Modelling of Coupled Nonlinear Axial and Lateral Vibrations of Drill Strings

Abstract

In this work a nonlinear mathematical model of coupled axial and lateral vibrations of a drill string under the effect of a longitudinal compressing force is investigated. The drill string is modelled in the form of a rotating elastic rod. To solve the model the Bubnov-Galerkin method and numerical stiffness switching method are applied. It is shown that the coupled axial and lateral vibrations of the drill string only arise at odd frequencies in Bubnov-Galerkin's expansion. Numerical analysis of the influence of the drill string geometrical and frequency characteristics on its vibrations is carried out, and the corresponding recommendations are provided.