Stress Analysis Of Bent Sucker Rods

Abstract

Abstract This paper describes an elastic analysis which can be applied to bent sucker rods to determine the effect of this imperfection on the stress behaviour or load-carrying capacity of the rod. It is shown that if the location of the bend in the rod is close to the sucker rod coupling, then high stresses can occur on the surface of the bend and this can seriously reduce the working capacity of the rod. Also, it is shown that for rods with bends in them a significant compressive stress can occur at the bend even though the rod is subjected to a large axial load. Experimental results are shown to agree quite favourably with the theory. The problem of residual stresses in the rod is also discussed and a mechanism for analyzing this, problem is described along with some experimental results. Introduction A sucker rod passes through many operations and handling procedures from the time it originally takes its shape in the manufacturing industry until it is placed in a well in the field. To what extent do bends in a sucker rod influence the life of that rod when placed down a well? When a rod is permanently bent, plastic deformation has taken place; this not only reduces the flexibility of the rod, but, in the area of the, bend, the residual stresses can accelerate corrosion. The object of this paper is to describe a means of evaluating the significance of bends on the -elastic behaviour of a sucker rod and provide a design formula for use in determining an acceptable degree of bend. Some experimental results are also presented which show the extent of plastic deformation that has occurred as a function of observable bends in a rod. Theoretical Considerations In the theoretical analysis, it was assumed that the initial shape of a bent rod could be represented by two straight lines, A-C and C-B, which meet at an apex called the bend position. The bend position is identified by dimension "a" and its location from one of the ends "c", as shown in Figure 1. It was also assumed that such a rod was bent before final heat treatment and therefore no residual stresses would be present when an axial load was applied. Thus, the analysis is a simple one of elastic behaviour of an initially bent circular rod. When the rod has been bent after heat treatment, there will be residual stresses and the total stress picture must be obtained by considering the elastic stresses added to the residual stresses. This is discussed in the treatment of the experimental program. The procedure for the elastic analysis was based on attempting to provide a mathematical model which could be checked by experiment. Because the experimental apparatus available for loading a sucker rod was limited to one of the testing machines in the laboratory it meant that the segment of the rod had to be kept within 6 feet.