钻柱纵向振动模型的建立及求解方法

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。

THE METHOD OF SOLUTION AND ESTABLISHMENT FOR AXIAL VIBRATION MODEL OF DRILLING STRING

Based on the interaction model of bit and formation, the force caused by rock and bit is defined as the bottom boundary condition of drilling string. Under some simplified condition and by means of elastic bar theory and unit method, the axial vibration model according to interaction between bit and formation and elastic deformation of drill string is established during drilling process. Based on the boundary condition and initial condition, the axial model is soluted by difference methods. It is a theoritical foundation for further understanding of the dynamic behavior and kinetics rule of drilling string and rock bit, modifying design method, controlling well track and preventing failure early.