Modeling of dynamic behavior of drillstring taking rock-bit interaction into consideration

Drillstring vibration is a dangerous dynamic phenomenon mostly happened. It may result in catastrophic and costly problems, such as failure of drillstring components and also leads to the wear of bit and decreased efficiency. Various studies were carried out to analyze the behavior of the drillstring; however, few of them took the bit-rock interaction into consideration. Therefore, a better understanding of the dynamic behavior of the drillstring in the presence of bits is necessary. In this paper, a new model is developed basing on Timoshenko beam theory to describe the dynamic behavior of drillstring. Firstly, several sources of excitation in vibration are analyzed in order to figure out their influences on the vibration. Then, boundary conditions and initial conditions are presented. Afterwards, the dynamic behavior of drillstring is considered as composed of axial-torsional vibration and lateral vibration, and governing equations are gotten by analyzing the equilibrium of tiny part of drillstring. These partial difference equations in space and in time are discretized by means of the finite element method and finite difference method, respectively. A computational code in Scilab is written to solve these equations and numerical simulations with this code are performed in several situations.