NUMERICAL ANALYSIS OF METAL TRANSFER IN GAS METAL ARC WELDING

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1 Unversty of Kentucky UKnowledge Unversty of Kentucky Doctoral Dssertatons Graduate School 007 NUMERICAL ANALYSIS OF METAL TRANSFER IN GAS METAL ARC WELDING Ge Wang Unversty of Kentucky Clck here to let us know how access to ths document benefts you. Recommended Ctaton Wang Ge "NUMERICAL ANALYSIS OF METAL TRANSFER IN GAS METAL ARC WELDING" (007). Unversty of Kentucky Doctoral Dssertatons Ths Dssertaton s brought to you for free and open access by the Graduate School at UKnowledge. It has been accepted for ncluson n Unversty of Kentucky Doctoral Dssertatons by an authorzed admnstrator of UKnowledge. For more nformaton please contact UKnowledge@lsv.uky.edu.

2 ABSTRACT OF DISSERTATION Ge Wang The Graduate School Unversty of Kentucky 007

3 NUMERICAL ANALYSIS OF METAL TRANSFER IN GAS METAL ARC WELDING ABSTRACT OF DISSERTATION A dssertaton submtted n partal fulfllment of the requrements for the degree of Doctor of Phlosophy n the College of Engneerng at the Unversty of Kentucky By Ge Wang Lengton Kentucky Co-Drectors: Dr. George P. Huang Professor of Mechancal Engneerng and Dr. Yu-Mng Zhang Professor of Electrcal and Computer Engneerng Lengton Kentucky 007 Copyrght Ge Wang 007

4 ABSTRACT OF DISSERTATION NUMERICAL ANALYSIS OF METAL TRANSFER IN GAS METAL ARC WELDING In gas metal arc weldng (GMAW) metal transfer plays a crucal role n determnng the qualty of the resultant weld. In the present dssertaton a numercal model wth advanced computatonal flud dynamcs (CFD) technques has been developed frst n order to provde better numercal results. It ncludes a two-step proecton method for solvng the ncompressble flud flow; a volume of flud (VOF) method for capturng free surface; and a contnuum surface force (CSF) model for calculatng surface tenson. The Gauss-type current densty dstrbuton s assumed as the boundary condton for the calculaton of the electromagnetc force. The droplet profles electrc potental and velocty dstrbutons wthn the droplet are calculated and presented for dfferent metal transfer modes. The analyss s conducted to fnd the most domnant effects nfluencng the metal transfer behavor. Comparsons between calculated results and epermental results for metal transfer under constant current are presented and show good agreement. Then our numercal model s used to study a proposed modfed pulsed current gas metal arc weldng. Ths novel modfed pulsed current GMAW s ntroduced to mprove the robustness of the weldng process n achevng a specfc type of desrable and repeatable metal transfer mode.e. one drop per pulse (ODPP) mode. Ths new technology uses a peak current lower than the transton current to prevent accdental

5 detachment and takes advantage of the downward momentum of the droplet oscllaton to enhance the detachment. The calculatons are conducted to demonstrate the effectveness of the proposed method n achevng the desred metal transfer process n comparson wth conventonal pulsed current GMAW. Also the crtcal condtons for effectve utlzaton of ths proposed method are dentfed by the numercal smulaton. The weldng operatonal parameters and ther ranges are also calculated and the calculated results further demonstrate the robustness of ths new GMAW technque n achevng hgh qualty weldng. KEYWORDS: Gas Metal Arc Weldng Metal Transfer Pulsed Current GMAW ODPP Metal Transfer Numercal Analyss Ge Wang 07/0/007

6 NUMERICAL ANALYSIS OF METAL TRANSFER IN GAS METAL ARC WELDING By Ge Wang George P. Huang Co-Drector of Dssertaton Yu-Mng Zhang Co-Drector of Dssertaton L. Scott Stephens Drector of Graduate Studes 7/0/007 Date

7 RULES FOR THE USE OF DISSERTATIONS Unpublshed dssertatons submtted for the Doctor s degree and deposted n the Unversty of Kentucky Lbrary are as a rule open for nspecton but are to be used only wth due regard to the rghts of the authors. Bblographcal references may be noted but quotatons or summares of parts may be publshed only wth the permsson of the author and wth the usual scholarly acknowledgments. Etensve copyng or publcaton of the dssertaton n whole or n part also requres the consent of the Dean of the Graduate School of the Unversty of Kentucky. A lbrary that borrows ths dssertaton for use by ts patrons s epected to secure the sgnature of each user. Name Date

8 DISSERTATION Ge Wang The Graduate School Unversty of Kentucky 007

9 NUMERICAL ANALYSIS OF METAL TRANSFER IN GAS METAL ARC WELDING DISSERTATION A dssertaton submtted n partal fulfllment of the requrements for the degree of Doctor of Phlosophy n the College of Engneerng at the Unversty of Kentucky By Ge Wang Lengton Kentucky Co-Drectors: Dr. George P. Huang Professor of Mechancal Engneerng and Dr. Yu-Mng Zhang Professor of Electrcal and Computer Engneerng Lengton Kentucky 007 Copyrght Ge Wang 007

10 ACKNOWLEDGMENTS Frst of all I would lke to epress my sncere thanks to my famly teachers frends and those who nspred and helped me to acqure a doctoral degree durng the entre process of ths study. Specal thanks should go to Dr. George P. Huang my maor professor and charman of the advsory commttee for hs contnuous support and encouragement nsghtful advce and nstructve comments on ths dssertaton. Carryng out ths research would not have been possble wthout the help from my co-drector Dr. Yu- Mng Zhang. I thank hm for generously sharng hs knowledge n weldng eperments and provdng contnuous gudance throughout ths research. At the same tme I would also lke to thank the other members of my advsory commttee: Dr. Raymond P. LeBeau and Dr. Vncent Capece for ther revew and gvng valuable suggestons toward ths dssertaton. I also would lke to acknowledge the fnancal supports from Department of Mechancal Engneerng at Unversty of Kentucky and Center for Robotcs and Manufacturng Systems at Unversty of Kentucky. Last but not the least I want to thank my wonderful husband Sean and my lovely daughter Wendy. I wsh I could epress n words how much I apprecate ther support understandng and patence.

11 TABLE OF CONTENTS Acknowledgements... Lst of Tables... v Lst of Fgures... v Lst of Fles... Chapter : Introducton.... Overvew of Metal Transfer Process.... Lterature Survey Motvaton and Obectves Dssertaton Organzaton...5 Chapter : Physcal Model of Metal Transfer...6. Physcal Process of Metal Transfer...7. Modelng of Metal Transfer...0 Chapter 3: Numercal Schemes Governng Equatons Numercal Modelng and Soluton for Governng Equatons Mesh Layout Dscretzaton of Governng Equatons and Algorthm Soluton...9 a. The Two-step Proecton Method...30 b. Advecton...3 c. Vscosty...33 d. Posson Equaton Trackng the Free Surface Modelng of Surface Tenson Calculaton of Electromagnetc Force...46 v

12 Chapter 4: Metal Transfer n Constant Current GWAW Introducton Results and Dscussons Effects of Surface Current Densty Dstrbuton Domnant Effects for Dfferent Metal Transfer Mode Summary...69 Chapter 5: Metal transfer n Pulsatng Current GMAW Introducton Proposed approach n modfed pulsed current GMAW Numercal Results and Dscussons Tradtonal Sngle Pulsed Current GMAW Modfed Pulsed Current GMAW Parameter Dagnoses for Phase Match The Operatng Range of T b The Influence of Pulsng Cycle Frequency and Peak Current Comparson wth Eperment Summary...4 Chapter 6: Conclusons...6 References...30 Vta...38 v

13 LIST OF TABLES Table Materal Propertes of the Electrode...9 v

14 LIST OF FIGURES Fgure. The sketch of metal transfer process n GMAW...7 Fgure. Schematc sketch of metal transfer process n GMAW wth ntal and boundary condtons: (a) A Schematc of metal transfer process; (b) Intal and eternal boundary condtons... Fgure 3. Flow dagram of numercal soluton...7 Fgure 3. Control volumes...8 Fgure 3.3 Checker-board dstrbuton for pressure...9 Fgure 3.4 Control volume for VOF functon...40 Fgure 3.5 Eamples of free surface shapes and reconstructons n the advecton of F through the rght cell face...4 Fgure 3.6 The transton zone wth thckness h at the nterface...44 Fgure 3.7 Layout of electromagnetc varables n a computatonal cell..48 Fgure 3.8 Eamples of free surface cells usng for boundary condton applcaton...50 Fgure 4. Comparson of predcted average droplet szes under dfferent current densty dstrbuton wth epermental results...59 Fgure 4. metal transfer process at the current of 60A: (a) Drop profles (b) Electrc potental and velocty dstrbutons wthn the droplet...6 Fgure 4.3 metal transfer process at the current of 300A: (a) Drop profles (b) Electrc potental and velocty dstrbutons wthn the droplet...66 Fgure 4.4 Metal Transfer Process at the Current of 50A: (a) Drop profles (b) Electrc potental and velocty dstrbutons wthn the droplet...68 Fgure 5. Current waveform for conventonal pulsed GMAW...73 Fgure 5. Current waveform used for modfed pulsed GMAW...77 Fgure 5.3 The relatonshp between the detached drop szes and weldng currents...80 Fgure 5.4 Metal transfer wth ODPP under conventonal pulsed current GMAW: (a) Droplet profles (b) Vertcal coordnate of droplet tp...84 Fgure 5.5 Comparson of calculated and epermental operatng ranges: (a) I p = 400A I b =80A I avg = 0A (b) I p = 400A I b =80A I avg = 9A (c) I p = 500A I b =80A I avg = 96A (d) I p = 500A I b =80A I avg = A...87 v

15 Fgure 5.6 Metal transfer wth ODMP under conventonal pulsed current GMAW...88 Fgure 5.7 Metal transfer wth MDPP under conventonal pulsed current GMAW...89 Fgure 5.8 Metal transfer wth ODPP under modfed pulsed current GMAW: (a) Current waveform (b) Droplet profles (c) Vertcal coordnate of droplet tp...9 Fgure 5.9 Metal transfer processes wth unsatsfed phase match condton: (a) Drop profles under a shorter duraton T b of 3ms (b) Vertcal coordnate of droplet tp...94 Fgure 5.0 Metal transfer processes wth unsatsfed phase match condton: (a) Drop profles under a longer duraton T b of 6ms (b) Vertcal coordnate of droplet tp...96 Fgure 5. The droplet response to ectng pulse: (a) Current waveform (b) Vertcal coordnate of droplet tp...97 Fgure 5. Development for vertcal coordnate of droplet tp n modfed pulsed current GMAW: (a) ODPP under T b of 3.5ms (b) ODPP under T b of 4.5ms (c) ODPP under T b of 5ms (d) ODPP under T b of 5.5ms...98 Fgure 5.3 Development for vertcal coordnate of droplet tp n modfed pulsed current GMAW (T p =4ms I avg =00A f=30hz I p =0A I b =40A): (a) ODMP under T b of.8ms (b) ODPP under T b of 3ms (c) ODPP under T b of 4ms (d) ODPP under T b of 4.5ms (e) ODPP under T b of 5ms (f) ODMP under T b of 5.5ms...0 Fgure 5.4 Development for vertcal coordnate of droplet tp n modfed pulsed current GMAW (T p =3ms I avg =00A f=30hz I p =0A I b =40A): (a) ODMP under T b of.5ms (b) ODPP under T b of.8ms; (c) ODPP under T b of 3ms; (d) ODPP under T b of 4ms (e) ODPP under T b of 5ms (f) ODMP under T b of 5.5ms...03 Fgure 5.5 Development for vertcal coordnate of droplet tp n modfed pulsed current GMAW (T p =6ms I avg =00A f=30hz I p =0A I b =40A): (a) ODMP under T b of 4ms; (b) ODPP under T b of 4.5ms; (c) ODPP under T b of 5ms; (d) ODMP under T b of 5.5ms...05 Fgure 5.6 Development for vertcal coordnate of droplet tp n modfed pulsed current GMAW (T p =7ms I avg =00A f=30hz I p =0A I b =40A): (a) ODMP under T b of 4ms (b) ODMP under T b of 5ms...06 Fgure 5.7 Metal transfer wth ODPP under modfed pulsed current GMAW: (a) Current Sgnal (b) Droplet profles (c) Vertcal coordnate of droplet tp...08 v

16 Fgure 5.8 Development for vertcal coordnate of droplet tp n modfed pulsed current GMAW: (a) ODMP under T b of.5ms; (b) ODPP under T b of 3ms; (c) ODPP under T b of 3.5ms; (d) ODMP under T b of 4ms...09 Fgure 5.9 Metal transfer wth ODPP under modfed pulsed current GMAW: (a) Current waveform (b) Droplet profles (c) Vertcal coordnate of droplet tp... Fgure 5.0 Development for vertcal coordnate of droplet tp n modfed pulsed current GMAW: (a) ODMP under T b of.5ms (b) ODPP under T b of 3ms (c) ODPP under T b of 4ms (d) ODMP under T b of 4.5ms... Fgure 5. Development for vertcal coordnate of droplet tp n modfed pulsed current GMAW (I p =0 I p =50): (a) ODPP under T b of 3ms (b) ODPP under T b of 4ms (c) ODPP under T b of 5ms (d) ODPP under T b of 6ms...4 Fgure 5. Metal transfer wth MDPP under conventonal pulsed current GMAW: (a) Vertcal coordnate of droplet tp (b) Droplet profles...6 Fgure 5.3 Development for vertcal coordnate of droplet tp n modfed pulsed current GMAW ( I p =0 I p =300 T p =5ms): (a) ODPP under T b of ms; (b) ODPP under T b of 4ms; (c) ODPP under T b of 6ms; (d) ODPP under T b of 7ms; (e) ODPP under T b of 0ms; (f) ODPP under T b of 0ms...8 Fgure 5.4 Drop veloctes toward weldng pool under dfferent detachng pulse current... Fgure 5.5 Comparson between the calculated results and epermental data: (a) Current waveforms (b) Vertcal coordnate of droplet tp from eperment (c) Vertcal coordnate of droplet tp from calculaton...3

17 LIST OF FILES. WangGe_Dssertaton.pdf: ~ 4 MB (Fle Sze)

18 Chapter Introducton In gas metal arc weldng (GMAW) many effects nfluence the weldng qualty. Among these metal transfer plays a crucal role n determnng the qualty of the resultant weld. Metal transfer descrbes the process of the molten metal movement from the electrode tp to the workpece across the arc n gas metal arc weldng. In order to acheve hgh qualty weldng the manner n whch the lqud metal transfers from the electrode to the weld pool has been the subect of much research. A better understandng of the metal transfer process not only helps to optmze and refne the weldng process but also provdes opportuntes to develop new technques for hgh qualty weldng. In the past emprcal approaches have been appled wth much success but ths approach s hghly tme consumng. A theoretcal analyss has the advantage of provdng nsght nto the underlyng physcs of the process. In ths thess a method has been proposed to pulsate the current n GMAW to acheve a specfc type of desrable and repeatable metal transfer mode. Etensve efforts have been made to eplore the mechansm of the metal transfer process and understand the underlyng physcs of the process numercally. The numercal analyss appled n ths thess not only provdes sgnfcant nsghts nto the metal transfer process n general but also provdes an effectve means to dagnose the optmum operaton parameters for the proposed new technque.

19 . Overvew of Metal Transfer Process Gas metal arc weldng s an mportant and wdely used metal onng method n many ndustral and manufacturng operatons. Durng gas metal arc weldng the electrode s melted and lqud droplets are formed at the tp of the electrode. The melted metal grows at the end of electrode and s detached from the electrode. Ths process s referred to as metal transfer process. Prevous studes [-5] showed that the behavor of metal transfer affects the weldng qualty n many ways. In gas metal arc weldng metal transfer can take place n three maor dstnct modes: globular spray and short-crcutng [6-8]. Spray transfer can be further classfed as drop spray or streamng spray dependng on the dameter of the detached droplet n relaton to that of the electrode: appromately the same n drop spray or much smaller n streamng spray. At low current globular transfer occurs f the arc length s suffcent. The droplets grow at the tp of the electrode wth a classc pendant drop shape due to the competton between gravty and surface tenson n the presence of relatvely small electromagnetc forces. Large droplets wth dameters much greater than the dameter of the electrode are detached prmarly by gravty. When the weldng current ncreases the electromagnetc force becomes the domnant droplet force so that small droplets wth dameter equal to or less than the dameter of the electrode can be detached. Ths s referred to as the spray transfer mode. It s found that there s an abrupt transton n the current whch dvdes the globular and spray transfer modes. Ths current or current range s referred to as the transton current. Hgh rregularty n the droplet detachment

20 frequency and the droplet sze has been observed n the mddle of the transton current range [8-0]. Short-crcutng transfer [] s a specal transfer mode whle the molten droplet makes drect contact wth the weld pool. It s characterzed by ntermttent arc etngushment and re-gnton. Globular and short-crcutng metal transfer typcally causes sgnfcant spatters and poor weldng qualty []. Its applcaton n producton s lmted. The spray transfer mode has advantages over the other metal transfer modes wth ts regular detachment accompaned by unform droplet sze drectonal droplet transfer and low spatters [3]. However spray transfer s only acheved at hgh current for constant current GMAW whch results n a thermal load too hgh to apply to thn sectoned or heat-senstve materals. Thereby ts applcaton s restrcted. In an effort to overcome ths dffculty pulsed current GMAW was ntroduced n 96 [4]. By usng a pulsed current a controlled spray transfer mode wth one droplet detached per pulse could be acheved at low average current whch typcally results n globular transfer for constant current GMAW. Such a metal transfer mode s referred to as one-drop per-pulse (ODPP). The change of the character of metal transfer affects the weldng qualty n many ways. For ths reason t has been and s stll beng nvestgated very ntensvely both epermentally and theoretcally by researchers around the world. 3

21 . Lterature Survey The epermental technques [5-4] whch have been wdely used n prevous studes of the metal transfer process nclude optcal methods sensor measurements and acoustc detectons. In the early 980 s an optcal technque ( frames per second) was developed at the M.I.T. weldng laboratory for vewng metal transfer process wth a relatvely small aggregate of optcal equpment [5]. Ths technque may be used to obtan the temporal evoluton of the profle of droplet detachment from a gasshelded weldng electrode. Lawrence A. Jones and hs assocates collected an etensve set of clear mages of drop detachment n 995 by usng a hgh-speed vdeo recorder wth speeds from 000 to 6000 frames per second [6]. The eperments recorded nclude a wde range of constant current and pulsed current welds usng steel and a smaller set of alumnum welds. The clear hgh-speed mages and assocated data provded by ths technque are a maor contrbuton to the study of metal transfer process n GMAW. Optcal methods manly nvolve hgh-speed vdeo systems and laser shadowng technques [5-8]. Ths makes the cost very hgh. The arc sensor s also wdely used n GMAW to study the process [9-]. By recordng and analyzng fluctuatons of the weldng voltage and/or current t s possble to predct the metal transfer mode. But t cannot provde any detal or sgnfcant nsghts about the metal transfer process. Its applcaton s better suted to weldng process control. As another approach Manz studed the relatonshp between the sound of a weldng arc and the metal transfer mode by acoustc measurement [3]. Snce acoustc sgnals can easly be dsturbed by the background nose the relablty of ths method s questonable. 4

22 Theoretcal descrpton of metal transfer n GMAW can provde a better understandng of the mechansm of ths process and the means to determne the optmal operaton parameters. However theoretcal descrpton of droplet formaton and detachment n GMAW are complcated by the followng effects: the dynamc nature of droplet growth thermal phenomena n the wre and heat transfer from the arc. Because of the completes assocated wth these effects models n the lterature for predcton of metal transfer n GMAW are typcally based on smplfed descrptons of the effects nfluencng the process of droplet formaton. Numerous models have been developed to study the metal transfer process n GMAW. The two best-known models developed from early studes of metal transfer analyss are the statc force balance theory (SFBT) [5-7] and the pnch nstablty theory (PIT) [8-30]. The statc force balance theory (SFBT) was frst proposed by Greene [5] and further developed by Amson [67] and Wasznk et al []. It predcts the detachng drop sze by smply comparng the balance between attachng and detachng forces. The man attachng force s the surface tenson force. Detachng forces nclude gravtatonal force electromagnetc force and plasma drag force. The drop detaches when the detachng force becomes greater than the attachng force. Snce ths model s based on statc force analyss the dynamc character of metal transfer cannot be consdered by SFBT. Also ths model does not take consderaton of droplet shape and neglects nteracton between 5

23 droplet shape and nfluental forces. Predcted results based on SFBT show severe devaton from epermental data at hgher current whle reasonable agreement s acheved at low current. As an etenson of the statc force balance model Cho et al [3] proposed a dynamc force balance model (DFBM) for metal transfer analyss. The dynamc force balance model predcts metal transfer n arc weldng by ntroducng the nertal force n addton to the conventonal forces used n the SFBT. The dynamcs of a pendent drop are modeled as a second-order mass sprng and damper system. Although the DFBM shows better agreement wth the measured drop sze than the SFBT both models are unable to accurately predct the detached drop sze n the hgh current range. The pnch nstablty theory (PIT) was frst appled to GMAW by Lancaster [6]. Allum [89] further used t to predct the detached drop sze n metal transfer. Rhee and Kannatey [30] etended the PIT to nclude effects of arc pressure. The PIT predcts the droplet sze based on consderaton of the nstablty of the current-carryng lqud cylndrcal column. The PIT consders perturbaton due to the radal magnetc pnch force actng on an nfnte cylndrcal column of lqud metal. Accordng to Raylegh nstablty theory the dsturbance n the flud cylnder can grow eponentally and break t nto droplets. The sze of the droplets depends on the wavelength of the fastest growng dsturbance. Ths model oversmplfes the droplet shape. Predctons made accordng to PIT provde the correct order of magntude of the detached droplet radus at hgher current but have maor dscrepances wth epermental data at low current. 6

24 Both SFBT and PIT fal to descrbe metal transfer properly over a wde current range due to the oversmplfcaton of those two models. Nether can predct the transton from globular transfer mode to spray transfer mode successfully. Other models have been proposed to predct metal transfer more accurately. In 994 Nemchnsky [3] developed a steady-state model to descrbe metal transfer by calculatng the equlbrum shape of a pendant droplet. An equaton to descrbe the droplet shape s proposed and solved. It calculates the mamum volume of droplet that can stll be attached to the electrode and then computes the radus of the detached droplet. Ths model s the frst to nclude effects comng from the couplng between surface tenson electromagnetc force and the droplet shape. It allows calculaton of the detachng droplet sze more accurately over a wder current range compared to the SFBT and PIT models. In 996 Joo et al [33] presented a numercal model based on the energy mnmzaton method to calculate the molten drop geometry. The gravtatonal surface tenson and electromagnetc forces are consdered n order to formulate the energy of the pendant droplet system and therefore nfluence the geometry of the statc pendant drop. The domnant effects are dentfed for dfferent metal transfer modes. The drop profle s manly affected by the surface tenson and electromagnetc force n the spray transfer mode. Effects of the gravtatonal force ncrease n the globular transfer mode. 7

25 Predctons agree favorably wth epermental data n the globular mode and the ntal stage of the spray mode. However the above two models are bascally statc approaches. They are stll unable to predct the dynamc behavor of the droplet growth and detachment durng metal transfer. The calculatons tend to dverge as soon as the nstablty occurs. The dynamc descrpton of the droplet development and detachment process s crtcal to understandng the detals of metal transfer n GMAW. In 995 Smpson and Zhu [34] developed a dynamc one-dmensonal model to predct droplet formaton and detachment. It ncludes dynamc development of droplet shape and sze under the acton of gravty electromagnetc forces and surface tenson. Ths model provded the frst predctons of droplet shape as a functon of tme. However t s not sutable for makng adequate predctons of the transton current between globular and spray transfer mode nor does t descrbe the detals of the metal transfer process. In 998 Jones and Eagar [3536] presented a dynamc model of drop detachment for low and moderate weldng currents n gas metal arc weldng. The dynamc model they developed eplctly consders the geometry of drops as they detach from an electrode thereby provdng a detaled vew of how the forces actng on the drops evolve. Ths dynamc model s a lumped parameter system n nature. Forces are appled to the center of mass rather than beng appled n a contnuum way to the dstrbuted mass of 8

26 the droplet. Comparsons wth eperment ndcate that the calculated aal magnetc forces are substantally too hgh when usng constant current. Recently the rapd development of hgh-speed computers has made sgnfcant contrbuton to the progress of Computatonal Flud Dynamcs (CFD) technques. Several transent two-dmensonal models have been developed to predct metal transfer process based on advanced CFD technques. In 996 Hadar and Lowke [38-40] developed a two-dmensonal dynamc model for the predcton of droplet formaton that ncluded the arc. Ths was the frst tme that an advanced CFD technque such as the VOF method was employed to study metal transfer and t made a great mpact on ths feld. Equatons of contnuty momentum energy and current were solved n two dmensons for the molten droplet and arc. Ths model predcted the transton current from the globular to the spray transfer mode n far agreement wth epermental data. However ths model faled to predct the presence of both small and large drops n the transton zone between the two modes. The droplet detachment was not addressed and the shape of drop was not very close to the mages gven by eperments. The accuracy of computatonal results s nfluenced by dscontnuty assumptons on the free surface such as a surface pressure boundary condton. In 998 a mathematcal model to descrbe the globular transfer was developed by Fan and Kovacevc [44]. The droplet formaton detachment and transport 9

27 phenomena are consdered together wth the mpngement effect on the weld pool. The flud flow and heat transfer n metal transfer are dynamcally studed by usng the VOF method n a two-dmensonal doman. An appromaton was used to obtan the current densty dstrbuton n the droplet by assumng unform aal current densty dstrbuton over the horzontal cross secton of the droplet. The sze and the transfer frequency of the droplets of globular transfer are determned by the balance of gravty surface tenson electromagnetc and arc drag forces. The calculated results agree well wth the epermental results recorded by a hgh-speed vdeo camera. However the calculaton was carred out only for globular transfer. Cho Km and Yoo [43] also conducted numercal smulatons of metal transfer n 998. They consdered the effect of the weldng arc under the assumptons of a unform and lnear current densty on the droplet surface. The dynamc characterstcs of the globular spray and short-crcut metal transfer modes were smulated by adoptng the VOF method. They noted that the current densty on the drop surface has sgnfcant effects on the shape and sze of droplet. They further dd a dmensonal analyss n order to determne the domnant factors that affect the metal transfer mode [44]. They found the rato of the electromagnetc force and the surface tenson force have the largest effects on the metal transfer characterstcs over the whole range of weldng condtons. The predcted results are n reasonably good agreement wth the epermental data although the transton current and characterstc of metal transfers occurrng n ths transton current range are not determned accurately. 0

28 In 00 Wang and hs assocates [45-47] successfully conducted numercal analyss for the droplet mpngement on the weld pool surface and the flud flow heat mass transfer n the weld pool for GMAW. The RIPPLE computer program whch models transent two-dmensonal ncompressble flud flows wth free surfaces by usng advanced CFD technques was ntroduced nto the study of GMAW. Whle ther study focused on the nteracton between the droplet and the weld pool the droplet growth and detachment process was not ncluded n ther paper. The necessary condtons to acheve the desrable one drop per pulse (ODPP) mode whch characterzes a stable perodcal and controllable metal transfer process were nvestgated n a number of works [48-57]. To ths end Uegur et al [48] analyzed the metal transfer n pulsed GMAW by usng statc force balance theory n 985. They ponted out the sgnfcance of the optmum current waveform on achevng the ODPP metal transfer mode. They also suggested the peak current should be set above a crtcal current to ensure that one droplet s detached per pulse. Amn [49] dentfed the crtcal current to ensure ODPP metal transfer whch was the transton current between the globular and spray transfer mode. In the pulsed current GMAW the current waveform s regarded as an mportant operaton condton to acheve ODPP metal transfer. In order to obtan one drop per pulse Quntno [505] suggested that the peak duraton T p should be decreased when the peak current I p ncreases. Smat [5] predcted the theoretcal pulsng frequency and

29 showed that one drop per pulse s realzed when the term I pt p remans constant. The work of Km [54-56] and hs assocates ponted out that there s a range of operatonal parameters wthn whch one droplet s transferred per current pulse. The operatng range of the pulsng frequency f whch provdes ODPP was found to ncrease when the peak current I p or load duty cycle T p f ncreased. The study conducted by Nemchnsky [57] consders the electrode-meltng rate under pulsed current GMAW. The results further confrmed that there s a range of pulsng frequency leadng to ODPP metal transfer. Prevous models for the metal transfer process have been unable to make accurate predctons of the transton between the globular and spray transfer modes. In the present study [5859] a new transent two-dmensonal model s developed on the base of RIPPLE [60] to smulate the droplet formaton detachment and transport n gas metal arc weldng. The transent shape of the droplet s calculated usng the fractonal volume of flud (VOF) method [6] whch s shown to be more fleble and effcent than other methods for treatng complcated free-boundary confguratons. Gravtatonal force surface tenson force and electromagnetc force play fundamental roles n the process of droplet growth and detachment. The contnuum surface force (CSF) model [6] adopted n ths study elmnates the need for nterface reconstructon smplfes the calculaton of surface tenson and enables accurate modelng of flud flows drven by surface forces. As the weldng current generates the electromagnetc force eerted on the pendant drop the effects of the current are ncluded wth assumpton of Gaussan current densty dstrbuton. The numercal results [58] show a very good agreement wth the epermental data. The transton current range and the specal behavor of metal transfer

30 durng ths range have been calculated and show good agreement wth epermental observatons. The analyss of the calculaton results provdes sgnfcant nsght nto the physcal mechansms whch nfluence the metal transfer procedure..3 Motvaton and Obectves Metal transfer wth one drop per pulse (ODPP) mode whch characterzes a stable perodcal and controllable process can produce hgh qualty weldng. Hence ts applcaton s the most desrable. In conventonal pulsed GMAW the peak current has to be set above the transton current along wth selecton of the approprate parameters to get the desrable one-drop per pulse mode (ODPP). On the other hand t has been shown that a peak current above the transton current wll easly brng accdental detachment.e. multple drops detached per pulse (MDPP) and overheat the droplet and weldng pool. Recently a novel actve control technology has been proposed by E Zhang and hs assocates [63-65]. A pulse cycle composed of two pulses ectng pulse and detachng pulse s used to detach a drop per pulse cycle durng gas metal arc weldng. A peak current below the transton current s used to detach the droplet prevent accdental detachment and realze the optmal ODPP metal transfer mode. The drop s detached by the combnaton of the downward momentum of the drop oscllaton and the ncreased electromagnetc force whch s nduced by an ectng pulse and a detachng pulse respectvely. The phase match between the downward movement and the ncreased pulse 3

31 current plays an mportant role to acheve ODPP metal transfer by utlzng ths modfed pulsed current arc weldng. The modfed pulsed current arc weldng has a maor advantage over the conventonal pulsed current GMAW n beng capable of lowerng the peak current under transton current to obtan ODPP metal transfer. On the other hand ths method ntroduces large amounts of addtonal weldng parameters due to the use of double pulse waveforms. These etra varables cause dffculty n selectng optmum combnatons of parameters for a wde range of weldng condtons to realze ODPP metal transfer. A tral-and-error method has been used to determne these parameters epermentally. However ths emprcal approach s very tme consumng and unpractcal. A theoretcal descrpton of metal transfer n GMAW not only provdes a better understandng of the technology s mechansm but also an effcent way to determne the optmum operaton parameters. The rapd development of Computatonal Flud Dynamcs (CFD) technques has made great contrbuton to the progress of the theoretcal study for GMAW. Hence advanced CFD technques have been adopted as an effectve means n the present numercal study of metal transfer n GMAW. An effort has been made to get calculated results n better agreement wth avalable epermental data by physcal modelng and use of advanced numercal schemes. The analyss of numercal results not only gve sgnfcant nsghts nto the metal transfer process n general but also provde an 4

32 effcacous means to dagnose the optmum operaton parameters for the proposed new technque and make ths novel actve control technology feasble n ndustry..4 Dssertaton Organzaton Frst of all the background lterature survey motvaton and obectves of ths dssertaton study have been ntroduced n Chapter. The physcal model of metal transfer n GMAW wll be presented n Chapter. The numercal schemes and algorthms to solve the governng equatons are shown n Chapter 3. Chapter 4 ncludes the calculated results for prelmnary test cases and the smulatons for metal transfer n GMAW under constant currents. The smulatons carred out for metal transfer under the pulsed current GMAW whch nclude the tradtonal pulsed current and modfed pulsed current GMAW and results are dscussed n Chapter 5. Some standard numercal test cases are also ncluded n ths chapter for valdaton purposes. Fnally conclusons are provded n Chapter 6. Copyrght Ge Wang 007 5

33 Chapter Physcal Model of Metal Transfer Metal transfer the process of transferrng weldng wre materal n the form of molten metal droplets to the workpece n gas metal arc weldng (GMAW) nvolves comple dynamc nteractons between many physcal phenomena. It ncludes the dynamc growth and detachment of molten droplets thermal phenomena n the wre heat transfer from the arc and the effect of electromagnetc feld due to weldng current. Because of the completes assocated wth these effects models n the lterature [5-57] for predcton of metal transfer are typcally smplfed and take only those maor effects nfluencng the process under consderaton. In ths work an unsteady two-dmensonal asymmetrc model s used to nvestgate droplet evoluton detachment frequency and the selecton of pulse parameters for optmal metal transfer n GMAW. The dynamcs of the droplet formaton and detachment process are formulated as an ncompressble vscous flow wth free surfaces. The forces whch sgnfcantly nfluence the metal transfer process are the gravtatonal electromagnetc and surface tenson forces. 6

34 . Physcal Process of Metal Transfer Fgure. shows the basc physcal process of metal transfer durng GMAW. An electrc arc s struck between the tp of an electrode the anode and the workpece the cathode. The consumable electrode s melted under the combned nfluences of heatng Fgure. The sketch of metal transfer process n GMAW 7

35 produced by weldng arc and Joule heatng. The molten metal grows at the end of electrode as a pendant droplet. After neck shrnkng the metal droplet breaks from the electrode and transfers downward through the arc nto the weld pool. Ths process s governed by a combnaton of factors ncludng the balance of forces thermal phenomena and electromagnetc feld. In the present study thermal phenomena are neglected by assumng the nput velocty of molten metal to be the same as the wre feed rate. In the molten droplet growth and detachment process the molten droplet eperences the gravtatonal force the surface tenson force whch arses from the free surface the electromagnetc force whch s generated by the nteracton of the weldng current wth ts self-nduced electromagnetc feld and the plasma drag force whch s nduced by the surroundng gas onzed n the weldng arc. Snce plasma drag force has less mpact compared wth the other forces t s neglected n the calculaton. The balance of forces determnes the droplet profle and detachment frequency. Whle the gravtatonal force tends to pull the droplet off and the surface tenson force tres to retan t on the tp of electrode the electromagnetc force s the most potent to accelerate the droplet off the end of the electrode as the weldng current ncreases. The competton between the gravtatonal surface tenson and electromagnetc forces determnes the mode of metal transfer and further nfluences the weldng qualty. Large pendant droplets are grown at low current under the domnance of the gravtatonal force and the surface tenson force n the presence of relatvely small electromagnetc forces. The globular transfer occurs wth the detachment of droplets havng a dameter much 8

36 greater than the dameter of the electrode. As weldng current ncreases the electromagnetc force becomes sgnfcant and accelerates the droplet detachment. The spray transfer occurs wth the detachment of small droplets havng dameter equal to or less than the dameter of the electrode. The vast maorty of eperments n the lterature were performed wth mld steel electrodes. Hence mld steel electrodes are also adopted n ths study. The materal propertes of mld steel are taken from the work of Cho Yoo and Km [43]. They are lsted n Table. Table. Materal Propertes of the Electrode Mass densty ρ 7860 kg/m 3 Knematc vscosty ν m /s Surface tenson coeffcent γ.-.8 N/m Electrcal Conductvty σ mho/m Permeablty µ 4π 0-7 H/m Among these propertes the surface tenson coeffcent s the most crtcal because t determnes the attachng force - surface tenson force. Furthermore the surface tenson coeffcent of the molten metal s senstve to the component of the electrode the temperature the sheldng gas etc. For the mld steel used n the present study t vares appromately n the range of.-.8 N/m dependng on the temperature of the molten steel. For the constant current GMAW the surface tenson coeffcent s assumed to be. N/m n the present study. For pulsed current GMAW the molten droplet temperature 9

37 s relatvely low due to the low average current therefore the surface tenson coeffcent s assumed to be.5 N/m. A thermal analyss should be ncorporated n the model to consder varatons of the materal propertes n the future study. The followng assumptons have also been made concernng the materal propertes durng the metal transfer process: () The physcal propertes of the materal are constant n the same phase ndependent of the temperature. () The molten metal s an ncompressble Newtonan flud. (3) Chemcal reacton and metal vaporzaton are neglgble.. Modelng of Metal Transfer Based upon the above analyss metal transfer n GMAW s modeled as an unsteady ncompressble vscous flow wth strong surface tenson on free surface. The electromagnetc force sgnfcantly nfluences the metal transfer process. The electrc feld whch s used to solve the electromagnetc force s assumed to be quas-steadystate. An asymmetrc geometrcal shape s used to model the shape of molten metal. Schematc sketches of metal transfer process n GMAW wth ntal and boundary condtons are shown n Fgure.. The followng assumptons have been made for the present study: 0

38 Electrode Wre federate v 0 4mm u ab = 0 v ab = v 0 p ab / y = 0 Φ ab = const. f ab = u bc = 0 v bc = 0 p bc / y = 0 Φ bc = 0 f bc = 0 a b c a b c y J s 4mm u ae = 0 v ae / = 0 p ae / = 0 Φ ae / = 0 f ae / = 0 Calculaton doman u cd = 0 v cd / = 0 p cd / = 0 Φ cd = 0 f cd / = 0 Calculaton doman Symmetrcal as mm e Wall d e y d u ed / y = 0 v ed = 0 p ed / y = 0 Φ ed = 0 f ed / y =0 (a) (b) Fgure. Schematc sketch of metal transfer process n GMAW wth ntal and boundary condtons: (a) A Schematc of metal transfer process (b) Intal and eternal boundary condtons () Incompressble lamnar flud flow s assumed; () The nput velocty of molten metal s assumed to be the same as the wre feed rate; (3) The problem s assumed to be asymmetrc. Hence the calculaton doman s taken as one sde of centerlne;

39 (4) Free slp at the sold boundares; (5) Momentum transfer from plasma to the droplet s neglected; the veloctes of the surroundng gas are specfed by settng them to zero; (6) The effects of pressure varatons n the surroundng gas have been neglected by settng the pressure to atmospherc condtons. The boundary condtons whch are used to determne the dstrbutons of the potental and current densty wthn the droplet and thus ncorporate the nfluence of the electromagnetc force are () An sopotental lne (Φ = 0) s set at the nlet secton; () There s symmetry about the centerlne; (3) The current densty on the droplet surface cell ( ) s J s. Snce there are no epermental measurements of the current densty on a GMAW droplet surface avalable n the lterature due to the dffculty of makng such measurements on the free surface of a metal droplet surrounded by the harsh envronment of weldng arc we assumed that current densty J s on the droplet surface s dstrbuted as followng J s = cf ( ) (.) By consderng the current contnuty I = J s S (.) the current densty on the droplet surface cell ( ) becomes

40 ( S f ( ) J s = I f ( ) ) (.3) n where I s the weldng current and S s the surface area of the free surface cell ( ). f ( ) s the dstrbuton functon whch has to be assumed. The two knds of current densty dstrbuton on the droplet surface assumed n the prevous study by Cho Yoo and Km [43] are as follows: Unform current densty dstrbuton: f( )= (.4) Lnear current densty dstrbuton: f( )=z (.5) where z represents the dstance between the free surface cell ( ) and the sold-lqud nterface of the electrode. It was found that the current densty dstrbuton on the droplet surface had sgnfcant effects on the molten droplet profle and sze. The calculated results were n broad agreement wth the epermental data and suggested that the assumpton of the lnear current densty predcted the epermental results more accurately than the unform current densty. However the transton current was not captured usng ether of these current densty dstrbuton models. s proposed: In the present work a Gaussan current densty dstrbuton on the droplet surface f ( ) = ξ = X D ep( ξ π / ) (.6) 3

41 where X s the arc (curve) length on the droplet surface between the lowest pont on the droplet and the free surface cell ( ) and D s dameter of the electrode when the weldng current s constant. The assumpton s proposed based on the current densty dstrbuton over the surface of the underlyng workpece for whch a radally symmetrc Gaussan dstrbuton has been detected by prevous eperments [6] and has been adopted frequently n the lterature. Copyrght Ge Wang 007 4

42 Chapter 3 Numercal Schemes Our numercal program s developed based on RIPPLE a computer program for solvng ncompressble flows wth free surfaces provded by Los Alamos Natonal Laboratory by addng electromagnetc feld calculaton. The numercal schemes employed are based on a fnte-dfference soluton of a coupled set of partal dfferental equatons governng unsteady ncompressble flud flow wth surface tenson on the free surface [60] and nfluence comng from the electromagnetc force. The two-step proecton method [66] s the basc algorthm for solvng ths set of partal dfferental equatons wth the pressure Posson equaton (PPE) solved by a robust ncomplete Cholesky conugate gradent (ICCG) technque. Free surfaces are captured by the volume of flud (VOF) method [6]. Surface tenson of free surfaces s modeled as a localzed volume force derved from the contnuum surface force (CSF) model [6]. The electromagnetc force s calculated based on assumpton of quas-steady-state electrc feld and Gaussan current densty dstrbuton over the free surface. A boundary condton must be enforced to a transent rregular surface the free surface. 5

43 3. Governng Equatons In order to smplfy the numercal model the physcal process of metal transfer s assumed to be asymmetrc and the materal propertes are assumed to be constant. The moton of flud wthn the droplet s governed by the two dmensonal ncompressble Naver-Stokes equatons (contnuty and momentum equatons) n Cartesan or cylndrcal ( = r y = z) coordnates: v = 0 (3.) Dv ρ = p τ F b (3.) Dt In the above v s the velocty ρ s the flud densty p s the scalar pressure F b s the body force whch ncludes the gravtatonal force surface tenson force and the electromagnetc force and τ s the vscous stress tensor. The element of vscous stress tensor τ y s v v y τ y = µ ( ) (3.3) y where µ s the dynamc vscosty coeffcent of the flud. 6

44 3. Numercal Modelng and Soluton for Governng Equatons When obtanng numercal soluton of the governng equatons some general steps should be followed:. Generate a layout of the fnte dfference mesh n the calculaton doman.. Formulate the dscretzaton form of the governng equaton. 3. Set ntal condtons accordng to the physcal model. 4. Add boundary condton accordng to the physcal model. 5. Solve the system of algebrac equatons. Fgure 3. shows a flow dagram of those steps. Start Fnte Dfference Mesh Dscretzaton Equaton Algorthm Soluton Boundary Condtons Intal Condtons Fgure 3. Flow Dagram of Numercal Soluton 3.. Mesh Layout The calculaton doman s parttoned nto a rectlnear mesh whch s composed of orthogonal cells wth varable wdth and heght y for a cell centered at the pont ( y ). The computatonal mesh s constructed from a number of sub-meshes wth each sub-mesh bult by quadratcally epandng cell spacng. Arbtrary varable cell spacng s acheved by properly choosng the specfed varables. 7

45 Fgure 3. shows layout of varables p ρ and v on a cell centered at y ). ( The pressure p and densty ρ are located at the cell center y ). The components ( of velocty are set at cell faces wth component u / at poston ( / y ) and y component v / at poston ( y / ). The control volumes for mass and momentum are marked n the fgure wth the mass control volume centered at y ) the - ( momentum control volume centered at y ) and the y -momentum control volume centered at y ). ( / ( / ( y ) ) y ) 3 ( y ( v / v / y ) ( y ) ( y ) y ρ ( p u / y ) ) y ) ( ( y ( u / Fgure 3. Control volumes 8

46 The staggered arrangement of pressure and veloctes results n second order accurate central dfferences. The key feature of ths staggered grd arrangement s that the mass flu across any face of the flud volume over whch contnuty s to be satsfed s drven by a pressure dfference evaluated wth pressures at nodes straddlng the mass flu nterfaces. Ths layout tends to prevent napproprate decouplng between the pressure and velocty felds whch yelds a false numercal soluton. The false soluton can be hghlghted by a checker-board dstrbuton for the pressure feld as shown n Fgure 3.3. It s apparently not a zero-pressure gradent feld n physcs. However a false p pe pw zero-gradent pressure feld = = 0 P EW s obtaned numercally when a nonstaggered grd arrangement of pressure and veloctes s appled. p W P E EE Fgure 3.3 Checker-board dstrbuton for pressure 3.. The Dscretzaton of Governng Equatons and Algorthm Soluton Gven a partal dfferental equaton and a fnte dfference mesh there are two prmary approaches to develop fnte dfference equatons: the pont approach and the control volume approach. The pont approach develops a fnte dfference appromaton 9

47 for ( φ ) by usng the Taylor seres epansons. The dscretzaton s derved n a mechancal way whle the physcal laws used n dervng the partal dfferental equatons are not scrutnzed. The control volume approach forces the fnte dfference equatons to follow the physcal laws or conservaton prncples that the partal dfferental equatons represent. Hence the control volume approach s adopted to buld fnte dfference equatons here. Usng the control volumes shown n Fgure 3. governng equatons 3. and 3. are dscretzed as frst order accurate n tme and second order accurate n space. The detals of the governng equatons dscretzaton wll be gven n the followng subsectons. a. The Two-step Proecton Method The two-step proecton method [66] s used as the basc algorthm to solve the set of partal dfferental governng equatons here. A tme dscretzaton form of the momentum equaton (3.) s v n n v n n n = ( v ) v p n t ρ n τ n ρ n ρ F n b (3.4) The basc scheme for the two-step proecton method s to break the computaton of the governng equatons for unsteady ncompressble flow (3.) and (3.4) nto two steps. Step : v * v t n = ( v n ) v n n ρ n τ n ρ F n b (3.5) 30

48 Step : n * v v = n t ρ n v = 0 p n ( n ρ p n v ) = t * (3.6) (3.7) In the frst step a velocty feld * v s computed from dffuson advecton and body forces.e. neglectng the nfluence from the pressure gradent. In the second step the velocty feld s changed under the nfluence of pressure gradent only. Snce the velocty feld must satsfy the contnuty equaton (3.) as well one Posson equaton (3.7) s obtaned for solvng the pressure feld. Ths Posson equaton s referred to as the pressure Posson equaton (PPE). The superscrpt n represents the value of varable when tme s n t. The tme step s varable wth ts value n n n cycles the tme s t = tk. k= 0 tk at the k th cycle ( k=0 ). After b. Advecton The fnte dfference form of advecton terms n the - and y-drectons are derved usng the momentum control volumes shown n Fgure 3.. For the advecton term n the -drecton t s calculated at (/) ( v ) u = u u v u / / / y / (3.8) where 3