Nonlinear analysis of axial-torsional vibration of drill string based on a 3 DOF model

Based on a model with three-degree-of-freedom, the nonlinear coupled axial-torsional vibration of drill string is numerically studied considering a modified contact model of bit-rock interaction. The effects of driving angular velocities, nominal drilling pressures, and formation stiffness on response are discussed. The simulation results show that response can be periodic, quasi-periodic or chaotic motion with the variation of system parameters. Increasing driving angular velocity is helpful to reduce the duration of sticking and even make the system stick-slip free. However, bit-bounce may occur if driving angular velocity is too large. Increasing nominal drilling pressure can cause the system to be more prone to stick-slip, but it has dampening effect on bit-bounce. The larger the formation stiffness is, the smaller the amplitude of the axial vibration response of the system is, and the driving angular velocity corresponding to the maximum amplitude of the axial vibration response is also larger, whereas the variation of the amplitude of torsional vibration is smaller. Compared with the results from two-degree-of-freedom model, the amplitude of torsional vibration of the present model is remarkable greater. Meanwhile, the present model is more prone to stick-slip than the one with two-degree-of-freedom, and it is not easy to bit bounce.