Nonlinear Modeling and Qualitative Analysis of Coupled Vibrations in a Drill String

Abstract

A coupled model for axial/torsional/lateral vibrations of the drill string is presented, in which the nonlinear dynamics and qualitative analysis method are employed to find out the key factors and sensitive zone for coupled vibration. The drill string is simplified as an equivalent shell under axial rotation. After dimensionless processing, the mathematical model for coupled axial/torsional/lateral vibrations of the drill string is obtained. The Runge–Kutta–Fehlberg method is employed for the numerical simulation, and the rules that govern the changing of the torsional and axial excitation are revealed. And the stability domains of the explicit Runge–Kutta method are analyzed. Furthermore, the suggestions for field applications are also presented. It is demonstrated by simulation results that the lateral/axial/torsional vibrations exist simultaneously and couple with each other. The system will obtain a stable period motion with an axial excitation zone before the coupled vibration in the three directions, and continue to increase the axial excitation to cause the coupled vibration easily. The torsional excitation of the drill string mainly contributes to the coupled vibration in the three directions when in a specific rotation speed zone. The system is more likely to obtain a periodic motion through adjusting the torsional excitation out of this zone.