Drilling response of drag bits: Theory and experiment

This paper presents a complete model of the drilling response of drag bits (or PDC bits as they are often referred to), i.e. a set of relations between the weight-on-bit W, the torque-on-bit T, the rate of penetration V, and the angular velocity Ω. This work complements an earlier paper [Detournay E, Defourny P. A phenomenological model of the drilling action of drag bits. Int J Rock Mech Min Sci 1992;29:13-23], in which the existence of a linear constraint between T, W, and the depth of cut per revolution d = 2 π V / Ω was established. The frictional contact process, shown previously to be a pervasive feature of the drilling response of drag bits, is here further characterized by the introduction of two new quantities: (i) the characteristic contact length ℓ, an objective measure of the bit bluntness and (ii) the contact strength σ, the maximum normal stress that can be transmitted by the cutter wear flat-rock interface. The proposed model distinguishes three successive regimes in the drilling response of PDC bits: (i) phase I, at low depth of cut per revolution, characterized by a dominance of the frictional contact process and by an increase of the contact forces with d, (ii) phase II, where the contact forces are fully mobilized, and (iii) phase III where the actual contact length increases beyond ℓ, due to poor cleaning. Experimental evidence obtained with a small drilling machine is given in support of this model.