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# Mill (grinding)

A grinding mill is a unit operation designed to break a solid material into smaller pieces. There are many different types of grinding mills and many types of materials processed in them. Historically mills were powered by hand (mortar and pestle), working animal, wind (windmill) or water (watermill). Today they are also powered by electricity.

The grinding of solid matters occurs under exposure of mechanical forces that trench the structure by overcoming of the interior bonding forces. After the grinding the state of the solid is changed: the grain size, the grain size disposition and the grain shape.

Grinding may serve the following purposes in engineering:

• magnification of the surface area of a solid
• manufacturing of a solid with a desired grain size
• pulping of resources

## Grinding laws

In spite of a great number of studies in the field of fracture schemes there is no formula known which connects the technical grinding work with grinding results. To calculate the needed grinding work against the grain size changing three half-empirical models are used:

• KICK for d > 50 mm

$W_K=c_k*\left(ln \left(d_A\right) - ln \left(d_E\right)\right),$

• BOND for 50 mm > d > 0.05 mm

$W_B= c_B*left\left(sqrtfrac\left\{1\right\}\left\{d_E\right\} - sqrtfrac\left\{1\right\}\left\{d_A\right\}right\right),$

• RITTINGER for d < 0.05 mm

$W_R=c_R*left\left(frac\left\{1\right\}\left\{d_E\right\} - frac\left\{1\right\}\left\{d_A\right\}right\right),$

with W as grinding work in kJ/kg, c as grinding coefficient, dA as grain size of the source material and dE as grain size of the ground material.

A reliable value for the grain sizes dA and dE is d80. This value signifies that 80% (mass) of the solid matter has a smaller grain size. The BOND's grinding coefficient for different materials can be found in various literature. To calculate the KICK's and RITTINGER's coefficients following formulas can be used

$c_K=1.151*c_B*\left(d_\left\{BU\right\}\right)^\left\{-0.5\right\},$

$c_R=0.5*c_B*\left(d_\left\{BL\right\}\right)^\left\{0.5\right\},$

with the limits of BOND's range: upper dBU = 50 mm and lower dBL = 0.05 mm.

## Grinding degree

To evaluate the grinding results the grain size disposition of the source material (1) and of the ground material (2) is needed. Grinding degree is the ratio of the sizes from the grain disposition. There are several definitions for this characteristic value:

• Grinding degree referring to grain size d80

$Z_d=frac\left\{d_\left\{80,1\right\}\right\}\left\{d_\left\{80,2\right\}\right\},$
Instead of the value of d80 also d50 or other grain diameter can be used.

• Grinding degree referring to specific surface

$Z_S=frac\left\{S_\left\{v,2\right\}\right\}\left\{S_\left\{v,1\right\}\right\}=frac\left\{S_\left\{m,2\right\}\right\}\left\{S_\left\{m,1\right\}\right\},$

The specific surface area referring to volume Sv and the specific surface area referring to mass Sm can be found out through experiments.

• Pretended grinding degree

$Z_a=frac\left\{d_1\right\}\left\{a\right\},$
The discharge die gap a of the grinding machine is used for the ground solid matter in this formula.

## Grinding machines

In materials processing a grinder is a machine for producing fine particle size reduction through attrition and compressive forces at the grain size level. See also crusher for mechanisms producing larger particles.

### Ball mill

A typical type of fine grinder is the ball mill. A slightly inclined or horizontal rotating cylinder is partially filled with balls, usually stone or metal, which grinds material to the necessary fineness by friction and impact with the tumbling balls. The feed is at one end of the cylinder and the discharge is at the other. Ball mills are commonly used in the manufacture of Portland cement.

### Rod mill

A rotating drum causes friction and attrition between steel rods and ore particles. But note that the term 'rod mill' is also used as a synonym for a slitting mill, which makes rods of iron or other metal.

### SAG mill

SAG is an acronym for Semi-Autogenous Grinding, and applies to mills that utilize steel balls in addition to large rocks for grinding. The SAG mills use a minimal ball charge of 6 to 15%.

A rotating drum throws large rocks and steel balls in a cataracting motion which causes impact breakage of larger rocks and compressive grinding of finer particles. Attrition in the charge causes grinding of finer particles. SAG mills are characterized by their large diameter and short length. The inside of the mill is lined with lifting plates to lift the material inside up and around the inside of the mill, where it then falls off the plates and falls back down.

SAG mills are primarily used in the gold, copper and platinum industries with applications also in the lead, zinc, silver, alumina and nickel industries.

### Autogenous mill

A rotating drum throws large rocks in a cataracting motion which causes impact breakage of larger rocks and compressive grinding of finer particles. It is similar in operation to a SAG mill as described above but does not use steel balls in the mill. Attrition in the charge causes grinding of finer particles. Also known as ROM or "Run Of Mine" grinding.

### Pebble mill

A rotating drum causes friction and attrition between rock pebbles and ore particles. May be used where product contamination by iron from steel balls must be avoided.

### High pressure grinding rolls

The ore is fed between two rollers which are pushed firmly together while their rotating motion pushes the ore through a small gap between them. Extreme pressure causes the rocks to fracture into finer particles and also causes microfracturing at the grain size level.

It consists of a pair of vertical cylindrical rollers through which material is passed. The two rollers rotate in opposite directions, "nipping" and crushing material between them. A similar type of intermediate crusher is the edge runner, which consists of a circular pan with two or more heavy wheels known as mullers rotating within it; material to be crushed is shoved underneath the wheels using attached plow blades.

### Buhrstone mill

Another type of fine grinder commonly used is the buhrstone mill, which is similar to old-fashioned flour mills.