Mechanical specific energy versus depth of cut in rock cutting and drilling

The relationship between Mechanical Specific Energy (MSE) and the Rate of Penetration (ROP), or equivalently the depth of cut per revolution, provides an important measure for strategizing a drilling operation. This study explores how MSE evolves with depth of cut, and presents a concerted effort that encompasses analytical, computational and experimental approaches. A simple model for the relationship between MSE and cutting depth is first derived with consideration of the wear progression of a circular cutter. This is an extension of Detournay and Defourny's phenomenological cutting model. Wear is modeled as a flat contact area at the bottom of a cutter referred to as a wear flat, and that wear flat in the past is often considered to be fixed during cutting. But during a drilling operation by a full bit that consists of multiple circular cutters, the wear flat length may increase because of various wear mechanisms involved. The wear progression of cutters generally results in reduced efficiency with either increased MSE or decreased ROP. Also, an accurate estimate of removed rock volume is found important for the evaluation of MSE. The derived model is compared with experiment results from a single circular cutter, for cutting soft rock under ambient pressure with actual depth measured through a micrometer, and for cutting high strength rock under high pressure with actual cutting area measured by a confocal microscope. Finally, the model is employed to interpret the evolution of MSE with depth of cut for a full drilling bit under confining pressure. The general form of equation of the developed model is found to describe well the experiment data and can be applied to interpret the drilling data for a full bit.