Abstract: The spatial buckling of sucker rod in tubing is important basis to analyze rod and tubing wear in vertical pumping well. In this paper, first, the spatial buckling model of entire sucker rod is divided into three-section model, four-section model and five-section model. Then the differential equations of each section of each model are established, and the continuity conditions of the displacement, rotation angle, bending moment and the tangential shear at the connecting points are derived respectively. Finally, numerical integration method is used to solve the equations, in which the differential equations are transferred into nonlinear algebraic equations, thus, the numerical simulation of the entire bucking configuration of sucker rod string is realized. The simulation results show that, when the bump end load of the rod is much higher than the spatial buckling critical load, the five-section model is more reasonable than the three- and four-section models. The contact force, helix angle of the helical section, the length of the helical section and bottom suspend section of three- and four-section models have certain gaps with five-section model. The results errors of the distribution contact force and the length of the helical section obtained by simplified reduced order equations in previous studies are larger compared with the solution of the complete helical buckling section equation. The wear position and contact pressure are different with different subsection methods. The simulation method may provide reference for further study of rod and tubing wear and prediction of rod life.

Key words: mechanical design, sucker rod string, spatial buckling, five-section, boundary constraint, numerical integration