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

Objective To propose a model for the coupled axial-torsional dynamics of a drilling bit with a non-uniform blade arrangement and to investigate the effects of multiple-regenerative effects and blade arrangement on the drilling vibration. Methods 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 bit-rock 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). Results 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 that the non-uniform arrangement of the cutting blades can reduce the vibration amplitude in some operating conditions. Conclusions The proposed model can capture the coupled axial-torsional dynamics of a drilling bit with a non-uniform blade arrangement and account for multiple-regenerative effects. The non-uniform arrangement of the cutting blades can be beneficial for reducing the drilling vibration in some cases. Disregarding the multiple-regenerative effects in the model can cause a considerable modeling error.