The stick-slip is one of the critical problems for the scientific drilling, because it causes a crushing of the sampled layer. The present study investigates the characteristics of stick-slip phenomena of the drill pipe with the model experiments and numerical methods. The model experiments are carried out using a 1m length drill pipe model made with the Teflon. The angular velocity at the top and the bottom of the pipe are measured with the gyro sensor on some conditions of rotating speed at the pipe top and the weight on bit (load at the pipe bottom). The numerical simulations are also carried out to reproduce the stick-slip phenomena of the model experiments. The stick-slip is a kind of torsional vibration which is governed by the convection equation. By considering the boundary condition at the top and bottom of the pipe, we can obtain a neutral delayed differential equation (NDDE). The solutions of the NDDE is depend on not the initial value but the initial history of the solution, because NDDE contains a delayed function term. Therefore, it should be solved carefully to avoid the numerical error. The NDDE is solved with the 4th order Runge-Kutta scheme with very small time increment until the truncation error could be neglected. And also, we have found out that the effect of the initial history on the solution become to be very small after a certain period of time. The experimental results are compared with the numerical results under the same rotating condition. The experimental results of the stick-slip suggest that the period of the slip is mainly depend on the rotation speed at the pipe top and the magnitude of the slip is mainly depend on the weight on bit. Those characteristics of the stick-slip such as the period or the magnitude of slip are also obtained with the numerical calculations. However, in order to obtain an acceptable numerical results of NDDE, we have to adjust the frictional torque acting on the drill bit. Though, the frictional torque model was determined by reference to the measured torque at the top of the drill pipe model in the present study, it is desired to be improved. Therefore, the physical model of the frictional torque on the drill bit should be evaluated much carefully for the precise estimation of the stick slip in the future.

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