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基于弹性大变形理论 ,考虑到轴力沿钻柱轴线的变化及其对钻柱弯曲变形的影响等因素 ,将受自重作用的铅垂井段钻柱在波动钻压激励下的振动转化为一个参数激励系统 ,用 Galerkin方法首次得到了描述此系统的 Mathieu方程 ,并通过将方程的解展成富里叶级数的方法 ,得到了该振动系统的动力分岔值曲线及其所包围的动力不稳定区。当钻井作业参数落在动力不稳定区时 ,钻柱将发生破坏性振动。根据钻柱的物理与几何性质及钻柱的工作状态 ,首次推导出了参数激励系统分岔参数的计算公式 ,并据此开发了相应的程序模块。该模块可以根据钻井现场的实际情况 ,提供合理的转速和钻压等作业参数 ,以避开动力不稳定区 ,改善钻柱的工作状态 ,延长其工作寿命。
Based on the large elastic deformation theory, taking into account the axial force along the drill string axis changes and its impact on the bending deformation of the drill string and other factors, will be under gravity of the vertical section of drill string vibration under fluctuating weight-pressure into a parameter The system is inspired by the Galerkin method for the first time. The dynamic bifurcation curve of the system and its dynamic instability zone are obtained by solving the equation into Fourier series. When the drilling parameters fall in a dynamic instability zone, the drill string will experience damaging vibrations. According to the physical and geometric properties of the drill string and the working status of the drill string, the formula for calculating the bifurcation parameters of the parametric excitation system is deduced for the first time and corresponding program modules are developed accordingly. According to the actual situation of the drilling site, the module can provide reasonable operating parameters such as speed and weight-on-bit to avoid the dynamic instability zone, improve the working status of the drill string and extend its working life.