H. Ahmadian - Department of Mechanical Engineering, Iran University of Science & Technology, Tehran.
S. Nazari - Department of Mechanical Engineering, Iran University of Science & Technology, Tehran.
H. Jalali - Department of Mechanical Engineering, Iran University of Science & Technology, Tehran.

The governing equations of motion for a drill string considering coupling between axial, lateral and torsional vibrations are obtained using a Lagrangian approach. The result leads to a set of non-linear equations with time varying coefficients. A fully coupled model for axial, lateral, and torsional vibrations of drill strings is presented. The bit/formation interactions are assumed to be related to the following parameters: bit motion, effects of gyroscopic moments, contact with the borehole wall, axial excitation due to bit/formation interactions, and hydrodynamic damping due to the presence of drilling mud. Simulation results show that parametric resonance and whirling may occur simultaneously within the range of operating conditions of drilling. The contact force between collar and borehole wall is calculated and its behavior is investigated. The dynamic behavior is quite complicated and may become non-periodic, suggesting a chaotic behavior.

Drill string, Critical speed, Whirling, Parametric resonance, Coupling effects