In this paper, the nonlinear vibration of a time-space coupled axial and torsional drill string system is investigated. Considering the surface morphology of rock, top drive system and mud, the drill string system is discretized by finite element method. The dynamic equations of the fully discrete drill string system based on rock surface morphology (SM) is established. Based on the surface morphology and strength of rock, the concept of rock surface state matrix is proposed. The stability and time domain response of the system are obtained by numerical simulation and compared with the multiple regeneration (MR) model. The results show that stick slip vibration and bit reversal are more likely to occur when drilling system cuts unhomogeneous rock, and stick slip vibration is the main reason to cause the drill bit impact rock. The stable driving torsional speed is lower than that of calculated by conventional models. In the calculation process, the volume conservation accuracy of the SM model is higher than that of the MR model. Moreover, the numerical convergence and efficiency of SM model are higher than that of MR model.

本文研究了时空耦合轴向和扭转钻柱系统的非线性振动。考虑到岩石，顶部驱动系统和泥浆的表面形态，采用有限元法离散化了钻柱系统。建立了基于岩石表面形态学（SM）的全离散钻柱系统动力学方程。根据岩石的表面形态和强度，提出了岩石表面状态矩阵的概念。通过数值模拟获得了系统的稳定性和时域响应，并与多再生（MR）模型进行了比较。结果表明，当钻井系统切割非均质岩石时，更容易发生粘滑振动和钻头反转，而粘滑振动是引起钻头冲击岩石的主要原因。稳定的驱动扭力速度低于传统模型计算出的扭力速度。在计算过程中，SM模型的体积守恒精度高于MR模型。而且，SM模型的数值收敛性和效率均高于MR模型。