A New Heat Source Model for Keyhole Plasma Arc Welding in FEM. analysis of the temperature

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1 Nw at Sourc Modl for Kyhol Plasma rc Wldng n FEM nalyss of th Tmpratur Profl Th modl taks nto consdraton kyhol confguraton and dcay of hat dstrbuton along th workpc thcknss BY C. S. WU,. G. WNG, ND Y. M. ZNG BSTRCT. It s a ky ssu to stablsh an approprat modl of th hat sourc n th smulaton of kyhol plasma arc wldng (PW). It rqurs that th modl account for th kyhol ffct and hav th charactrstc of volumtrc dstrbuton along th drcton of th plat thcknss. For avalabl hat sourc modls, nthr Gaussan nor doubl llpsodal mods of hat sourc s applcabl to th kyhol PW procss. Consdrng th forc of th hgh-spd plasma jt and th assocatd strong momntum, a modfd thrdmnsonal concal hat sourc modl s proposd as th bass for th numrcal analyss of tmpratur flds n th kyhol PW procss. Furthr, a nw hat sourc modl for quas-stady stat tmpratur fld n kyhol PW s dvlopd to consdr th bugl-lk confguraton of th kyhol and th dcay of hat ntnsty dstrbuton of th plasma arc along th drcton of th workpc thcknss. Basd on ths hat sourc modl, fnt-lmnt analyss of th tmpratur profl n kyhol PW was conductd and th wld gomtry was dtrmnd. Th rsults showd that th prdctd locaton and locus of th mlt-ln n th PW wld cross scton ar n good agrmnt wth xprmntal masurmnts. Introducton Plasma arc wldng (PW) offrs sgnfcant advantags ovr convntonal gas tungstn arc wldng (GTW) n trms of pntraton dpth, jont prparaton, and thrmal dstorton (Rfs. 1, ). Th arc usd n PW s constrctd by a small nol and has a much hghr gas vlocty ( m/s) and hat nput ntnsty C. S. WU and. G. WNG ar wth th Insttut for Matrals Jonng, Shandong Unvrsty, Jnan, Chna. Y. M. ZNG s wth th Cntr for Manufacturng and Dpartmnt of Elctrcal and Computr Engnrng, Unvrsty of Kntucky, Lxngton, Ky. ( w/m ) than that n GTW (gas vlocty 8 15 m/s, hat nput ntnsty w/m ) (Rfs., 4). s th plasma arc mpngs on th ara whr two workpcs ar to b jond, t can mlt matral and crat a moltn lqud pool. Bcaus of ts hgh vlocty and th assocatd momntum, th arc can pntrat through th moltn pool and form a hol n th wld pool, whch s usually rfrrd to as a kyhol (Rf. 5). Movng th wldng torch and th assocatd kyhol wll caus th flow of th moltn mtal surroundng th kyhol to th rar rgon whr t rsoldfs to form a wld bad. Th kyhol mod of wldng s th prmary attrbut of hgh-powr dnsty wldng procsss (PW, lasr wldng, and lctron bam wldng), whch maks thm pntrat thckr pcs wth a sngl pass. Compard to lasr wldng and lctron bam wldng, kyhol PW s mor cost ffctv and mor tolrant of jont prparaton, though ts nrgy s lss dns and ts kyhol s wdr (Rf. 4). Thus, kyhol PW has found applcatons on th wldng of many mportant structurs (Rfs. 6 14). lthough kyhol PW has th potntal to rplac GTW n many applcatons as a prmary procss for prcs jonng (Rf. 1), th stabl stat of th kyhol s an mportant ssu n applyng PW (Rf. 15). In kyhol PW, th qualty of th wld dpnds on th kyhol stablty, whch tslf dpnds on a larg numbr of factors, spcally th physcal charactrstcs of th matral to b KEYWORDS Fnt Elmnt nalyss Plasma rc Wldng Kyhol Wldng at Transfr Thrmal nalyss wldd and th wldng procss paramtrs to b usd (Rf. 5). Thus, kyhol PW s suscptbl to th varaton of wldng procss paramtrs, whch maks t hav a narrowr rang of applcabl procss paramtrs for good wld qualty so that kyhol PW s stll lmtd n ts wd applcaton n ndustry (Rf. 16). Th tmpratur profl around th wld pool has grat nflunc on th formaton and stablty of kyhol. Through numrcal smulaton of th tmpratur fld and th wld pool bhavor n kyhol PW, th procss paramtrs can b optmd for obtanng hgh-qualty of wld structur. Thrfor, t s of grat sgnfcanc to modl and smulat th tmpratur dstrbuton and wld pool gomtry n th kyhol PW procss. Th ky ssu for numrcal analyss of tmpratur fld n kyhol plasma arc wldng s how to dvlop a hat sourc modl that rflcts th thrmo-physcal charactrstcs of th kyhol PW procss. Bcaus of th complxty of th phnomna assocatd wth th formaton of a kyhol, only a lmtd numbr of thortcal studs tratng th PW procss hav bn rportd, ach of varyng dgrs of approxmaton, and ach focusng on dffrnt aspcts of th problm (Rfs. 11, 17 1). Gnral Gaussan or doublllpsodal hat sourc modls usd wdly n smulaton of arc wldng procsss ar not sutabl for kyhol PW. s th frst stp n a srs of study, ths papr focuss on dvlopng a sutabl hat sourc modl for fnt-lmnt analyss of tmpratur profl n kyhol PW. Modls of at Sourc n Kyhol PW s mntond abov, th ky problm n FEM analyss of kyhol PW s how to modl th wldng hat sourc. Most rsarchrs mployd a Gaussan dstrbuton of hat flux (W/m ) dpostd on th sur- 84-s DECEMBER 6

2 Fg. 1 Schmatc of TDC modl. Fg. Schmatc of MTDC modl. Fg. Schmatc of kyhol and wld pool. Fg. 4 Schmatc of QPW modl. fac of th workpc (Rfs. 4). lthough such a surfac mod of hat sourc may b usd for th shallow pntraton arc wldng procsss lk GTW, t dos not rflct th acton of arc prssur on th wld pool surfac so that t s not sutabl for modlng th wldng procsss wth dpr pntraton lk gas mtal arc wldng (GMW). Goldak proposd a doubl-llpsodal hat sourc modl, whch has th capablty of analyng th thrmal hstory of dp pntraton wlds lk GMW (Rf. 5). owvr, th doubl-llpsodal dstrbuton of hat ntnsty (W/m ) s stll not applcabl to th hgh-dnsty wldng procsss wth hgh rato of th wld pntraton to wdth, such as kyhol PW (Rf. 6). Kyhol PW producs a wld wth hgh rato of dpth to wdth. Th cross scton of th wld s of th bugl-lk confguraton. To consdr th strong acton of th plasma jt and th rsultd bugl-lk wld confguraton n kyhol PW, nw typs of wldng hat sourc modls must b proposd. Thr-Dmnsonal Concal at Sourc Thr-dmnsonal concal hat sourc (TDC) s a volumtrc hat sourc that consdrs th hat ntnsty dstrbuton along th workpc thcknss. s shown n Fg. 1, th hat ntnsty dpostd rgon s maxmum at th top surfac of workpc, and s mnmum at th bottom surfac of workpc. long th thcknss of th workpc, th damtr of th hat dnsty dstrbuton rgon s lnarly dcrasd. But th hat dnsty at th cntral axs (-drcton) s kpt constant. t any plan prpndcular to -axs, th hat ntnsty s dstrbutd n a Gaussan form. Thus, n fact, TDC s th rpatd addton of a srs of Gaussan hat sourcs wth dffrnt dstrbuton paramtrs and th sam cntral maxmum valus of hat dnsty along th workpc thcknss. In ths way, th hatng acton of th plasma jt through th workpc n kyhol PW s consdrd. t any plan prpndcular to th - axs, th hat ntnsty dstrbuton may b wrttn as r QV ( r, )= Q xp r (1) whr Q s th maxmum valu of hat ntnsty, r s th dstrbuton paramtr, and r s th radal coordnat. Th ky problm s how to dtrmn th paramtrs Q and r. s shown n Fg. 1, th hght of th concal hat sourc s =, th - coordnats of th top and bottom surfacs ar and, rspctvly, and th damtrs at th top and bottom ar r and r, rspctvly. Th dstrbuton paramtr r s lnarly dcrasd from th top to th bottom surfacs of th conc rgon, and t can b xprssd as r ( )= r r r () Through complt drvaton (s ppndx), Equaton 1 s of th followng form WELDING JOURNL 85-s

3 Fg. 5 Th grd systm. Fg. 6 Th thrmal conductvty vs. tmpratur. Tabl 1 Th Paramtrs Usd for at Sourc Mods at Sourc Mods r (mm) r (mm) (mm) (mm) D h (mm) TDC MTDC QPW Tabl Kyhol PW Wldng Procss Paramtrs Cas Wldng Currnt rc Voltag Wldng Spd Plasma Gas Flow Shldng Gas Flow () (V) (mm/mn) Rat (L/mn) Rat (L/mn) Tabl Comparson of th Prdctd and Exprmntal Wld Wdth Top Wld Wdth (mm) Bottom Wld Wdth (mm) at Sourc Prdctd Masurd Prdctd Masurd TDC MTDC QPW ηUI QV ( r, )= π 1 1 r rr r + + r xp r () whr η s th plasma arc powr ffcncy, U s th arc voltag, and I s th wldng currnt. Modfd Thr-Dmnsonal Concal at Sourc lthough th thr-dmnsonal concal hat sourc taks consdraton of th hat ntnsty dstrbuton and dcay along th workpc thcknss, ts charactrstc of lnar dcln s not approprat. In kyhol PW, a bugl-lk wld confguraton was th rsult. To rflct ths fatur, a modfd thr-dmnsonal concal (MTDC) hat sourc s proposd, whch s shown n Fg.. For th MTDC hat sourc, th dstrbuton paramtr r dcrass no longr as lnarly as for TDC, but n a curvlnar way. s shown n Fg., th hght of th modfd thr-dmnsonal concal (MTDC) hat sourc s =, th - coordnats of th top and bottom surfacs ar and, rspctvly, and th damtrs at th top and bottom ar r and r, rspctvly. Lt r rprsnt th dstrbuton paramtr at. r s dcrasd nonlnarly and can b xprssd as r ( )= a+ b (4) ftr complt drvaton and manpulaton (s ppndx), th hat ntnsty for MTDC can b wrttn as UI η 1 r QV ( r, )= xp ( ) π 1 r whr ( + ) + = a ( + ) + aa ( b) r r a = r r b = r r r ( )= ( ) ( ) r 1 + n r ( ) ( ) (5) + b (6a) (6b) (6c) (6d) 86-s DECEMBER 6

4 Fg. 7 Th hat transfr coffcncy and spcfc hat vs. tmpratur. Fg. 8 Comparson of prdctd PW cross scton wth xprmntal rsults. B Fg. 9 Th cross scton of a plasma arc wld undr wldng condton Cas 1. Th prdctd rsult basd on modl QPW; B macrograph. Quas-Stady Stat PW at Sourc s aformntond, th arc usd n th PW procss s constrctd by a small nol and has a much hghr gas vlocty and tmpratur than that n GTW. Th hgh plasma gas vlocty and th assocatd momntum forc th plasma jt to pntrat th bas mtal, formng a kyhol n th wld pool of complt pntraton. Thus, th plasma jt mrgs from th undrbad at th bottom of th workpc Fg.. s th torch movs along th wld, ths kyhol progrssvly cuts through th mtal wth th moltn mtal flowng bhnd to form th wld bad. Th s and shap of th kyhol producd by PW dpnd manly on th prssur of th mpngng gas. It was found that a typcal plasma arc kyhol n 6-mm-thck stanlss stl, -mm nol bor damtr, and 8 1 mm torch standoff s a concal hol wth a crcumfrntal damtr of 5 mm at th top and about 1.5 mm at th bottom nd (Rf. 7). Th forcs that tnd to form and mantan th kyhol nclud th plasma stram prssur, vapor prssur, and rcol prssur (Rf. 7). Th xstnc of kyhol, on on hand, maks th hat ntnsty from th plasma arc dstrbut through th workpc thcknss, but on th othr hand, causs som vaporaton, whch rsults n som hat losss. Thrfor, th nt hat nput s not dpostd on th workpc totally. To consdr ths pont, part of th hat dnsty at th uppr scton of th kyhol s xcludd. s shown n Fg. 4, th hat ntnsty s dstrbutd wthn a doman boundd by th curvs f () and f 1 () at th uppr scton of th kyhol, whl at th lowr scton of th kyhol, th hat ntnsty s dstrbutd as a modfd concal hat sourc. Ths modl of hat sourc s proposd for th quas-stady stat PW procss, so t s rfrrd to as QPW for short. It can b xprssd as For th uppr part, ( D h ) IU η r QV ( r, )= xp, π 1 f ( ) f1 r f whr r f1 ( )= + Dh Dh (7) (8) (9) For th lowr part, ( D h ), t s of th sam xprsson as Equatons 5 and 6. FEM nalyss r r f ( )= ( ) ( ) r 1 + n r ftr stablshng a sutabl hat WELDING JOURNL 87-s

5 Fg. 1 Comparson btwn th prdctd and masurd wld cross scton for Cas 1. sourc modl for kyhol PW, th tmpratur profl and wld pool gomtry ar abl to b dtrmnd by th fnt lmnt mthod (FEM). In a movng coordnat systm o-xy n whch th orgn concdd wth th ntrsctng pont btwn th torch cntrln and th bottom surfac of workpc, x-axs along th wldng drcton and -axs normal to th workpc surfac, th quas-stady stat tmpratur fld durng kyhol PW s govrnd by th followng quaton T ρc v x x k T P = x + y k T y + + k T (1) whr ρ s dnsty, C P s spcfc hat, v s wldng spd, T s tmpratur, k s thrmal conductvty, and Q V s volumtrc hat sourc. Th boundary condtons for Equaton 1 ar as follows: On th workpc surfac, k T = α T T T Q V (11) whr T s th ambnt tmpratur, and α T s th combnd hat transfr coffcnt. t th symmtrc plan xo, T = y (1) So only half of th workpc s takn as th calculaton doman. Th workpc dmnson s mm n lngth, 8 mm n wdth, and 9.5 mm n hght. Th half doman s dvdd nto 8-nod hxahdrons. s aformntond, part of hat dnsty at th uppr scton of kyhol s xcludd bcaus of vaporaton loss and kyhol ffct. To rflct ths charactrstc and match th dstrbuton mod of hat sourc QPW, som lmnts n th uppr scton of th kyhol ar tratd as dad. Th dscrt grds ar shown n Fg. 5. Rsults Th workpc matral s stanlss stl 4. Its thrmal conductvty k, spcfc hat C P, and th combnd hat transfr coffcnt α T ar shown n Fgs. 6 and 7. Its dnsty s ρ = 786 (kg m ), and ambnt tmpratur s T = K. Th paramtrs usd for dscrbng hat sourc mods ar gvn n Tabl 1. Kyhol PW xprmnts ar conductd undr two wldng condtons (Tabl ). Th arc powr ffcncy η taks a valu of.66 basd on th ltratur (Rf. ). ftr wldng, a macrograph of th wld s mad to show ts cross scton. Frstly, two knds of volumtrc hat sourc modls,.., thr-dmnsonal concal (TDC) and modfd thr-dmnsonal concal (MTDC), ar usd to prdct th plasma arc wld gomtry. Fgur 8 shows th comparson of th xprmntal rsults wth th prdctd ons basd on dffrnt modls. Tabl gvs th data of wld wdth. From th pont of vw of agrmnt, th calculaton prcson of TDC s poorr. It can b sn that TDC s not sutabl for dtrmnng kyhol plasma arc wld dmnsons. Though th prcson of MTDC s mprovd compard to TDC, spcally th wld wdth at both top and bottom surfacs, th calculaton prcson for th locaton and locus of th mlt-ln n th wld cross scton s stll lowr. Fg. 11 Th cross scton of a plasma arc wld undr wldng condton Cas. Th prdctd rsult basd on modl QPW; B macrograph. Scondly, th dvlopd hat sourc modl for quas-stady stat kyhol PW,.., QPW, s mployd to calculat th wld gomtry. Fgurs 9 1 show th comparson of xprmntal rsults wth th prdctd ons basd on QPW modl for wldng condtons Cas 1 and Cas, rspctvly. In Fgs. 9 and 11, th dottd lns ar drawn along th sothrm of mltng tmpratur. It can b sn that th prdctd wld gomtry agrs wll wth xprmntal masurmnts. Snc th modl QPW dpcts th charactr of th kyhol PW procss through consdrng th bugl-lk confguraton of th kyhol and th dcay of hat ntnsty dstrbuton of th plasma arc along th drcton of th workpc thcknss, th calculaton prcson of th wld gomtry at th cross scton s qut satsfactory. Concluson B Bcaus of th kyhol ffct, a plasma arc wld has a larg pntraton-to-wdth rato. For numrcal analyss of wldng tmpratur profl n kyhol PW, an 88-s DECEMBER 6

6 Fg. 1 Comparson btwn th prdctd and masurd wld cross scton for Cas. approprat hat sourc modl must b dvlopd to consdr th hgh-spd plasma jt and th assocatd strong momntum actd to th wld pool and th dstrbuton of hat ntnsty along th drcton of th workpc thcknss. Bcaus nthr th doubl-llpsodal mod of th hat sourc nor th thr-dmnsonal concal mod of th hat sourc can b approprat for th fnt lmnt analyss of th kyhol PW procss, a modfd thr-dmnsonal concal hat sourc modl (MTDC) s put forward to rflct th nonlnar dcay of hat ntnsty dstrbuton along th drcton of th workpc thcknss. lthough MTDC can b usd to calculat th wld wdth on both th top and th bottom surfacs of th workpc, for th locaton and locus of th mlt-ln n th wld cross scton, ts calculatng prcson s lowr. nw hat sourc modl for th quasstady stat kyhol PW,.., QPW, s proposd, whch dpcts th charactrstc of th kyhol PW procss qut wll, bcaus t consdrs both th bugl-lk confguraton of th kyhol, and th dcay of hat ntnsty dstrbuton of th plasma arc along th drcton of th workpc thcknss. Th QPW hat sourc modl s appld n fnt lmnt analyss of th tmpratur fld. Th rsults show that th calculatd wld gomtry at th cross scton s n good agrmnt wth th xprmntal on. cknowldgmnts Th authors wsh to thank th fnancal support for ths rsarch from th Natonal Natural Scnc Foundaton of Chna (Grant No ) and th Ky Projct of Chns Mnstry of Educaton (Grant No.1419). Rfrncs 1. Grag, E Th plasma arc wldng rvw. Wldng Journal 67(): Tomsc, M., and Barhost, S Kyhol plasma arc wldng of alumnum wth varabl polarty powr. Wldng Journal 6(): 5.. Mtcalf, J. C., and Qugly, M. B. C at transfr n plasmaarc wldng. Wldng Journal 54(): 99-s to 1-s. 4. Lancastr, J. F Th Physcs of Wldng, chaptr 8, Prganon Prss, Oxford. 5. Mtcalf, J. C., and Qugly, M. B. C Kyhol stablty n plasma arc wldng. Wldng Journal 54(11): 41-s to 44-s. 6. Martkann, J. K., and Moso, T. J. I Invstgaton of th ffct of wldng paramtrs on wld qualty of plasma arc kyhol wldng of structural stls. Wldng Journal 7(7): 9-s to 4-s. 7. Vlkas, E. P Plasma arc wldng of xhaust pp systm componnts. Wldng Journal 7(4): Irvng, B Why arn t arplans wldd? Wldng Journal 76(1): Irvng, B Plasma arc wldng taks on th advancd sold rockt motor. Wldng Journal 71(1): Nuns,. C Varabl polarty plasma arc wldng on th spac shuttl xtrnal tank. Wldng Journal 6(9): Kann, R. G., and Rubnsky, B Plasma arc wldng undr normal and ro gravty. Wldng Journal 69(6): Zhang, Y. M., and Lu, Y. C.. Modlng and control of quas-kyhol arc wldng procss. Control of Engnrng Practc 11(1): Lu, Y. C. 4. Control of dynamc kyhol wldng procss. PhD thss. Unvrsty of Kntucky. 14. Chn, K. X, L,. Q., and L, C. X. 4. Survy of varabl polarty plasma arc wldng. Transactons of th Chna Wldng Insttuton 5(1): Zhang, Y. M., and Zhang, S. B Obsrvaton of th kyhol durng plasma arc wldng. Wldng Journal 75(): 5-s to 59-s. 16. Dong, C. L, Wu, L., and Shao, Y. C.. Th hstory and prsnt stuaton of kyhol plasma arc wldng. Chns Mchancal Engnrng 11(5): su, Y. F., and Rubnsky, B Transnt mltng of a mtal plat by a pntratng plasma arc. SME J at Transfr 19(5): su, Y. F., and Rubnsky, B Twodmnsonal hat transfr study on th kyhol plasma arc wldng procss. Int. J at Mass Transfr 1(7): Nhad,. K Enthalpy tchnqu for soluton of Stfan problms: pplcaton to th kyhol plasma arc wldng procss nvolvng movng hat sourc. Int. Comm. at Mass Transfr (6): Kann, R. G., and Rubnsky, B Thr-dmnsonal smulaton of th plasma arc wldng procss. Int. J at Mass Transfr 6(1): Fan,. G., and Kovacvc, R Kyhol formaton and collaps n plasma arc wldng. J Phys D: ppl. Phys. : Kou, S., and Wang, Y Computr smulaton of convcton n movng arc wld pools. Mtall. Trans. 17: Fan,. G., Na, S. J., and Sh, Y. W Mathmatcal modl of arc n pulsd currnt gas tungstn arc wldng. J Phys D: ppl. Phys. : Wu, C. S., and Yan, F. 4. Numrcal smulaton of transnt dvlopmnt and dmnuton of wld pool n gas tungstn arc wldng. Modlng and Smulaton n Matrals Scnc and Engnrng 1: Goldak, J., Chakravart,., and Bbby, M nw fnt lmnt modl for wldng hat sourcs. Mtall. Trans. B 15(6): Wang,. X., Wu, C. S., and Zhang, M. X. 5. Fnt lmnt mthod analyss of tmpratur fld n kyhol plasma arc wldng. Transactons of th Chna Wldng Insttuton 6(7): Brtoluo, G. O Plasma varabl polarty pulsd arc wldng 1.7 mm thck alumnum. Proc of IIW san Pacfc Wldng Confrnc, uckland, Nw Zaland. pp ppndx 1 Drvaton for at Intnsty Dstrbuton Equatons For a volumtrc dstrbuton of hat ntnsty, th followng assumptons ar mad: 1) Th hat ntnsty dpostd rgon s maxmum at th top surfac of workpc, and s mnmum at th bottom surfac of workpc. ) long th thcknss of th workpc, th damtr of th hat dnsty dstrbuton rgon s dcrasd n som way. But th hat dnsty at th cntral axs (drcton) s kpt constant. t any plan prpndcular to -axs, th hat ntnsty dstrbuton may b wrttn as r QV ( r, )= Q xp r (1) whr Q s th maxmum valu of hat ntnsty, r s th dstrbuton paramtr, and r s th radal coordnat. Th ky WELDING JOURNL 89 -s

7 problm s how to dtrmn th paramtrs Q whn th dcay rul of r s known. Bcaus of thrmal nrgy consrvaton, w hav π r ηui = QV ( r, ) rdrdθdh π r r = Q xp rdrdθ dh r πq r r = r xp r r d dh r πq 1 = r dh () whr η s th plasma arc powr ffcncy, U s th arc voltag, and I s th wldng currnt. Thr-Dmnsonal Concal at Sourc (TDC) s shown n Fg. 1, r dcrass lnarly for TDC. Th hght of th concal hat sourc s =, th -coordnats of th top and bottom surfacs ar and, rspctvly, and th damtrs at th top and bottom ar r and r, rspctvly. Th dstrbuton paramtr r can b xprssd as or h r = r + ( r r) h, = Snc Substtutng 5 nto, thn πq ( 1 ) ηui = r + rr + r 9 9ηUI 1 Q = π 1 r rr r Fnally, substtutng 6 nto 1, w gt 9ηUI QV ( r, )= π 1 1 xp ( ) r + rr + r ( r ( )= r r r Modfd Thr-Dmnsonal Concal at Sourc () (4) (5) (6) (7) s shown n Fg., th hght of th modfd thr-dmnsonal concal (MTDC) hat sourc s =, th -coordnats of th top and bottom surfacs ar and, rspctvly, and th damtrs at th top and bottom ar r and r, rspctvly. Lt r rprsnts th dstrbuton paramtr at. r can b xprssd as r () = a +b ( + + ) ) h r dh r r r dh = + ( ) r r r = + + r r r (8) Bcaus thus r = a +b r = a +b Substtutng 9 and 1 nto 8, r r r ( )= ( ) ( ) r 1 + n r ( ) ( ) ( ) Lt h =. Snc r dh a b = ( 1 + ) dh = a1 ( h + )+ b n n dh = a ( h + ) dh + ab ( h + ) dh + b Basd on th Mathmatcs andbook, udu = uu u + C udu = u u udu = u u ( uu u)+ C = r dh a ( h + ) dh + ab 1 n( h+ ) dh+ b = a ( h+ ) ( h+ ) ( h+ ) ( + )+ ( + ) h h + ab ( h+ ) ( h+ ) ( h+ ) + b = a ( + ) ( + ) aa ( b) ( + ) ( + ) + b Substtutng 1 nto πq ( 1 ) πq ( ) ηui = r 1 dh= ηui Q = ( 1) Substtut 14 nto 1, w obtan ppndx Nomnclatur a Lt UI η r QV ( r, )= xp π 1 r Equaton 9 r r a = r r b = = r dh= a ( + ) ( + ) aa ( b) ( + ) ( + ) + b varabl, dfnd n varabl, dfnd n (9) (1) (11) (1) (1) (14) (15) 9-s DECEMBER 6

8 Equaton 1 b varabl, dfnd n Equaton 1 C P spcfc hat D h varabl, dfnd n Fg. 4 bas of natural lagarthm f functon, dfnd n Fg. 4 f 1 functon, dfnd n Fg. 4 h k thrmal conductvty Q maxmum valu of hat ntnsty hat ntnsty dstrbu Q v ton functon r x + y r radal coordnat n hat sourc mod r varabl, dfnd n Fgs. 1,, 4 r varabl, dfnd n Fgs. 1,, 4 T tmpratur T ambnt tmpratur U arc voltag v wldng spd x, y, coordnat varabl, dfnd n Fgs. 1,, 4 varabl, dfnd n Fgs. 1,, 4 hat loss coffcnt α T η θ ρ arc powr ffcncy angular varabl dnsty WELDING JOURNL Instructons and Suggstons for Prparaton of rtcls Txt approxmatly 15 5 words n lngth submt hard copy submssons va dsk or lctronc transmsson prfrrd format s Mac but common PC fls ar also accptabl accptabl dsks nclud floppy, p, and CD. Format nclud a ttl nclud a subttl or blurb hghlghtng major pont or da nclud all author nams, ttls, afflatons, gographc locatons sparat papr nto sctons wth hadngs Photos/Illustratons/Fgurs glossy prnts, slds, or transparncs ar accptabl black and wht and color photos must b scannd at a mnmum of dp ln art should b scannd at 1 dp photos must nclud a dscrpton of acton/objct/prson and rlvanc for us as a capton prnts must b a mnmum s of 4 n. x 6 n., makng crtan th photo s sharp do not mbd th fgurs or photos n th txt accptabl lctronc format for photos and fgurs ar EPS, JPEG, and TIFF. TIFF format s prfrrd. Othr llustratons should accompany artcl drawngs, tabls, and graphs should b lgbl for rproducton and labld wth captons rfrncs/bblography should b ncludd at th nd of th artcl Edtoral Dadln January ssu dadln s Novmbr 11 Fbruary ssu dadln s Dcmbr 1 March ssu dadln s January 1 prl ssu dadln s Fbruary 1 May ssu dadln s March 1 Jun ssu dadln s prl 9 July ssu dadln s May 1 ugust ssu dadln s Jun 1 Sptmbr ssu dadln s July 11 Octobr ssu dadln s ugust 11 Novmbr ssu dadln s Sptmbr 1 Dcmbr ssu dadln s Octobr 1 Suggstd topcs for artcls cas studs, spcfc projcts nw procdurs, how to appld tchnology Mal to: ndrw Cullson Edtor, Wldng Journal 55 NW LJun Road Mam, FL 16 (5) 44-95, xt. 49; FX (5) cullson@aws.org WELDING JOURNL 91 -s