Professor Bello’s notes on grinding, sieve analysis and filtration

Prof Bello notes on sieve etc.eve et al

Principle

A ball mill works on the principle of impact: size reduction is done by impact as the balls drop from near the top of the shell.

Construction

A ball mill consists of a hollow cylindrical shell rotating about its axis. The axis of the shell may be either horizontal or at a small angle to the horizontal. it is partially filled with balls. The grinding media is the balls, which may be made of steel (chrome steel), stainless steel or rubber. The inner surface of the cylindrical shell is usually lined with an abrasion-resistant material such as manganese steel or rubber. Less wear takes place in rubber lined mills. The length of the mill is approximately equal to its diameter.

Working

In case of continuously operated ball mill, the material to be ground is fed from the left through 60° cone and the product is discharged through a 30° cone to the right. As the shell rotates, the balls are lifted up on the rising side of the shell and then they cascade down (or drop down on to the feed), from near the top of the shell. In doing so, the solid particles in between the balls are ground and reduced in size by impact.

Applications

The ball mill is used for grinding materials such as coal, pigments, and felspar for pottery. Grinding can be carried out either wet or dry but the former is carried at low speed.

Description

1

Professor Bello’s notes on grinding, sieve analysis and filtration

Bench top ball mill

Laboratory scale ball mill

High-energy ball milling

A ball mill, a type of grinder, is a cylindrical device used in grinding (or mixing) materials like ores, chemicals, ceramic raw materials and paints. Ball mills rotate around a horizontal axis, partially filled with the material to be ground plus the grinding medium. Different materials are used as media, including ceramic balls, flint pebbles and stainless steel balls. An internal cascading effect reduces the material to a fine powder. Industrial ball mills can operate continuously, fed at one end and discharged at the other end. Large to medium-sized ball mills are mechanically rotated on their axis, but small ones normally consist of a cylindrical capped container that sits on two drive shafts (pulleys and belts are used to transmit rotary motion). A rock tumbler functions on the same principle. Ball mills are also used in pyrotechnics and the manufacture of black powder, but cannot be used in the preparation of some pyrotechnic mixtures such as flash powder because of their sensitivity to impact. High-quality ball mills are potentially expensive and can grind mixture particles to as small as 5 nm, enormously increasing surface area and reaction rates. The grinding works on the principle of

2

Professor Bello’s notes on grinding, sieve analysis and filtration

critical speed. The critical speed can be understood as that speed after which the steel balls (which are responsible for the grinding of particles) start rotating along the direction of the cylindrical device; thus causing no further grinding.

Ball mills are used extensively in the mechanical alloying process[1] in which they are not only used for grinding but for cold welding as well, with the purpose of producing alloys from powders.[2]

Lead antimony grinding media with aluminium powder.

A ball mill inside the Mayflower Mill near Silverton, Colorado.

The ball mill is a key piece of equipment for grinding crushed materials, and it is widely used in production lines for powders such as cement, silicates, refractory material, fertilizer, glass ceramics, etc. as well as for ore dressing of both ferrous and non-ferrous metals. The ball mill can grind various ores and other materials either wet or dry. There are two kinds of ball mill, grate type and overfall type due to different ways of discharging material. There are many types of grinding media suitable for use in a ball mill, each material having its own specific properties and advantages. Key properties of grinding media are size, density, hardness, and composition.

3

Professor Bello’s notes on grinding, sieve analysis and filtration

Size: The smaller the media particles, the smaller the particle size of the final product. At the same time, the grinding media particles should be substantially larger than the largest pieces of material to be ground.

Density: The media should be denser than the material being ground. It becomes a problem if the grinding media floats on top of the material to be ground.

Hardness: The grinding media needs to be durable enough to grind the material, but where possible should not be so tough that it also wears down the tumbler at a fast pace.

Composition: Various grinding applications have special requirements. Some of these requirements are based on the fact that some of the grinding media will be in the finished product. Others are based in how the media will react with the material being ground.

o Where the color of the finished product is important, the color and material of the grinding media must be considered.

o Where low contamination is important, the grinding media may be selected for ease of separation from the finished product (i.e.: steel dust produced from stainless steel media can be magnetically separated from non-ferrous products). An alternative to separation is to use media of the same material as the product being ground.

o Flammable products have a tendency to become explosive in powder form. Steel media may spark, becoming an ignition source for these products. Either wet-grinding, or non-sparking media such as ceramic or lead must be selected.

o Some media, such as iron, may react with corrosive materials. For this reason, stainless steel, ceramic, and flint grinding media may each be used when corrosive substances are present during grinding.

The grinding chamber can also be filled with an inert shield gas that does not react with the material being ground, to prevent oxidation or explosive reactions that could occur with ambient air inside the mill.

Advantages of the ball mill

Ball milling boasts of several advantages over other systems:

the cost of installation, power and grinding medium is low; it is suitable for both batch and continuous operation, similarly it is suitable for open as well as closed circuit grinding and is applicable for materials of all degrees of hardness.

4

Professor Bello’s notes on grinding, sieve analysis and filtration

Varieties

Aside from common ball mills there is a second type of ball mill called a planetary ball mill. Planetary ball mills are smaller than common ball mills and mainly used in laboratories for grinding sample material down to very small sizes. A planetary ball mill consists of at least one grinding jar which is arranged eccentrically on a so-called sun wheel. The direction of movement of the sun wheel is opposite to that of the grinding jars (ratio: 1:-2 or 1:-1 or else). The grinding balls in the grinding jars are subjected to superimposed rotational movements, the so-called Coriolis forces. The difference in speeds between the balls and grinding jars produces an interaction between frictional and impact forces, which releases high dynamic energies. The interplay between these forces produces the high and very effective degree of size reduction of the planetary ball mill.

History

Devices for shaking materials along with hard balls might be old, but it was not until the industrial revolution and the invention of steam power that a machine could be built. It is reported to have been used for grinding flint for pottery in 1870.[3]

Also available

Cement mill

Vertical roller mill

Tumble finishing.

References:

1. Florez-Zamora, M. I. et al. (2008). "Comparative study of Al-Ni-Mo alloys obtained by mechanical alloying in different ball mills". Rev. Adv. Mater. Sci. 18: 301.

2. Mechanical Alloying Technology , Institute of Materials Processing3. Lynch, A., Rowland C (2005). The history of grinding. SME. ISBN 0-

87335-238-6.

5

Professor Bello’s notes on grinding, sieve analysis and filtration

mmmmmmmmmmmmmmmmmmm

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

6

Professor Bello’s notes on grinding, sieve analysis and filtration

hhhhhhhhhhhhhhhhhhhhhhhhhhhh

mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

Vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

7

Professor Bello’s notes on grinding, sieve analysis and filtration

Particle Size Reduction MachinesSize reduction equipment

The principal types of size-reduction machines are as follows:

A. Crushers (coarse and fine)

1. Jaw crushers( Stag or Dodge)2. Gyratory crushers3. Crushing rolls

B. Intermediate Crushers/Grinders (intermediate and fine)

1. Disc Crusher2. Edge Runner Mill3. Hammer mills; impactors4. Rolling-compression mills5. Pin Mill6. Attrition mills7. Tumbling mills

C. Ultrafine Crushers ( grinders )

1. Hammer mills with internal classification2. Buhrstone Mill3. Roller Mill4. Griffin Mill5. Ring roller Mill6. Ball Mill7. Tube Mill8. Hardinge Mill9. Babcock Muill

D. Cutting machines

Knife cutters; dicers; slitters

What is Size Reduction?

8

Professor Bello’s notes on grinding, sieve analysis and filtration

"Adding energy to a material to make large pieces smaller"

Energy + Material = Size Reduction

Different types of size reduction equipment are available and each has its own method of reduction. The right machine for the task is the one that can add energy most efficiently for the application.

From the beginning of time, humans have found it necessary to make little pieces out of big ones – stone, ore, ice, grain and more. It was a slow, laborious process for many centuries. Then in the Stone Age came the first breakthrough – we call it a hammer – and it worked better than ever. It worked so well, in fact, that it's still one of the most widely used tools in the world.

Today, there are many different size reduction machines available to make little pieces out of big ones. Particle size-reduction equipment includes

i. primary impact crushers and ii. secondary crushers as well as iii. milling machines - cage mills, hammer mills, pulverizers

and grinders.

Hammer Mill Crushers

What is a Hammer Mill?

A hammer mill is a crusher that can grind, pulverize, and crush a wide range of materials. This crusher employs a rain of hammer blows to shatter and disintegrate the material. Hammer mills produce a finish product size that is dependent upon the following:

1. Openings in perforated screens or grate bars2. Number, size and type of hammers3. Grinding plate setting4. Rotor speed

The servicability of a Stedman Machine is second to none. Standard service can be performed with common hand tools. Their product contact points is available in carbon and stainless steel. Their machines can also be rebuilt over and over, saving money. The special combination of features in a Stedman Hammer mill is the result of over 90 years' experience in the field.

9

Professor Bello’s notes on grinding, sieve analysis and filtration

Wood hammer mills, also called wood hogs are special heavy duty Stedman Hammer mills specifically designed to process wood and fibrous waste without the use of high maintenance knives. Their machines have simple designs with rugged construction that makes them easy to operate and maintain. 

Stedman Hammer mill Features

Large opening for flexibility Fully lined crushing chamber for longevity  Liners are bolted for easy change out Grate bars and screens for accurate product sizing that are easily replaceable Hammers or rings allowing flexibility Forged alloy steel and extreme duty shaft allowing reduced vibration and

longer bearing life Positive lock housing for extra security from blow outs and dusting Adjustable grinding plate for process control Multiple rotor configurations to suit any material Large discharge opening

Hammer mill Applications Animal Tankage Coal Limestone Biomass & Biofuels Bagasse Wood Corn Stalks Barley Shorts Bran Cocoa Shells Feed Grains

Crab, Clam & Oyster Shells Fish Meal Gelatin Gypsum Meat Scraps Oats Salt Cake Corn Soy Bean Expeller Cake Steamed Bone Hops Wheat

10

Professor Bello’s notes on grinding, sieve analysis and filtration

Impact Crushers

What is an Impact Crusher?

Impact size reduction incorporates striking to pulverize material. The primary types of impact crushers include:

horizontal shaft impactors (HSI), cage mill pulverizers , and vertical shaft impactors (VSI).

Each impactor can be further designated as primary and secondary rotor crusher as well as tertiary and quaternary crushers. This particular designation is dependent on which processing stage the equipment is being utilized.

Every Stedman crusher is engineered for a maximum feed size, target output size, and total capacity, but selecting a crusher on these criteria alone is merely half the task. Every size reduction project requires evaluation of the complete process to maximize production and keep operating costs low. From start to finish Stedman provides the information to make the correct choices for your processing needs.

11

Professor Bello’s notes on grinding, sieve analysis and filtration

Crusher Throughput Production

Feed enters the crushing chamber and meets the breaker bars or plates propelling feed against the breaker plates resulting in impact reduction. There are no screens or grates holding material inside impact crushers, so material is efficiently processed at high rates for low costs.

What Industries Use Crusher?

The following are of useful importance:

Aggregate Coal, Energy & Biomass   Minerals & Mining Brick, Clay & Ceramics Industrial Applications and many more…

Industrial Fine Grinding Mills

What is a Fine Grinder?

The number and kind of grinders are as diverse as the materials they are designed to reduce. The earliest examples are as simple as a mortar and pestle and have evolved to include the horse mill, windmill and watermill.

Today, Stedman fine grind products include modern air swept material handling and classification methods to efficiently produce consistent finely ground powder products.

Fine Grinding Applications

A wide variety of industries that rely on fine grinders includes:

Agricultural Processing Chemical Processing Feed Processing Food Processing Mineral Processing Pharmaceutical Rendering Soap & Detergent

12

Professor Bello’s notes on grinding, sieve analysis and filtration

Fine Grinding Mill Equipment

The range of fine grinders assists in the production of materials from A-to-Z making efficient work of breaking down particles to the required or desired product gradations.

LUMP BREAKER

What is a Lump Breaker?

Lump-breaking equipment is able to reduce lumps created in the production, storage or transportation of bulk solids and powders - without generating excessive dust and fines. The rotation of specially shaped blades through a fixed comb gives an efficient lump breaking action.

Where to find Lump Crushing Applications Soda Ash Coal Sodium Bicarbonate Pet Coke Fertilizer Salt Herbicide Gypsum Filter Cake Detergent Sugar Frozen Vegetables

Crushing efficiency

Empirical relationships: Rittinger’s and Kick’s law

The work required in crushing is proportional to the new surface created. This is equivalent to the statement that the crushing efficiency is constant and, for a giving machine and material, is independent of the sizes of feed and product.

13

Professor Bello’s notes on grinding, sieve analysis and filtration

If the sphericities a (before size reduction) and b (after size reduction) are equal and the machine efficiency is constant, the Rittinger’s law can be written as

where P is the power required, is the feed rate to crusher, is the average particle diameter before crushing, is the average particle diameter after crushing, and Kr is Rittinger’s coefficient.

Kick’s law: the work required for crushing a given mass of material is constant for the same reduction ratio, that is the ratio of the initial particle size to the finial particle size

where Kk is Kick’s coefficient.

Bond crushing law and work index

The work required to form particles of size Dp from very large feed is proportional to the square root of the surface-to-volume ratio of the product, sp/vp. Since s = 6/Dp, it follows that

where Kb is a constant that depends on the type of machine and on the material being crushed.

The work index, wi, is defined as the gross energy required in KWH per ton of feed to reduce a very large feed to such a size that 80% of the product passes a 100 m screen. If Dp is in millimetres, P in KW, and in tons per hour, then

If 80% of the feed passes a mesh size of Dpa millimetres and 80% of the product a mesh of Dpb millimetres, it follows that

14

Professor Bello’s notes on grinding, sieve analysis and filtration

Example: What is the power required to crush 100 ton/h of limestone if 80% of the feed pass a 2-in screen and 80% of the product a 1/8 in screen? The work index for limestone is 12.74.

Solution: =100 ton/h, wi =12.74, Dpa =2 25.4=50.8 mm, Dpb =25.4/8=3.175 mm

Screening

Screening is a method of separating particles according to size alone.

Undersize: fines, pass through the screen openings

Oversize: tails, do not pass

A single screen can make but a single separation into two fractions. These are called unsized fractions, because although either the upper or lower limit of the particle sizes they contain is known, the other limit is unknown. Material passed through a series of screens of different sizes is separated into sized fractions, i.e. fractions in which both the maximum and minimum particle sizes are known.

4.1.1 Screening equipment

Stationary screens and grizzlies; Gyrating screens; Vibrating screens; Centrifugal sitter.

Cutting diameter Dpc: marks the point of separation, usually Dpc is chosen to be the mesh opening of the screen.

Actual screens do not give a perfect separation about the cutting diameter. The undersize can contain certain amount of material coarser than Dpc, and the oversize can contain certain amount of material that is smaller than Dpc.

4.1.2 Material balances over a screen

Let F, D, and B be the mass flow rates of feed, overflow, and underflow, respectively, and xF, xD, and xB be the mass fractions of material A in the

15

Professor Bello’s notes on grinding, sieve analysis and filtration

streams. The mass fractions of material B in the feed, overflow, and underflow are 1- xF, 1- xD, and 1- xB.

F = D + B

FxF = DxD + BxB

Elimination of B from the above equations gives

Elimination of D gives

4.1.3 Screen effectiveness

A common measure of screen effectiveness is the ratio of oversize material A that is actually in the overflow to the amount of A entering with the feed. These quantities are DxD and FxF respectively. Thus

where EA is the screen effectiveness based on the oversize. Similarly, an effectiveness EB based on the undersize materials is given by

A combined overall effectiveness can be defined as the product of the two individual ratios.

Filtration

Filtration is the removal of solid particles from a fluid by passing the fluid through a filtering medium, or septum, on which the solids are deposited.

16

Professor Bello’s notes on grinding, sieve analysis and filtration

The fluid may be liquid or gas, the valuable stream from the filter may be fluid, or the solid, or both. Sometimes it is neither, as when waste solid must be separated from waste liquid prior to disposal.

Filters are divided into three main groups: cake filters, clarifying filters, and crossflow filters. Cake filters separate relatively large amount of solids as a cake of crystals or sludge. Often they include provisions for washing the cake and for removing some of the liquid from the solids before discharge. At the start of filtration in a cake filter, some solid particles enter the pores of the medium and are immobilised, but soon others begin to collect on the septum surface. After this brief period the cake of solids does the filtration, not the septum; a visible cake of appreciable thickness builds up on the surface and must be periodically removed. Clarifying filters remove small amount of solids to produce a clean gas or a sparkling clear liquid such as beverage. The solid particles are trapped inside the filter medium or on its external surfaces. Clarifying filters differ from screens in that the pores of the filter medium are much larger in diameter than the particles to be removed. In a crossflow filter, the feed suspension flows under pressure at a fairly high velocity across the filter medium. A thin layer of solids may form on the surface of the medium, but the high liquid velocity keeps the layer from building up. The filter medium is a ceramic, metal, or polymer membrane with pores small enough to exclude most of suspended particles. Some of the liquid passes through the medium as clear filtrate, leaving a more concentrated suspension behind.

The theory of filtration

In cake filters, the particles forming the cake are small and the flow through the bed is slow. Streamline conditions are invariably obtained. From Kozeny equation,

(1)

where u is the velocity of the filtrate, L is the cake thickness, S is the specific surface of the particles, is the porosity of cake, is the viscosity of the filtrate, and P is the applied pressure difference. The filtrate velocity can also be written as

(2)

where V is the volume of filtrate which has passed in time t and A is the total cross-sectional area of the filter cake.

17

Professor Bello’s notes on grinding, sieve analysis and filtration

For incompressible cakes can be taken as constant and the quantity 3/[5(1- )2S2] is then a property of the particles forming the cake and should be constant for a given material. Therefore

(3)

where

(4)

Eq(3) is the basic filtration equation and r is termed the specific resistance. It is seen to depend on and S. For incompressible cakes it is taken as constant, but it will depend on the rate of deposition, nature of particles, and on forces between the particles.

In Eq(3), the variables V and L are connected, and the relation between them can be obtained by making a material balance between the solids in the slurry and in the cake.

Mass in the filter cake is (1- )AL s, where s is the density of the solids.

Mass of liquid retained in the filter cake is AL , where is the density of the filtrate.

If J is the mass fractions of solids in the original suspension

(5)

That is

(6)

Therefore

(7)

and

18

Professor Bello’s notes on grinding, sieve analysis and filtration

(8)

If v is the volume of cake deposited by unit volume of filtrate then:

or (9)

and from Eq(8):

(10)

Substituting for L in Eq(3)

or

(11)

Eq(11) can be regarded as the basic relation between P, V, and t. Two important types of operation will be considered: 1). where the pressure difference is maintained constant and, 2). where the rate of filtration is maintained constant.

Constant pressure difference

Eq(11) can be re-written as

(12)

Integrating Eq(12) gives

19

Professor Bello’s notes on grinding, sieve analysis and filtration

or (13)

Thus for a constant pressure filtration, there is a linear relation between V2 and t. Filtration at constant pressure is more frequently adopted in practical conditions.

Constant rate filtration

constant (14)

Therefore

or (15)

In this case, P is directly proportional to V.

Flow of filtrate through the septum and cake combined

Suppose that the filter septum to be equivalent to a thickness Ls of cake, then if P is the pressure drop across the cake and septum combined Eq(3) can be written as:

(16)

i.e.

(17)

For constant rate filtration we have

(18)

For constant pressure filtration we have

20

Professor Bello’s notes on grinding, sieve analysis and filtration

(19)

21