游梁式抽油机分析的数值法

A numerical method for analysis on walk-beam pumping units

当游梁式抽油机的结构比较复杂时,用解析法来分析比较烦琐,采用数值法就成为明智的选择。为此,建立了抽油机运动所满足的1组控制方程,用数值法求出一个曲柄转动周期的一系列悬点位移的离散值,利用这些离散值对悬点位移进行Fourier级数逼近,再对逼近后的表达式连续求导分别得到悬点速度和悬点加速度。在此运动分析的基础上,应用动能定理的功率方程,分别考虑游梁式抽油机各部件对曲柄输出轴扭矩的影响,得到求解曲柄输出轴扭矩的表达式。给出用数值法对常规型游梁式抽油机进行分析的例子,应用表明,数值法通用性强,精度可以控制,是一种可靠的游梁式抽油机分析方法。

When the structure of a walk-beam pumping unit is complicate, it is tedious to analyze and contrast with analytical method, while numerical method is a proper choice. Thus a group of dominating equations satisfied with the motion of pumping units are established. A series of discrete solutions of displacement with the period of crank rotation are calculated by using numerical method. The discrete values are used to conduct a Fourier progression approximation on the displacement and the approximated expressions are used calculate the velocity and acceleration. On the basis of kinematic analysis, the power equations of kinetic energy theorem are introduced to calculate the influence of each part of the beam pumping unit on the output axle torque of crank respectively, and the expressions for solving the crank output axle torque are derived. Examples are given for analyzing the conventional beam pumping units with numerical method. Application indicates that the numerical method is universal; its precision is controllable and it is a reliable method for analyzing the walk-beam pumping units.