To clarify the effects of the contact between a drill string and a borehole wall

the torque dissipation of the drill string

and the borehole’s trajectory on the dynamic characteristics of a drill string system

the lateral and torsional coupled nonlinear dynamic model of the drill string in an inclined well is established with the Lagrange equation. The contact behavior between the drill string and the borehole wall is modeled with the linear elastic contact model. Then

the discrete torque-drag model is used for describing the transfer characteristics in the drill string system. Finally

the dynamic properties of the drill string system are determined through numerical simulations. The simulation results indicate that the friction losses of the torque in the drill string system increase with the increasing inclination angle. The stick-slip vibration of the drill string is obvious when the inclination angle of the inclined well in its inclined part becomes big. The effect of the dead weight of the drill string on the vibration of the drill string system is significant as the inclination angle of the inclined well's trajectory becomes big.