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Abstract: In this paper a nonlinear model was developed for a drillstring system in deviated well with axially moving motion and axial loading, using the perturbation techniques. The drillstring was considered as a simply supported axially moving rotor. Governing equations of motion were obtained based on Hamilton''s principle and method of multiple scales was employed to solve the nonlinear motion equations in order to obtain the steady state response and stability region of the system. Then the effects of rotating speed, axial compression load, imbalance mass and nonlinear fluid force on the drillstring responses were investigated in detail and nonlinear natural frequencies and their corresponding mode shapes were presented. Analytical and numerical results reveal the rich and interesting nonlinear phenomena such as primary and parametric resonance that is being investigated for the first time in this study on the nonlinear vibration of the drillstring system. Finally in effort to validate the theoretical approach employed in this study, the numerical solutions obtained here were compared with a set of existing experimental data. [Copyright &y& Elsevier]

Abstract: This paper studies self-excited stick-slip oscillations of a rotary drillstring with a drag bit. In previous researches coupling between torsional and axial vibration was studied for a system with two degrees of freedom and without considering the effects of rotary table, damping of drilling mud and active damping system. In this research, for the first time a complete model is considered. This model is a discrete model with two degrees of torsional freedom and one degree of axial freedom. Both frictional contact and cutting process at bit-rock interface have been considered by bit-rock interaction law. There is a coupling between torsional mode and the axial mode through this law. In this paper, the effects of damping, active damping ratios and bit-rock interaction number have been studied on stick-slip motion. The equations of motion have been solved by numerical method. The technique of solution is Euler-forward finite difference technique. This research shows that by increasing the damping of drilling mud, bit parameter and by appropriate selection of active damping ratios, stick-slip oscillation of bit can be avoided and oscillation of rotary table be damped. [Copyright &y& Elsevier]