Analysis of Drill-String Nonlinear Dynamics Using the Lumped-Parameter Method

Symmetry, vol. 14, pp. 1495

Abstract

This work aims at studying the nonlinear dynamics of drill strings using the lumped-parameter method (LPM). The study is based on the good consistency of the results of the test problem where the model of the longitudinal vibrations of a horizontal drill string with a static compressive load at the left end is considered. In this paper, this method is applied to discretize linear and nonlinear models of the lateral vibrations of a vertical drill string under the effect of a supersonic gas flow. The obtained results are verified with the previously published data. The optimal number of the drill-string partitions is determined using the developed application, which allows us to estimate the accuracy of the loaded data. The numerical solution of the model is obtained using the fourth-order Runge–Kutta method. The optimization of the numerical algorithm using parallel-programming tools is carried out, and the efficiency of the method is analyzed.

Authors 4

1. Lelya Khajiyeva

   Al-Farabi Kazakh National University

   Affiliation as printed

   Department of Mathematical and Computer Modelling, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan

2. Igor V. Andrianov corresponding Aachen Institute of General Mechanics chair

   RWTH Aachen University

   Affiliation as printed

   Chair and Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, D-52062 Aachen, Germany

3. Yuliya F. Sabirova

   Al-Farabi Kazakh National University

   Affiliation as printed

   Department of Mathematical and Computer Modelling, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan

4. Askar K. Kudaibergenov

   Al-Farabi Kazakh National University

   Affiliation as printed

   Department of Mathematical and Computer Modelling, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan