Mathematical Modeling and Analysis of Drill String Longitudinal Vibration with Lateral Inertia Effect

Comparative analysis whether considering the lateral inertia or not, aiming at the longitudinal vibration of the drill string in drilling progress, is proposed. In the light of the actual condition, the mechanical model of the drill string about vibration is established on the basis of the theoretical analysis. Longitudinal vibration equation of the drill string is derived from the Rayleigh-Love model and one-dimensional viscoelastic model. According to the Laplace transform method and the relationships among parameters of the model, the solutions to complex impedance at the bottom of the drill string are obtained, and then the comparison results are analyzed, which is the lateral inertia effect on longitudinal vibration characteristics. The researches show that the smaller the length of the drill string, the greater the cross-sectional area of the drill string, the greater the damping coefficient of bottom hole on the bottom of the drill string, and the more evident the effect on the dynamic stiffness of the drill string with lateral inertia effect. The Poisson ratio of the drill string only has some effects on it taking account of the lateral inertia effect, and the influence is relatively small compared with the former three conditions.