NEW METHOD FOR DETERMINING COOLING TIME AND PREHEATING TEMPERATURE IN ARC WELDING. Prof. Dr, University of Belgrade, High Technical School

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1 NEW METHOD FOR DETERMINING COOLING TIME AND PREHEATING TEMPERATURE IN ARC WELDING Valnina M. NEJKOVIĆ 1, Miroslav S. MILIĆEVIĆ *, Zoran J. RADAKOVIĆ 3 1 Assisan, Prof. Dr, Univrsiy of Niš, Faculy of Elcronic Enginring Prof. Dr, Univrsiy of Blgrad, High Tchnical School 3 Prof. Dr, Univrsiy of Blgrad, Faculy of Mchanical Enginring * Corrsponding auhor; milicvic.miroslav@ms.rs Sudy and rsarch on arc wlding hav providd idnificaion of rrors in formulas for calculaing h cooling im 8/5 and ohr dpndn paramrs. I is concludd ha larg rrors ar prsn in crain inrvals which had causd failurs in wlding chnologis. Incorrc approximaion of cooling mpraur is rplacd by a mor accura approximaion usd for dfining of h nw prcis algorihm for drmining rlvan wlding paramrs. Kywords: cooling im, mpraur, wlding, prhaing, prcis mhod 1. Inroducion Th opic of rsarch of his work is arc wlding, for which, according o rlvan liraur [1-9], a nw prcis algorihm for calculaing h pos-wld criical cooling im and cooling ra afr wlding can b obaind. Also, h nw procdur for drmining h cooling im and prhaing mpraur is providd. Fusion wlding procsss ar of concrn, including gas wlding, arc wlding, and high-nrgy bam wlding. Fusion wlding is a joining procss ha uss h fusion of h bas mal o cra h wld. Thr major yps of fusion wlding procsss ar givn: 1. Gas wlding: oxyacyln wlding (OAW).. Arc wlding: shildd mal arc wlding (SMAW); gas-ungsn arc wlding (GTAW); plasma arc wlding (PAW); gas-mal arc wlding (GMAW); flux-cord arc wlding (FAW); submrgd arc wlding (SAW); and lcroslag wlding (ESW). 3. High-nrgy bam wlding: lcron bam wlding (EBW); lasr bam wlding (LBW). Sinc h lcric arc is no involvd in h lcroslag wlding procss, i is no xacly an arc wlding procss. For convninc of discussion, i is groupd wih arc wlding. Basic work in his ara is sudid, rsarchd and prsnd in [10, 15]. According o our xprinc and from publishd rfrncs [16-19], a nw approach for solving problms of arc wlding and h calculaion of imporan paramrs has bn dvlopd. I is worh o mnion ha h main rsul of his rsarch includs a corrcion of h rror found also in h Briish Sandard.

2 . Exising hory for calculaing h cooling im in arc wlding Bfor prsning h algorihm for drmining spcific arc wlding paramrs, a prsnaion of xising analyical dpndncis is includd. Thy all dfin links bwn criical cooling im 8/5, h wlding inpu ha and prhaing mpraur. Th liraur [1-15] provids D and 3D modls of analyical dpndncis. Hnc, hr is a known rlaion givn by E.(1) for calculaing h cooling im, 8/5, in funcion of prhaing mpraur for h adopd D modl: Q 1 1 8/5 =, (1) 4 πλρcd (500 Tp) (800 Tp) whr: d - ransiion hicknss; Q -ha inpu; T p - prha mpraur; 8/5 - cooling im; λ - hrmal conduciviy [J (s m C) 1 ]; c - spcific ha [J (kg C) 1 ] and ρ - dnsiy [kg m 3 ]. I is known ha Q = /v, whr for arc wlding is = UIη. U is wlding volag [V] and I is wlding currn [A], η is h cofficin of wlding fficincy ha dpnds on wlding yp. Q is h ha inpu for a crain wlding ra [kj mm 1 ]. Euaion () is rcognizd for h 3D modl in drmining wlding paramrs: 8/5 Q 1 1 = πλ 500 Tp 800 T Euaion (3) is usd for h slcion of h wlding modl: d gr Q 1 1 = + ρc 500 T p 800 T p p. () 0.5. (3) Th modl of D yp is usd for dfining h hicknss for wlding if i is ual or lss han h valu givn in E.(3), ohrwis h 3D modl should b usd. All hs acions ar usd for improving h accuracy of calculaions. Euaions (1) and () hav bn usd for a long im whil hr was no criical simaion in pracical applicaions which includd h nir scop of us of variabls wihin diffrn yps of arc wlding. As an xampl, in h book [0] h following formulas ar providd, and in h PhD hsis [1], Es.(1) and () ar usd, which implis on h us of hs rlaions unil h priod of dvloping his rsarch. Th smallr numbr of rsarchs has drmind h dviaion of h calculad cooling im, bu hr wr no corrcions and no confirmaions of proof for obaining h corrc soluion. Thrfor, during h dvlopmn of h Briish Sandard in his ara of wlding [], h corrcion for a mor accura calculaion is givn by Es.(4) and (5), rspcivly, for h D and 3D modl. Q /5 = ( Tp ) 10 F, (4) d (500 Tp) (800 Tp) 1 1 8/5 ( T p ) Q = Tp 800 T F. (5) p Auhors of his work usd applid rsarchs of numrical xaminaions and concludd ha Es.(4) and (5) hav significan dviaions in som pars of h scop of us. Th work in [3] has dvlopd a nw modl.5d for calculaing h cooling im:

3 .5D 3D D 8/5 γ 8/5 β 8/5 = +. (6) I is usd for calculaion of nwly inroducd cofficins hrough us of rsuls from h D and 3D modls and xprimnal rsuls. Such calculaions offr corrc rsuls for on scop of variabls, bcaus h auhor has no confirmd and provd i horically. According o h rsarchd problms, auhors of his work applid a rlaion for obaining h corrc rsuls for all arc wldd marial hicknsss. 3. Dvlopmn of rlaions and forming of algorihm for prcis calculaion Dvlopmn of analyical dpndncy for cooling mpraur is conducd according o xprinc from [4] and from [10-13]. For xampl, for wo sl plas ha nd o b wldd, h mpraur disribuion can b dscribd by h ha uaion: T T T = a +, x y (7) whr h hrmal conducanc is givn by λ a =. (8) cγ If h mpraur T is uad by hicknss of plas and no dpndn on h z axis, h wlding is conducd along h x axis. Th sourc of ha is an lmn of volum dxdy and high d. According o [10, 11], h soluion of E.(7) is prsnd in h form of 0.5 vx v b Trx (, ) = xp K 0 r πλd a +, 4a a (9) whr: K 0 is modifid Bssl funcion of nd kind and 0 class. Sinc h cas of arc wlding includs highr valus of, E.(9) can b ransformd ino h form y T ( y0, ) = xp b. vd 4πλcγ 4a (10) Euaion (10) dvlops in h cas whn h highs cooling ra is in h wlding zon. Hnc, i can b confirmd ha y = 0 and xp( b) = 1, T () =. (11) vd 4πλcγ Cooling im for arc wlding, 8/5, can b dfind as a im diffrnc bwn 5 and 8. In his cas, 8 is a im whn T() rachs 800 C by cooling, and 5 is a im whn i rachs 500 C, 8/5 = 5 8. (1) Whn 8/5 is lss han ral for wldd sl, prhaing a mpraur T p should b conducd. Th ims 8 and 5 can b calculad if E.(11) is suard and solvd for : 1 =. (13) vd 4 πλcγ ( T T) p

4 and (15): Rplacmn in E.(13), T = 800 C will provid 8, or T = 500 C will provid 5 in Es.(14) = 8 vd 4 πλcγ (800 Tp ) = 5 vd 4 πλcγ (500 Tp ) 1 1, (14). (15) If h rplacmn is placd for Es.(14) and (15) in E.(1), w arriv a E.(1), prsning h D Rosnhal modl for calculaion of im 8/5. Howvr, auhors of his work alrady concludd ha his rlaion dos no provid accura valus in many applicaions. Thrfor, in cas whn y = 0, h E.(10) bcoms T ( ) = xp( b). (16) vd 4πλcγ Th following xampl is providd for drmining h dviaion of E.(11) rlaing o E.(16). Exampl 1. Thr is ha in h amoun of 1 = J/cm for arc wlding, whr sl plas of hicknss 7.4 [mm] ar wldd wih prhaing o T p = 180 C. Thr should b T() graphics drawn and im of cooling 8/5 should b providd in cas of applicaion of Es.(11) and (16). Th valu 1 is drivd from xprssion 1 = /v, so afr rplacmn of valus for consans, h rlaion E.(11) bcoms and E.(16) bcoms T () 453 =, (17) b T ( ) = 453. (18) Th valu b is a funcion of h applid sl for wlding and is gomry which can b confirmd in [5-8]. Figur 1 shows h diagram for cooling mpraurs in his xampl as a funcion of im. I can b sn ha funcion T 1 () has a slowr dcrasing ra and is cooling im is ual o 8/5 = 50 s. Th mpraur T () has a fasr dcrasing ra and cooling im valu 8/5 = 15 s. If hr is only on xampl of wlding, i can b concludd ha h curv T 1 () for highr valus of im can hav largr dviaions rgarding h curv T (). Thrfor, i is concludd ha h D Rosnhal modl of h uaion for calculaing 8/5 [5, 8] dvlops larg dviaions. A confirmaion of his lis in a sris of paprs [6, 7] which hav mphasizd ha his uaion dmands larg valus for cooling im 8/5 which can b considrd as a paradox.

5 Figur 1. Cooling mpraurs T 1 () and T () wih rlaiv rror of dviaion. Figur 1 prsns rlaiv rror ε in funcion of im, whr incras of incrass h rror. Thrfor, h approximaion using E.(17) is possibl only for small valus of. Th rlaiv rror of dviaion T 1 () rlaing o T () can b prsnd by xprssion T1() T() 100 ( b ε = = 1) 100 [%]. (19) T () According o rlaion (19), for = 0, h rror ε has h valu ual o zro and i is also considrd as small for small valus of which corrspond o vn smallr valus of insrd ha. Du o incrasing of im, and o h im T() dcrass o 500 C, h rror of dviaion incrass, which shows ha rlaion (18) should b usd for mpraur T (). Figur 1 shows ha hr ar wo plos for cooling mpraur, afr wlding, whr T 1 () corrspondd o Es.(1) o (5) for calculaion of D and 3D of h Rosnhal modl. Sinc T 1 () significanly dvias from h accura valu T (), i shows h rason why hr is a larg dviaion during h drminaion of 8/5 in full scop of im. Th plo for ε prsns a rlaiv prcnag dviaion which dscribs h dpndncy, E.(19). 4. Iraiv calculaion and corrcion of formulas in h Briish Sandard Problmaic formulas ar usd for dcads by xprs and rsarchrs in h ara of ha ransfr and as such, hy ar also incorporad ino h Briish Sandard. Evn improvd vrsions had producd significan dviaions in numrical calculaions. I is provn ha E.(16) should b usd for calculaion. I is ranscndn rgarding variabl. Also, i is imporan o drmin 8 and 5, bu i is impossibl o provid his xplicily. Auhors of his work inroducd h Nwon iraiv mhod ino h calculaions. For h funcion f() = 0, i is

6 i 1 = i f( i) f ( i), i= 0,1,,, (0) + whr: i - is h numbr of iraions; f( i ) - funcion from which i is calculad; and f '( i ) is h firs drivaiv of h funcion. Th procss of iraions i = 0 is sard by iniial slcion of xpcd valu. Du o good convrgnc of h iraiv procss and lack of good iniial soluion, h procdur xamins h soluion for wihin o 3 iraions. On xampl is givn for illusraing h applicaion of h prcis algorihm. Exampl. Arc wlding includs ha inpu 1 = J/cm, h sh hicknss is d = 7.4 mm and h prhaing mpraur T p = 180 C. This xampl is akn from [6] in ordr o compar rsuls. Afr rplacmn for known consans, h xprssion is as follows b For calculaing 8 h valid xprssion is as follows T ( ) = (1) T ( ) = = 60 C, () and for 5, h E.(1) can b usd: T ( ) = = 30 C. (3) Thr is or b f( ) = 0, (4) b f( ) = 0, (5) and h firs drivaiv has h form b f () b. (6) Th soluion is obaind from 3 iraions, whil h saring iraion providd 8,0 = 15 s = 8.71 s 8,1 8, 8,3 = s (7) = s Th similar for 5 can b obaind, whr 5,0 = 5 s, as shown in E.(6): = s Finally, h cooling im 8/5 is providd in h form 5,1 5, 5,3 = s (8) = s

7 8/5 = = 7.6 s. (9) Through h dilaomric mhod, dscribd in dail in [7] and prsnd hrough works of auhors [6, 7], h valu of 3.5 s is obaind. Th soluion drivd from h prcis mhod of h auhor of his work is valid, sinc soluions providd hrough h dilaomric mhod according o [7] dpnd on chmical-mchanical propris of h sl, and h pr-procss of sl producion. Ths ar wo diffrn ways for dfining h sam paramr, h cooling im 8/5. In ordr o obain valus for 8 and 5, in Es.(14) and (15) using h drivaion from E.(11), i can b providd hrough E.(16), which furhr provids h xprssions = b8 8 vd 4 πλcγ (800 Tp ) = b5 5 vd 4 πλcγ (500 Tp ) Finally, h soluion for 8/5 : = b5 b8 8/5 4 πλρc( vd) (500 Tp) (800 Tp) and (30). (31), (3) which prsns h nw rlaion for drmining 8/5, from which h prcis and xac rlaion of all variabls in h wlding procss can b dfind. Howvr, i is much asir o apply a spcial iraiv procss for drmining h spcial valus for 8 and 5, and o dfin 8/5 by simpl subsiuion. Th rason for his is h fac is ha E.(3) is much mor difficul for solving in pracic. 5. Rsuls and discussion Accuracy of h obaind rsuls by using h mhod in his work shall b sd firs by using fini lmn mhod (FEM) simulaion and calculaion via wo xampls. Th firs xampl is rlad o wlding of hin sl plas and h scond is rlad o a hickr sl. All h xampls includ D and 3D mhods of h Rosnhal modl. Exampl 3. Arc wlding of sl shs of hicknss 7.4 mm, inpu ha 1 = J/cm and prhaing mpraur of 180 C. Calculaion of h cooling im 8/5 by using h D horical modl has improvd h formulas in h Briish Sandard, h nw mhods from his work and h FEM mhod, succssfully ar applid in paprs [6, 7]. Also, h xprimnal daa ar obaind by dilaomric mhod for drmining h cooling im 8/5. Afr h calculaion, h daa ar prsnd in Tabl 1. Tabl 1. Comparaiv valus of cooling im 8/5 (s = 7.4 mm) wih prha mpraur, including FEM rsuls. Cooling im 8/5 [s] Inpu ha [kj cm 1 ] Prha mpraur Euaion D or xprimn FEM/nw prcis uaion [ C] E.(4) Exprimn FEM Euaion in his papr

8 Tabl 1 prsns h largs dviaion by D Rosnhal modl corrcd for Briish Sandard in E.(4). This rsul significanly dvias from h xprimnal rsul. Applicaion of h FEM mhod provids a rsul 31 s, which is nar o h xprimnal rsul of 7 s. Th rsul obaind by using h algorihm in his work is 31.6 s, which is narly h sam as h rsul from h FEM mhod. Exampl 4. Th sl sh of hicknss 9 mm is wldd [6, 7] wih inpu ha of 16.5 kj/cm and prhaing mpraur of 04 C. Calculaions ar mad as in Exampl 3. Th calculad daa ar givn in Tabl. Tabl. Comparaiv valus of cooling im 8/5 (s = 9 mm) wih prha mpraur, including FEM rsuls. Cooling im 8/5 [s] Inpu ha [kj cm 1 Prha mpraur Euaion 3D or xprimn FEM/nw prcis uaion ] [ C] (1) Exprimn FEM Euaion in his papr Tabl shows ha 8/5 has h valu of 1 s, h FEM analysis provids a rsul of 11.5 s and h algorihm from his work provids a rsul of s. Sinc h rsuls of FEM analysis and prsnd in his work ar narly h sam, i provs h jusificaion ha h algorihm hr prsnd rally displays a nw prcis way for calculaing h cooling im 8/5. Sinc h analysis of rsuls from prvious wo xampls in a viw of saisical rasoning is small, hr ar largr rsarchs found hrough h rsuls of numrous works [6, 7, 9-35]. Also, all hs rsuls ar compard o rsuls obaind in his work. Rsuls ar rviwd in Tabl 3, from whr i is obvious ha a largr dviaion is providd hrough E.(1). Som bi smallr dviaions ar givn by E.(4) which prsns h formula from h BS. Thr ar rsuls providd hrough xprimns [6, 7]. Howvr, h rsuls obaind in his work [31] ar no prsnd, sinc his work provs ha hr is no uod formula. In h work [8], rsuls ar includd for cooling im 8/5. Ths rsuls hav a largr rror. As final and major rsuls, daa obaind using h nw prcis algorihm from his work ar impord. Th jusificaion of implmning hs mhods is largly confirmd du o a fac ha hy ar narly h sam as rsuls from h FEM analysis. Tabl 3. Comparaiv valus of h cooling im 8/5 (s = 7.4 mm) wih prha mpraur. Cooling im 8/5 [s] Inpu ha [kj cm 1 Prha mpraur Euaion D Exprimn/nw prcis uaion ] [ C] E.(3) E.(4) Exprimn Euaion in his papr

9 Nowadays, hory and pracic us fiv formulas. Som of hs formulas ar vry hard for solving sinc hir form is no appropria and hy ar complx. Th algorihm shown hr uss only on formula and i is vry simpl for calculaing 8/5. Ths faurs provid rsuls appropria o many rsarchrs and praciionrs, du o shor im of calculaion. Th calculaion of 8/5 is prsnd hr sinc numrous paprs hav applid his paramr, and also h Es.(1)-(5). Rsuls usd in his papr mak i possibl o calcula also h prhaing mpraur whn 8/5 is dfind for paricular yps of sl. This can b don by formulaing uaions (16) as h diffrnc bwn T( 8 ) and T( 8 + 8/5 ), whos numrical valu is 300 C, and 8 is calculad by a subsun applicaion of h iraiv mhod, E.(0). Th prhaing mpraur T p is hn drmind by subsiuing his valu ino E.(30). 6. Conclusion Rsarch in his work is conducd in a way o includ a long priod of arc wlding, saring from h firs horical soluions, profssional and scinific works, books, PhD paprs and diffrn sandards. According o rsuls achivd hrough h rsarch, including h rsuls from ha ransfr, hr ar assumpions for idnifying h dviaions and rrors in his ara of sudy. I is concludd ha crain rlaions produc larg dviaions, so h auhors had found and provd h corrc formulas, using mahmaical and numrical analyss, which hlpd hm o form a nw and prcis mhod of calculaing h spcific paramrs. Also, hr ar rrors idnifid in h Briish Sandard, and hy hav also bn rmovd by driving h xac formulas wihou any rrors or dviaions. Nowadays, h hory uss mor of hs formulas, so unsolvd problms and soluions wih significan dviaions ar includd in pracic. Problms in hs horis hav bn solvd by h auhors of his work by inroducing only a singl formula and a simpl way of calculaion which could b favourabl for furhr work and rsarch. Apar from idnifying poor approximaions in Es.(1) o (5), an xac rlaion has bn drivd, E.(3). Th procdurs for calculaing h criical cooling im 8/5 or h prhaing mpraur T p ar dfind in his work, dpnding on h ruirmns in solving wlding paramrs. Hr, h arc wlding procdur is paricularly considrd, du o h bulk numbr of paprs ha dal wih his chnology and also bcaus of h involvd Briish Sandard, ha also dals wih arc wlding, and in h favour of a suggsd corrcion. I is also ru ha his procdur may b applid o ohr yps of wlding chnology. Nomnclaur d ransiion hicknss, [mm] Q ha inpu, [kj mm 1 ] T p prhaing mpraur, [ C] 8/5 cooling im, [s] v wlding spd, [mm s 1 ] U wlding volag, [V] I wlding currn, [A] Grk lrs λ hrmal conduciviy, [J kg 1 C 1 ]

10 ρ dnsiy, [kg m 3 ] c spcific ha, [J kg 1 C 1 ] η ha fficincy Rfrncs [1] Simpson, P.G. Inducion Haing: Coil and Sysm Dsign, McGraw Hill, Nw York, USA, [] Wlding Handbook, Vol.3, 7 h Ed., Rsisanc and solid sa wlding and ohr joining procsss, Amrican Wlding Sociy, Miami, FL: , [3] Wlding Handbook, 9 h Ed., Vol.4, Par 1: Marials and Applicaions, AWS, Ann O-Brin Ed., Miami, FL, USA, 011, p.860. [4] Sindo, K., Wlding Mallurgy, nd Ed., Wily-Inrscinc, Hobokn, Nw Jrsy, USA, 003, p.480. [5] Choong/Mzoung, al., Hong Ik Univrsiy; Kora, Tub and Pip Tchnology, January/Fbruary, 001. [6] Suzuki, S., Takamm, T., Th formaion mchanism of whi lin wldd joins of ERW sl pips, Tsu o Hagan (1984), 40(10): [7] Schuman, H., Mallography, Lipzig, VEB Duchr Vrlag fur Grunsoffindusri, [8] Gaulois, M.W., Jr., Dsign Principls for Oxid Thrmolcric Marials, Ph.D. Thsis, Univrsiy of California, Sana Barbara, USA, 015. [9] Adams, C.M., Jr., Wld. J (1958), 37(5): 10s-15s. [10] Rosnhal, D., Wld. J (1941), 0: [11] Rykalin, N.N., Calculaion of ha flow in wlding, Trans. Z. Paly and C.M. Adams, Jr., Documn , Inr. Ins. of Wlding, London, [1] Rykalin, N.N., Nikolav, A.V., Wlding arc ha flow, Wlding in h World (1971), 9(3/4): [13] Rosnhal, D., Th hory of moving sourc of ha and is applicaion o mal ramns. Transacions ASME (1946), 68(8): [14] Chrisnsn, N., al., Disribuion of mpraurs in arc wlding, Briish Wlding J (1965), 1: [15] Aburuga, T.Kh.S. al., Numrical Aspcs for Efficin Wlding Compuaional Mchanics, Thrmal Scinc (014), 18, Suppl. 1: S139-S148 [16] Milićvić, M., Th applicaion of a nw formula of Nakaoka cofficin in HF induciv wlding, J Mchanical Enginring (010) 56(7-8): [17] Milićvić, M., Radaković, Z., Qualiy improvmn of sl pips by sam wlding wih nw magno-dilcric impdr, Marials Transacions, Th Japan Insiu of Mals (006), 47(06):

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