Size Reduction

Particle size reduction

It is a critical process in numerous industries such as mining, pharmaceuticals, and materials processing.

Comminution

Particle size reduction is also known as __________

Particle Size Reduction

Its main objectives are to achieve desirable particle sizes for improved chemical reactions, enhanced material recovery, and better handling.

1%

Despite the importance of this particle size reduction, it is notably energy-intensive, with current industrial practices often achieving less than ___ efficiency.

Particle Size Reduction

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

• Create specific particle sizes and shapes

• Increase surface area for reactions

• Liberate valuable minerals

What are the purposes of Size Reduction?

• mechanical grinding

• crushing

• cutting

• milling

The size reduction process can be achieved through various methods, such as:

5%

_____ percent of all electricity generated is used for size reduction

1%

Industrial particle size reduction processes are less than _____% efficient

Attractive Forces

These forces pull the ions towards each other.

equilibrium distance

The strength of these forces is significant when the ions are at their

equilibrium distance

the distance at which the attractive and repulsive forces are balanced

Repulsive Force

As the ions come too close (beyond a certain threshold), these forces between their electron clouds increase.

Inversely proportional

As the ions come too close, the repulsive forces increase.

What is the relationship between repulsive forces of ions and the distance between them?

equilibrium distance

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

compression

In _________, forcing ions closer together increases repulsive forces, which can cause structural failure if stress surpasses the elastic limit.

tension

In __________, increasing the distance between ions reduces attractive forces until they can no longer maintain the lattice structure, potentia ly leading to bond breaking and fracture if the distance is further increased

Hooke’s Law

states that strain is directly proportional to applied stress.

Young’s Modulus

It describes this proportionality between stress and strain

elastic

In this range, the deformation is ______; the ions can return to their original positions once the applied forces are removed

elastic limit or yield stress

The ___________________ refers to the maximum stress that the material can withstand while still returning to its original shape.

plastic deformation

Beyond the elastic limit, _____________ occurs, indicating the transition to fracture.

Sometimes, defined as "material's strength."

Elastic limit or yield stress is also known as the ____________

Material Strength or Yield Stress

The strength of a material can be estimated based on the attractive and repulsive forces between its ions.

• Overestimated Strength

• Underestimated Strength

What are the Theoretical Approaches to Fracture?

Overestimated Strength

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

Underestimated Strength

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

Strain energy

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

strain energy

A body under tension stores __________.

area under the appropriate stress-strain graph

The amount of strain energy stored under tension is given by the ___________________________

Strain energy

_________ is not uniformly distributed throughout the body but is concentrated around holes, corners, and cracks

Inglis (1913)

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

stress concentration factor

The ______________ is a ratio that compares the maximum stress in a structure to the nominal stress

Griffith (1921)

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

Griffith theory of fracture (Crack propagation theory)

The _____________________ is a theory in fracture mechanics that explains how cracks in brittle materials propagate

Griffith (1921)

He proposed that for a crack in the surface of a body to propagate, there are criteria must be satisfied

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:

Griffith

_________ also found that tensile stresses always occur in the vicinity of crack tips, even when the applied gross stresses are compressive.

30 degree

Griffith also showed that the largest tensile stresses are produced at cracks having a __________ angle to the compressive stress

Evans et al. (1961)

According to him, For a disc acted upon by opposing diametrical loads, there is a uniform ensile stress acting at 90 degrees to the diameter.

Kendal (1978)

He discovered that as particle size decreases, the fracture strength increases.

Evans et al.

They also extended the analysis to three-dimensional particles to show that even when particles are stressed compressively, the stress pattern set up by virtue of the shape of the particle may cause it to fail in tension, whether cracks exist or not

Inversely proportional

What is the relationship between Particle Size and Fracture Strength?

Kendal (1978)

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

Remomize

• Rittinger’s Law

• Kick’s Law

• Bond’s Law

There are three well-known postulates predicting energy requirements for particle size reduction

Rittinger (1867)

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

200–300

However, since in practice the energy requirement is usually __________ times that required for creation of new surface, it is unlikely that energy requirement and surface created are related

Kick (1885)

__________ 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 law

_______ states that the work required to reduce particle size is proportional to the inverse square root of the size

Bond’s Work Index

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.

Bauxite - 9.45 kWh/short ton

Coke (coal) - 20.7 kWh/short ton

Gypsum Rock - 8.16 kWh/short ton

Common Values of Wi

Bauxite -

Coke (coal) -

Gypsum Rock -

Bond’s work index

_____________ is the work required to reduce a unit weight from a theoretical infinite size to 80 percent passing 100 μm

TRUE

TRUE or FALSE

The work index may be found experimentally from laboratory crushing and grinding tests or from commercial mill operations

Holmes (1957) and Hukki (1961)

They derived a general formula that includes all three size reduction laws as special cases.

What are the values for n for each of the three postulates?

Rittinger’s Law - energy ∝ surface area increase

Kick’s Law - energy ∝ volume ratio

Bond’s Law - energy ∝ inverse square root of size

Summary Property Relationships for each of the three postulates

Rittinger’s Law

Kick’s Law

Bond’s Law

• Rittinger’s Law - ultra-fine grinding

• Kick’s Law - coarse crushing, crushing

• Bond’s Law - industrial grinding processes

When to use each formula for the three postulates?

RITTINGER’S LAW (1867)

• shape factors and density are constant

• gives ridiculously low values if data gathered for large product sizes are extrapolated to predict energy requirements for small product sizes

Kick’s Law

• based on stress analysis theory for plastic deformation

Kick’s Law

The energy required in any comminution process is directly proportional to the ratio of the volume of the feed particle to the product particle.

BOND’S LAW (1952)

The work required to form particles of size from a very large particle size is proportional to the square root of the surface to volume ratio of the product.

BOND’S LAW (1952)

gives a fairly reliable first approximation to the energy requirement provided the product top size is not less than 100 m

• Crushing

• Grinding

• Cutting

• Attrition

• Impact

• Compression

What are the different operations in Size Reduction?

Crushing

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

• Jaw Crushers

• Gyratory Crushers

• Cone Crushers

What are the different types of crushing equipment?

Jaw crushers

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

Gyratory crushers

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

Cone crushers

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

Grinding

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

• Ball Mills

• Rod Mills

• Hammer Mills

What are the different grinding equipments?

Ball mills

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

Rod mills

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

Hammer mills

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

Cutting

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

Cutting machines

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

Attrition

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

Attrition mills

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

IMPACT

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

Impact crushers

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

Compression

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

Compression crushers

__________ apply a 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 w/ other unit operations

Factors affecting Choice of Machine

• Stress applied between two surfaces at low velocity (0.01 - 10 m/s)

• Stress applied at a single solid surface at high velocity (10–200 m/s)

• Stress applied by carrier medium–usually in wet grinding to bring about disagglomeration

What are the Stress Mechanisms Responsible for Particle Size Reduction

• Jaw Crusher

• Gyratory Crusher

• Crushing Roll Machine

• Horizontal table mill

Comminution Equipment using Mechanism 1 (Crushing)

Jaw crusher

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. The lumps of material are crushed between the jaws and leave the crusher when they are able to pass through a grid at the bottom

Gyratory Crusher

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. Material is discharged when it is small enough to pass through the gap between the jaws

Crushing Roll Machine

has two cylindrical rolls rotate in opposite directions, horizontally and side by side with an adjustable gap between them. As the rolls rotate, they drag in material which is choke-fed by gravity so that particle fracture occurs as the material passes through the gap between the rolls. The rolls may be ribbed to give improved purchase between material and rolls

Horizontal table mill

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

• Pin mill

• Fluid energy mill

Comminution Equipment using Mechanism 2 (High velocity impact)

Hammer mill -

consists of a rotating shaft to which are attached fixed or pivoted hammers. This device rotates inside a cylinder. The particles are fed into the cylinder either by gravity or by gas stream. In thegravity-fed version the particles leave the chamber when they are small enough to pass through a grid at the bottom.

Pin mill -

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. Particles are carried in air into the centre and as they move radially outwards are fractured by impact or by attrition.

Fluid energy mill

- 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. Material is conveyed from the grinding area near the jets at the base of the loop to the classifier and exit situated at the top of the loop

Fluid energy mill

- these mills have a very high specific energy consumption and are subject to extreme wear when handling abrasive materials. These problems have been overcome to a certain extent in the fluidized bed jet mill in which the bed is used to absorb the energy from the high-speed particles ejected from the grinding zone

• Sand mill

• Colloid mill

• Ball mill

Comminution Equipment using a Combination of Mechanism 1 & 2 (Crushing and impact with attrition)

Sand mill

It is a vertical cylinder containing a stirred bed of sand, glass beads or shot. The feed, in the form of a slurry, is pumped into the bottom of the bed and the product passes out at the top through a screen which retains the bed material

Colloid mill

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

It is a rotating cylindrical or cylindrical–conical shell about half filled with balls of steel or ceramic. The speed of rotation of the cylinder is such that the balls are caused to tumble over one another without causing cascading. This speed is usually less than 80% of the critical speed which would just cause the charge of balls and feed material to be centrifuged.