关键词: 数学模型, 抽油杆, 三维振动, 有杆泵抽油, 偏微分方程组, 抽油井, 油管, 故障诊断, 有限差分法, 非线性特征

Abstract: Three-dimensvonal vertical vibration of the sucker rod string,tubing and liquid column in the sucker rod beam pumping system has been comprehensively atudied in this paper,a new set of partial differential equations describing the movement regularity of sucker rod beam pumping system have been obtained,and numerical solution of the partial differential equations have been obtained with finite山fference technique in a manner of lineAR and non-linear analysis.This mathematical model is better theoretically than one-dimensional and two-dimensional models which take sucker rod string only or sucker rod string and liquid column(unanchored tubing) only into consideration,so it may give a powerful tool for predicting the dynamic parameters of a sucker rod pumping system and well site diagnosis can be also.