在建立了牙轮钻头与井底岩石互作用模型的基础之上 ,将钻头与井底岩石互作用力矩作为钻柱的下端边界条件。在适当简化的条件下 ,利用弹性杆理论和单元法 ,建立了在钻井过程中由于钻头与岩石互作用和钻柱弹性变形而导致钻柱产生扭转振动的动力学模型。在给定初始条件和边界条件的情况下 ,采用数值计算方法求解了钻柱扭振模型。为进一步弄清钻头、钻柱在井底的实际运动规律和动力学性能 ,控制井眼轨迹 ,预防钻杆早期失效奠定了理论基础。 Based on the model of rock interaction between roller cone bit and bottom hole, the interaction moment between bit and bottom hole rock is taken as the lower boundary condition of drill string. Under proper simplified conditions, the dynamic model of torsional vibration of drill string due to the interaction between drill bit and rock and the elastic deformation of drill string was established by using the theory of elastic rod and the element method. Given the initial conditions and the boundary conditions, the torsional vibration model of the drill string is solved numerically. In order to further understand the drill, drill string in the bottom of the actual movement and dynamic performance, control wellbore trajectory, drill pipe to prevent the early failure of the theory laid the foundation.