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`Page 1 of 66
`
`Petitioners' Exhibit 1015
`John Crane v. Finalrod
`IPR2016-01786
`
`
`
`

`
`Issued by Sandia National Laboratories, operated for the United States
`Department of Energy by Sandia Corporation.
`NOTICE: This report was prepared as an account of work sponsored by an
`agency of the United States Government. Neither the United States Govern-
`ment nor any agency thereof, nor any of their employees, nor any of their
`contractors,
`subcontractors. or
`their employees, makes any warranty.
`express or implied, or assumes any legal liability or responsibility for the
`accuracy, completeness, or usefulness of any information, apparatus, prod»
`uct, or process disclosed. or represents that its use would not infringe pri-
`vately owned rights. Reference herein to any specific commercial product,
`process, or service by trade name, trademark, manufacturer, or otherwise,
`does not necessarily constitute or imply its endorsement, recommendation,
`or favoring by the United States Government, any agency thereof, or any of .
`their contractors or subcontractors. The views and opinions expressed
`herein do not necessarily state or reflect those of the United States Govern-
`ment, any agency thereof, or any of their contractors.
`
`Printed in the United States of America. This report has been reproduced
`directly from the best available copy.
`
`Available to DOE and DOE contractors from
`Office of Scientific and Technical Information
`P.O. Box 32
`Oak Ridge, TN 37831
`
`Prices available from (615) 576-8401. F’l‘S 626-8401
`
`_ Available to the public from
`National Technical Information Service
`U.S. Department of Commerce
`5235 Port Royal Rd
`Springfield, VA 22161
`
`NTIS price codes
`Printed copy: A04
`Microfiche copy: A01
`
`Page 2 of 66
`
`

`
`SAND97-1652
`Unlimited Release
`Printed September 1997
`
`.
`
`Distribution
`Category UC-122
`
`Finite Element Analysis of Sucker Rod Couplings with
`Guidelines for Improving Fatigue Life
`
`Edward L. Hoffman
`Engineering and Structural Mechanics Division
`Sandia National Laboratories
`
`Albuquerque, New Mexico 87185
`
`Abstract
`
`The response of a variety of sucker rod couplings to an applied axial load was simulated using
`axisymmetric finite element models. The calculations investigated three sucker rod sizes and
`_ various combinations of the slimhole, Spiralock, and Flexbar modifications to the coupling. In
`addition, the effect of various make-ups (assembly tightness) on the performance of coupling
`was investigated. The make-up process, based on measured circumferential displacement of
`the coupling from a hand-tight position, was simulated by including a section of an axially
`expanding material in the box section which, when heated, produced the.desired mechanical
`interference which would result from making-up the coupling. An axial load was applied to
`the sucker rod ranging from -5 ksi to 40 ksi, encompassing three load cycles identified on a
`modified Goodman diagram as acceptable for indefinite service life of the sucker rods. The
`simulations of the various coupling geometries and mal<e—ups were evaluated with respect to
`how well they accomplish the two primary objectives of preloading threaded couplings: (1) to
`lock the threaded coupling together so that it will not loosen and eventually uncouple, and (2)
`to improve the fatigue resistance of the threaded connection by reducing the stress amplitude
`in the coupling when subjected to cyclic loading. A coupling will remain looked as long as the
`mating surfaces of the pin and box sections remain in compression, resisting rotational motion
`or loosening. The fatigue evaluation was accomplished in two parts: nominally and locally. In
`the nominal evaluation, a set of equations based on the gross dimensions of the coupling were
`derived which describe how a load applied to a sucker rod is distributed throughout a
`preloaded coupling. The local fatigue evaluation characterized the fatigue performance of the
`various couplings using the local stresses predicted in the finite element simulations and a
`stress equivalencing criterion for multiaxial stress states. This criterion is based on Sines’
`equivalent stress theory which states that the permissible effective alternating stress is a linear
`function of the mean hydrostatic stress. Perhaps the most significant finding in this study was
`the characterization of the coupling parameters which affect these two stress measures. The
`mean hydrostatic stress, which determines the permissible effective alternating stress, is a
`function of the coupling make-up. Whereas, the alternating effective stress is a function of the
`relative stiffnesses of the pin and box sections of the coupling and. as long as the coupling
`does not separate, is unaffected by the amount of circumferential displacement applied during
`make-up. The results of this study suggest approaches for improving the fatigue resistance of
`sucker rod couplings.
`
`
`
`Page 3 of 66
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`

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`Page 4 of 66
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`

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`Contents
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`2.1 Finite Element Model of the Coupling Geometry . . .
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`2.2 Preload of Sucker Rod Couplings . .
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`2.3 Materials and Load History .
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`2.4 Summary of Analysis Cases . . .
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`Analysis Results . .
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`3.1 Yielding in the Sucker Rod Coupling .
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`3.2 Load Distribution in Threaded Coupling During Load Cycling . . . . . . . . .
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`3.3 Estimating Fatigue Life of Sucker Rod Couplings . . .
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`3.3.1 Considerations in Life Prediction .
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`3.3.2 Fatigue Damage Criterion for Multiaxial Stress ..................... .
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`Identification of Critical Fatigue Locations . . . . .
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`3.3.4 Equivalent Stress at Critical Locations .
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`Root ofLast Engaged Box Thread ................... .f. ...... ..s3
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`3.3.5 Effect of Make-up on Service Life .
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`4 Conclusions and Recommendations . . .
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`References .
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`' Distribution .
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`Page 5 of 66
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`

`
`Figures
`
`Figure 1.
`
`Illustration of sucker rod pump.
`
`Figure 2.
`
`Threaded pin and shoulder at each end of the sucker rod.
`
`9
`
`10
`
`Figure 3. Modified Goodman diagram for allowable stress and range of stress for sucker rods
`in non-corrosive service.
`11
`
`Figure 4. Detailed illustrations of the 7/8-inch coupling, with dimensions of the coupling and
`the threads.
`'
`12
`
`Figure 5. Axisymmetric finite element model of 7/8 inch sucker rod coupling, showing the
`pin and box sections.
`13
`
`Figure 6. Existing sucker rod coupling designs and proposed design modifications under
`investigation.
`
`14
`
`Figure 7. Modified Goodman diagram for API Grade C carbon steel, identifying load cycles
`and extreme loads selected for analysis.
`16
`
`Figure 8. Von Mises stress distribution (ksi) in the 7/8-inch API standard coupling (Analysis
`1) at preload, maximum compression, and maximum tensile loads.
`“
`19
`
`Figure 9. Von Mises stress distribution (ksi) in the 7/8-inch Spiralock coupling (Analysis 12)
`at preload, maximum compression, and maximum tensile loads.
`A
`20
`
`Figure 10.
`
`Illustration of sucker rod coupling.
`
`Figure 11. Pin load and coupling force as a function of axial load for the 3/4, 7/8, and
`1-inch coupling sizes (S6, S7, and S8, respectively).
`
`21
`
`26
`
`Figure 12. Pin load and coupling force as afunctiou of axial load for the 7/8-inch standard API
`coupling size (S7) with make-ups of 0.0, 1.0, and 1.5.
`27
`
`Figure 13. Pin load and coupling force as‘ a function of axial load for various combinations of
`.
`the Flexbar (FB), Spiralock (SL), and slimhole (SH) geometry modifications to the
`base geometry (S7).
`29
`
`Figure 14. Pin load and coupling force as a function of axial load for the base geometry (S7)
`with Spiralock threads (SL) and make-ups of 0.0, 1.0,1.5, 2.0. 2.5, and 3.0.
`30
`
`Figure 15. Schematic S-N curves for steel at various stress ratios.
`
`Figure 16. Maximum principal stress directions in the 7/8-inch API standard coupling at
`minimum (-5 ksi) and maximum (40 ksi) loads.
`
`34
`
`35
`
`Figure 17. Distribution of the fatigue safety factor with respect to indefinite service life for the
`7/8-inch API standard coupling subjected to the three load cycles.
`39
`
`Figure 18. Distribution of the effective alternating stress in the 7/8-inch API standard
`'
`coupling subjected to the three load cycles.
`
`40
`
`Figure 19. Distribution of the hydrostatic mean stress in the 7/8-inch API standard coupling
`subjected to the three load cycles.
`41
`
`6
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`Pae 6 of 66
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`Page 6 of 66
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`

`
`Page 7 of 66
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`

`
`Figure 20. Difference between the effective alternating stress and the alternating effective
`stress in the 7/8-inch API standard coupling subjected to the threeload cycles. 42
`
`Figure 21. Von Mises and hydrostatic stress at the root of the first engaged pin thread as a
`function of applied axial load for various coupling sizes.
`
`45
`
`Figure 22. Von Mises and hydrostatic stress at the root of the first engaged pin thread as a
`function of applied axial load for various make-ups of the 7/8-inch API coupling.
`46
`
`Figure 23. Von Mises and hydrostatic stress at the root of the first engaged pin thread as a
`function of applied axial load for various combinations of the Flexbar (FB),
`slimhole (SH), and Spiralock (SL) modifications to the base coupling (S7).
`
`47
`
`Figure 24. Von Mises and hydrostatic stress at the root of the first engaged pin thread as a
`function of applied axial load for the Spiralock coupling with make-ups of 0.0, 1.0,
`1.5, 2.0, 2.5, and 3.0.
`49
`
`Figure 25. Von Mises and hydrostatic stress at the pin neck as a function of applied axial load
`for various coupling sizes.
`50
`
`Figure 26. Von Mises and hydrostatic stress at the pin neck as a function of applied axial load
`for various make-ups of the 7/8-inch API coupling.
`51
`
`Figure 27. Von Mises and hydrostatic stress at the pin neck as a function of applied axial load
`for various combinations of the Flexbar (FB), slimhole (SH), and Spiralock (SL)
`modifications to the base coupling (S7).
`52
`
`Figure 28. Von Mises and hydrostatic stress at the pin neck as a function of applied axial load
`for the Spiralock coupling with make-ups of 0.0, 1.0, 1.5, 2.0, 2.5, and 3.0.
`54
`
`Figure 29. Von Mises and hydrostatic stress at the root of the last engaged box thread as a
`function of applied axial load for various coupling sizes.
`Figure 30. Von’ Mises and hydrostatic stress at the root of the last engaged box thread as a
`function of applied axial load for various make-ups of the 7/8-inch API coupling.
`57
`
`55
`
`Figure 31. Von Mises and hydrostatic stress at the root of the last engaged box thread as a
`function of applied axial load for various combinations of the Flexbar (FB),
`slimhole (SH), and Spiralock (SL) modifications to the base coupling (S7).
`
`58
`
`Figure 32. Von Mises and hydrostatic stress at the root of the last engaged box thread as a
`function of applied axial load for the Spiralock coupling with make-ups of 0.0, 1.0,
`1.5, 2.0, 2.5, and 3.0.
`59
`
`Figure 33. Fatigue safety factor distribution in the 7/8-inch Spiralock coupling (with make-
`ups of 1.0, 1.5, and 2.0) subjected to the full axial load range (-5 ksi to 40 ksi). 61
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`1
`
`Introduction
`
`Oil and gas production in the US has reached a point where significant effort is required to
`forestall declining production and stop the abandonment of significant unproduced resources.
`New technology developments are needed. However, because lifting costs are high relative to
`oil prices, the petroleum industry is downsizing and investing less effort in the development of
`new technology. The goal of Sandia National Laboratories’ Applied Production Technology
`(APT) project is to extend the life of marginally economic wells by reducing the negative
`impacts of persistent production problems. The approach is to use “Sandia Technology” to
`rapidly diagnose industry-defined production problems and then propose or develop improved
`technology utilizing the capabilities of industry. One task of the APT project
`is the
`investigation of sucker rod and sinkerbar failures. Sucker rods and sinker bars are the primary
`components of rod pumping systems, the most common artificial lift technology utilized in
`domestic oil production. Thus, high sucker rod failure rates have a large economic impact on -
`the domestic oil industry and threaten the domestic oil reserves with high abandonment rates.
`If the level of technology and understanding of the rod pumping system can be increased,
`there will be significant benefit to both the domestic industry and domestic energy security.
`
`illustrated in
`A sucker rod pump,
`Figure 1, brings underground oil
`to
`the earth's surface. The primary drive
`motor turns a flywheel with a crank
`arm. Attached to the crank arm is a
`Pitman Ann which links the crank to
`
`the walking beam. The walking bean
`is a lever arm which pivots at
`its
`midsection. At the other end of the
`
`walking beam is the horsehead. A
`hanger cable hangs off the horsehead
`and is clamped to the rod string. This
`mechanism converts
`the
`rotary
`motion of the drive motor
`to a
`
`translational pumping motion. Two
`valves are ‘used to maintain the
`
`direction of flow. A traveling valve,
`often just a ball in a cage, is attached
`to a plunger at the end of the rod
`string. At the base of the well is a
`stationary valve (another ball
`in a
`cage) called a standing valve.
`
`The rod string, capable of reaching
`lengths of over 10,000 ft, consists of
`individual sections of steel rods called
`
`.--Tubinfl
`
`Rod String
`
`Traveling Valve
`Standing Valve
`
`sucker rods. Sucker rods come in
`bngths ranging from 25 to 30 ft and
`
`_
`Figure 1.
`
`.
`Illustration of sucker rod pump.
`
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`nominal diameters ranging from 0.5 to 1.125 inches. Each rod contains a threaded pin at each
`end as shown in Figure 2. Threaded couplings, known as boxes, are used to connect the sucker
`rods to produce the rod string. These pin and box coupling are tightened to a specified
`preload, known as the joint make-up, so that it will not loosen during normal operation.
`
`In addition to supporting the pumping forces, each sucker rod must be strong enough to
`support the weight of the rods below it. Hence, loads are greater on the sucker rods farther up
`the rod string. The diameter of each sucker rod is specified by the well designer based on the
`strength of the rod material and the loads it will be exposed to. As most rod strings are made
`up of a single material, the resulting optimized rod string tapers down in diameter with
`distance down the well. Because the rod string is extremely long relative to its diameter,
`elastic stability of this long slender column is of concern to pump designers. The rod string
`must translate the force to the pump in both stroke directions. Because the entire length of the
`rod string will be in tension on the upward stroke, elastic stability of the rod string is not a
`problem. Furthermore, if the weight of the rod string exceeds the required pumping force on
`the downward stroke (as it typically does), then the upper sucker rods will also be in tension
`on the downward stroke. The lower rods, on the other hand, will be in compression on the
`downstroke, a condition which could result in downstroke compression buckling of the lower
`rods. To keep the rod string straight and in tension throughout the pump cycle, a section of
`large diameter bar, known as a sinker bar, is placed just above the pump. The sinker bar,
`typically consisting of large-diameter sucker rods (such as 7/8 or 1-inch), replaces an equal
`length of sucker rods immediately above the pump. This large diameter section of the rod
`string is both heavy enough to keep the sucker rods in tension and stiff enough to resist
`buckling. The sinker bar may also increase pump plunger overtravel (on the downstroke)
`which increases fluid production.
`
`Rod string failures are very expensive to repair since the entire string must be disassembled
`and removed to access the failed rod. The rod string must then be reassembled. Wells with
`low production rates may not warrant the cost of repairing a failed rod. To maximize system
`reliability, safety and simplify system design, nearly every aspect of sucker rod system design,
`manufacturing and assembly has -been standardized by the American Petroleum Institute
`(API). Because sucker rods are exposed to cyclic stresses, they are at risk of fatigue failure.
`Fatigue is the process of cumulative damage caused by repeated fluctuating loads whose
`magnitude is well below the material’s ultimate strength under monotonic loading. To ensure
`a long fatigue life of the sucker rods, the API uses the modified Goodman stress diagram
`
`D; = Pin shoulder Diameter
`W, = Wrench Square Width
`
`polished rod
`
`Figure 2. Threaded pin and shoulder at each end of the sucker rod.
`
`10
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`(shown in Figure 3) to determine the allowable range of stress for a sucker rod. Based on the
`ultimate tensile strength of the material, the modified Goodman diagram defines a stress
`envelope (shaded area) within which a structural component can operate such that it will
`provide an infinite service life. Using this system, the well designer can determine the
`appropriate rod diameter based on a knowledge of the minimum load (on the downstroke) and
`the maximum load (on the upstroke). The modified Goodman diagram provides the
`fundamental rating which can be used where corrosion is not a factor. Since all well fluids are
`corrosive to some degree, the stress values determined from this diagram must be adjusted by
`an appropriate service factor based on the severity of the corrosion.
`
`In spite of the thorough efforts of the API to ensure performance within the fatigue limits of
`the selected materials, sucker rod failures still occur. Pin failures comprise a large fraction of
`all rod pumped system failures. Not much is known about the perfonnance of sucker rod
`couplings as they have not been extensively studied in the past. Because the coupling diameter
`is much larger than that of the rod, it has been assumed that the oversized coupling falls within
`the stress range specified by the Goodman diagram for the rod. This may not be true as the
`coupling is a complex preloaded mechanism which will react differently to axial loads than a
`solid rod. This report documents finite element simulations of the sucker rod coupling which
`were performed to provide a better understanding of sucker rod couplings and attempt to
`explain pin failures. All of the simulations were performed with JACZD [1], a quasistatic '
`finite element analysis code developed at Sandia National Laboratories.
`
`s, = (0.25T + 0.5625 S,,,;,,)SF
`ASA = SA ' Smln
`
`Where:
`
`T = Minimum Tensile Strength
`SF = Service Factor
`8,. = Maximum Allowable Stress
`ASA =Maximum Allowable Range of Stress
`
`Minimum Stress
`
`"3
`
`Figure 3. Modified Goodman diagram for allowable stress and range of stress for sucker
`rods in non-corrosive service.
`
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`between the extremes to assure that the stress path was repeated for every point in the
`coupling.
`
`2.4 Summary of Analysis Cases
`
`A variety of geometries and preloading options have been presented. The particular cases
`selected for analysis are listed in Table 2. To simplify the presentation of the analysis results,
`the abbreviation FB is used to identify a coupling with the Flexbar modified pin, SH to
`identify a slimhole coupling, and SL to identify a coupling with Spiralock threads. In addition,
`the 3/4, 7/8 and 1-inch coupling sizes are identified as S6, S7, and S8, respectively. The
`Table 2: Summary of Analysis Cases
`
`A at
`
`'
`
`C
`
`Ii
`
`Fl
`
`(1
`
`..
`
`'
`
`1 2 3 4 5 8 7 8 9
`
`—l O
`
`-L i
`
`THE 1-°
`NINE ‘-5
`fflflfl °-°
`HEW ‘—°
`Eflflflflfl 1-°
`SHE ‘-°
`NINE 1-°
`IIII ‘-°
`3 1-°
`II *-°
`-ZEN °-°
`II ‘~°
`IHEI ‘-5
`KIN 2-°
`2-5
`*6 -HE 3-°
`
`.5 M
`
`.5 W
`
`.5 -K
`
`.5 U!
`
`' F = full bore. SH = elinhole
`*' API Indicates standard API threads. FB indicates Flexbar extended pin with shoulder
`"’ SL = Splralock threads In box section
`
`standard 7/8-inch sucker rod coupling (Analysis 1) was selected as the base case by which to
`benchmark the other cases. A make-up of 1.0 indicates that the joint is made-up according to
`the API recommendations. Analyses 2 and 3 are of the same geometry but with make-ups of
`1.5 and 0, respectively. A make-up of 1.5 indicates that the joint is made-up to one and a half
`times the recommended circumferential displacement. Analysis 4 adds the Flexbar pin to this
`base geometry, while Analysis 5 looks at the slimhole configuration of the base case. Analysis
`
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`‘
`
`6 combines both the Flexbar pin and the slimhole box section into a single analysis. Analyses
`7 and 8 look at the 3/4 inch and 1 inch versions of the same base coupling. Analysis 9 takes a
`look at the base coupling geometry with the addition of the Flexbar pin and Spiralock thread
`modifications. Analysis 10 examines the slimhole version of the base geometry with
`Spiralock threads. Finally, Analyses 11 through 16 are of the same geometry (base 7/8 inch
`' coupling with Spiralock threads), but with make-ups varying from 0.0 to 3.0.
`
`3 Analysis Results
`
`The purpose of preloading a threaded coupling is to (I) lock the threaded coupling together so
`that it will not loosen and eventually uncouple, and (2) improve the fatigue resistance of the
`threaded connection by reducing the stress amplitude in the threaded coupling when subjected -
`to cyclic loading. Hence, the “relative goodness” of the various coupling geometries and
`preloads analyzed here will be based on how well they accomplish these two objectives.
`
`3.] Yielding in the Sucker Rod Coupling
`
`If the coupling yields at the same location on every cycle, a condition known as plastic
`ratcheting, then it will fail in a relatively small number of cycles. Even if the coupling only
`yields on the first cycle, this will reduce the preload in the coupling. If the preload is reduced
`enough to cause separation of the coupling, then the coupling integrity and the fatigue life can
`be compromised.
`
`Figure 8 is a plot of the von Mises distribution in the 7/8-inch API standard coupling at
`preload (no axial load), maximum compression (-5 ksi), and maximum tension (40 ksi).
`Recall that the yield strength of the API Grade C steel is 60 ksi. Hence, a red contour is
`indicative of regions which have yielded. As the figure shows, during preload the steel yields
`in the pin shoulder, the pin neck, and at the root of the first three pin threads. Yielding during
`preload was predicted in all of the simulations except for those which had a zero makeup.
`When subjected to the maximum compressive load, the pin shoulder yields further while no
`further yielding is experienced in the threads. Finally, when subjected to the maximum tensile
`load, the pin threads and pin neck yield even more while no further yielding is experienced in
`the pin shoulder. Yielding during the first load cycle was predicted in all of the simulations.
`However, none of the simulations experienced further yielding on the second load cycle.
`
`The von Mises stress distributions in all of the simulated couplings using the API thread form
`are very similar to that shown in Figure 8. Only the Spiralock modification produced a
`significant change in the coupling mechanics. Figure 9 is a plot of the von Mises distribution
`in the 7/8-inch Spiralock coupling _(Analysis 12) at preload (no axial load), maximum
`compression (-5 ksi), and maximum tension (40 ksi). The major difference between the
`Spiralock and API simulations is that the stresses in the pin and box bodies are much smaller
`in the Spiralock case than in the API case, indicating that the Spiralock coupling is not
`generating as much preload. This will be better quantified in the following section. During the
`make-up process the Spiralock coupling yields only at the tips of the pin threads. This differs
`from the API coupling which yielded in the threads. the pin neck, and the pin shoulder. The
`reason for the thread yielding is the very localized point contact between the pin and box
`threads. This point contact generates very high deviatoric stresses in the pin threads upon
`
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`loading. The deformation of the pin thread tips is so great that it reduces the preload in the
`coupling. No further yielding occurs when the coupling is subjected to the maximum
`compressive load. This is indicated by the fact that the maximum yield stress at the maximum
`compressive load (68.8 ksi) is less than that at preload (74.7 ksi). Finally, when subjected to
`the maximum tensile load, the pin threads yield even more, conforming to the shape of the
`box threads. No further yielding was predicted to occur in the second load cycle. Although the
`yield regions in the above examples appear to be small, these nonlinear deformations have a
`profound effect on the performance of the couplings as will be observed in the following
`section.
`
`3.2 Load Distribution in Threaded Coupling During Load Cycling
`
`The sucker rod coupling joint is basically a bolted joint in tension. A better understanding of
`the numerical results presented in this report is facilitated by a review the theory of bolted _
`joints [3]. The illustration in Figure 10 defines many of the terms used in this discussion.
`
`applied axial load
`
`axisofsymmetry
`
`
`
`pin shoulder
`
`/ pin neck
`
`
`grip length
`
`first engaged thread
`
`last engaged thread
`
`Figure 10. Illustration of sucker rod coupling.
`
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`
`
`Treating both the pin and the box sections as elastic members, the deflection (8) of each under
`simple tension or compression can be expressed as '
`
`_ Fl
`- A-1;
`
`(2)
`
`where F is force, A is the cross-sectional area of the pin or box section, E is the modulus of
`elasticity, and l is the grip length. As shown in Figure 10, the grip length is assumed to extend
`from the pin shoulder (where it contacts the box) to a distance just below the first engaged
`threads. The actual grip length, though difficult to calculate, is slightly longer. The threads can
`be neglected when calculating the cross~sectional areas of the pin and box sections since, in
`most cases, the majority of the grip length is not threaded (see Figure 6). Therefore, the
`stimess constant of each can be expressed as:
`
`i
`
`k = Q = I-‘TE
`
`I
`
`(3)
`
`Note that the bolt theory presented below is primarily concerned with the material between
`the pin shoulder and the first engaged thread. It is this material which carries and benefits
`from the initial preload F,-.
`'
`
`When an external load P is applied to the preloaded sucker-rod coupling, there is a change in
`the deformation of the pin and the box sections. The pin, initially in tension, gets longer. This
`increase