Mill (grinding)

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 semi-empirical models are used. These can be related to the Hukki relationship between particle size and the energy required to break the particles. In stirred mills, the Hukki relationship does not apply and instead, experimentation has to be performed to determine any relationship.[1]

• Kick for d > 50 mm

${\displaystyle W_{K}=c_{k}(\ln(d_{A})-\ln(d_{E}))\,}$

• Bond[2] for 50 mm > d > 0.05 mm

${\displaystyle W_{B}=c_{B}\left({\frac {1}{{\sqrt {d}}_{E}}}-{\frac {1}{{\sqrt {d}}_{A}}}\right)\,}$

• Von Rittinger for d < 0.05 mm

${\displaystyle W_{R}=c_{R}\left({\frac {1}{d_{E}}}-{\frac {1}{d_{A}}}\right)\,}$

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

A reliable value for the grain sizes d_A and d_E 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

${\displaystyle c_{K}=1.151c_{B}(d_{BU})^{-0.5}\,}$

${\displaystyle c_{R}=0.5c_{B}(d_{BL})^{0.5}\,}$

with the limits of Bond's range: upper d_BU = 50 mm and lower d_BL = 0.05 mm.

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

${\displaystyle Z_{d}={\frac {d_{80,1}}{d_{80,2}}}\,}$

Instead of the value of d₈₀ also d₅₀ or other grain diameter can be used.

• Grinding degree referring to specific surface

${\displaystyle Z_{S}={\frac {S_{v,2}}{S_{v,1}}}={\frac {S_{m,2}}{S_{m,1}}}\,}$

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

• Pretended grinding degree

${\displaystyle Z_{a}={\frac {d_{1}}{a}}\,}$

The discharge die gap a of the grinding machine is used for the ground solid matter in this formula.

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. In general, grinding processes require a relatively large amount of energy; for this reason, an experimental method to measure the energy used locally during milling with different machines was recently proposed.[3]

Operation of a ball mill

SAG mill

Principle of SAG Mill operation

SAG is an acronym for semi-autogenous grinding. SAG mills are autogenous mills that also use grinding balls like a ball mill. A SAG mill is usually a primary or first stage grinder. SAG mills use a ball charge of 8 to 21%.[6][7] The largest SAG mill is 42' (12.8m) in diameter, powered by a 28 MW (38,000 HP) motor.[8] A SAG mill with a 44' (13.4m) diameter and a power of 35 MW (47,000 HP) has been designed.[9]

Attrition between grinding balls and ore particles causes grinding of finer particles. SAG mills are characterized by their large diameter and short length as compared to ball mills. The inside of the mill is lined with lifting plates to lift the material inside the mill, where it then falls off the plates onto the rest of the ore charge. SAG mills are primarily used at gold, copper and platinum mines with applications also in the lead, zinc, silver, alumina and nickel industries.

Buhrstone mill

Table top hammer mill

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

• Windmill, wind powered
• Watermill, water powered
• Horse mill, animal powered
• Treadwheel, human powered (archaic: "treadmill")
• Ship mill, floats near a river bank or bridge
• Arrastra, simple mill for grinding and pulverizing (typically) gold or silver ore.
• Roller mill, an equipment for the grinding or pulverizing of grain and other raw materials using cylinders
• Stamp mill, a specialized machine for reducing ore to powder for further processing or for fracturing other materials
• A place of business for making articles of manufacture. The term mill was once in common use for a factory because many factories in the early stages of the Industrial Revolution were powered by a watermill, but nowadays it is only used in a few specific contexts; e.g.,
  • Bark mill produces tanbark for tanneries
  • Cider mill crushes apples to give cider
  • Gristmill grinds grain into flour
  • Oil mill, see expeller pressing, extrusion
  • Paper mill produces paper
  • Sawmill cuts timber
  • Starch mill
  • Steel mill manufactures steel
  • Sugar mill (also called a sugar refinery) processes sugar beets or sugar cane into various finished products
  • Textile mill
    • Silk mill, for silk
    • Flax mill, for flax
    • Cotton mill, for cotton
  • Huller (also called a rice mill, or rice husker) is used to hull rice
  • Powder mill produces gunpowder

• "Mill" . Encyclopædia Britannica. 18 (11th ed.). 1911.
• Video of fine grinder in mining application
• Flour Mill Details
• Image of SAG mill during installation
• Grinding Media Grinding Media Guide