螺杆泵采油杆柱扭转振动固有频率的计算方法

Research on the mechanical model and natural frequencies of torsion vibration of the rod string of screw production systems

考虑地面驱动与传动系统转动惯量对铅垂直井螺杆泵采油杆柱扭转振动的影响,建立了顶端具有等能转动惯量Je的自由转动圆盘、下端自由的多级组合杆柱扭转振动的力学模型,给出了单级、二级与三级组合杆柱自由扭转振动固有频率的计算公式。分析结果表明,等效圆盘的转动惯量与采油杆柱转动惯量的比值Je/J0对杆柱扭转振动的固有频率有一定影响,当Je/J0=5和Je/J0=25时,基频相差7.38%。当Je/J0≥5时,固有频率随Je/J0的增加而增加,并趋近于将螺杆泵采油杆柱顶端简化成固定端时的固有频率。当Je/J0≥10时,将螺杆泵采油杆柱顶端简化成固定端所产生的基频计算误差为5%左右。对于目前实际应用的螺杆泵采油系统,采油杆柱第1阶与第2阶扭转振动的固有频率一般处于螺杆泵常用的工作转速范围内,因此应合理选择螺杆泵的工作转速或合理设计下泵深度与杆柱组合,以避免系统在基频或二次谐波共振区工作。

The affecting of rotating inertia of driving and actuating system to the torsion vibration of the rod string of screw production systems is considered, a new mechanical model of torsion vibration of the rod string is setup. The natural frequency equations of torsion vibration of the combined rod string are established. It is showed by the analysis results that the natural frequency is affected by the ratio Je/Jo. When Je/Jo =5 and Je/Jo=25, the difference between the natural frequencies is 7.38%. When Je/Jo≥5, the natural frequency increases with the increasing of Je/Jo, and the natural frequency tends to reach the natural frequency of that the top of rod string is simplified into fixed top. If Je/Jo≥10 and the top of rod string are simplified into fixed top, the calculating error of the first natural frequency is about 5%. Because the first and second natural frequencies are in the range of the working rotating speeds of present practical screw production systems, it is necessary to optimize the design of the working parameters that contain the rotating speed, pump depth and the combination of rod string and to avoid making resonance in the first and second natural frequencies.