Rock is a random-composite material, and rock cutting diamonds are randomly shaped tools. Based on this, a research program has been planned, starting from single diamond operation on actual rock specimens. Points to be elucidated are the forms of the mathematical linkages between cutting force, normal force, cross section of the kerf produced and rock micro-hardness; the last point, due to obvious scale effects, does not seem to be reasonably predictable from conventional geo-mechanical tests and macroscopic scale cutting tests, nor from conventional rock mechanics theories. Following a synthetic discussion of the problem, the experimental apparatus is described and the results of tests under different conditions are presented. These tests cover the range of the normal and tangential forces applied by a single diamond of a wire saw bead, on different rock types. The results are then analysed, and a mathematical model of the single diamond action, in a form suitable to the application to a simulation of the multi diamond cutting tool, is presented. In the meantime, the most suitable way to characterise the rock in diamond cuttability problems is discussed and, in particular, the problem of obtaining quantitative micro-strength distribution data from conventional mineralogical-petrographic description is treated. Report by M. Cardu, E. Michelotti and E. Lovera.

Any attempt aimed to establish a model of diamond wire sawing for rock materials should take into account the following points:

The medium on which the wire acts is inhomogeneous: the single diamonds 'see’ the medium as a random sequence of mechanically different elements, having, as a common feature, only the approximately elastic-brittle behaviour (Fig 1).

The elementary tools (the diamonds) are randomly shaped and can be practically modelled only as point like concentrations of forces: the cross sections of the single incisions can not be usefully put into relationship to the cross sections of the individual diamonds. The case of metal cutting is entirely different: the cross sections of the single incisions practically coincide with the cross section of the diamonds, due to the elastic-plastic behaviour of the metallic media (Fig 2).

The elementary tools are organised in small groups forced to follow parallel paths with fixed mutual distance by a rigid body (the bead) on which they are mounted. The total normal force and the total parallel force acting on the group is easily calculated, but the distribution of the forces amongst the single diamonds of the group is essentially random, depending on the random distribution of the elements of the medium on which the diamonds act. On the other side, the paths of the beads are not determined by a rigid guidance, rather by the balancing of forces, and depend on the amounts of rock removed by the diamonds instead of being imposed by the feeding mechanism. An idealised behaviour of the wire is easily described, and the aim is to verify what of the idealised model should be retained and what should be corrected.

Conclusions

Wire saw production can be increased by increasing the wire speed or by increasing the tension, which means the pressure. Having the available power an upper limit, to increase the speed it’s necessary to reduce the tension, and vice versa. Tests developed indicate that specific cutting energy in most rocks depends on pressure, and decreases as pressure increases, which suggests that an increase of the tension, even at the expense of a reduction of the speed, can be fruitful. This is not, however a general rule. In granite, probably, due to the great inhomogeneity of this rock type, the specific cutting energy is not much affected by pressure. The measured values of single diamond incision specific energy are of the same order of magnitude of commercial sawing operations (5 to 25 kWh/m2, being the width of the cut 1 cm, mean 0.00181012 to 0.0091012 J/m3), and of the current microhardness values (1000 MPa mean 0.0011012 J/m3). The use of the single diamond incision and of the microhardness test as indicators of the energetic cost of stone sawing seems promising also for this reason [4]. Rocks are more often described in terms of mineralogical composition. A quantitative mineralogical analysis can be converted to a microhardness frequency distribution, provided that rock-forming minerals are grouped in narrow microhardness classes (Mohs scale lacks the required resolving power). A specific research is under way on this subject. Obviously, a greater variety of rock types has to be tested to obtain a general rule. As to the other doubtful points of the simplified model of wire operation, data should come from tests with an instrumented cutting machine; a test campaign is still under way.