Mill (grinding) - Grinding Laws

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. 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.

• Kick for d > 50 mm

• Bond for 50 mm > d > 0.05 mm

• Von Rittinger for d < 0.05 mm

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

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

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

• Grinding degree referring to specific surface

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

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