A fractal comminution approach to evaluate the drilling energy dissipation

Abstract

SUMMARYThe drilling comminution is theoretically and experimentally analysed by a fractal approach. An extension of the Third Comminution Theory is developed to evaluate the energy dissipation in the process: it occurs in a fractal domain intermediate between a surface and a volume. The theoretical assumption of a material 'quantum' is experimentally observed. The experimental fragment analysis evidences the characteristic size of separation between primary cutting and secondary milling. A global power balance for the drilling process is also presented and permits the prediction of drilling velocity. It shows also how the dissipation energy density (drilling strength) is not a constant parameter, but decreases considerably with the size scale.

A multifractal comminution approach for drilling scaling laws

“…One can assume a material ''quantum'' of size r min = constant [21,36,37,42,43], and the hypothesis of self-similarity, i.e., r max ¼k ffiffiffiffi V 3 p , k = constant [38,42]. The energy dissipated to produce the new free surface in the comminution process, which is provided by the product of fracture and friction energy C F (for drilling C F i30G F , being G F the fracture energy, [42]) and total surface area A/2 (and not A the surface being in common between fragments) [39,40], is:…”

Evolutionary fractal theory of erosion and experimental assessment on MIR space station

“…the energy W dissipated in the comminution processes is proportional to the length L/surface A/volume V of the element, raised to fractal exponents γ i , for which well defined limits are given. Γ * i is the so-called fractal fragmentation strength and appears to be a constant, differently from the usual fragmentation strength S [17]. Strong size effects on classical fragmentation strength S are in fact clearly observed from an experimental viewpoint [17,18].…”

“…Γ * i is the so-called fractal fragmentation strength and appears to be a constant, differently from the usual fragmentation strength S [17]. Strong size effects on classical fragmentation strength S are in fact clearly observed from an experimental viewpoint [17,18].…”

Fractal coupled theory of drilling and wear

“…Drilling (Carpinteri and Pugno, 2002a) can be considered simply artificial fragmentation. On the other hand, wear is studied in the Tribology science.…”

“…In the present paper, we propose a coupled theory, based on statistical and fractal concepts (Mandelbrot, 1982;Feder, 1988;Turcotte, 1992;Carpinteri and Pugno, 2002a,b), to describe the phenomena from a global point of view. According to Carpinteri and Pugno (2002a), the drilling process is described in terms of drilling velocity. A similar global parameter, the wear rate, is introduced to describe the tool wear.…”