Theoretical Forces for Prescribed Motion of a Roller Bit

This paper presents a systematic method for determining The forces on a simplified roller bit. The kinematics of an actual roller bit drilling in rock is complex; nevertheless, it is desirable to obtain an accurate analytical model. As a preliminary study, the roller bit is represented here by a preliminary study, the roller bit is represented here by a simple two-dimensional bit and the rock by a Coulomb plastic material. Results from previous work, plus plastic material. Results from previous work, plus additional assumptions, are incorporated into a computer program to determine the forces required to move the bit in a specified manner. Example problems are worked by use of this program. By problems are worked by use of this program. By studying similar but less complex drilling problems and by supporting laboratory work, one could eventually obtain an accurate analytical model for drilling an actual roller bit. This could lead to the compilation of a catalog of results that, in turn, would allow selection of the optimum drill bit for any given situation. Introduction The kinematics of an actual roller bit drilling in rock is complex so complex that it is not appropriate for basic analytical study. However, it is desirable to obtain eventually an accurate analytical model of rock drilling; with such a model the optimum drill bit for any given situation could be selected. As a first step toward obtaining a model, the actual roller bit is replaced by a simplified one and the rock is idealized as a more predictable material. Previous work, with appropriate modifications, has Previous work, with appropriate modifications, has been incorporated into this study. The previous work includes force-indentation studies of single teeth, and prediction of the path of fracture in both brittle and plastic stressed material. The work presented here is based primarily on a thesis. STATEMENT OF THE PROBLEM The problem solved here is the determination of the forces on a simplified roller bit when the bit is moved in a specified manner across a rock that is assumed to behave as a Coulomb plastic material. A Coulomb plastic is a time-independent (therefore, nonviscous), non-strain-hardening material characterized by a conical yield surface. The yield envelope is determined by the cohesive strength, C, and the angle of internal friction, both of which are properties of the material. When Mohr's stress circle properties of the material. When Mohr's stress circle is large enough to be tangent to the plane-strain yield envelope, the material is assumed to flow plastically. plastically. The idealized drill bit (Fig. 1) is two-dimensional and has sharp teeth. It is driven across a flat rock surface with the bit center held a given distance above the surface (constant maximum depth of penetration). penetration). SPEJ P. 473