On Lateral and Helical Buckling of a Rod in a Tubing
Bibliographic record
Abstract
Abstract The paper analyzes lateral and helical buckling of a rod sub-merged in fluid in tubing. The purpose of the paper is to revisit the controversy regarding the formula for the helical buckling load that still exists in the literature. The relation between the critical helical buckling force and the helix-pitch has been reexamined. Our analytical calculations and experimental tests confirm the results obtained by Cheatham and P.D. Pattillo(1). The effect of the pressure acting on the rod was included in the analysis to explain the so-called "fictitious forces" introduced by Lubinski(2). Introduction In the oil and gas industry, Lubinski's equation(2) for the critical buckling load for a rod in a tube has been given high credibility. However, this equation causes some controversy [see Equation (15) of the present paper]. Lubinski's equation is often used to evaluate the stability of tubes. It is also important in the analysis of the stability of sucker rods. The oil pressure and the forces resulting from pump action cause the compressive force acting on the rod at the bottom of the well. Often this compressive force causes the rod to buckle; specifically, to buckle in a helical form. The rod first buckles laterally. However, with the increase of the compressive force, the helical buckling occurs. The rod coils around the inside of the tube and the axial stiffness of the rod is reduced significantly. The buckling of the rod can produce large negative effects on the work of the pump. The helically-buckled sucker rod has muchlower axial stiffness and reduces the stroke of the plunger. The buckling-related lateral deformations cause much greater wearing of the rod, the tubing, and the pump. It is therefore important to determine the correct value of the critical buckling force. There are different opinions about Lubinski's equation. For example, J.B. Cheatham and P.D. Pattillo(1), solving the problem by means of virtual work principle, found that the critical helical buckling force is two times smaller than the force predicted by Lubinski. They are of the opinion that there are two critical force relations corresponding to loading and unloading and that the value of the real critical buckling force lies between these two forces. Y.W. Kwon(3), solving the problem using the beam-column equation, obtained a result identical to Lubinski's formula. In this paper, the lateral and helical buckling of a rod submerged in a fluid in a tube has been reexamined. Using virtual works and modifications that allow for the elimination of some approximations used in Cheatham and Pattillo's(1) work, an equation for the critical helical buckling force has been developed. This equation sets the buckling force two times lower than Lubinski's equation. The formula for the critical helical buckling load for the rod or tube submerged in a liquid has been derived for a case of constant compressive force and side surface pressure. It has been assumed that the weight of the rod is negligible as compared to other forces.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".