PartTech - Size Reduction

Size Reduction

This refers to the process of breaking down solid materials into smaller, more manageable particles.

Comminution

What is the other term for “size reduction“?

• Create specific particle sizes and shapes

• Increase surface area for reactions

• Liberate valuable minerals

Give some of the purposes of size reduction or comminution (3)

FALSE

Size reduction process is energy intensive and a highly inefficient process.

TRUE or FALSE. Size reduction process is energy intensive and a highly efficient process.

5%

What percent of electricity generated is used for size reduction?

1%

Industrial processes are less than ___% efficient.

Attractive Forces

These forces pull the ions towards each other. The strength of these forces is significant when the ions are at their equilibrium distance.

Repulsive Force

This force prevents the ions from getting any closer together and contributes to the stability of the crystal lattice.

Equilibrium Distance

____________ is where the attractive and repulsive forces are equal in magnitude but opposite in direction, resulting in zero net force

Equilibrium Distance

This distance represents the most stable configuration for ions in the lattice.

FALSE

In compression, forcing ions closer together increases repulsive forces.

TRUE or FALSE. In compression, forcing ions closer together decreases repulsive forces.

FALSE

In tension, increasing the distance between ions reduces attractive forces until they can no longer maintain the lattice structure,

TRUE or FALSE. In tension, decreasing the distance between ions reduces attractive forces until they can no longer maintain the lattice structure.

Hooke’s Law

This law states that “strain is directly proportional to applied stress.“

Young’s Modulus

This describes the proportionality (stress/strain)

Plastic Deformation Regime

When the applied force exceeds a certain threshold, the material enters the _____________. Here, the deformation becomes permanent, resulting in the breaking of bonds.

Elastic Limit or Yield Stress or Material’s Strength

This refers to the maximum stress that the material can withstand while still returning to its original shape. Beyond this limit, plastic deformation occurs, indicating the transition to fracture.

Overestimated Strength

This assumes all bonds in a crystal plane break simultaneously under tensile stress, leading to a theoretical strength much higher than reality.

Underestimated Strength

This assumes only the bonds about to break are stretched, resulting in a theoretical strength much lower than reality

TRUE

TRUE or FALSE. Actual fracture mechanism is more intricate than these simplified models, requiring deeper analysis to accurately predict material behavior.

Strain Energy

This is the stored energy when an object stretches or when there is a change of length because a force is being applied to it.

Tension

A body stores strain energy under ___________.

FALSE

Strain energy is not uniformly distributed throughout the body but is concentrated around holes, corners, and cracks.

TRUE or FALSE. Strain energy is uniformly distributed throughout the body but is concentrated around holes, corners, and cracks.

Inglis (1913)

Who proposed the working formulas for the stress concentration factor (K).

Stress Concentration Factor

This is a ratio that compares the maximum stress in a structure to the nominal stress.

Griffith (1921)

Who proposed the criteria that must be satisfied for a crack in the surface of a body to propagate.

Griffith Theory of Fracture

This theory in fracture mechanics explains how cracks in brittle materials propagate.

1. The strain energy that would be released must be greater than the surface energy created.

2. There must be a crack propagation mechanism available.

Griffith (1921) proposed that for a crack in the surface of a body to propagate, the following criteria must be satisfied (2)

30 degree angle

Griffith showed that the largest tensile stresses are produced at cracks having a ____ degree angle to the compressive stress.

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Kendal (1978)

Who showed that as the particle size decreases, the fracture strength increases until a critical size is reached when crack propagation becomes impossible.

TRUE

TRUE or FALSE. As particle size increases, the fracture strength decreases.

FALSE

Large particles are less difficult to break than small particles.

TRUE or FALSE. Large particles are more difficult to break than small particles.

• Rittinger’s Law

• Kick’s Law

• Bond’s Law

What are the three well-known postulates predicting energy requirements for particle size reduction.

Rittinger (1867)

Who proposed that the energy required for particle size reduction was directly proportional to the area of new surface created.

Kick (1885)

Who proposed that the energy required in any comminution process was directly proportional to the ratio of the volume of the feed particle to the product particle.

Bond’s (1952) law

This law states that the work required to reduce particle size is proportional to the inverse square root of the size.

Bond’s Work Index

This is defined as the energy required to reduce the size of unit mass of material from infinity to 100 µm in size.

Bond’s Work Index

It is determined experimentally and depends on the material type but is independent of the final product size.

Holmes (1957)

Hukki (1961)

Who were the people who derived a general formula that includes all three size reduction laws as special cases.

According to Holmes (1957) and Hukki (1961), the three proposals can be considered as being the integrals of the same differential equation:

1.5

From the given differential equation, in Bond’s Law, N is equal to ____.

2

From the given differential equation, in Rittinger’s Law, N is equal to ____.

1

From the given differential equation, in Kick’s Law, N is equal to ____.

Rittinger’s Law

For small particle sizes (ultra-fine grinding), what postulate predicting energy requirements for particle size reduction should be applied?

Kick’s Law

For large particle sizes (coarse crushing, crushing), what postulate predicting energy requirements for particle size reduction should be applied?

Bond’s Law

For intermediate particle sizes, what postulate predicting energy requirements for particle size reduction should be applied?

1. Crushing

2. Grinding

3. Cutting

4. Attrition

5. Impact

6. Compression

Enumerate the Operations in Size Reduction mentioned (6)

Crushing

The process of breaking large pieces of material into smaller pieces.

Grinding

The process of breaking large pieces of material into smaller pieces using abrasion and shear forces.

Cutting

The process of breaking large pieces of material into smaller pieces using a sharp knife.

Attrition

A size reduction method that uses rubbing or scraping to break down solid materials into smaller particles.

Impact

The process of breaking down a material into smaller particles by forcefully striking it against another surface

Compression

A size reduction technique that uses force to crush materials between rollers or plates

• Jaw Crushers

• Gyratory Crushers

• Cone Crushers

Enumerate equipment used for CRUSHING (3)

Jaw Crushers

Identify what equipment is being described: CRUSHING

These are used for coarse size reduction and operate by compressing the material between two plates, one fixed and one moving.

Gyratory Crushers

Identify what equipment is being described: CRUSHING

These consist of a conical head gyrating inside a larger conical shell, crushing the material as it moves downward.

Cone Crushers

Identify what equipment is being described: CRUSHING

These operate similarly to gyratory crushers but are typically used for secondary or tertiary crushing

• Ball Mills

• Rod Mills

• Hammer Mills

Enumerate equipment used for GRINDING (3)

Ball Mills

Identify what equipment is being described: GRINDING

These cylindrical devices used for fine grinding, where the grinding media (balls) are tumbled with the material to be ground.

Rod Mills

Identify what equipment is being described: GRINDING

These are similar to ball mills but use long rods as the grinding media, which grind the material by rolling and cascading action.

Hammer Mills

Identify what equipment is being described: GRINDING

These use rotating hammers to impact and break the material into smaller pieces.

Cutting Machines

Identify what equipment is being described: CUTTING

These are used when a specific particle shape is required. They operate by slicing the material into smaller pieces using sharp blades or edges.

Attrition Mills

Identify what equipment is being described: ATTRITION

These involve the rubbing or grinding of particles against each other, leading to the removal of small fragments from the surface.

Impact Crushers

Identify what equipment is being described: IMPACT

These equipment use the principle of rapid impact to shatter the material, typically using hammers or blow bars.

Compression Crushers

Identify what equipment is being described: COMPRESSION

These apply force to the particles, causing them to fracture along their weakest planes.

• Stressing mechanism

• Size of feed & product

• Material properties

• Carrier medium

• Mode of operation

• Capacity

• Combination with other unit ops.

What are the Factors Affecting the Choice of Machine? (7)

0.01 - 10 m/s

What is the range of velocity if the stress is applied between two surfaces at low velocity?

10 - 200 m/s

What is the range of velocity if the stress is applied between two surfaces at high velocity?

• Jaw crusher

• Gyratory crusher

• Crushing roll machine

• Horizontal table mill

Enumerate the comminution equipment for CRUSHING (mechanism 1) (4)

• Hammer mill

• Pin mill

• Fluid energy mill

Enumerate the comminution equipment for HIGH VELOCITY IMPACT (mechanism 2) (3)

• Sand mill

• Colloid mill

• Ball mill

Enumerate the comminution equipment for CRUSHING and IMPACT WITH ATTRITION (mechanism 1&2) (3)

Jaw Crusher

Identify what equipment is being described:

Behaves like a pair of giant nutcrackers. One jaw is fixed and the other, which is hinged at its upper end, is moved towards and away from the fixed jaw by means of toggles driven by an eccentric.

Gyratory Crusher

Identify what equipment is being described:

Has a fixed jaw in the form of a truncated cone. The other jaw is a cone which rotates inside the fixed jaw on an eccentric mounting

Crushing Roll Machine

Identify what equipment is being described:

Has two cylindrical rolls rotate in opposite directions, horizontally and side by side with an adjustable gap between them.

Horizontal Table Mill

Identify what equipment is being described:

The feed material falls on to the centre of a circular rotating table and is thrown out by centrifugal force. In moving outwards the material passes under a roller and is crushed

Hammer Mill

Identify what equipment is being described:

Consists of a rotating shaft to which are attached fixed or pivoted hammers. This device rotates inside a cylinder.

Pin Mill

Identify what equipment is being described:

Consists of two parallel circular discs each carrying a set of projecting pins. One disc is fixed and the other rotates at high speed so that its pins pass close to those on the fixed disc.

Fluid Energy Mill

Identify what equipment is being described:

Relies on the turbulence created in high velocity jets of air or steam in order to produce conditions for interparticle collisions which bring about particle fracture.

Fluid Energy Mill

Identify what equipment is being described:

These mills have a very high specific energy consumption and are subject to extreme wear when handling abrasive materials.

Sand Mill

Identify what equipment is being described:

Is a vertical cylinder containing a stirred bed of sand, glass beads or shot.

Colloid Mill

Identify what equipment is being described:

The feed in the form of a slurry passes through the gap between a male, ribbed cone rotating at high speed and a female static cone

Ball Mill

Identify what equipment is being described:

Is a rotating cylindrical or cylindrical–conical shell about half filled with balls of steel or ceramic.

1-0.1 m

Terminology Used in Comminution

Size range: __________

Term used: Coarse Crushing

Crushing

Terminology Used in Comminution

Size range: 0.1 m

Term used: __________

Fine crushing or coarse grinding

Terminology Used in Comminution

Size range: 1 cm

Term used: ___________

1 mm

Terminology Used in Comminution

Size range: __________

Term used: Intermediate grinding, milling

100 um

Terminology Used in Comminution

Size range: __________

Term used: Fine grinding

Ultrafine grinding

Terminology Used in Comminution

Size range: 10 um

Term used: _________

• Crushers

• Table mills

• Edge runner mills

Categorizing Equipment according to product size:

Equipment that are DOWN TO 3 MM (3)

• Ball mills

• Rod mills

• Pin mills

• Tube mills

• Vibration mills

Categorizing Equipment according to product size:

Equipment that are 3 MM - 50 UM (5)

• Ball mills

• Vibration Mills

• Sand mills

• Perl mills

• Colloid mills

• Fluid energy mills

Categorizing Equipment according to product size:

Equipment that are LESS THAN 50 UM (6)

a. Crushers (down to 3 mm)

Categorizing Equipment according to product size:

Which does not belong to the group

a. Crushers

b. Ball mills

c. Tube mills

d. Vibration Mills

d. Vibration mills (3mm-50um or less than 50 um)

Categorizing Equipment according to product size:

Which does not belong to the group

a. Crushers

b. Edge runner mills

c. Table mills

d. Vibration Mills

Hardness

Identify what Material Property is being described:

This property is a measure of the resistance to abrasion.

Graphite - ranked 1

Diamond - ranked 10

In the Mohs’ scale of hardness, graphite is rank number ____, and diamond is rank number ____.

Abrasiveness

Identify what Material Property is being described:

This is linked closely to hardness and is considered by some to be the most important factor in selection of commercial mills.

Toughness

Identify what Material Property is being described:

This is the property whereby the material resists the propagation of cracks.

Cohesivity/adhesivity

Identify what Material Property is being described:

The properties whereby particles of material stick together and to other surfaces.

TRUE

TRUE or FALSE. Decrease of particle size or increasing moisture content increases the cohesivity and adhesivity of the material.