钻柱力学特性分析的剪变形理论

Shearing deformation theory for mechanical behavior analysis of drill string.

在现有三维空间钻柱力学基本方程的基础上 ,考虑横向剪应力和剪应变两因素对钻柱挠曲变形的作用 ,参照S P Timoshenko剪切梁理论 ,针对空间钻柱受力与变形特征 ,引入 ψN 和ψB2个广义位移函数 ,建立了钻柱力学剪变形理论的通用基本方程。以某水平井一单跨钻柱两端简支情况下的二维横向振动为具体算例 ,给出了计算公式。该公式综合描述了横向剪切变形和轴向钻压对钻柱横向振动固有频率的影响 。

Based on the existing 3-D mechanical equation of drill string, considering the influence of lateral shearing strength and shearing strain on flexural deflection of drill string, the universal basic equations for the shearing deformation of drill string are established according to the deformation and force characteristics of the drill string. Two ideal displacement functions,ψ N and ψ B,are introduced to the equations. An example of calculation is presented, and relevant calculating equation is given. This equation describes comprehensively the influence of lateral shearing deformation and axial WOB on the natural frequency of the lateral vibration of the drill string, and it is a supplyment of the existing basic mechanical theory of the drill string.