Forced vibration analysis of an axially moving and spinning drill string system based on Green’s functions

A drill string is a critical structural component in the petroleum industry, subject to various influences such as high temperature, high pressure, torsional forces, drilling fluids, and frictional interaction at the drill bit during operation, especially the frictional interaction at the drill bit, which produces complex friction torques or forces that could induce stick-slip vibrations and complicated nonlinear vibrations of the drilling string. This paper formulated a systematically novel nonlinear dynamic model of a drill string that considered combined effects of axially moving and spinning motions, the frictional interaction at the drill bit, and internal and external drilling fluid circulation. For the aim of investigating the combined effects of axially moving and spinning motions, a degenerated linear dynamic model of the axially moving and spinning drill string (ASDS) is studied analytically. A novel aspect of this work is that firstly the effects of axially moving and spinning motions, with both internal and external drilling fluid circulation on forced vibration of the drill string are all considered. The extended Hamilton principle is used to establish the systematical nonlinear dynamic model of the drill string. The Green’s function and the Laplace transform are then applied to obtain the fundamental solution of the vibration equation, which is general and can be adapted to various boundary conditions. In the numerical results section, the effectiveness of the proposed method is validated by comparing it with existing results from references. The influence of factors such as axially moving velocity, spinning velocity, internal drilling fluid velocity, and the viscous damping coefficient on the vibration response of the drill string is discussed, providing a theorewtical basis for the vibration control of drill strings.