CA2232925C - Sucker rod coupling - Google Patents

Abstract

An improved connection and method for making the connection for connecting sucker rods in a sucker rod string used to drive downhole pumps for producing fluid from an underground formation, the connection having an outside diameter no greater than one and one half times the outside diameter of the sucker rod and which uses the contact between the mating threads of the connection for transferring loads between connected sucker rods coupling.

Description

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, 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 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 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.

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.

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 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 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:

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 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 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 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 T ~Z77aylL (d h)2d d =d -tz t = do -d, = (do -h)-(d~ -h) 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 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 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~

&...~ ..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 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 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:

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.) 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 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.

Claims (13)

1. An improved connection for use in connecting sucker rods having an outside diameter and a full load capacity in a sucker rod string used to drive downhole pumps that pump fluids from an underground formation to the surface including a pin formed on an end of the sucker rod to be coupled, wherein the pin includes a tapered, threaded portion for coupling with a box having a correspondingly tapered, threaded bore to provide a box and pin connection having a taper, a thread length and a connection load capacity, the improvement comprising sizing the box and pin connection to have a maximum outside diameter when mated that is no greater than about one and one half times the outside diameter of the sucker rod to be coupled and wherein the tapered, threaded portion of the pin has opposing ends defining the tapered, threaded portion therebetween and is comprised of a core having threads formed thereon, wherein the core has a core diameter and a core length and wherein the taper is defined as the difference between the core diameters at opposing ends of the tapered, threaded portion divided by the core length between the opposing ends of the tapered, threaded portion and the taper is between .1 and .44 such that the connection load capacity meets or exceeds the full load capacity, including torsional load, of the sucker rod across the connection.

2. The improved connection of claim 1 wherein the connection further includes a make-up section and wherein the make-up section has its maximum nominal outside diameter no larger than the maximum outside diameter of the box and pin connection when mated.

3. The improved connection of claim 1 wherein the box is comprised of a separate box having an internal bore inwardly tapering from opposing ends and having threads formed on the bore which are configured to mate with the threaded portions of the pins of successive rods to be coupled.

4. The improved connection of claim 1 wherein the ratio of the thread length to the diameter of the sucker rod to be coupled is between .9 and 6.5.

5. The improved connection of claim 1 wherein the preselected thread form includes a flat pin crest and opposingly sloping load and stab flanks.

6. A connection for connecting sucker rods in a sucker rod string used to pump fluids from an underground formation to the surface comprising:
a pin formed on an end of a sucker rod to be coupled having threads formed on a tapered core to provide a threaded portion of the core, wherein the threaded portion of the core of the pin has a terminal end and an opposite end and wherein the threaded portion of the core of the pin is outwardly tapered from its terminal end, and wherein the core has a core diameter and the threaded portion of the core defines an axial length between the terminal end and the opposite end of the threaded portion, and the outward taper of the core is defined by the ratio of the core diameter at its terminal end minus the core diameter at its opposite end to the axial length of the threaded portion and said ratio is between .1 and .44;
and a box having a correspondingly tapered bore therein with mating threads on the bore for coupling with the pin to provide a box and pin connection in which all coupling load in use is born by the mating threads.

7. The connection of claim 6 wherein the ratio of the thread length to the diameter of the sucker rod to be coupled is between .9 and 6.5.

8. A method for optimizing the dimensions of a sucker rod connection comprised of a connection material and having an outside diameter for use in connecting sucker rods in a sucker rod string used to drive downhole pumping mechanisms to pump fluids from an underground formation to the surface comprising:
Providing a threaded box having an internal, tapered bore, the bore defining a bore taper, and a correspondingly tapered pin formed on an end of a sucker rod to be coupled, the pin having corresponding threads formed on a core of the pin for coupling with the threaded box, the core defining a corresponding core taper, wherein the corresponding pin and box threads have a thread length which satisfies the equation and wherein the corresponding core and bore tapers satisfy the equation where:
dc is the outside diameter of the connection;
ae is the ratio of the thread diameter to the outside diameter of the connection at a terminal end of the pin thread;
ao is the ratio of the thread diameter to the outside diameter of the connection at a terminal end of the box thread;
E is the Young's modulus material property for the connection material;

sin (.PHI. / 2) is an effective friction coefficient, where µ is the nominal friction coefficient of the thread interface, and .PHI. is the thread flank angle;

.sigma.y is the yield strength of the connection material;
v is Poisson's ratio material property for the connection material; and I is the coupling yield interference defined by the equation:

9. A method for making a sucker rod coupling having a coupling outside diameter and including a threaded pin portion and correspondingly threaded box portion for use in connecting sucker rods having a rod outside diameter in a sucker rod string used to drive downhole pumping mechanisms to pump fluids from an underground formation to the surface comprising the steps of:

(a) selecting a coupling outside diameter no greater than about one and one half times the rod outside diameter of the sucker rod to be coupled and a coupling inside diameter no greater than the square root of the coupling outside diameter squared minus the square of the rod outside diameter;

(b) determining the coupling yield interference for the selected coupling using a thick wall pressure vessel as the mathematical model for the calculated interference to determine radial and tangential stresses for the coupling and thereby determining the torque required for the coupling when the pin portion and box portion are mated; and (c) forming a coupling with corresponding threads formed on the box portion and pin portion which satisfy the torque requirements as determined in the selecting and determining steps.

10. A sucker rod coupling including a threaded pin portion and correspondingly threaded box portion for use in connecting sucker rods having a rod outside diameter in a sucker rod string used to drive downhole pumping mechanisms to pump fluids from an underground formation to the surface comprising:

(a) a tapered, threaded pin formed on an end of a sucker rod to be coupled and a correspondingly tapered, threaded box for coupling with the pin which, when coupled have a coupling outside diameter no greater than about one and one half times the rod outside diameter of the sucker rod to be coupled and a coupling inside diameter no greater than the square root of the coupling outside diameter squared minus the square of the rod outside diameter, each of the box and pin having threads having a thread form that satisfies the torque requirements for the mated coupling wherein the torque requirements are defined by calculating the coupling yield interference using a thick wall pressure vessel as the mathematical model for the calculated interference to determine radial and tangential stresses for the coupling.

11. The connection of claim 1 wherein the box has a terminal end and wherein the connection includes an entrance defined by the terminal end of the box and further comprising a seal between the box and pin adjacent the entrance to prevent migration of production fluids into the mating threads.

12. The connection of claim 6 wherein the box has a terminal end and wherein the connection includes an entrance defined by the terminal end of the box and further comprising a seal between the box and pin adjacent the connection entrance to prevent migration of production fluids into the mating threads.

13. A threaded box and pin connection for connecting sucker rods having a rod outside diameter in a sucker rod string used to pump fluids from an underground formation to the surface comprising:

(a) a pin formed on an end of a sucker rod to be coupled and having external threads formed on a tapered core having a core diameter, wherein the core has a proximal end and a distal end and wherein a thread length and a taper axe defined therebetween, wherein the ratio of the thread length to a largest diameter of the core is between .9 and 6.5 and wherein the taper, defined by the ratio of the core diameter at its proximal end minus the core diameter at its distal end to an axial length between the core diameters, is between .1 and .44; and (b) a box having a correspondingly threaded and tapered counterbore for coupling with the pin, wherein an outside diameter of the mated coupling corresponds to an outside diameter of the box, which outside diameter of the box is no more than about one and one half times the core diameter at its proximal end, which corresponds to the rod outside diameter of the rod to be coupled.