Analysis of Surface Set Diamond Bit Performance (1969)

Abstract With, the assumption of perfect cleaning, a theory of the drilling performance of surface set diamond bits has been developed. The analysis is based on the previously developed theory of the cutting action of a single diamond, in which it was assumed that rock behavior during cutting may be approximated by that of a rigid-plastic, Coulomb material. With specified drilling conditions and rock formation, expressions for bit torque and bit weight are obtained in terms of bit penetration rate. Expressions also are obtained for the depths of cut of the diamonds. Note that depth of cut and diamond cutting force vary considerably over the cutting surface of the bit. Theoretical results are compared with experimental results for full hole bits and core bits. The agreement is reasonable. Introduction A theoretical analysis of single diamond cutting action on rock has been presented. Equations were established for the stress distribution on the cutting surface of the diamond, for the normal and the tangential cutting forces, and for the chip volume removed by the diamond. These relations were obtained by assuming that the principal, mode of material removal is by "ploughing", and that the rock formation may be approximated by a rigid-plastic, Coulomb material. It is pertinent to consider the drilling performance of a surface set diamond bit, since the over-all performance is determined by the total effect of the individual diamonds on the cutting surface of the bit. A complete analysis of surface set diamond bit performance should take into account the interaction performance should take into account the interaction of the drilling fluid with the mechanics of the cutting action. All material loosened by the diamonds must be carried away by the drilling fluid as it flows between the cutting face of the bit and the rock being cut. The geometry of the clearance between bit and rock is dependent on the diamond catting action as well as the bit geometry. Still there are many factors related to chip generation and removal. that are not understood, and hence, a complete analysis of bit performance including bit hydraulics effects has not been attempted. The present study relates primarily to the mechanics of cutting. It will be assumed that all of the material removed by the diamonds is immediately flushed away by the drilling fluid. The performance of a diamond bit will be determined for conditions of "perfect cleaning". Theoretical results for penetration rate will, therefore, correspond to the upper limit insofar as cleaning is concerned. Using the previous theory of cutting action, one important step remains in order to determine diamond bit performance. The depth of cut of the diamonds must be determined in terms of bit geometry and drilling rate. Most bits have a relatively large number of diamonds spaced rather closely, together. Various spacing patterns are used. However, irregularities in diamond shape and variation due to manufacturing procedures result in deviations that are as large or procedures result in deviations that are as large or larger than the average depth of cut of the individual diamonds. On a new bit it is probable that there are some diamonds that do not cut at all. It seems impractical to attempt to determine the depth of cut of each individual diamond. Statistical treatment of the depth of cut is perhaps the most desirable. Since there is a large number of cutting points, it has been assumed that the performance of the bit as a whole does not depend significantly on the exact nature of the variation in depth of cut and spacing at each radius. We assumed that at any given radius on the bit cutting surface, the diamonds are either randomly spaced or uniformly spaced and that the diamonds along the circumference at any given radius share the work equally. Also, we assume that the drilling conditions and the rock formation remain constant and that steady-state conditions prevail.