Nonlinear Self-Excited Vibration Mechanism for Under-Actuated Oil-Well Drilling System with Stick-Slip Vibration

Exploration of oil or gas wells is usually carried out by using drilling system. When the kilometers of drilling system is externally disturbed, the drilling system is prone to undesired stick-slip vibration of the drill-string. The stick-slip vibration of the drill-string belongs to the nonlinear self-excited vibration. In order to study the vibration mechanism, the model for the nonlinear torque on the bit by using Karnopp friction model and the two degrees of freedom model for drilling system were established. The equivalent damping torque formula and the energy variation formula of the drilling system were proposed. The mechanism of the nonlinear self-excited vibration of the drilling system was explained. The simulation results indicated that the stick-slip vibration of the drill-string was caused by the negative value of the equivalent damping force of the drilling system. The equivalent damping torque made the positive work on the system, so that the system absorbed the vibration energy from the outside, which destroyed the stability of the system equilibrium point. The feedback effect in the speed of the drill-bit regulates the system energy to maintain constant vibration without attenuation. In each vibration cycle, the energy input by the system is equal to the energy dissipated by the system. The energy absorbed by the drilling system is mainly converted into the potential energy. 油气井钻柱系统受到外部扰动容易引发非线性自激振动。以钻柱黏滑振动为例，建立了钻具与岩石间的非线性扰动扭矩模型及钻柱系统双自由度集中参数模型。首次提出了钻柱系统的等效阻尼扭矩公式和相对于平衡位置的能量公式，揭示了等效阻尼扭矩对激发钻柱黏滑振动所起的作用，探索了发生黏滑振动时钻柱系统能量的变化规律，分析了钻柱系统的非线性自激振动机理。仿真结果表明，在非线性扰动的作用下，钻柱系统出现负阻尼，等效阻尼扭矩对系统做正功，系统从外界吸收振动能量，破坏了系统平衡点的稳定性。钻具转速反馈作用调节能量输入使钻柱系统维持不衰减的持续振动，每个振动周期内系统输入的能量等于系统耗散的能量。钻具转速振幅较小时能量增加，转速振幅较大时能量减少，且钻柱系统吸收的能量主要转化为系统的势能。