Forward and backward natural frequencies of a drill string for different boundary conditions

The main goal of this research is to analyze the effect of angular velocity on forward and backward natural frequencies of a drill string for different boundary condition. To this end, non-dimensional kinetic and potential energies are written while lateral vibration, centrifugal force, shaft moment inertia, gyroscopic effect and bending deformation by Euler-Bernoulli theory are considered. Finite element method is employed to discrete the formulations andvibrational equations are derived by Lagrange method. These results represent the significant effects of centrifugal terms and rotational speed. Also the effects of different boundary conditions and slenderness ratio are examined. Increasing rotational speed leads to decreasing of forward and backward natural frequencies. In addition, instability threshold of a drill string is investigated. These formulations can be used to choose the safe working conditions for a drill string

Keywords:

drill string , vibration , forward and backward natural frequencies