Theoretical and experimental determination of the preload as a nonlinear function of circumferential displacement for a precise sucker-rod makeup for the use of fatigue tests

Circumferential displacement (CD) based sucker-rod makeup is more reliable than the makeup using torque as there is an explicit and strict mechanical relation between preload and CD. In this study, a robust and pragmatic framework has been developed to improve the sucker-rod makeup quality by theoretically and experimentally determining the preload as a nonlinear function of CD, allowing us to minimize the risk of abnormal cracks on a rod-pin during fatigue tests. More specifically, by analyzing the dynamics on a threaded connection of a rod-sample, explicit formulae have been derived and subsequently modified with a nonlinear format as a function of CD to determine the preload. Meanwhile, the stress on a stress-relief groove (SRG) induced by an external force has also been modeled. The original model results in a large deviation of 117.5% to the experimental measurements, while the modified model yields a minor deviation of 6.1%, bringing remarkable improvements of preload prediction. Experimentally, a large number of 7/8 in (22 mm) rod samples have been made, connected with screws, and then utilized for fatigue tests. The connections of rod samples are preloaded with the CDs calculated from the modified models, i.e., such CDs are recommended as 13.5-15.1 mm and 15.1-16.3 mm, for the Grade D and Grade H sucker-rods, respectively. Meanwhile, with the recommended CDs, the fatigue-safety of the SRG is theoretically proved by employing the modified Goodman diagram method. The results of 137 fatigue tests using 7/8 in sucker-rods indicate that, such recommended CDs significantly relief abnormal cracks on the screw threads and SRGs. Compared with either the torque-controlling manner or using the CDs stipulated for sucker-rod working in oil wells, the application of CDs determined from the new model proposed in this study greatly promotes the success of fatigue tests.