant items to cement plants. We can supply all castings and wear parts for cement plants as per existing design to meet the original specifications and design of plant supplier. We can also advise improvement in existing design and specifications of parts to achieve better performance.

In some cases, we can also arrange visit of our expert to your cement plant to obtain necessary drawing and data of required part and then offer exactly same. We are professional and understand requirements of cement plants.

We supply Roller tires and Table segments as per original specifications and design of vertical mill. No matter whatever type of vertical grinding mill you are using, we can provide you parts in improved metallurgy to fit your requirement.

We also serve our client with their procurement requirements of Vertical Mill Seals and other accessories. We are one of few companies who supply vertical mill wear parts in Metal-Ceramic composite as well as High Chromium.

We are company based in GermanyWe supply industrial machinery, equipment
and spare parts to industries in the World. We provide complete solution for warehousing,
procurement and shipping of material.

## ball mill: operating principles, components, uses, advantages and

A ball mill also known as pebble mill or tumbling mill is a milling machine that consists of a hallow cylinder containing balls; mounted on a metallic frame such that it can be rotated along its longitudinal axis. The balls which could be of different diameter occupy 30 50 % of the mill volume and its size depends on the feed and mill size. The large balls tend to break down the coarse feed materials and the smaller balls help to form fine product by reducing void spaces between the balls. Ball mills grind material by impact and attrition.

Several types of ball mills exist. They differ to an extent in their operating principle. They also differ in their maximum capacity of the milling vessel, ranging from 0.010 liters for planetary ball mills, mixer mills, or vibration ball mills to several 100 liters for horizontal rolling ball mills.

Im grateful for the information about using a ball mill for pharmaceutical products as it produces very fine powder. My friend is working for a pharmaceutical company and this is a good article to share with her. Its good to know that ball mills are suitable for milling toxic materials since they can be used in a completely enclosed for. Thanks for the tips!

## ball mills - zimaksan co

Ball mills are the best and most effective method for crushing and powdering a variety of dry and wet materials, including minerals, types of building materials, sand and cement, lime and ceramics, and many other materials.

Zimaxon Industrial Group engineers have been able to design and sell many types of ball mills of high quality based on their knowledge and expertise, with the backing of years of useful experience. Currently, Horizontal Ball Milling Machine of this company is recognized as a fully reliable device for use in various industries.

After cutting the plates, bend them and welded Partitioned plates together and eventually expose them to extreme heat to strengthen them. Then, using the non-destructive and engineered tests, the whole machine is checked and verified. All ball mills part like ball bearings and machine are carefully tested to ensure their accuracy and efficiency.

On the oscillating sweeping blades of the ball mill they are fitted with Shoe-type bearings that for lubricated using a dynamic diesel lubrication system. They are designed and constructed to fit the shape of the rings easily and fit perfectly. Engineers at Zimaxon Industrial Group have designed the mill creatively on trunnion bearing.
Generally, the ball mill contains a DMG 2, two large gear and a gearbox, a small gear for the mill and a shaft counter. In addition, these ball mills also have an auxiliary drum for use at the time of the main drum failure.

Iron cement, cement and many other similar materials are usually crushing and milling used in two part mills or two chamber cement mills. Both parts of this mill are embedded in a high performance VTP.

According to Blaines theory, these mills can cut up and pour up to 6500 cm2 /g of material. The mill is equipped with an armored lift in the initial part, which uses larger grinding mills with high grinding power. In the next section, mills use a smaller mill that is used to end the cutting and milling process.

In the classified diaphragm, a control sensor is also installed to allow only a certain amount of milling material in each mill segment. In the roller mill, materials are transferred to another part by using an external wall and molded.

When the material is heated, the equipment for cooling the material transmits them to two rooms embedded in the mill to cool the water using embedded water spray. If the mill is equipped with a compact drive and a roller, part of the mill is equipped with an armored classifier without an aperture.

The materials used in the kiln lines are usually made using mills with one to two compartments with a special compartment for pre-dryer chamber. These types of mills are equipped with a circuit and use high-performance VTP for separation.

The material is dried by using a furnace or heating gas, and a cooling room is also used to cool it. This kind of ailment is often applied to materials that have a moisture content of more than 8%. After the process done on the material in this type of mill, the crushed material is less than 0.5% moisture and is crushed or powdered at 12 to 14% R90.

To use this ball mill, first all the materials are placed in the dryer compartment to get their moisture well before entering the damper stage. In the Damper area, the materials are separated and the coarser and heavier materials are directed to the mill ball. The same seats and drivers used in cement mills are used precisely for this mill.

This type of mill has a pre-dryer for milling and a compartment for milling materials. After the pre-drying step, the materials are placed on the floor of the mill and directed to the LRTs high-quality separation unit. The product will ultimately be packed in a filter or cyclone. Usually materials that have a very high humidity are grinding through a pneumatic grinder.

The mill is used to dry the material from a high temperature using a gas injected into the dryer, and then the milling and separation work is done. Pneumatic mill is very popular because of its simple design and high performance. Pneumatic mills are generally used for grinding coal and petroleum coke, which are designed in a high separation environment LTR-U with a pressure drop of over 3.5 times.

Our engineers at Zimaxon Co., as one of the most advanced mills company in Iran, have been designing and manufacturing a large number of ball mills, unique and classical on swing trunnion bearings, which are used in many industries.

In this article, the latest methods and practices of producing, modeling and controlling the grinding process in the ball mill are discussed. It should be noted, however, that this paper also focuses on basic kinetic and the energy models in the ball mill process, and our intention, therefore, to present and review these materials is to actually describe and analyze the various strategies available for more control strategies.

Today, in many industries, ball mills are used as one of the most advanced and best methods for grinding and reducing the size of various types of particles with different physical, chemical and mechanical characteristics and nature, which each of these ball mills may have a different conditions and may be a different technology.

Although ball mills are often used to grind and crush materials such as ores, minerals, limestone and many other such materials, ball mills in todays industries have many more and more diverse applications.

Generally, ball mills are used in industries such as minerals and mining, metallurgy, cement processing and production, petrochemical industry and various chemical industries, in the pharmaceutical industry, in the cosmetics industry, in the tile and ceramic industry, agriculture, and any other industry in which the need for crushing materials, the preparation of coarse and hard materials, etc., is used in many test laboratories and factories.

Contrary to many imaginations, ball mills are not only made for crushing and reducing the size of particles and materials. Ball mills can also be used for mixing, blending, dispersing and amorphous materials, or even for the preparation of mechanical alloys.

The ball mill building is made up of a cylindrical vessel, which is carefully connected to the two ends to allow rotation around the central axis to be rotated easily. This grinding mill uses a girth gear to connect the shell and the shaft moves it with the main drive to rotate it.
For ball mills, commonly used synchronous motors equipped with an air clutch or gear, it can be easily circulated by connecting to the main gear mill. The power of these transfer motors is usually considered to be enough to grind and grinding various types of raw materials such as stones, ore, etc., depending on the performance of the ball mill.

The ball mill is very diverse and is often made in different sizes and designs, and even the materials used in the production of these mills are different. Generally speaking, what determines the type of ball mill in different industries is issues such as material size, equipment used for loading raw materials (feeders) and even the system of discharge of produced materials. Given this, it should be noted that the size of the mill is usually determined by the ratio of length to diameter, which is about 0.5 to 3.5.

Usually, a spout feeder or a single or double helical scoop feeder is used to load raw material into the ball mill.
The drainage system or discharge system is different in the ball, and each one may be designed differently. The ball mill, in terms of the drainage system, can have an overflow discharge system, a diaphragm or grate discharge mill and a center-periphery discharge mill.

Ball mills with an internal surface are usually the best choice for industrial applications because they have a steel body of grinding and the other equipment used in these mills is perfectly suited to industrial applications depending on the types of industry. For this reason, the contents of the mill can be built with the best possible weight to prevent falling or dropping or cascades down.

Usually, balls are made from any type has a standard sizes range from 10 to 150 mm and are used depending on the type of mill. Although most types of steel and other metals are used to manufacture and supply these types of balls, ceramic types and other types of balls are sometimes made and used.

The Clypeus balls have a slightly conical shape in the cylinders of a grinding ball mill and the edges of each of these balls are round, their diameter and length are considered equal and they have different dimensions, generally in the state of 8 x 8 to 45 x 45 mm depending on the type of application they are made.

In order to get maximum efficiency from the ball, due to the high density and specific surface of the balls, their shape has been well developed.
Porcelain balls are a high-density ceramic ball that, in order to withstand high wear resistance by using aluminum oxidized in the ball structure, these balls are produced with a very high thickness and hardness.
The main characteristics of the mill body and their higher efficiency depend on the mass and size, ware rate, the impact on the failure rate and the efficiency of grinding energy.

The ball mill speed usually identifies three main types of operating modes of the milling machine: low speed (cascading), rapid rotational speed (cataract) and very high spin speed or super speed (centrifuge). The effect of each of these speed, varies on materials on the ground, because each of these speeds has a specific trajectory of motion charging path in the mill.

In addition, it should be kept in mind that other factors may also affect the milling process, such as dry or wet substances, or that wet materials may be added to the milling material during the milling process. For this reason, in this research, the dimensions of different mills in dry conditions or wet conditions are also mentioned.

In general, the ball mill in the process of grinding or crushing raw materials into smaller particles depends on several factors, most notably:
Various material specifications such as mass, volume, size, hardness, density, charge size, type and other specifications of raw materials that are loaded in the mill
Specifications such as type, mass, density, or ball size distribution in the ball mill
Spin rate or speed of rotation of the mill
Density and volume of Slurry in the wet mill operation

Of course, it should not be forgotten that the ball mills production capacity depends on several factors, the most important of which is the size of the mill, the type of grinding structure (overflow or grate discharge), the speed of rotation, the size of the raw material loaded in the mill, the size of the desired final product Based on feed size (reduction coefficient), type of material, shaft power used in the ball mill, and raw material gravity.

We intend to consider all the parameters defined in the ball mill in this study and finally we propose an experimental relationship that will measure the mill capacity as a ratio of power to shaft and energy consumption in the grinding process to describe well.

Due to the fact that the ball mill usually operates in industrial conditions in milling circuits, it is usually possible to achieve the best particle size by classifying the materials according to their required size. The open and closed circuit ball in Figure 1 is shown as simple as possible.

In the second case, the grinding material is returned to the mill feed using a classifier, and the process continues so that all the materials are converted into the final product. Usually, in order to increase the grinding efficiency, different interconnections between the ball mill and dividers may exist.

The main purpose of grinding raw materials is to reach the final product with the desired size and structure in such a way that all the materials in the same size and shape are mined and there is no impurity in it, such as a variety of metals or other pollutants that May affect the final product. This process will further increase the power of the grinding circuit and even reduce the final cost of production.

In this paper, we will attempt to examine the most important principles for modeling the grinding process by examining some of the most important of these methods and strategies, and then we will analyze various strategies to identify the best design and control of the structure and Finally, using the obtained data, we chose a suitable method for controlling the process, depending on the type of ball mill operation.

The unveiling of the mill process and the main idea in modeling all crushing processes is necessary to obtain a good and proper mathematical relationship between the feed size and the size of the final product.

However, the passage of time makes the main raw material, or the chopped feed used in the process of production, has a decreasing trend, because the increased energy of grinding media creates disturbances in the bonding forces.

When abrasive process is used to cause local low tension stress occurs, as a result of this wear, particles that are attached to the particle mother or larger particles are separated from the mother and particles that are approximately the same size as themselves. (Figure 2a)

Of course, it should not be forgotten that these three different mechanisms will never fall apart alone, and issues such as the type of mill, the different operating conditions, or even the type of material that is being grinded, also greatly affects the process of reducing particle size, and probably leads to Exacerbate or reduce each of these three mechanisms.

Generally, a number of major concepts are commonly used in modeling the grinding process. Certainly there are raw materials that define the classes of different particle size because these particles naturally exist in different sizes.
A standard sieves should be used to measure the quantity of particles in each class. Generally, solid state theory is used in a series of steps in the partitioning process with two main operations:

Using this operation, two structures can be identified: the Si function in this function is Si, i = 1, 2, , n, and the breaking function bij, n i j 1. In this function, n shows the number of size classes. In this structure, the fracture performance or failure rate with the selective Si performance is shown. Xi to indicate the probable size of the particles in each step, according to the piece given to the mill for the milling, and in this operation we consider xi as the least probable particle size.

In this regard, S1, S2, , Sn denotes the mass of material in each class, depending on the size of the mill that is considered for the mill and converted to smaller particles. The mill operation or the breaking of bij, which, of course, can be called the distribution function, is generally described by the distribution of the size of the parts produced after grinding and breaking the particle size Xj.

Therefore, b1j, b2j, , bnj is the mass fractions of the particles after milling process and the breaking of particles in the class size j, that are essentially related to the particle mass in classes 1, 2, , n.

Fig. 3 graphically illustrates the particle fracture process. In the left column, an initial distribution sample of the primary feed is shown to the milling machine. Using solid arrows, the use of the different forces described in each class is show, and using dash arrows to describe the movement of parts of the same size or slightly less on each floor.

The fracture functions are displayed in the third column and finally displayed in the fourth column of the final product that has been produced at the desired and smaller sizes. During this process, in the lower-level categories, the level of crude feed is distributed in class 1 size.
Ultimately, with the milling process and the breakdown and distribution of raw material or feed over a given time, the mass of mass 1 is eliminated in general, although ultimately the total mass remains constant.

Having a communication process in modeling performance and breaking performance is one of the most important parameters that should be considered in this modeling. In the milling literature in general, three types of models have to be considered: the matrix model, the kinetic model and the energy model.

To give a specific principle to a general principle for the development of any model, such as establish mass balance or energy equilibrium equations, which relates to mass or energy components involved in the process, should not be forgotten. Matrix models should be used at times when the size reduction is mainly in a discrete process with each discrete step including three selection breakdown classification.

The important thing to keep in mind is that when a fixed mill is in steady state for batch milling modeling, the milling process and the reduction of raw material size should be seen as a continuous process. In this case, the mathematical models must be combined with the combination of time parameters and considers the working time. Therefore, in this case, matrix models are less responsive to kinetic models and energy models.

Currently, various types of grinding mill machines and even different milling circuits are used when modeling the grinding process. The basic assumption that is often taken into account is that the content of the crushed matter is the same and is completely mixed with the movement and rotation of the mill and the displacement of the grinding media. For this reason, they call this model a very complex model, or sometimes as a perfectly mixed model.

Of course sometimes, the grinding of the mill is well-mixed in the radial direction, but it is not thoroughly grinding in the axial direction. The second assumption is that particles of any size are ultimately broken up uniformly and in the normal or in the same way, and that no agglomeration process occurs during the milling process of this raw material and during the breaking of the material.

Given this, perhaps the best method for grinding processes is kinetic models, since they perform process descriptions over different size intervals based on mass equilibrium equations. In this case, it is assumed that the mill in the radial direction completely mixes the material and, in the axial direction, to some extent mixes the material, and in the second step a more kinetic model must be used. For this purpose, the following model should be used:

The first and second stage, which relate to the particle masses and particles in this class, are shown on the right. Thirdly, describes the degree of dispersion of the axis, and in the fourth stage, which is the last step, the conveyance of the material or particles will be shown axially at the speed of the UI. With this description, a differential equation (1) has the following boundary conditions:

With conditions 2-4 in Equation 1, we are actually showing the basic kinetic model of the process. Of course, this kinetic model has a number of well-known models that determine the specific operating conditions of the mill.

Now the basic assumption is that the mixture is mixed in the direction of axially and in radial direction uniformly and completely, and for this reason, fully mixed model or completely mixed or complex model for this equation is used. The third and fourth equations can exceptionally be ignored in this particular case and design the kinetic model of the mill as follows [3, 25, 46]:

We can even use the cumulative form of Equation 5 to model the grinding process. for example:Now, in class size, we see that the conditions are equal to the mass of the feed. For this relation, the most accurate and most suitable formula is wi (t) i = 1, 2, , n, which is used as the Reid solution for the batch mill equation and is shown in [3, 23].
is the cumulative fractional mass fraction of particle that have a size larger than xi and is smaller than the size of the particles of class i.
For the pre-supposes, a basic knowledge of the breakage and selection functions bij and Si, we can use the solution obtained in the solution of equations 5 and 8.is the cumulative fractional mass fraction of particle that have a size larger than xi and is smaller than the size of the particles of class i.
Of course, experimental procedures and successive therapies can also be found for some particular processes, although, because these types of topics do not have known basic functions, achieving the results of a purely experimental, is not easy-to-learn match. Several different methods can be used to determine the fracture functions and some of the usual breaking performance charts. In the explicit form of the cumulative equation of grinding 8 is also shown in Figure 3.
To describe the grinding process, you can even use mathematical models based on energy-balance equations. In model 21, a linear model that is similar to model 5 is used, which has been further developed, in which we chose the batch milling kinetics for a particular energy as an independent variable and instead of milling time.
Even in many cases, mathematical models can be used based on energy balance equations to describe the grinding process. Accordingly, in model 21, which is a kind of linear model similar to model 5, is shown with the difference that more development has been given. In fact, in this model, the kinetics are known as milling for a particular energy as an independent variable and the place of milling time.
So far, many scholars and scientists have been conducting precise and specific tests to measure the specific energy consumed in ball mills in various conditions and operations, and even in the case of different materials.
Generally, the results of these experiments in raw mill conditions and with detailed analyzes showed that the dispersive failure rate of the measurement with the specific energy entering the mill and even the fracture distribution functions can be constant and constant. So, using a model like the following model can be well responsive in a structure that equations modeling for energy balance:
the
is the energy-normalized breakage rate parameter and E
SiE
is the specific energy entering to the

We can even use the cumulative form of Equation 5 to model the grinding process. for example:Now, in class size, we see that the conditions are equal to the mass of the feed. For this relation, the most accurate and most suitable formula is wi (t) i = 1, 2, , n, which is used as the Reid solution for the batch mill equation and is shown in [3, 23].

For the pre-supposes, a basic knowledge of the breakage and selection functions bij and Si, we can use the solution obtained in the solution of equations 5 and 8.is the cumulative fractional mass fraction of particle that have a size larger than xi and is smaller than the size of the particles of class i.

Of course, experimental procedures and successive therapies can also be found for some particular processes, although, because these types of topics do not have known basic functions, achieving the results of a purely experimental, is not easy-to-learn match. Several different methods can be used to determine the fracture functions and some of the usual breaking performance charts. In the explicit form of the cumulative equation of grinding 8 is also shown in Figure 3.

To describe the grinding process, you can even use mathematical models based on energy-balance equations. In model 21, a linear model that is similar to model 5 is used, which has been further developed, in which we chose the batch milling kinetics for a particular energy as an independent variable and instead of milling time.

Even in many cases, mathematical models can be used based on energy balance equations to describe the grinding process. Accordingly, in model 21, which is a kind of linear model similar to model 5, is shown with the difference that more development has been given. In fact, in this model, the kinetics are known as milling for a particular energy as an independent variable and the place of milling time.

So far, many scholars and scientists have been conducting precise and specific tests to measure the specific energy consumed in ball mills in various conditions and operations, and even in the case of different materials.

Generally, the results of these experiments in raw mill conditions and with detailed analyzes showed that the dispersive failure rate of the measurement with the specific energy entering the mill and even the fracture distribution functions can be constant and constant. So, using a model like the following model can be well responsive in a structure that equations modeling for energy balance:

milldefined as
In order to better understand this issue, we have compared the simplified model of the mass balancing presented in Form 5 with the equilibrium energy model presented in Form 10. The two linear models presented in the formulas of equations 5 and 9 are almost straightforward and can easily be used, and each of them has a high degree of kinetics for studying first-order breakage kinetics in the process.Note that in Equation (10) we consider p as the input of power to the mill and Was the mass of the feed material in the mill.
In the model 5, we made a detailed study using differential equations in exact and complete forms, and in literature with different hypotheses and degrees of approximation. Generally, in Model 5, we examined the best solution in milling time in particle size as a solution, and we came to the conclusion and recognized it.
But to do this, we can estimate the model, like the model 9, rather than the exact time of the analysis of the breakage kinetics using the specific energy consumed by the model.
In addition, as a fully functional control parameter in the process, we can measure the accuracy of the input power to the mill, instead of using the measured data. However, for the purpose of milling, in an analysis of other crushing systems such as the roll mill, an energy model such as that given in model 21 can be used in a more useful way. It should also be kept in mind that apart from linear models, more developed nodes and mathematical models can be used in grinding, such as the choice of nonlinear models, time dependent models, or breakage functions [7, 20].
Often, the methods mentioned and many other methods for studying the dynamic properties of the breaking process, the computer method that simulates the work process is based on a discrete element [31, 32, 38].
III. Process control methods
It is very difficult to control a grinding machine because of factors such as nonlinear character, unspecified processes, possible and unpredictable mistakes in mathematical models, the existence of variables of the process of interaction with different dynamics, the effect of unwanted disturbances, delay time Extremely high operating conditions are unclear and dependent on various and violent factors and the use of tools such as precision sensors and reliable all-in-one control of grinding machines.
In addition, it is also important to achieve different factors, such as increasing the output power of the circuit and the quality of the expected final product, or minimizing production costs in order to achieve greater efficiency and more efficient control of the mill process.
III.1. Process variables and characteristics
By the control viewpoint, the ball mill grinding circuit should be operated as a multivariate connected system that has very strong interactions between all process variables.
For example, in a very simple and integrated structure, a closed loop circuit in a wet mill has a ball mill, a sump and a spliter or divider [10, 13, 33, 39]. What is shown in Figure 4.
Fig. 4
Types of process input variables depicted in the figure above
u1: water flow rate of mill feed
U2: feed rate of fresh ore
U3: speed fraction in the mill critical
U4: rate of water flow of sump dilution
U5: flow rate of sump discharge
The values of these variables are used to control the output variables listed below and are shown in the figure:
Y1: The mass fraction of products or feed given with smaller particle sizes than the quantities available
Y2: Concentration of product solids
Y3: product flow rate
Y4: sumps slurry level
Y5: Concentration of sump solids
Of course, it should be kept in mind that some of the possible malformations may occur in this process, which are most likely to have the greatest impact on the process, ore hardness changes, and changes in feed size. For this purpose, in the form of a matrix form, we can define the inputs and outputs of this model.
(11)
,
.
where
is the transfer function relating the i-th input and j-th output for
i, j = 1, , 5.
In this circumstances, it is attempted to determine the transfer functions by applying the step change test and measuring the dimensions of the output of the final product.
There is no doubt that a lot of experiments are to be conducted to get accurate results. In addition, some of the parameters, such as configuration and grinding circuit equipment, are factors that sometimes require different sets of input and output variables to make a model [8, 33, 40].
What is certain is that there are many obstacles and problems to control the ball mill process, the most well-known and most important of which can be as follows:
Non-linear mills, such as ball mills, have measurable disturbances that do not have a dynamic model for them.
There are tight interconnections between the variables of this type mill, so that each input variable may be associated with several output variables.
Although a lot of time constant can be defined in the process, it should be kept in mind that many of the input / output pairs require a much longer and more unpredictable time.
The system model of the ball mill has many integrals.
In the milling process of some parameters, time as the age of the circuit is variable
Ball mills still sometimes have technological constraints that can sometimes be seen in manipulated and controlled variables.
Finally, you cannot be sure of the measurements and rely on a high-end model.

In order to better understand this issue, we have compared the simplified model of the mass balancing presented in Form 5 with the equilibrium energy model presented in Form 10. The two linear models presented in the formulas of equations 5 and 9 are almost straightforward and can easily be used, and each of them has a high degree of kinetics for studying first-order breakage kinetics in the process.Note that in Equation (10) we consider p as the input of power to the mill and Was the mass of the feed material in the mill.
In the model 5, we made a detailed study using differential equations in exact and complete forms, and in literature with different hypotheses and degrees of approximation. Generally, in Model 5, we examined the best solution in milling time in particle size as a solution, and we came to the conclusion and recognized it.
But to do this, we can estimate the model, like the model 9, rather than the exact time of the analysis of the breakage kinetics using the specific energy consumed by the model.
In addition, as a fully functional control parameter in the process, we can measure the accuracy of the input power to the mill, instead of using the measured data. However, for the purpose of milling, in an analysis of other crushing systems such as the roll mill, an energy model such as that given in model 21 can be used in a more useful way. It should also be kept in mind that apart from linear models, more developed nodes and mathematical models can be used in grinding, such as the choice of nonlinear models, time dependent models, or breakage functions [7, 20].
Often, the methods mentioned and many other methods for studying the dynamic properties of the breaking process, the computer method that simulates the work process is based on a discrete element [31, 32, 38].
III. Process control methods
It is very difficult to control a grinding machine because of factors such as nonlinear character, unspecified processes, possible and unpredictable mistakes in mathematical models, the existence of variables of the process of interaction with different dynamics, the effect of unwanted disturbances, delay time Extremely high operating conditions are unclear and dependent on various and violent factors and the use of tools such as precision sensors and reliable all-in-one control of grinding machines.
In addition, it is also important to achieve different factors, such as increasing the output power of the circuit and the quality of the expected final product, or minimizing production costs in order to achieve greater efficiency and more efficient control of the mill process.
III.1. Process variables and characteristics
By the control viewpoint, the ball mill grinding circuit should be operated as a multivariate connected system that has very strong interactions between all process variables.
For example, in a very simple and integrated structure, a closed loop circuit in a wet mill has a ball mill, a sump and a spliter or divider [10, 13, 33, 39]. What is shown in Figure 4.
Fig. 4
Types of process input variables depicted in the figure above
u1: water flow rate of mill feed
U2: feed rate of fresh ore
U3: speed fraction in the mill critical
U4: rate of water flow of sump dilution
U5: flow rate of sump discharge
The values of these variables are used to control the output variables listed below and are shown in the figure:
Y1: The mass fraction of products or feed given with smaller particle sizes than the quantities available
Y2: Concentration of product solids
Y3: product flow rate
Y4: sumps slurry level
Y5: Concentration of sump solids
Of course, it should be kept in mind that some of the possible malformations may occur in this process, which are most likely to have the greatest impact on the process, ore hardness changes, and changes in feed size. For this purpose, in the form of a matrix form, we can define the inputs and outputs of this model.
(11)
,
.
where
is the transfer function relating the i-th input and j-th output for
i, j = 1, , 5.
In this circumstances, it is attempted to determine the transfer functions by applying the step change test and measuring the dimensions of the output of the final product.
There is no doubt that a lot of experiments are to be conducted to get accurate results. In addition, some of the parameters, such as configuration and grinding circuit equipment, are factors that sometimes require different sets of input and output variables to make a model [8, 33, 40].
What is certain is that there are many obstacles and problems to control the ball mill process, the most well-known and most important of which can be as follows:
Non-linear mills, such as ball mills, have measurable disturbances that do not have a dynamic model for them.
There are tight interconnections between the variables of this type mill, so that each input variable may be associated with several output variables.
Although a lot of time constant can be defined in the process, it should be kept in mind that many of the input / output pairs require a much longer and more unpredictable time.
The system model of the ball mill has many integrals.
In the milling process of some parameters, time as the age of the circuit is variable
Ball mills still sometimes have technological constraints that can sometimes be seen in manipulated and controlled variables.
Finally, you cannot be sure of the measurements and rely on a high-end model.

In order to better understand this issue, we have compared the simplified model of the mass balancing presented in Form 5 with the equilibrium energy model presented in Form 10. The two linear models presented in the formulas of equations 5 and 9 are almost straightforward and can easily be used, and each of them has a high degree of kinetics for studying first-order breakage kinetics in the process.Note that in Equation (10) we consider p as the input of power to the mill and Was the mass of the feed material in the mill.

In the model 5, we made a detailed study using differential equations in exact and complete forms, and in literature with different hypotheses and degrees of approximation. Generally, in Model 5, we examined the best solution in milling time in particle size as a solution, and we came to the conclusion and recognized it.

In addition, as a fully functional control parameter in the process, we can measure the accuracy of the input power to the mill, instead of using the measured data. However, for the purpose of milling, in an analysis of other crushing systems such as the roll mill, an energy model such as that given in model 21 can be used in a more useful way. It should also be kept in mind that apart from linear models, more developed nodes and mathematical models can be used in grinding, such as the choice of nonlinear models, time dependent models, or breakage functions [7, 20].

Often, the methods mentioned and many other methods for studying the dynamic properties of the breaking process, the computer method that simulates the work process is based on a discrete element [31, 32, 38].

It is very difficult to control a grinding machine because of factors such as nonlinear character, unspecified processes, possible and unpredictable mistakes in mathematical models, the existence of variables of the process of interaction with different dynamics, the effect of unwanted disturbances, delay time Extremely high operating conditions are unclear and dependent on various and violent factors and the use of tools such as precision sensors and reliable all-in-one control of grinding machines.

In addition, it is also important to achieve different factors, such as increasing the output power of the circuit and the quality of the expected final product, or minimizing production costs in order to achieve greater efficiency and more efficient control of the mill process.

By the control viewpoint, the ball mill grinding circuit should be operated as a multivariate connected system that has very strong interactions between all process variables.
For example, in a very simple and integrated structure, a closed loop circuit in a wet mill has a ball mill, a sump and a spliter or divider [10, 13, 33, 39]. What is shown in Figure 4.

The values of these variables are used to control the output variables listed below and are shown in the figure:
Y1: The mass fraction of products or feed given with smaller particle sizes than the quantities available
Y2: Concentration of product solids
Y3: product flow rate
Y4: sumps slurry level
Y5: Concentration of sump solids

Of course, it should be kept in mind that some of the possible malformations may occur in this process, which are most likely to have the greatest impact on the process, ore hardness changes, and changes in feed size. For this purpose, in the form of a matrix form, we can define the inputs and outputs of this model.

There is no doubt that a lot of experiments are to be conducted to get accurate results. In addition, some of the parameters, such as configuration and grinding circuit equipment, are factors that sometimes require different sets of input and output variables to make a model [8, 33, 40].