Axial–Torsional Dynamics of a Drilling Bit with Non-uniform Blade Arrangement

Abstract

In this paper, a model for the coupled axial-torsional dynamics of a drilling bit with a non-uniform blade arrangement is proposed. The neutral-type time-delay model is used to model the drill pipes, which transfer the actuation force and torque to the bit. The employed bitrock interaction law is a rate-independent law including both cutting and frictional effects. A novel method for determining the depth of cut, which is the key component in estimating the cutting forces, is developed to capture different phenomena, including multiple-regenerative effects. In this method, a functional description of the well surface pattern is presented to determine the depth of cut. Unlike the previous studies, the well surface pattern evolution is represented by an algebraic equation rather than a partial differential equation (PDE). Illustrative simulation results are presented for a representative case study, which demonstrates the validity of the proposed model even in the presence of multiple-regenerative effects. The effect of the non-uniformly arrangement of the blades on the drilling vibration is also discussed. It is shown