Note: Descriptions are shown in the official language in which they were submitted.
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SUCKER ROD COUPLING
5 Field of the Invention
This ul~_.~on relates to sucker rods and their c~ f~ and in particular to
UJllJlU._ll_~:i in design ofthe pin and box cn----f~ c
Bacl~u~,d ofthe Ir.~ iu.-
Strings of individually coupled sucker rods have been used in oil and gas wells for
10 Il~ ~.C~ g ",e~ ir~l power to a~ devices used in the prod~lctinn of ûil and gas.
Sucker rods generally transfer power by a~al load, driving pumps with a rc~,;ylu~aLil~g motion
along the well bore (e.g., beam or rod pumps). In recent years, there has been i~lcred~ use
of sucker rods to drive pumps that operate in a rotary motion (e.g., p~u~ g cavity pumps).
This rotary type of pl~mring ~ ....ls power by a torsional load, or torque, along the rods.
Fttings for co~ og~,~l,_ a series of sucker rods to reach the dow '- -'e purnps in the
r~ n from which ~uids are being pumped have long been s~.~d;~d, and ~,o.l~nal
Lt~ulgs indude a uniform diameter thread and a shn~ on whidh the pin end and box end meet.
An . , le of this type of cc.nn~h~n can be found in U.S. Patent 1,671,458 to Wllson. This
cû..~_~o~ design limits the length of thread make-up and hence its ability to wi~ d to. ~
20 stress, which is more acute in sucker rods ~q~ qted with rotary pur.,ps than with l_l~JlU~ltUlg
pumps.
It is co"~ ional to include as the upper nost rod in a sucker rod string a poli~l,ed rod,
which provides a polished surface to accommr)date a ,,.~ l dynarnic seal, co.. only
referred to within the industry as the "stuffing box," at the wellhead b~ ,n the high pre~
25 annulus of the well and the qtmosph~re. A conV~ntiollql polished rod has a partially tapered
pinlbox arrqngempnt with the taper occurring at the end of the threaded section only, and with
the taper obtained by red~lction of the thread height and not by reduction in ~ .... t~ ~ of the
threaded section as a whole. The ~ ",ose of the polished rod taper is to allow the rod to
pen~lale through the stuffing box without causing darnage to the sealing materials co~ d
30 within. An example of such a conventional tapered pinlbox al".,-~,e....~ is shown in U.S.
Patent 2,690,934 to ~olc~".be.
The American p~ lm Institute has se~ ls for the ~ onc of sucker rods and
their qccû.~ ~ co..rlingc which c n be found in API Spe~ 1 lB, 25th Edition, January 1,
1995. For suclcer rod pin co~ l;r~llc these ~L~nda ds include minimum and ...~ .. threads,
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35 pin-shoulder face p.u~llel~;u.., miniml-m and ~ t~ ofthe ssress relief aec~on of the pin,
mil~irnurn and .. -~;.. ~;- .. t~ r for pin-shoulder and upset bead, mnnirnurn and ~ .. pin
length and pin stress relief lengths. Similarly, box cQn..~l;nl- a~ld~da are ~ , ;A. ~ g
nominal thread ~ ~, total box depth, total thread lengths in the box, in~ ing counter bore,
minirnum box m~or ~~: .. t~."..-~ box pItch ~I;- - t~ and . .;; . - .. box minor
40 diarneter and ~ ... t~ of the box counter bore. Pin and box contact ~1; .. .- --n~ are si~larly
sy~ ;~ Thread forrns are ~I Q ;~A with ~ lce to the ANSIIASME Bl. 1 ~ ~"rt;on
All of these ~1:.... ~- onal standards are directed to CO~JYI ~ that are ;.~ AI to transrnit
power by axial lew~,lucdion. The c~-- r~ ;nn upset reduces the fatigue stress asaoaated with
l~.loc~on and the mating l.n~YI~I~ faces ofthe box and pin pro~ide a positive m-~ke up indicator~5 and prevent the co....f~ n from '~.~.g out" during op~lion. High torque capacity is a
col~d.,.~L,on in the industry-standard design.
In addition to the specific dirnensions just listed, external ~ ~nc of couplings and
~I,c~ c are listed for each a~ d suclcer rod size for both coll~ .l~iondl couplings and "slim
hole" cu pli ~ Whether ' ' - '- or standard, prior art cu..~ design has ;..- l~dtd as its largest
50 .1;- ... ~.~ 11;.l....-: n an upset on the pin end which rnalces the l.; .-:~;ol- from the shoulder to the
base of the wrench aats, which provides the metal mass needed for the torque ~h---~lA~ . to transfer
torque through the cr,....~./;~ n The ~ ofthat upset relative to the rod body ~ can be
referred to as an upset ratio, which for nonnal cU~ y~ ; under the API cl)e~ ,,,c is about two
and one eighth to one, and for slirnhole couplings under the API .~I.e~ ;r."~ is two to one.
5~ As can be ~pl~;aled, the space occupied by the Co~ ng withinthe annulus throughwhich
auids are drawn to the surface ~I;.,,;.~:ch. ~ the space available in the annulus for plo-ln- I;.~n ~uid to
aOw, resulting in higher friction losses in the ~uid. A larger co -~ling d;&..~ te. also IllW~S the
tubing .li- ... t~ required for a desired level of plod~ ;ol~ It would Ill~fu~c be desirable to
de~se the space occupied by the cu~ yet maintain the structural integrity needed for the
~4~ g, while in service under axial and tO~ load c4r~ c Fl -- ~ the need for a
torque chollld~r would ci~ . .l ly reduce the upset ratio thaeby providing more annulus space for
a given tubing size or parnit the use of smalla tubing for effiective auid prodnc~ion
R~1u~ng the co..pling d;- ..- t~ also de~,~s the standoff between the rod and tubing.
This reduccs the fatigue we~n;ng co...~ in the rod body adjacent to com~lL.ol~al pinlbox
6~ cr~ l;onc that are subjected to c~ ed axial and torsional loads in well intervals with Illod~
to high curvature. It can be ~,.~;aled tha~ rods in deviated wells are subjected to cyclic bending
stresses as the rod rotates. Fu~ll.e.lllure, axial tension on the rod g -le-~L~s a loc~~;~ aLul~;
co~ don arlj~r~nt to co....~ ~ jonC because ofthe standofffrom the tubing wall. By r~l~.g the
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CQ~ upset ratio, the standoff is lowered, thereby d~...g the culvature c~ l;nll in
70 the adjacent rod, thus u..~..u~u-g the fatigue 1~ - . .rP
Summa~y ofthe L~ ,on
The ...~_.~on includes an irnproved sucker rod c4uy~ or CQnnr -l ;on that eliminates the
mating pin and box shoulders and provides for torque transfer solely by way of the pin and box
ma~ng threads. The invention in~ de~c a cr-~--f- 1;~ n having pin threads fonned on a tapered pin
75 body and co..~ Ol~ gly tnating threads formed in the bore of the box. In particular, the
cn....~ n includes a pin having its thread formed on a core that is outwardly tapered from its
tenr~nal end to the end of the llu~ed portion of the pin and a non-~eaded section to
~ ......... ~.l~e a box u._}~g portion, with the non-tl.~ d portion having an outside diameter
app.~).;...-l. 1~ the same as the largest diameter of the llu~ded portion and having a slightly
80 radiused transition between the o _.l~-g and a wrench fats section of the pin. Wlth this
am.~,f ... ~1, the largest outside .1;~ of the torque make-up or wrench ~ats section of the pin
can be no greater than the outside .l;- . . te of the mated Cn~ n rhe box portion of the
c~ ;ol- is C~ Oh~; ~yJy shaped and llu~dod to mate with the pin with load transfer contact
between the pin and box provided only by way of the mating threads.
As can be ~p~;ded the coupling can be entirely integral with a rod body, i.e. pin end
formed on one rod body end and box on the OIJlJG5i1~ or could include a separate box C4..~ 0
ha~ing two oppo~u.~, boxes for mating with rods ha~qng pins formed on both rod ends.
T:he irlvention further indudes a method for o~d;...;: ~g the ~imPn ;onC and cc...r~ of
a cn....~ n which eliminates the need for a torque ch~ ~. The method includes matd~ing the
90 wrench fiats section ~1:----- t~r to the sucker rod to be coupled, S~IF,:~ g a thread profile or form and
thread length, and sPI~ bore and core tapers to match the thread length and profile. One
feature of the method is 5~ of a thread forrn fûr the conn~l;ol- which, when pin and box
portions are ~g~ results in contact on both the load and stab fianlcs of the thread to provide for
load transfer between rods to occur in the mated threads.
95 BriefDes~.;~on ofthe Draw~n~
A better u..de~ n~; .g of the present invention can be gleaned from the following detailed
de~.i~ on of a plcf~-~d embodirnent read in light ofthe A.-r4".~.-..y~lg Drawing in which:
Figure 1 is a side view of a suclcer rod pin formed in acco..l~-ce with the instant invention,
Fgure 2 is a side view of a sucker rod mated conl.~l;ol- formed in accul~ce with the
100 instantinvention;
Figure 3 is a side, cross sff~on~ ;C view of a box and pin mated connÇ~o~
illustrating the c4nn~ n geo.ll~ly,
Fgure 4 is a side view showing a ~I ~;îe l vd thread form for the mated c~. .n~ ;on of
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FlgUre2;
105 F~gure S is an exploded view sl,u~ g the detail of a ~ d thread forrn for use in the
cr.. ~ ofthe invention;
F~gure 6 is a graph ..hu~."g radial load on a coupled rod as a fiunchon of the depth of the
box counter bore for a one inch rod using a 1.25 inch C4~ F~:I;ol~ in a~lJ~nce with the present
inv~ ion, and
11() Flgure 7 is a gl_rl ~~ql C~ p~~ of two prior art CQ~ I;nl~C with a c4nn~ n in
aK4ld~lce with the present i~ n i~ atulg improved area available around the cnn~ on for
plU~ n through plO~ iLion tubing
Detailed De~ ;ol- of a P~ d Embodiment
1 l S; The basic colL~Ludi~n of the e~ l ;nn ac~l~,~ to the invenhon is shown in Fgures 1
and 2 showing the pin and box polLions ofthe c~ .l;o~ th l~ .,ce to Flgure 1, pin 10 is
shown fonned on the end of rod body 12 and includes a make-up section 14 having wrench ilats 16
for ~ g and tol~ up the cr,..nr l;- l- Cc,ll~ iol~lly, the mi~i mlm d;~... t~ across the
centers ofthe wrench ~ats matches or is only slightly larger than the outer ~1; ..r t~ ~ ofthe rod body,
120 and comers 18 ofthe make-up sechon 14 are sized to provide the notch for holding a wrench in the
~ats 16.
The pin 10 inrlllde5 a csntimlouc pin thread 20 formed on tapered core 22. The pin
thread 20 and tapered core 22 extend from terminal end 24 of the pin up to a short ulllL~ded
pin co,~P~,I;nn e.ltlance section 26. The pin e.llla.~ce section 26 preferably inc~udes a laL.Ised
125 transition 28 to the point where it meets the corners 18 of the make-up section 14. Wlth
reference to Figure 2 mated co-~-~F~,I;on 29 is shown having opposing ellLI~ces 26', box 30
mated with a pair of pin ends of a sucker rod string. As shown, the box 30 includes an
ull~ aded c.,llance 26" and a tapered bore 31 having a cor-tin..ous thread 32 formed for
mating with the pin thread 20. As can be app-e.,;aLed, the co~ l ;on can be made either with
130 a rod forrning opposing pin ends on the rod body and providing a sepal~Le box having
opposing boxes for mating with the rod body pin ends or by providing a rod body with one
shaped pin end and an opposing end shaped as a box. As can be apprc~,ated, to ~ e the
chance for well fluid contact with the threads 22 and 32, it may be desirable to include a
cou~ p seal such as seal 25 illustrated in Figure 1. As will be appl c~,;ated, any type of sealing
135 ~I.e~ ;c... suitable for use with equipment subjected to produced fluids can be used with the
coupling of the instant invention. Thread dope should also be used for this purpose as well as
for 111;.1;...;~ friction on make-up ofthe col..le~,lion, as ~iccucced below.
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The C4....~ 1;n.- ofthe instant i..~_~on can~ configured to provide the minimurn overall
cnnnr~.l;nn .li~ wh;le providing ~lu~ e strength to transfer the full load capacity, in
140 tension, torsion, or cl~ d.-nr~ loading, of a suclcer rod body across the CO....e~.l;o~ To that end, the
cr.. ~.l;o.- should be co,~d for a particular rod body size. It has been found that high torque
loads can be L.~ "~d through a conl-~ without inr~ ng a torque shoulder in the co....~. ~;nl~
uQng a tapered pin core and box bore and using only the tlu~ ~ed; ~ ce for load transfer by
r~l.no~ g an app.u~,l;~ taper and thread length for the col- -r 1;~-l- It is also ad~ c to
145 provide a thread ge~ y which ...~ contact b~ the pin and box lluuugl.ùu1 the thread
length.
Flgure 4 schematically illustrates c4~ ~r ~ n g~lll.,l~y and the nanner in which a tapaed
thread core is used to produce radial ultwfww-ce when the pin 10 is advanced in the box 30. One
key feature of the u~ tiùll is the ;... ~ -n of box ovwl~g 34 outside of the tlu~d~d ~g~i
150 length of the co..~ g This u~wL_~g 34 l~uducesc a raaial force co~c~on at tne mated
ro ~l~r~l;nll c.~t.~ce section 26'. Ree~ cç the box wall is thinnest in the mated C~-nn~ r~;
section 26', the lowest inward radial forces are seen in this section, some of which are ~ ..,d
from the overhang 34. It has been found that an optimal length of the overhang 34 can be
--.;--rri usingbendingwavee~ c asdr~. ihe~ below.
155 ~hhm~gh any thread design can be used, there are some thread types that are known to be
more ~~ at ~ f. .;.~g torque. For most e~ective torque transfer, the threads 20 and 32
p..,f~dltly include straight ~anks, e.g., load ~anks 36 and stab flanks 38 and a fat root/crest, e.g.,
pin crest 40 and box root 42 as best seen in Flgure 5. In general, the thread height should be kept
small to ..... ;-.~ the effect ofthe thread on co~ ng wall thicknecs.
160Turning now to the method for Gpt;~ the physical phl~l... e~ of the couplin~ the
following will first address the forces ûn the critical section~c of the couplin~ as secured to a
rod body, inclu~ing the rod body 12, the pin cQnn~inn entrance 26, the collpling make-up or
mid-section 14 and its thread section inr~ ing the threads 20 and 32. Load transfer e4~!-l;nnC
are then applied to the results of the critical section designs. A key feature of the design
165 o~Jt;~ ;on method of the invention is to use as a model for the couplin~ load a thick-wall-
p.~,saule-vessel. It has been found that, although a col~pling is not a p.~ ule-vessel,
;c~i models developed for stresses in such a vessel lead to design results that are
effective tO produce a couplin~ capable of effective torque transfer and of 5l~ffiri~nt structural
hl~c~;Ly to w;lh~l~nd the rigorous forces to which a sucker rod ct nl~k~;l;on is subject in use.
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170 Critical Sections
Rod Body 12
The rot body section is a circular section. Hollow rods have an opening down thecentre ofthe rod. The rod body section c~pa~;l;fc are given in terms ofthe rod t1;A ~ t~ . and
rod bore .liz.,,~ t~ as follows:
F = ~ = a ~(d, -dl )
175 Y Y 4 (axial load capaci~y)
T _ ay ~r(d, -d, )
Y ~ 16 (tola;onal yield capa~ y)
ay J~(d3-d3)
T" = ,~ 12 (tol..;onal~ ~capacity)
where:
ay = tensile mqt~riql
180 d, = rod ~I;z~.. r l, and
di = rod bore d;~ .. t.~ (hollow rods).
In the following, only solid rods will be con~ ered for ~impliçity~ However, as will be
al)p..,~,;a~ed the o~ Al;on method can Iso be applied to hollow rods. Since hollow rods
have lower section load car~ C, cc~ l;ol- designs mPieting load l~luilc~ Ls for solid
185 rods will more than meet loads for hollow rods.
Mated Connection Entrance 26'
Load is l~ r~lled across the threads from the pin to the box along the taper of the
threaded zone. Torsional load is L,~,~r~ d by friction, while axial load is l~iu~..r~ d
ll~r.hA~ .Ally by bearing loads on the thread flanlcs. If the load transfer rate with respect to
190 location is imllffici~nt the section ~,apac;Ly is reduced by the taper faster than the load is
t~l;,r~led out ofthe pin, which would lead to a failure in the pin.
Given the taper, t, of the thread in terrns of the initial and final ~ng~ged thread
. tr-~ ~ (do and d~ .e~ ely) and the ~ng~ged thread length (L,) as shown in Figure 3,
t do - d,
195 where the thread pitch ~i~m~ter, d, at any location, shown exploded in Figure S, can be
eA~,.eJsed as
d =do - tz
The ~ltim~te section capacity gradients can be shown to be:
dFU = -a ~Zz(dO - tz)
dz Y 2
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dT~ ay ~(do_tz)2
20~ 3 4
These rel~tion~hirs show that the largest section capacily gradient occurs where the
thread d;-...."~ r iS largest and the box 11~ rL ~P~c iS ~mqllest, at the mated conl-e~ion L,lt.~lce
26'.
Coupling Make-Up Section or Mid-Section 14
20'i With contin~ing ~,,ference to Figures 3, 4, and 5, the mid-section 14 of the ~u~ipl:~g
carries the full rod body 12 loads b~ pins. In ~ -B the co~p~ 8 mid-section 14
cd~,a~ y to the rod body 12, only the ul~ le ~ itips need be considered. The section limits
are ~yl~,.,s~ ~I;l~ly to those for the rod body 12:
F ~(dc2-d2)
4 (tensile limit)
T _ ay J~(dc - d, )
210 J~ 12 (torsional limit)
where dc is the outside .1i~.... t~ ~ of the box.
For a given box diqmptpr~ dc~ the ~ ;-------- end ~ia"~Pl~ to match the rod body 12
c~-~ities can be determined, qCsllming similar material strengths for the rod and box:
d""~, = ~Id 2 _ d 2
215 d 3 ~
The box ~ ct~ is e"l"-,;,sed in terms ofthe nominal rod di-qmPter and an upset pa.~ ter, ~:
dc = ~d,
d~(~orJlona~=dr3 ~
d,(a~"", = dr ~ Fqu~qtinn I
220 The smallest box inside di~.. te~ must be used to ensure the section strength is
adequqte over the range of cG~l~billed load contlitiom that may be encoun~el,:d. Conceq~lpntly~
the axial load criterion governs the inside ~~iqnnptpr of the couplil-D If mqmlfq~lring
COh~ impose a mq~imllm coupling inside di-q-met~Pr7 then this rel-qtiomhir can be used to
define the coupling upset required.
225 Thread Sections 20 and 32
Loads are ~ lled across the contact surfaces on the threads and into the bodies of
the pin and box through the base of the threads. In most cases the frictional characteristics
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require a sllfflripntly long threaded section that the thread limits are not of csnrprn However,
for heavier upset CQn~ nc~ the thread ah~ can govern the design.
230 Figure 4 shows the critical section for one thread. The thread width over which the
load is ll~lar.,~l~,d is a fraction of the total thread pitch. The. .,fol e, the stress l~r.~c.l~d across
the critical thread sections 20 and 32 can be c,.~ressed in ter ns ofthe average load ll~,~
p a~,
a, =tJo~ 7 F~ ti--n 2
235 where w is the thread width at the critical lo~?tir~n and P is the thread pitch. The thread
effiri~nry factor ~ in~ir~t~5 what plopo.tion of the thread cone carries the load. For fully
Pn~ g~d V-threads, the thread ell~4:~ - y approaches 100%. For square threads, the thread
Pffir,j~nry is roughly 50%, and for partially ~~n~ V-threads the thread Pffir.;~nr,y can be
25% to 50%. ~ccllming a 50% thread PffiriPnr,y is slightly cons~,.valhre for the thread type
240 plefe.led for this applin /;on
The thread sections 20 and 32 will fail when the stress state on the entire thread
sc~l;onc 20 and 32 (i.e. on all threads) reaches the yield lirnit:
F 2F
A 7r(dO +d,)L,
T 6T~ 6T
d ~ dz J~ - (do ~ ~L~ do2 + dod, + d 2
~o 2
245 Couplin~ Hoop Limit
The couplin~ is expanded by radial il~lc.rcie"ce as the pin is advanced into the box,
developing the radial stress ie.~ulred to produce the ch~ trcl~,lLial friction force. The radial
force that can be developed is limited by the ~llen~ of the couplin~ material, and by the
Ih'L~-f~S of the coupling. If the friction factor is inc~ffirient, or the length of the co,..~ ;or- is
250 too short, the radial force required to produce the nece~C~. y torque may exceed the capa~iily of
the co--l,lin~ This leads to failure of the co~lplin~ by hoop PYp~nciQn~ perhaps to the point
where the coupiin,P splits.
Load Transfer Equations
Frictional Torque
255 Torque is developed by friction produced by the radial load resulting from radial
hltc~r~.~,nce. The couplin~ thir~nPcc is ,ci~ific~nt relative to the co..~ P .li~.fter, so thick
wall pl~ llt; vessel equations are ap~rop~;ale to relate the radial force to the hlL~l~..,..ct. In
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this developm~nt the radial il~le-r ~_nce will be ~CC~m-~d COfi'~ over the length of the
threads. It is a simple matter to extend the design criteria to account for a linear u,L~.r~ ce
260 distribution ~ccoc:-~ed with a taper ~--;c--~ b~L~ n the pin and box.
Flgure 5 shows a free body diagram of an ;..~..;les; ~l intenal of the co~ subject
to radial ulL~,Ç~ ce. The thick wall ~re..~e vessel equations for an u~c_pl)ed vessel can be
eAI,iessed giving the contact stress C in terms of the dia..,etlical il,lt~L.~nce I (twice the radial
i~lte~rc;re~lCe), ,~eG~ nic characteristics, and elastic material p.opc.l;es.
C~ IE(dc-d )
265 dL( l+v) dC2+( 1-2v) d2]
where ~ is the elastic morl~ lc and v is Poisson's ratio.
The cou~ling inside di~ t~ r (or thread ~l;a..,. t~ ~) iS e~yl~saed in terms of the co!lpl; ~8
outside ~ -. t ~ by a factor a, and the contact stress is upd~ted CGIll ~Jon~ y.
d=adc
IE(l _a2
270 C~C [(1 + v) + at ~1- 2v);
~ The friction torque associated by this contact stress on the ~ ;t~ l interval
d~t.-~lc on the eIL~ e frictional charactP~i~t~
dT=~r~.IEdc a( l-a2) dz
2 [ (l+v)+a2( 1-2v) ]
sin(~/2) Fqu~ti~rl 3
275 This di~el~ ial equ~tion is the basis for two of the most i~ )oll~u.l design equations
for the co~ F~ n First, the lll~ lll allowable thread taper can be c~lc~ ted to prevent a
failure in the pin connection entrance section 26 of the mated co~ ;on 29. From this
c~ tion the threaded length can be delel..,.l~ed and the total torque lr~lar~ d can be
c~ ted from the integration ofthe di~ ial eql~tiQn
280 The torque transfer rate must be greater than the section torque capacity gradient at the
mated co~e~ ~ion entrance 26":
dT~ >_dTu
d~ dz
~r~Ed ~( l-a ) ~Jy 7Zt( do~~Z)
2 [( I + v) + ~-( 1 - 2v) ] ~ 4
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2~r~E (l-a2)
ayad~ [ ( 1 + v) + a2( 1- 2v) ] Fqll~tiltn 4
285 The tot.,l fi~çtionql torque l~L-~. d across the threads is evaluated from illte~a~ g
the di~,..,..L;al equvtion First7 the ratio ac of the thread pitch ~ t~ do to the cu .~ g
d;~ r dc is e,~p~ sed in tenns of the ~xial position z:
a = aO - mz, wherem = ~' L
dz =--da
m
290 r r:~. - 2m ( 1 + v) + a2( 1 - 2v)
The following i ll,,~alion fonnula can be used with ap~lu~u.iate variable ;,.~ nc
to i~le~ale the equqtion
I u(l-u2)d a+bl ( +bu2) u2
a=(l+v),b =(1-2v),u =a
295 The total fi;ctil-nql torque is thus:
T ~ cIEdcL 2-v 1~( l+v) +( 1-2v) a2~ aO2-a2
4 aO-a~) ( 1-2v) 2 ~( I+V) +( 1-2v) aC2) 1-2v
Fq~l~ti :~n 5
This expression is v. lid as long as the co~ remains elastic. The effective stress in
the coupling is largest on the co!lpling inside d;~ ,te~ at the end of the thread, adj,qc~nt to the
300 col-p~ g mid-section 14. The elastic torque capacity of the thread is reached when the
,.L,~"ce produces a von Mises effective stress at this location. The amount of i~llc;lr~ ce
at the yield limit is determined using the thick wall pressure vessel equations:
C _~ry( l-aC)
~ (contact stress at first yield)
I = C d ( I + v) +( I _ 2v) a2
aV[ ( I+v) +( 1-2v) a~
' E J~ F.q~qti~ 6
l~e int~ ence ~sociqted with first yield of the coupling is used to dete-~lune a
coupling geometry that can transfer the ~lltimqte rod body 12 torque. The ~qd~litionql plastic
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capacity of the conne~ n aCcQun~c for the m~ ;f-.n~l stress effects resulting from the
rod body 12 loads that are tl~l~L,.~ d through the co.lpling mid-section 14 sim-~ Qu~ly with
310 the ,ll~.r~ e loads.
Axial Force
The l..N.h~ l load transfer rate is govemed by the shear capa.,;~y of the critical
ehread s~PctiQnC 20 and 32 ofthe mated con ~ n 29:
315 Axial load transfer ,~ u.. ,.. l~.lti at the mated co~ e~l;o~ e.lt,~lcc 26' are similarto
those for torque:
, 2 - dFY
~Y 2~ ~(do-tz)
t < 2
3 F.qu~tion 7
320 ~ practical ~p~ I;onC the .. ~ .. taper allowed by the axial load transfer ~,.;I.,.;on
is much larger than that allowed by the torque transfer rritP.rion
Thread Load Limits
Thread load limits are c-~lc~ tPd based on the as~u~,lt,Lion that the stress l.~f.,..~,d
across the critical thread sef~ionc 20 and 32 reaches the material yield limit over the entire
325 threaded region. A thread capac;~y safety factor is dele.l..uled from the quotient b~ .,., the
thread load capacity and the rod body 12 capacity. Since the threads are also subjP,cted to large
bearing forces on the thread flank, it is l~,cO.. f ~~ed that at thread capacity safety factor of at
least two be ...~; .l;.; .ed in the design. For most minimal upset designs frictional torque transfer
rate con~;~prations govern, producing thread capacity safety factors ci~ifir.~ntly higher than
330 two. It is possible for the thread capacity to govem when the coul)ling upset bccol..es more
cigJIifir~nt
For design, the c~lsnl~tirJns for thread capacity is based on the area ofthe cone defined
by the thread roots. This introduces a slight conservatism in the design because this cone
di~rnPtP. is slightly smaller than that of the critical thread area. The dilTelence b~,L~ ,n the
335 thread pitch ~i~rnPtPr and the root ~i~,--ct~ is equal to the thread height, h.
Torsional Thread Capacitv
The ultimate torsional load capacity, TT, of the critical thread sectionc 20 and 32 under
pure shear is given by the following integration:
Il
CA 02232925 1998-03-24
T ~Z77aylL (d h)2d
d =d -tz t = do -d, = (do -h)-(d~ -h)
340 L
Tr = 7rr,7~y ¦ (do ~ h - ~z)2dz
T _ 7~77ay [do - h - tz~
2~ - 3t 0
Tr = 6~t [(do -h~ - (d~ -h)3¦
Tr = ~ [( do-h) 2+( do~h) ( dC-h) +( d~-h) 2]
~4S where,
do = thread ~ ter at co~ ing e.~ ce 26,
d~ = thread ~3;~.. ,t~l in centre of couplin~,
h = thread height
77 = thread ef~it iPn~y factor~50 Axial Thread Capacity
The IlltiTn~te axial load capacity Fr of the critical thread sections 20 and 32 under pure
shear is given by the following il~Lc~al~on~ using similar sub~ ;on~ to those used in the
torsional thread capa~,;ly:
F ~ YIL (d h)d
Fr = 7r7~ Y I (do - h-~Z)dz
Fr = ~( do + d~ - 2h)
~ Equation 9
COU"L~ O~ O~ l;on
If the connçction entrance or coupling mouth extends past the thread i"Le,r~.~.,ce zone,
e.g., inril~e5 unthreaded section 44 shown in Figure 3, elastic d~rol,.,alion energy g~"~,~l.,s an
360 a~ition~l radial force in the first threads. This radial force is modest because the D/t ratio is
largest at that location, where D is one half of the average of the coupling outside and inside
rn~ters, and t is one half of the di~el .".ce between the cou~ ,.e outside and inside d;~ " t~ ~.
The additional radial force at the mated cQnnec~ion e~ nce 26' can ~ngrnPnt the initial torque
12
CA 02232925 1998-03-24
transfer and reduce the ~Iu.adPd length ~equu~d to transfer torque, or provide a modest safety
36'i factor in the torque transfer .,,f..l,~ .. The box wall ~I..rL..~ in the COU~lt~,.bOr~ iS relatively
small in cG...p- ;~on with the co~ f~;nn ~li~ - ter, so the equ~tinn~ for a beam on an elastic
ru~ ;on can be used to es~ e the ring force produced by the o~,.Lang 34.
The spring stiffnecc~ k and Wa~_lCY~ ,tcr"~, are given as:
4Et
k= d2
12(1-v )
The eql~tiom for ~ di~pl~cernPnt and ~.. n.. ~ in a short beam on an elastic
r~,u~ l;on are:
u = P~ cosh~+cos~L+2
2k sinh ~ + sin
M P cosh~L-cos~Z;
~ 4,B sinh ~ + sin ~
375The length ofthe short beam, L, is tvnce the overhang length for the co.. yl;.~ Lc~ and P
is also t~vice the ~1~....~1A~;sn load Pc.
The ~ sF'-~PmPnt is equal to half of the ~~ lte~r~ ,"ce I. Solving for the
on load P and graphing with respect to the COUII~ JOI~ Iength (Flgure 6 for a 1nc- nn~l;on) illustrates that the primary benefit is developed within 0.25 inches, which
380 cG"~onds to one halfofthe characterisdc wa~.,lcn~lh.
When the coullL~,.l,ore length has been fin~liced the torque ~C~o~ cd with the
coul.~,l,ore al~ l;on is c~icl~l~tPd by:
T = ~r~PCdc
2 Equation 10
Using the above P~U.7l ;Ollc and p ~ re. ~, opdmal ll; - - .- on.c of a cou~ p in accol~ce
385 with the present invendon that is suitable for use in the field can be dc~ as follows:
Design o~ ;Qn Method
Coupling diameter selection: The Cu!~l lin~ mid-section area is IIIAI~hf'li to the rod area
using Equation 1. For designs cohsl.~ined by mqmlf~ lring limitqtio~ on the inside ~ ... t.Fr
of the box, the co~plin~ upset is defined by the rod ~ ."~r nd minimllm allowable (by
390 msmlf~lring limits) coupling inside .1;~..,. ter. If a larger di~m~.tPr co~pl;.~g is re~ u~d to
f~ itqte hqn~ling procedures, the coul7ling inside ~i-qmetpr is defmed by the rod and collpling
diqmPters. ~ g the couplin~ inside ~iqmPter increases the torque tl~laL.Ied over a
CA 02232925 1998-03-24
given thread length, so there is no &l~ tage fo reduçing the inside l~ . fwther than
n~cr7--.y for a given coupli.~g upset.
395 l' '- '- couplingyicldintc.rele r~ Usingthesele~lcdcouyl;~d:~-.,t~ ,thee~ g
yield ul~e.r.,.vnce is dete...l.nvd using Fqustinn 6.
Thread profile selection: The thread profile should then be selected to define the elTvvLi~,v
friction coPffir;Pnt for the fnctional torque load transfer rql~llstinn . nd the thread f~ y
par~.lvtvr for the critical thread section load c~p~c;l;Fs The .,ILvli~v friction co~ l is
400 given by Fquvti~)n 3, and the thread e~ r is defined in FqlJstiQn 2. The thread height must
be reduced as much as possible to ~ . the impact on the co~ g hoop strength and
stiffness at the mated cQl.l-r. l;nn ~ t,~lce 26'. Thread dope should be selected to give the
.. : ~;.. friction coPffiripn~ at make-up. This ensures that the torque capaviLy will not degrade
if well bore fluids migrate into the threads over time. Co~-~-e~ nc should be made-up to the
405 ~pt~;r;rd torque limit.
Thrcad length calculations for load transfer in threads: Four load transfer ~ l...l~l;..,.c
are p~rulllled to rq-lr,u~qte the .. ;~.: .. lhl~ded length rv~luir~ to transfer load for all critical
sectinnc Ty-pically, the torque transfer criteria govern. Threaded lengths required for torque
trànsfer are cqlr~llqted using F.~ ;nn~ 4 and 5. The threaded length based on an a~al load
410 transfer ul;l~,.iùll is çqle.~lqtrd using Equation 7. The longest thread length e~aled from
these c~l. ..15l;..,~c is used in the ;, ~l~s~ step.
Threaded section capacities check: The thread capacities are rhÇC~od by evaluating the
safety factors, using the llueaded length det~lluulv~ in the previous step. F~ ;ol~c 8 and 9
give the llltimqtç thread capacity ofthe cC~ ~nr~ Dividing these results by the l,,~yevli~e rod
415 body ultimQte cq-paritiçs gives the safety factors with respect to thread section limits. If the
safety factor is less than that desired, the thread length should be scaled up in plOpOI lion to the
d~
Coupling counterbore r~lcnlqt~ The cou,lLelbole torque is cqlrulQted by Fquqtinn 10.
This torque, or a portion of it, can be used to provide an Q~itionql safety factor. If the thread
420 length is govellled by the frictional torque transfer criterion, the portion of this value that isn't
used for a safety margin can be used to reduce the threaded length further, as desvlil,ed in the
following step.
Revise thread length for designs governed by friction: If r~ ;ol~l torque transfer
governs the threaded length, the cuullt~llJole torque load can be used to further oytill~lae the
425 coupling size.
To illustrate the use of the method of the present ul~ tiol~ the fol'o . . u~g Sample Design
Cqlrnlq*nn iS pl~S~ILCd. As c_n be a~yl~idt~ the ~.~e ltion is not ~nited to the p~vul~
14
CA 02232925 1998-03-24
&...~ ..c ~ ,lL,.g from any r~ n of optim;i~esign, but rather the scope of the il,~_.~ol~ is
defned by the scope ofthe claims at the end ofthis dr ~ The s. mple is p,~l merely to
430 ~ and ill~~ e one method for o~ g the design of a co ,pli.~C for a particular
c.~.. -.. sucker rod d;~ ,t~ in accordance with the ,.,~ on.
Sample Design Cql I~l;on
A sample design is ~ .,Led to d~ ~-or~ le one optimicqtion approacl, using the new
design eqllqtionc In this ~ plP, a cr~l1ne~;on design is de~loped for a 1 inch solid rod with
435 a 0.25 inch upset col~n~v~ - on the d;~ ~ t~-. A mqtPnq1 sh.,.-~Lh of 100,000 psi is ~ d
for the ~ ,;se, and the co, .~ values for elastic m~d~ s and Poisson's ratio are used:
30X106 and 0.3, I~ l,e~ ely. The following does not include design consid~.alioi~ for
tole.~ncin~, or mqm-f~ ring
Step 1: Cql~lqtç the bore .l;-~... te- using Fq~lqtir~n 1. The upset ratio is cqlenlqted from the
440 cQ!~Jling and rod .1;~.. t~ .~ and the l..~ .. allowable co!~pl;n~, bore ~ trr is d~,t~ .fd
using the axial section capacity:
d,
d~ = d, ~ .252 - 1= 0.562
Step 2: C~lrlllqtç the thread ,llt~.r~.~,..ce (on the .l:~ .. t~ l) to produce first yield in the co..~ g
445 using Fql~qtion 6:
d, 0.5626 0 45
' dC 1.2S
I=d ~Y [(l+V)+(1-2V ~,2]
C E ~
I =d ~V [(l+V)+(l-2v ~,2]
1 25 10Q000 [(1 + 0.3)+ (I - 2x o.3p.452]
30x lo6 ~/3 + o.452
450 I= 0.003215
Step 3:Define the basic thread fonn characteristics so that an effective friction factor and
thread Pffiri~nry may be defined. For this exercise a thread height of 0.025 is defined with
S~ll----.,LI;C load and stab flanks at 22.5~ from the plane ~ .l;c.llqr to the rod axis for an
in~ ded angle, ~, of 45~ between the two flanlcs. A sy-""-.,."c thread giving equal thread
455 width to the pin and box is used to optimise the thread effiri~nry. In the ~ ,;l-le:, the threads
CA 02232925 1998-03-24
are ~cllmed to mate p~r~;lly and transfer load only on the thread flanks. A coarse thread
pitch of 4 TPI (threads per inch) is used.
A cons~.valive friction coeffiri~nt of 0.1 is ~5l~me(1 The effective friction factor is
c~lcvl~ted using Fqu~tion 3
0.1 0 26
460 ' sin(~/2) sin(22.5~)
The thread Pffirienr,y is the ratio of the thread shear area to the total thread area. The
total thread width at the pitch line is 0.125 inches, and the width at the base ofthe thread is:
w=0.125+2tan(22.5~)(0.025/2)=0.135
=--= = 0.54
P 0.250
465 Step 4- C~lrul~tç the engaged thread length required for various critical sec,tion criteria. The,se
eqv~tionc are defined in terms of the thread pitch f~ t~ Therefore, the di~. ~,t~, ~ used in
these c~lc~ tinn~ reflect the pitch di~mpt~r of the thread.
The torque transfer rate criteria dPfining the ...~ allowable thread taper is given
by Fq~tion 4. The c~lc~ tion is made for the mated connection c.,l,ance 26' of the couFlinp
470 where the torque transfer requi~ e..l is most dP "~ g
< 2~,~ a2)
a~C [(1 + v) + a2(1 - 2v)]
d +h 1.0+0.025
=~X = ~ = =0.82
~ dC 1.25
< 2J~(0.26)(0.003215)(30x 106) (1 -0.822)
- (100,000)(0.82)(1.25) ~(1 + 0.3)+ 0.822(1 - 2(0.3))
tsO.178
475 The .on~g~d thread length is c.~lc--l~ted from the taper equation:
d -d
Lt
L do-d~ 1 0- 5625=2.45inches
t 0.178 (a)
The axial load transfer rate cnteria gives a m~xim--rn taper by Equation 7. This would
not normally govern the design, but is incl~lded here for completeness. The maximum taper
480 allowed by the axial load transfer rate criterion is given by
S 2J7
16
CA 02232925 1998-03-24
t ~ 2(0.54) o 62
~ (b)
This value is over three times larger than that based on the torsional transfer rate
.ion and ll,. ,~ rO,~ does not govern the design.
485 The total to,a;onal load transfer capacity is given by Fquation 5:
T 7~clEdcL 2-v 1r~( l+v) +( 1-2v) ~OZ~ ~OZ-aCz
4( aO-~x~) ( 1-2v) 2 ~ +V) +( 1-2v) aC2) 1 2
The ultimate torque capacity of the rod body is given by
ay ~ 100,00o ~(1-0) = 15 100in - Ibs.
Y ~/~ 12 ~ 12
The value for a~ is also upda-ted to the thread pitch line, inclea~lg its value to 0.47
490 from 0.45. Solving for L so that the torque transfer capacity equals the l~ltimate rod body
cdpaciLy gives:
L = 1.35 inches (c)
The length based on the torque transfer rate is higher than that based on the total
torque transfer. Because the ~ngaged length c~ ted from the taper equation of 2.45 inches
495 is longer (L~ above), it is used in the l~ design steps because it results in the other
criteria being s ~icfied
StepS:Check load safety factors on the thread shear area using Fqu~tionc 8 and 9. The
torsional load capacity for the thread shear area is (Equation 8) in terms of the thread pitch line
g~ tly is:
Tr = ~T7 v [(do ~ h)2 + (do ~ hXd~ - h)+ (d, _ h)2
500 6~
T = ~r(0 54)(100~ooo)(2 45)(l oZ +(l.0)(0.5625)+(0 56252)
T, = 75,300in.- Ibs.
Torque Saftey Factor = 75~300 = 4 6
15,100
The axial load capacity of the thread is col.")a.~d with the lllSim~te rod body
505 axial load capacity. The rod body capacity is:
~:avd2 ~r(100,000)(l ~) = 78,500 Ibs.
The thread capacity is given by Equation 9:
CA 02232925 1998-03-24
ayL(d d 2h) ~(0.54)(10Q~00)(2.45)(1 025+05875-0.05)
~ = 376,0001bs
,~xi~ fetyFactor= 37~'000=4.79
510 78,500
Both axial and torsional safety factors indicate adequate thread shear area capacity, so
the e ~ d thread length remains at 2.4S inches.
Step6:The cou..l~o,e torque is ç~lc~ tPd from Fqllatinn lO~Most ofthe a-~ n
load is developed with a length of 0.2S inches, at which Pc is 463-lbs./in. Fqll-~inn 10 giYes a
515 cu~ .L~olc torque as:
T ~a2Pcdc2 ~(0.82)2(~(1.2S)2
T~, = 1280 in. - lbs.
In this PY~mplP the effective cou,,l~-l,o,c length and the a~ I;nn torque are small
because of the wall th;~nPss in the coul,l~,.bore. An actual design would probably accept this
520 as a modest (8%) improvement in the overall safety factor.
Step 7: O~ ;on with cou"lc,l,ore could be done to reduce the overall thread length. The
;nn torque can be used to reduce the effective co~ r.,l;n~ c..l,~nce ~ in the
thread taper and thread length c~lcul~tion~ in Steps 4a and 4c. ~c~...,.;.,~ the ~-1~",..,1i.1;nn
torque is ll~la~ d at the first ~ng~gPd thread, the ~ torque is:
525 Tyl =~ru-To = l~,lO0-1,280=13,800in.-lbs
The critical t~i~mPtPr for ca.,y;"g this torque is c~lc~ tPd from the ultimate torque
eq~-ation
ay ~3
T"= ~
d = 3112~l2l~(l378oo)
V ~cry~(100,000)
530 Step 4 can be re-evaluated with dol repl~ ing do. ~jllcting the tli~nnptpts to thread
pitch ~i~metçrs gives:
dol +h 0.971+0.025 0 797
ol dc 1.25
The thread lengths determined in Steps 4 then become:
L, = 1.98 in. (compared with 2.45 in.)
18
CA 02232925 1998-03-24
535 L, = 1.12 in. (co.~lparcd with 1.25 in.)
However, this is the length from the effective J;~ t~r (0.973 inches), not from the
thread start. The criteria from step 4a governs, so using the thread taper from that ç~ lA~;nn
gives the total e-~g~ thread length required:
(d - d 1) 6
L,, 1 979 (1.0-.971) 2 12i ches
540 0.21
~ this example the thread length can be reduced by 13% if the cou,l~.l,o~eop1;~..;C~l;on is used. For thicker wall cuu.lt~-l,ol~,s the i~ u~ can be even greater,
provided the torque transfer rate (Step 4a), or the total torque criteria (Step 4b) governs.
The final sample co~ ;nn dim~nci~nc are ~he.~rul~ as follows:
545 Rod ,I;,.. t~ ~ (d.) = 1.00 in. 25.4mm
Coupling ~ -.- t~ (&) = 1.25 in. 31.75mrn
Coupling bore diarn. (d~-h) = 0.5625 in. 14.29mm
Co~lnt~,.l,û.c diam. (do+h) = 1.05 in. 26.67mm
Cou-~ o,c length (Lc) = 0.25 in. 6.35mm
550 Thread height (h) = 0.025 in 0.64mm
Flank angle (~) = 22.5~ (45O in~lnded angle)
Pitch~ .. t~-.,
co~ g e.l~ ce(dO) = 1.025 in. 26.04mm
collpling centre (&) = 0.5875 in. 14.92mm
555 Threadlength (L) = 2.12in. 53.85mm
Thread pitch (defined term) = 4 threads per inch (0.25 in./thread) (6.35
mm/threaad)
Figure 7 illustrates the benPfici~l end result ûf the con~ ;Qn of the instant invention
over prior art collrlingc which include a torque shoulder, where Figure 7A shows a ~ d~d 1
560 inch courlinE~ within a typical 2.875 inch ~ tubing, Figure 7B a one inch conv~,.l ional
rlimhole co--pling and Figure 7C a co~-pling in accordance with the present invention. As
illustrated, a co.~.~P~I;on dPcignPd using the above opl;~ ;on method for a nominal one inch
sucl~er rod would have a maximum outside rli~m~t~or of 1.25 inches (3.175 cm) and a length of
5.8 inches (14.73 cm) and will provide as much as 263 percent more flow area about the
565 co~rling than prior art convention~l courlingc decignP,d for- the same rod body 12.
Furthc..l.ol~, with respect to fatigue stresses, the rednc.tion in st~n~offreduces fatigue stresses
appleciably. For e~..ple, for the 1" rod in the sample design under a 15,000 Ib. tensile load in
19
CA 02232925 1998-03-24
a well section with a curvature of 15 degree/lOOft, the bending COI~C~ a~iOniS only 2.3 times
the n-min~l curvature or 53% the bendi~lg co~ .l.dlion of 4.3 produced by co.,~ ional
570 co~ 8c
As can now be app,.,~,;ated, the invention is not limited to the pa,~.,~,lers and e-- - plts
which are given above for the purpose of teachin~ how to practice the invention, but rather is
defined by the following claims.
