Vibration characteristics of the drill string subjected to spinning motion and multiple stabilizers by means of Green's functions

Abstract

This article analyzes the vibration characteristics of the drill string system with elastic boundary conditions and stabilizers. According to Hamilton's principle, the dynamic equations of the drill string system are established. The expressions of the mode shapes and frequency equations of the transverse vibration of the drill string without stabilizer are obtained by using the Laplace transform. Similarly, the Laplace transform is used to obtain Green's functions of the transverse vibration of the drill string system with stabilizers, and the mode shapes and frequency equations of the transverse vibration of the drill string with stabilizers are obtained by means of the linear superposition principle. The analytic form mode shapes and closed form frequency equations of the drill string subjected to spinning motion and multiple stabilizers obtained in this paper have high accuracy. Taking a drill string simply supported at both ends as an example, the effects of internal flow velocity, viscous damping coefficient, the positions of stabilizers, number of stabilizers, and the stiffness coefficients of stabilizers on the natural frequencies and mode shapes of the system are discussed. The results show that the number, position, and stiffness coefficient of stabilizers have significant effects on the frequency characteristics of the drill string.