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


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: Qx=(CS.Sx)n or Qx=(CS.f)n.x2n where: x the size of the particle, Sx the surface area, f the surface coefficient, while CS and n are constants >0. The specific energy (energy per unit mass) for the same created particle is: qx=(CS.f)n.x2n-3/(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 Wo, size modulus y and distribution modulus is: , for (2n-3+) > 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 (2n-3+) = 0 the energy is given by:

Keywords: Crushing; Comminution; Particle size; Energy

* Corresponding author
   E-mail : elistach@mred.tuc.gr