Two-Dimensional Study of Rock Breakage in Drag-Bit Drilling at Atmospheric Pressure
Authors: Gray Kenneth E. , Armstrong Frank , Gatlin Carl 
Published: December 2007

Abstract
This paper presents some preliminary results of two-dimensional cutting tests of dry limestone samples at atmospheric pressure. Cutting tips having rake angles of + 30, + 15, 0, –15 and - 30 were used to make cuts on Leuders limestone samples at six depths of cut ranging from .005 to .060 in. at cutting speeds of 15, 50, 109 and 150 ft/min. The vertical and horizontal force components on the cutting tips were recorded with an oscilloscope equipped with a polaroid camera. Motion pictures of the cutting process at camera speeds of 5,000 to 8,000 frames/sec were taken at strategic points in the variable ranges. The movies provide considerable insight into the brittle failure mechanism in rocks. It appears that chip-generating cracks usually have an initial orientation which is related to the resultant of the externally applied forces. The latter part of the crack curves upward toward the free surface being cut, this part being governed by some type of cantilever bending or prying. The linear and angular motion of the loosened chips also indicate the tensile nature of brittle failure. Analyses of the forces on the cutting tips indicate that:relatively small increases in vertical loading result in large cut-depth increases for sharp tips (rake angles 0 degrees);tool forces increase at an increasing rate as the rake angle decreases, particularly for rake angles less than 0 degrees; andfor the range of this study, rate of loading had little effect on the maximum forces.
Both the movies and visual inspection of the cuttings indicated that the volume of rock removed by chipping was much larger than that by any grinding mechanism, even for tips having negative rake angles. Cutting size increases with increased cut depth and rake angles, and decreases slightly at high cutting speeds, the depth of cut having by far the most influence. The amount of contact between the rock and the cutting tip was always less than the depth of cut and rarely exceeded 0.010 in. even for cuts of 0.060 in.

Introduction
The planing (or slicing) of various materials with a fixed blade has long been practiced by workers' in many industries. For example, the farmer's plow, the carpenter's plane and the housewife's paring knife all employ this basic action. The casual observer might suspect that something so common must be quite simple; however, as in all problems involving the failure of materials, such is not the case. Industries concerned with the machining of metals have long studied these problems, and their literature on the subject is voluminous. Despite these efforts, basic knowledge is not very advanced, as may be noted from recent and comprehensive analyses of their literature. Metals are more subject to analysis by classical theories of elasticity and/or plasticity than are rocks, since their elastic constants and strengths are reasonably well established in many cases. In spite of this relative "simplicity", Hill prefaces his discussion with an admission that the mathematical solution to the machining problem is not known. Photoelastic studies of both machining and milling have been performed and are discussed thoroughly by Coker and Filon. Rotary drilling of rocks with fixed blade or drag bits has long been practiced by the mining and petroleum industries, and considerable study has been given to defining their cutting action in terms of the pertinent variables. Essentially all the published mechanistic research on drag-bit drilling has been performed by mining engineers and has been concerned only with rocks in the brittle state. Fairhurst has worked extensively in this area and employed photographic techniques quite similar to those reported here, except at much lower speeds. His studies showed the periodic or cyclical nature of the brittle failure mechanism, in which instantaneous loads on the bit varied from some maximum value to near zero. Goodrich has presented further data on the subject as well as a qualitative description of the process. Again the postulated mechanism is cyclical, with alternate chipping and grinding periods. The ploughing of coal is a practiced method and has been studied in some detail by English mining engineers. Their findings have considerable general application to drag-bit drilling. Evans, in particular, has extended Merchant's metal-cutting theory to brittle materials with some success, although certain aspects of his theory are open to question.
JPT
P. 93^