考虑横向惯性效应的钻柱纵向振动特性研究

Longitudinal Vibration of Drilling String with Transverse Inertia Effect

在理论分析的基础上,提出利用改进Rayleigh-Love杆模型,研究考虑横向惯性效应的钻柱纵向振动问题。根据钻柱实际工作情况,以钻柱整体为研究对象,假设钻柱为能被分成若干个有阻尼特性的Rayleigh-Love杆,以及钻柱内外的钻井液为性质相同的弹性层,据此建立其力学模型和振动微分方程;利用模型中的边界条件和参数之间的关系,得到钻柱底部复阻抗的求解方法,求出钻柱底部动刚度的具体表达式;并分析了不同相关参数对钻柱动刚度的影响。研究结果表明:钻柱动刚度随着频率的增大呈现振幅逐渐增大的周期性变换规律;其他相关参数保持不变,频率相同时,动刚度的绝对值与钻柱长度成反比,与钻柱横截面面积成正比;阻尼系数越大,导致井底对钻柱的作用力也越大,钻柱动刚度的振幅反而越小;钻柱的泊松比越大,随着频率的增加,动刚度的变化周期越长。

The longitudinal vibration of the drill string is the principal factor causing drill bit failure and drill pipe wear, on which the transverse inertia effect has an important influence. Based on this point, the longitudinal vibration control of drilling string is studied considering its lateral inertial effect by using the Rayleigh-L0ve rode model. Assuming that the drilling string can be divided into several parts with material damping of Rayleigh-Love rod, and drilling fluid around drill string are elastic layers with common attributes. According to the actual working condition of drilling string and regarding the whole drill string as the object, simplified mathematical models and vibration equations are established. According to the relationships between parameters and the boundary conditions of the models, we obtain the solutions to complex impedance and the differential equations of dynamic stiffness at the bottom of the drill string, and the influences of different parameters on the dynamic stiffness of drill string are analyzed by MATLAB. The results show that dynamic stiffness of the drilling string increases gradually with the frequency in the form of periodic change, while the vibration period increases; when other related parameters remain unchanged, the absolute value of dynamic stiffness increases with the increase of the length and cross- sectional area of the drill string ; damping coefficient is bigger, which means that the force of bottom-hole to drilling string is bigger, so the amplitude of dynamic stiffness is smaller; when Poisson＇s ratio increases, its dynamic stiffness period increases with the frequency.