


Impact crushing approach to the
relationship of energy and particle size in comminution
E. Th. Stamboliadis*
Department of Mineral Resources Engimeering,
laboratory of Mineral Processing Technical University of Crete 73100 Chania
Received 12 June 2002; accepted 14 March 2003
ABSTRACT
The
theories of Rittinger, Kick and Bond, that relate the energy required for comminution to
the particle size of the feed and product do not provide for a size distribution of the
material. The present theory tries to incorporate the concept of particle size
distribution into the existing ones. Charles, firstly presented such an approach, but he
used a different model of size reduction. He borrogh the model of Walker and Shaw
according to which, the size of a particle is continuously reduced to an infinetly smaller
particle at a time. The present model accepts that breakage of a mother paricle produces
more than one daughter particles, which have a certain size distribution.
The energy required to create each individual particle, by exposing all of its surface, is
given by the formula: Q_{x}=(C_{S}.S_{x})^{n} or Q_{x}=(C_{S}.f)^{n}.x^{2n}
where: x the size of the particle, S_{x} the surface area, f the surface
coefficient, while C_{S} and n are constants >0. The specific energy (energy
per unit mass) for the same created particle is: q_{x}=(C_{S}.f)^{n}.x^{2n3}/(k.) where:
the
particle density and k the volume coefficient. Assuming a GGS size distribution of the
daughter particles, the energy required to produce an assembly of particles having a total
mass W_{o}, size modulus y and distribution modulus
is:
, for (2n3+) > 0 . In
this case the laws of Rittinger and Bond are derived as partial cases for values of n
equal to 1 and 1.25 respectively. For (2n3+) = 0 the energy is given by:
Keywords: Crushing; Comminution; Particle size; Energy
* Corresponding author
Email : elistach@mred.tuc.gr 
