SANDIA REPORT
`SAND97-1652 • UC-122
`Unlimited Release
`Printed September 1997
`
`Finite Element Analysis of Sucker Rod
`Couplings with Guidelines for Improving
`Fatigue Life
`
`.MASTER
`~-tS'r_. ___ :_· ___ lll!ll1r!ON Of 1HIS DOCUMENT IS UN!JMIT!{Jy~t .
`
`
`
`Edward L. Hoffm.~q;(··
`
`. ,. .
`'"'"'' •v
`•-
`Sandia National Labo.rilto.ries
`: J>r~, <:;alifornia 94550
`Albuquerque, New Mexico 87181$''
`·~~-~fi~-9/f!,'· ·
`Sandia is a muai~rogram l~boik~W!
`Corporation, a Lockhe~d Martin_ · .•.. ;any, or ~n§ u'lilted States
`D!i~~1tment· of Energy under Contr:ji'(ii[DE-ACQ4-'94Ala?OOO.
`:r;U:J~::~_}J;~-i
`'/~}'~:·~;·i
`~ · ..
`A~proved for public r~iease; distribufi~~[J,s unlimit:
`
`,' .!'-'- .,
`
`. nes
`
`SF29000(8-81 \
`
`Page0000001
`
`Pet'rs Exhibit 1015
`John Crane v. Finalrod
`IPR2016-00521
`
`

`
`Issued by Sandia National Laboratories, operated for the United States
`Department of Energy by Sandia Corporation.
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`
`Printed in the United States of America. This report has been reproduced
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`
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`
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`Page0000002
`
`

`
`SAND97-1652
`Unlimited Release
`Printed September 1997
`Finite Element Analysis of Sucker Rod Couplings with
`Guidelines for Improving Fatigue Life
`
`Distribution
`Category UC-122
`
`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 make-ups were evaluated with respect to
`how well they accomplish the two primary objectives ofpreloading 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 locked 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.
`
`3
`
`Page0000003
`
`

`
`4
`
`Page0000004
`
`Page0OO0004Page0OO0004
`
`

`
`Contents
`
`Figures .................................................................... 6
`
`Tables ..................................................................... 8
`
`1
`
`Introduction ............................................................. 9
`
`2 Analysis Model .......................................................... 12
`2.1 Finite Element Model of the Coupling Geometry .......................... 12
`2.2 Preload of Sucker Rod Couplings ...................................... 13
`2.3 Materials and Load History ........................................... 15
`2.4 Summary of Analysis Cases ........................................... 17
`
`3 Analysis Results ........................................................ 18
`3.1 Yielding in the Sucker Rod Coupling ................................... 18
`3.2 Load Distribution in Threaded Coupling During Load Cycling ............... 21
`3.3 Estimating Fatigue Life .of Sucker Rod Couplings .......................... 31
`3.3.1 Considerations in Life Prediction .................................. 32
`3.3.2 Fatigue Damage Criterion for Multiaxial Stress ....................... 34
`Identification of Critical Fatigue Locations .......................... 38
`3.3.3
`3.3.4 Equivalent Stress at Critical Locations .............................. 38
`Root of First Engaged Pin Thread ............................... 44
`Pin Neck .................................................. 48
`Root of Last Engaged Box Thread .............................. 53
`3.3.5 Effect of Make-up on Service Life ................................. 60
`
`4 Conclusions and Recommendations ......................................... 63
`
`References ................................................................ 65
`
`· Distribution ............................................................... 66
`
`5
`
`Page0000005
`
`

`
`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
`16
`and extreme loads selected for analysis.
`
`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.
`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
`l-inch coupling sizes (S6, S7, and S8, respectively).
`
`21
`
`26
`
`Figure 12. Pin load and coupling force as a function 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
`39
`7/8-inch API standard coupling subjected to the three load cycles.
`
`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
`41
`subjected to the three load cycles.
`
`6
`
`Page0000006
`
`

`
`DISCLAIMER
`
`Portious of this document may be Ulegi'ble
`ill electronic image products. . Images are
`produced from the best Jmlilable original
`docmneat.
`
`Page0000007
`
`

`
`Figure 20. Difference between the effective alternating stress and the alternating effective
`stress in the 7/8-inch API standard coupling subjected to the three load 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.
`55
`
`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
`
`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
`
`7
`
`Page0000008
`
`

`
`Tables
`Table 1. API Sucker Rod Joint Make-up Recommendations ....................... 15
`
`Table 2. Summary of Analysis Cases ......................................... 17
`
`Table 3. Pin and Box Cross-Sectional Areas and Load Partitioning Factors for Various Cou-
`pling Geometries ............................................................ 24
`
`Table 4. Summary of Coupling Performance for Various Analysis Cases ............. 31
`
`8
`
`Page0000009
`
`

`
`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.
`
`A sucker rod pump, illustrated in
`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 Arm 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
`sucker rods. Sucker rods come in
`lengths ranging from 25 to 30 ft and
`
`Horse Head
`
`Traveling Valve
`
`Standing Valve
`
`Figure 1.
`
`lllustration of sucker rod pump.
`
`9
`
`Page0000010
`
`

`
`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 upwarp 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 l-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
`
`D1 = Pin Shoulder Diameter
`W8 =Wrench Square Width
`
`Figure 2. Threade:d pin and shoulder at each end of the sucker rod.
`
`10
`
`Page0000011
`
`

`
`(shown in Figure 3) to detennine 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 detennined 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 performance 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 JAC2D [1], a quasistatic
`finite element analysis code developed at Sandia National Laboratories.
`
`T
`+]
`
`Minimum Stress
`
`SA= (0.25T + 0.5625 Smin)SF
`/).SA= SA· Smin
`
`Where:
`T =Minimum Tensile Strength
`SF = Service Factor
`SA= Maximum Allowable Stress
`/).SA =Maximum Allowable Range of Stress
`
`T
`3
`Figure 3. Modified Goodman diagram for allowable stress and range of stress for sucker
`rods in non-corrosive service.
`
`11
`
`Page0000012
`
`

`
`2 Analysis Model
`2.1 Finite Element Model of the Coupling Geometry
`
`Detailed illustrations of the 7 /8-inch coupling, with dimensions of the coupling and threads,
`are shown in Figure 4. An axisymmetric finite element representation of the sucker rod
`coupling is shown in Figure 5 with the axis of symmetry on the left side of the model.
`Although the threaded connection is a three-dimensional geometry, it can be adequately
`represented with an axisymmetric: model since the thread pitch is small relative to the other
`dimensions of the coupling. Because the lower boundary of the box section is modeled with a
`symmetry plane, the model repres:ents the coupling of two rods. The pin is modeled up to the
`shoulder and does not include the narrower rod section. This simplification was made to avoid
`modeling the asymmetric wrench flats which are located between the rod and the coupling
`shoulder. Since the applied loads are specified (from the Goodman plots) as stresses in the
`rod, the resulting stress at the larger diameter coupling shoulder was required as input into the
`model. This was accomplished by specifying a pressure multiplier equal to the ratio of the rod
`area to the shoulder area.
`
`Four existing sucker rod designs ~md five proposed design modifications were the subjects of
`this computational study. The various sucker rod pin designs and proposed pin modifications
`are shown in Figure 6. The four existing sucker rod couplings studied here include the
`standard couplings for 3/4, 7/8, and l-inch sucker rods. In addition, a 7 /8-inch slimhole
`
`{Cross-sectional View)
`
`(Exploded View)
`DISTANT END OF PIN
`
`718" API Box and Pin
`Sucker Rod Connection
`
`(Thread Detail)
`
`=~""'.;......;+t-1- '-'1~;::~.~;~r
`r ~--"H""r- ROOT ~.f~T BOX
`~-,...;.,tf-t- FIRS~~=E;O
`
`BOX
`
`Figure 4. Detailed illustrations of the 7/8-inch coupling, with dimensions of the
`coupling and the threads.
`
`12
`
`Page0000013
`
`

`
`pressure boundary
`condition
`
`Pin Section
`
`axially
`expanding
`material
`
`-.- Box Section
`
`symmetry boundary
`condition
`Figure 5. Axisymmetric finite element model of 7/8 inch sucker rod coupling, showing the
`pin and box sections.
`
`coupling, used in applications of low well bore clearance, is also studied. The five modified
`geometries are variations of two basic modifications: the Flex bar pin, and Spiralock box. The·
`Flexbar pin uses the same coupling as the standard sucker rod coupling designs. However, the
`pin is slightly longer and incorporates a shoulder on which the coupling rests. The second
`modification consists of a proprietary thread design, called Spiralock threads, which are used
`in the box section of the coupling. The pin retains the standard API threads in this
`configuration.
`
`2.2 Preload of Sucker Rod Couplings
`
`The API sucker rod tables contain recommendations for t:he assembly or preloading of sucker
`rod couplings, also known as make-up. The recommendations are based on a circumferential
`displacement, measured at the shoulder of the sucker rod, while tightening from a hand-tight
`position. These recommendations are summarized in Table 1 for the 3/4, 7/8, and l-inch
`diameter sucker rods. The axial displacement of the pin (or interference at the shoulder) can
`be calculated as:
`
`13
`
`Page0000014
`
`

`
`3/4" Sucker Rod
`API Threads
`
`7/8" Sucker Rod
`API Threads
`
`7/8" Sucker Rod
`API Threads
`Slimhole Coupling
`(a) Existing Sucker Rod Coupling Designs
`
`1" Sucker Rod
`API Threads
`
`7/8" Sucker Rod
`Flexbar Pin
`
`7/8" Sucker Rod
`Flexbar Pin
`Slimhole Coupling
`
`7/8" Sucker Rod
`Spiralock Threads
`
`7/8" Sucker Rod
`Spiralock Threads
`FlexbarPin
`
`7/8" Sucker Rod
`Spiralock Threads
`Slimhole Coupling
`
`(b) Proposed Modifications to Sucker Rod Coupling Designs
`
`Figure 6. Existing sucker rod coupling designs and proposed design modifications
`under investigation.
`
`14
`
`Page0000015
`
`

`
`Pdc
`d-=-
`nD
`f
`
`1
`
`(1)
`
`where P is the thread pitch, de is the circumferential displacement, and D1 is the shoulder
`diameter. All of the sucker rod sizes listed in Table 1 have a thread pitch of 0.1 inches.
`Simulating the preloading of the threaded coupling posed a particularly difficult problem. The
`interferences listed in Table 1 were large enough that the initial stress-free mesh required a
`significant amount of mesh overlay at the pin-shoulder/box interface. The contact and solution
`algorithms of JAC2D had difficulty pushing back the overlapping meshes and converging on
`a solution. This was further complicated by the fact that in some cases the pin and box
`sections exhibited a slight amount of yielding on preload, making joint preload a nonlinear
`event. To circumvent these difficulties, a section of material was added to the box section
`which is identical to the box material except that it has an axial thermal expansion coefficient
`(see Figure 5). Preload was obtained by heating the model so that this section of material
`expanded, producing the required amount of displacement to preload the joint.
`
`2.3 Materials and Load History
`
`Since the API specifies allowable stress ranges for sucker rods based on the grade of steel
`used, the load history is coupled to the material selection. The API specifies many grades of
`steels for use in sucker rods and box couplings, depending on the particular application and
`load history. An API Grade C carbon steel was selected as the subject for this study. The API
`Grade C specification includes any steel with a minimum yield strength of 60 ksi, and a
`minimum tensile strength of 90 ksi. Hence, these inelastic properties were used in the present
`
`Table 1: API Sucker Rod Joint Make-up
`Recommendations
`
`Rod Size
`(in)
`
`Pin
`Shoulder
`OD (in)
`
`Minimum
`Circumferential
`Displacement (in)
`
`Calculated axial
`displacement or
`interference (in)
`
`3/4
`
`7/8
`
`1
`
`1.500
`
`1.625
`
`2.000
`
`7/32
`
`9/32
`
`12/32
`
`4.64x1o·3
`
`s.s1x1o·3
`
`5.97x1o·3
`
`Scribed
`vertical
`Line
`
`Measured circum·
`ferenlial displace·
`men!
`
`Hand-tight joint
`
`Made-up joint
`
`15
`
`Page0000016
`
`

`
`study. The post yield behavior was modeled with a linear hardening modulus of 100 ksi. In
`addition, an elastic modulus of 29 x 106 psi and a Poisson's ratio of 0.3 were used.
`
`The fatigue limits of API Grade C sucker rods were determined specifically from the modified
`Goodman plot shown in Figure 7. This diagram shows the allowable stress range for API
`Grade C steel and identifies thre(~ load scenarios selected for analysis in the present study:
`cycling between -2 ksi and 8 ksi, between 2 ksi and 23 ksi, and between 15 ksi and 30 ksi. In
`the presentation of the analysis results these load cycles are identified as Cycles 1, 2, and 3,
`respectively. The three load cycles. identified in the modified Goodman diagram (Figure 7) are
`load cycles which will provide an indefinite service life with respect to rod failure. In addition
`to the above load cycles, extreme loads of -5 ksi and 40 ksi were chosen for analysis to
`determine if the threaded coupling behaves elastically under these allowable extreme loads.
`Assuming that the coupling deformations are linearly elastic while cycling between the
`extreme loads, then all three load cycles can be studied from a single calculation following
`this load path. Hence, following preload, all of the models were first subjected to the
`maximum compressive load (-5 ksi) followed the maximum tensile load (40 ksi). If the
`coupling were to experience inelastic deformation during this first load cycle (e.g. in the
`threads), then the coupling stresses would not follow the same path in subsequent load cycles.
`To determine if this was the case, the models were. subjected to an additional load cycle
`
`90ksi
`
`Minimum Stress
`
`Figure 7. Modified Goodman diagram for API Grade C carbon steel, identifying load cycles
`and extreme loads sele:cted for analysis.
`
`16
`
`Page0000017
`
`

`
`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 si:J;nplify 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 l-inch coupling sizes are identified as S6, S7, and S8, respectively. The
`Table 2: Summary of Analysis Cases
`
`Analysis Coupling
`Size*
`No
`
`Rod
`Size
`
`Pin**
`
`Box*** Make-Up
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`F
`
`F
`
`F
`
`F
`
`SH
`
`SH
`
`F
`
`F
`
`7/8"
`
`7/8"
`
`7/8"
`
`7/8"
`
`7/8"
`
`7/8"
`
`3/4"
`
`1"
`
`API
`
`API
`
`API
`
`FB
`
`API
`
`FB
`
`API
`
`API
`
`API
`
`API
`
`API
`
`API
`
`API
`
`API
`
`API
`
`API
`
`1.0
`
`1.5
`
`0.0
`
`1.0
`
`1.0
`
`1.0
`
`1.0
`
`1.0
`
`8
`
`9
`
`10
`
`11
`
`12
`
`13
`
`14
`
`15
`
`16
`
`F
`
`SH
`
`F
`
`F
`
`F
`
`F
`
`F
`
`F
`
`7/8"
`
`7/8"
`
`7/8"
`
`7/8"
`
`7/8"
`
`7/8"
`
`7/8"
`
`7/8"
`
`FB
`
`API
`
`API
`
`API
`
`API
`
`API
`
`API
`
`API
`
`SL
`
`SL
`
`SL
`
`SL
`
`SL
`
`SL
`
`SL
`
`SL
`
`1.0
`
`1.0
`
`0.0
`
`1.0
`
`1.5
`
`2.0
`
`2.5
`
`3.0
`
`• F = full bore, SH = slim hole
`** API indicates standard API threads, FB indicates Flexbar extended pin with shoulder
`*** SL = Spiralock 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
`
`17
`
`Page0000018
`
`

`
`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), ibut with make-ups varying from 0.0 to 3.0.
`
`3 Analysis Results
`
`The purpose ofpreloading a threaded coupling is to (1) 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.
`
`3.1 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 Mi.ses distribution in the 7/8-inch API standard coupling at
`preload (no axial load), maximum compression (-5 ksi), and maximum tension (40 ksi).
`