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在牙轮钻头与井底岩石互作用模型的基础之上，将钻头在井底作纵向往复运动的位移作为钻柱纵向振动的下端边界条件，在适当简化的条件下，利用弹性杆理论和单元法建立了钻柱在钻井过程中由于钻头与岩石互作用及钻柱的弹性变形而导致钻柱产生纵向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纵振模型。为进一步弄清钻头、钻柱在钻井过程中的实际运动规律和动力学性能，改进钻头、钻柱的设计方法，预防钻头、钻柱早期失效奠定了基础。
Based on the interaction model of roller cone bit and rock bottom, the displacement of longitudinal reciprocating motion of drill bit at bottom hole is taken as the lower boundary condition of longitudinal vibration of drill string. Under the condition of simplified and simplified, Method was used to establish the dynamic model of the drill string during longitudinal drilling due to the interaction between the drill bit and the rock and the elastic deformation of the drill string. Under given initial conditions and boundary conditions, the numerical method was used to solve the problem Longitudinal vibration model of drill string. In order to further understand the drill and drill string in the drilling process of the actual movement and dynamic performance, improve the drill, drill string design method, prevent drill bit, drill string early failure foundation.