A phenomenological model for the drilling action of drag bits

This paper is concerned with an investigation of the drilling response of drag bits (or PDC bits, as they are often referred to), i.e. with the study of the relations between weighht-on-bit W, torque T, angular velocity ω and rate of penetration v. Following an early suggestion (Fairhurst and Lacabanne, Min. Quarry Engng, 157–161, 194–197, 1957) that the bit-rock interaction is characterized by the coexistence of rock cutting and frictional contact, the torque and weight-on-bit are each decomposed into two components associated with these basic processes. By postulating that the cutting component of T and W is proportional to the depth of cut per revolution, δ = 2πv/ω, and that a linear constraint exists between the frictional component of T and W, a linear relation is derived between the specific energy E and the drilling strength L two quantities with dimensions of stress, that are respectively proportional to T and W, and inversely proportional to δ. The original assumptions appear to be justified when the model is tested against published experimental results, as the data point cluster along a line in the E-L diagram. Interpretation of experimental data suggests that the contact friction coefficient actually reflects the internal frictional property of the rock. It is also proposed that the influence of the bit design on the drilling response is embodied in a single number γ, which depends on the shape of the cutting edge and on the distribution of cutters on the bit body.