钻柱动态数学模型的建立及求解

钻井用钻柱在使用过程中受力比较复杂，钻柱不仅存在纵向振动、横向振动，还存在扭转振动，并且3个振动相互耦合，用一般受力分析方法很难确定，采用能量法求出单元的动能和势能，利用拉格朗日方程建立起钻柱系统动力学有限元模型，求出了系统质量矩阵、刚度矩阵、阻尼矩阵及系统载荷矩阵，利用微分方程的数值计算方法对钻柱过程进行计算机仿真。通过研究得出了一套研究钻柱系统动力学模型及求解方法，。对新形钻柱的设计和钻井力学的研究具有指导意义。

Dynaical Mathematical Model of String

In the process of oil drilling, drilling string and rock bit are main drilling tools. The fact of their failure would cause serious accidents. To solve this problem, the vibration law of string should be found. The longitudinal vibration model, torsional model and lateral vibration model are founded simultaneity. Many methods are used to build up this model, including finite element technique, numerical technique and computer simulation. The dynamic model reveals the dynamic action of string, it is instructive to design new rock bit and study drilling mechanics.