Acoustics and Signal Processing Laboratory, Department of Mechanical Engineering, Texas A&M University, 3123 TAMU, College Station, Texas 77843-3123, USA.
J Acoust Soc Am. 2013 Sep;134(3):1920-31. doi: 10.1121/1.4816539.
In order to understand critical vibration of a drill bit such as stick-slip and bit-bounce and their wave propagation characteristics through a drill string system, it is critical to model the torsional, longitudinal, and flexural waves generated by the drill bit vibration. Here, a modeling method based on a vibration transfer matrix between two sets of structural wave variables at the ends of a constant cross-sectional, hollow, circular pipe is proposed. For a drill string system with multiple pipe sections, the total vibration transfer matrix is calculated by multiplying all individual matrices, each is obtained for an individual pipe section. Since drill string systems are typically extremely long, conventional numerical analysis methods such as a finite element method (FEM) require a large number of meshes, which makes it computationally inefficient to analyze these drill string systems numerically. The proposed "analytical" vibration transfer matrix method requires significantly low computational resources. For the validation of the proposed method, experimental and numerical data are obtained from laboratory experiments and FEM analyses conducted by using a commercial FEM package, ANSYS. It is shown that the modeling results obtained by using the proposed method are well matched with the experimental and numerical results.
为了理解钻头的临界振动，如粘滑和钻头跳动，以及它们通过钻柱系统的波传播特性，对钻头振动产生的扭转、纵向和弯曲波进行建模是至关重要的。在这里，提出了一种基于两端结构波变量之间振动传递矩阵的建模方法，该矩阵位于等截面空心圆管的两端。对于具有多个管段的钻柱系统，通过将所有单个矩阵相乘来计算总振动传递矩阵，每个矩阵都是为单个管段获得的。由于钻柱系统通常非常长，传统的数值分析方法（如有限元法（FEM））需要大量的网格，这使得对这些钻柱系统进行数值分析在计算上效率低下。所提出的“解析”振动传递矩阵方法需要的计算资源明显较少。为了验证所提出方法的有效性，从实验室实验和使用商业有限元包 ANSYS 进行的有限元分析中获得了实验和数值数据。结果表明，使用所提出的方法获得的建模结果与实验和数值结果非常吻合。
