Mathematical modelling of the mechanics of core drilling in geomaterials

A new, rational model is proposed for simulating the process of core drilling in geomaterials. The model describes in a consistent manner the complicated process of core drilling in quasi-brittle materials. After reviewing a model from the literature, based only on the balance of forces at the cutting edge, a new approach is introduced, considering a fundamental kinematical constraint to the rotary drilling process, namely, the helicoidal trajectories of the cutters. At the same time, the mechanical balance of engine power supply and drilling energy consumption must hold. The concept of drilling strength, i.e., the energy consumed to remove the unit volume of base material, is discussed, showing that the expression of the drilling strength depends on the fracture mechanisms occurring in the base material, and thus depends also on the shape of the indenters (back rake angle, wear-flat). A simple estimate of the wear effects at the cutting edges, based on experiments, is proposed. In conclusion, a global formulation of the core drilling process is obtained by coupling the kinematical and mechanical conditions. The model comprises a set of physical parameters, which can be determined according to drilling tests.