Axial-torsional coupling vibrations are dangerous and complex vibrations that can cause abnormal working conditions in the drilling system. Therefore, the vibration mode correlation is essential in the dynamic analysis of the response complexity of the system to reduce the vibration risk level. In this paper, an axial-torsional lumped parameter model with 5-DOF (degrees of freedom) is proposed to investigate the axial-torsional mode correlation of a drill string system with non-smooth characteristics. Numerical simulations are carried out by using the 4th-5th order Runge-Kutta method with adaptive time steps, and the simulation results are compared and verified by the 5-DOF torsional lumped parameters model and field measurement data. It also performs time domain, frequency domain, and correlation coefficient analysis. The results reveal the mode shape and correlations of an axial-torsional mode in coupled vibrations with and without a bit-bounce. Bit-bounce and stick-slip coupling vibration can be produced by increasing the rotary table speed. The torsional angular velocity of the proposed model is smaller than that of the comparative model, which is in good agreement with the field data.

轴扭耦合振动是一种危险而复杂的振动，会导致钻井系统出现异常工作状态。因此，振动模态相关性在系统响应复杂度的动态分析中对于降低振动风险水平至关重要。本文提出了一种具有5自由度（自由度）的轴扭集总参数模型来研究具有非光滑特性的钻柱系统的轴扭模态相关性。采用具有自适应时间步长的4-5阶Runge-Kutta方法进行数值模拟，并通过5自由度扭转集总参数模型和现场测量数据对模拟结果进行了比较和验证。它还执行时域、频域和相关系数分析。结果揭示了轴向扭转模式在有和没有位反弹的耦合振动中的模式形状和相关性。通过提高转台速度可以产生钻头弹跳和粘滑耦合振动。所提模型的扭转角速度小于对比模型，与现场数据吻合较好。