Computer simulation of the submerged arc welding process on the basis of self-consistent physicomathematical

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1 International Journal o Engineering Research and Technology. ISSN Volume 11 Number 1 (018) pp International Research Publication House Computer simulation o the submerged arc welding process on the basis o sel-consistent physicomathematical model S.S. Miller Welding Department Tula State University Tula Russia ABSTRACT Computer simulation o the submerged arc welding process is based on solving a sel-consistent physico-mathematical model. This means that the developed simulation is based on the some o the most complete physicalmathematical model o the submerged-arc welding process. This model includes submodels o the heat sources heat transer electromagnetic phenomena in the weld pool hydrodynamic phenomena in the weld pool and submodel o ree suraces o the weld pool. This physicomathematical model is the basis o the developed sotware or the simulation o the submerged-arc welding process (SAW). Keywords: Computer engineering numerical model simulation welding. I. INTRODUCTION When creating new products and innovative technologies we have to perorm timeconsuming experimental research the task o which is to optimize the technological process. The need or research usually arises when creating new objects using new materials and equipment. To reduce the cost o such research and to optimize the manuacturing technology o the object it is advisable to use a preliminary theoretical study based on computer simulation o the phenomena in the object o study i.e. computer-aided engineering. In the modern world computer-aided engineering (CAE) systems are widely used allowing simulate various physical processes occurring in the objects o study. There are known theoretical models o arc welding [1-8] which are based on the system o heat transer equations and equilibrium o the weld pool surace. These models reproduce well the ormation o the weld pool and weld in shielded gas welding. However these models were not able to reproduce the ormation o a seam during arc welding under a layer o lux. In particular the known models o arc welding do not reproduce the ormation o speciic seam ormation under a lux layer which is characterized by the mushroom-

2 1838 S.S. Miller shaped cross section o the seam (Fig. 1) as well as the strong dependence o this orm on the arc voltage and the electrode diameter (Fig. ). Fig.1. Proiles o weld penetrations in carbon dioxide (a) and under a layer o lux (b) in the same welding conditions Fig.. The eect o voltage 5V (a) and 35V (b) on the cross-proile o the weld during welding under lux at the same arc current and welding speed. II. PHENOMENOLOGICAL ANALYSIS Obviously the main dierence between submerged-arc welding and gas-shielded arc welding is that the arc is in the gas cavity ormed by lux vapors. As the arc moves the lux in ront o the arc melts and partially evaporates and behind the arc it condenses and hardens. These phenomena signiicantly change the heat transer in the ormation zone o the weld pool and can explain the dierence in the seam proiles. The eect o arc voltage on the seam proile can be explained by the act that as the arc voltage increases the length and power o the plasma arc column also increases hence the volume o the lux vapor in the arc cavity increases. Increasing the arc length increases the cavity height and redistributes the energy o the lux vapor to the metal surace which increases the seam width on the surace o the weldment. At low voltage and short arc the gas cavity is located deep in the metal respectively narrow seams are ormed. A noticeable eect o the electrode diameter on the ormation o a weld in submerged-arc welding is associated with the use o large-diameter wires. Since with an equal arc current the same amount o electrode metal is melted as the wire diameter increases the electrode eed rate should be reduced to obtain a given arc current. Accordingly the pressure o the droplets o the electrode metal on the surace o the weld pool will decrease which will reduce the delection o the surace o the weld pool and reduce the depth o penetration.

3 Computer simulation o the submerged arc welding process 1839 III. MATHEMATICAL MODEL To explain the above eatures o submerged-arc welding submodels o these phenomena were introduced into the well-known model o weld ormation. III.I. SIMULATION SPACE AND COORDINATE SYSTEM In the simulation process was used ixed Cartesian coordinate system х у z (Fig. 3) in which the metal o the welded joint is immobile and the electrode and the arc move with a welding speed vw in the direction o the x coordinate. Fig.3. The structure o the simulation zone: 0 base metal 1 powder lux electrode 3 molten slag 4 solid slag 5 molten metal 6 solid-liquid metal 7 lux vapor and 8 weld metal. Internal interphase boundaries are deined as intersections o sets and denoted by: Z0=Ω1Ω3 (powder lux - slag) is determined by the decomposition o the solidiication lux isotherm; Z1=Ω7Ω5) (lux vapor - molten metal) is determined by the solution o the equilibrium equation o the surace o the weld pool; Z=Ω7Ω (electrode - arc) deined as the distance rom the surace o the weld pool equal to the length o the arc; Z3=Ω3Ω5 (molten metal - molten slag) is determined by solving the equilibrium equation o the surace o the weld pool; Z4=Ω0Ω1 (solid metal - powder lux) determined by the proile o the groove; Z5=Ω4(Ω6Ω8) (solid slag - metal) is determined by the location o the surace o the weld pool on the crystallization line; Z6= Ω7Ω3 (lux vapor - slag) is determined by the location o the isotherm o evaporation o the lux; Z7= Ω0Ω8 (base metal - seam) is determined by the limiting distribution o the melting point o the metal.

4 1840 S.S. Miller III.II. DIFFERENTIAL HEAT EQUATION The main equation in the simulation is a nonstationary nonlinear heat equation with boundary conditions which determines the enthalpy change rate at dierent points o the weld metal (1). H t T T T H vx q (1) x x y y z z x where H = H(xyzt) is a bulk enthalpy J/cm 3 ; λ=λ(xyzt) coeicient o thermal conductivity W/cm grad vx movement speed o liquid metal q=q(xyz) heat intensity distribution o the welding arc W/cm 3. The enthalpy H=H(xyzt) is related to the temperature T by a non-linear unction that takes into account the usion heat HLS and the heat capacity cρ o the substance located at a given point in the simulation space (Fig. 3). Boundary conditions: At the boundaries o the simulation area x=0 y=0 z=0 x=xm y=ym z=zm linear interpolation T(xyzt) o the equation to the boundaries is used: where n is the normal to the boundary surace. Initial conditions: T 0 () n t = 0 T (x y z) = T0 (3) correspond to the beginning o the welding process i.e. it is assumed that at the initial moment the temperature o the usion aces in all points is equal to the ambient temperature. The structure o the modeling space (Fig. 3) was taken in accordance with the moment o arc initiation: the location o the metal corresponds to the geometry o groove the lux is in a powder state the electrode contacts the metal surace the welding pool and the gas cavity are absent. III.III. HEAT INTENSITY DISTRIBUTION OF THE WELDING ARC q=q(xayz) in the modeling space is determined according to physical phenomena in the arc cavity and adjacent zones as well as with the movement o the arc axis xa=x0+vwt in the modeling zone with the welding speed vw. The heating o electrode stick-out by arc current (zone ): dt dz e j c ym y v (4)

5 Computer simulation o the submerged arc welding process I where T temperature o electrode stick-out ρe= ρe(t) volume resistivity j - current density I in an electrode with a diameter d сρ volumetric heat capacity o the electrode material v electrode eed. The anode area o the arc (surace Z=Ω7Ω): d dq dz ju a (5) where Ua voltage drop in the anode region o the arc. The heat liberation in the plasma lame o the arc is described as the distribution o radiation o the arc column over the surace o the arc cavity Ω7 (surace Z1=Ω7(Ω3Ω5)): dq dn EIL r where E potential gradient in arc column IL arc current and arc length r the distance between the point o the surace Z1 and the center o the arc column. The cathode region o the arc (surace Z1=Ω7Ω5): (6) dq dn IU k exp r 0 R R (7) where Uk cathode arc voltage R eective arc radius r0 the distance between the point o the surace Z1 and the point o intersection o the arc axis with the surace Z1. Heat transer by droplets o an electrode metal is described as heat release on the surace (surace Z1=Ω7Ω5): dq dn 4cT v 4r 0 exp d k d (8) where Tk temperature o droplets. Heat liberation in the liquid slag is practically absent so the slag does not have direct contact with the electrode which has a temperature below the melting point o the lux and the electrical resistance o the powder lux is very high.

6 184 S.S. Miller IV. EQUILIBRIUM EQUATION OF THE WELD POOL SURFACE The location o the surace o the weld pool Z(xy)=Ω5(Ω7Ω3) is determined by the pressure equilibrium equation (9): capillary pressure pσ gravitational pressure pg the low o the electrode metal droplets p hydrodynamic pressure o metal low in a weld pool pv electrodynamic pressure arc pa internal pressure o liquid metal pm. p pa p pv pg pm 0 (9) Capillary pressure is determined by the curvature o the surace Z(xy) and or small delections it is determined as: Z Z p (10) x y where σ - surace tension coeicient. Gravitational pressure is determined by the weight o a column o substance above the surace point o the weld pool: pg gz zmax hzh (11) where - g acceleration o gravity ρ ρh metal and slag densities zmax maximum surace height o the weld pool Zh thickness o the liquid slag layer. Electrodynamic pressure o the arc is determined by the arc current: k ai x0 vwt y p exp (1) a Rp Rp where - ka - electrodynamic coeicient Rp- arc orce radius. The low pressure o the droplets o the electrode metal is determined by the speed and mass o the low: v x0 vwt y p exp (13) R The velocity o liquid metal vx in the weld pool Ω5 is determined by the ratio between the low o liquid metal and the cross section o the weld pool: Z1 x y Z5x y vx x v (14) w Z1x y Z7x y where - vw welding speed. The hydrodynamic pressure o the weld pool metal low is determined by the change rate o the weld pool cross-section area (15). ds5 pv v (15) x dx

7 Computer simulation o the submerged arc welding process 1843 This pressure component increases the pressure beore the arc and decreases it behind the arc. The internal pressure in the melt pm is determined rom the equality o equality o the area o the weld metal to the amount o electrode metal consumed in solving the variation problem: pm var S8 0( xm) S0(0) r v v w (16) where - S ( 80 xm) the cross-sectional area o the seam at the end o the modeling area x=xm S (0 0 ) - the initial cross-sectional area o the groove edges at x=0. V. CURRENT AND WELDING ARC LOCATION The arc current I is set by the eed rate v and the diameter d o the electrode:' I v d 4 c T k T H LS (17) where - Tk is the temperature o the electrode droplets HLS is the volume heat o usion. The length L o the welding arc is given by the voltage U0 o the power source and depends on the electrical resistance o the current-carrying elements R0 and electrode stick-out R: L 1 E U0 Ua Uk I R0 R (18) The electrode stick-out resistance depends on its length L and the temperature T distributed over the length: R 4 d L 0 e T VI. CORRECTION OF THE SIMULATION AREA STRUCTURE The initial uncertainty o the weld pool geometric structure ormation requires a continuous change in the location o the interacial suraces depending on the results o solving the equilibrium equation o the weld pool. When transerring the surace Z(xy)=Ω5(Ω7Ω3) it is assumed that the temperature o the metal and slag in the zone o displacement is equal to the surace temperature and their enthalpies change in accordance with this temperature. The resulting error is deined as the rate o change o enthalpy during surace transiguration: z dz (19)

8 1844 S.S. Miller d 3 Hd dt 3 d 5 Hd dt 5 (0) These errors are compensated by changing the enthalpy o the zones Ω3 and Ω5 depending on the temperature distribution: H x y z 3 1 Tx y z TL Tx y z T L 3 3 d (1) where - TL liquidus temperature. As the thermodynamic state approaches the steady state the transormation error is deined as ΛΩ 0. The condition or the end o the simulation is the stabilization o the solidus isotherm length: d xmax 6 0 () dt Solving the model equation systems in the orm o temperature distributions T(xyzt) and the geometric structure o the modeling zone Ω(t) allows the initial stage o the process to be reproduced rom the moment o arc initiation until the steady-state weld pool. VII. NUMERICAL SOLUTION OF THE SELF-CONSISTENT PHYSICO- MATHEMATICAL MODEL A eature o the submerged arc welding model is the complexity o the weld pool ormation zone or the numerical description o which a discrete space is used which consists o a set o points evenly spaced with a step Δ. The continuous coordinates xyz o points are replaced by indices ijk. The structure o a discrete space is deined by an array o pointers Ωijk belonging to a point ijk to a lux in a powder liquid vaporous and melted state or to a metal in a solid or liquid state. Depending on the current result o solving the system o equations o the model the structure o the array Ωijk varies. To solve the equations o heat conduction and equilibrium o the weld pool surace the inite dierence method on conjugate grids was used. On the interacial suraces the coeicient o thermal conductivity was determined as the average harmonic value o thermal conductivities o adjacent phases.

9 Computer simulation o the submerged arc welding process 1845 To reduce the size o the modeling zone as the electrode moves to the grid step i.e. in time τ=δ/vw the array o pointers is translated on one node against the direction o welding: t t H T i j k i 1 j k t H t i j k i 1 j k t T t i j k i 1 j k In this case the coordinate o the arc axis returns to its original position xa=x0. Figure 4 presents the algorithm or numerical simulation o the submerged-arc welding process. Initial data: geometry o groove ater the previous pass the thermophysical properties o steel and lux welding parameters Determination o the initial geometry o the numerical solution zone Calculation o electrode melting parameters and energy characteristics o the welding arc The cycle o non-stationary numerical simulation o the thermodynamic state o the ormation o the weld pool Determination o distribution o heat luxes on metal and slag suraces Solution o heat equation The solution o the variation problem o the location o the welding arc in the groove The solution o the equilibrium equation o the surace o the weld pool when exposed to capillary gravitational electrodynamic hydrodynamic and internal pressures Calculation o the internal pressure o the weld pool according to the condition o mass balance o the weld and electrode eed until equal masses o suracing and electrode eed Correction o the location o the interphase boundaries "vapor-slag-powder luxsolid slag" "solid-liquid metal" by solving the equation o heat conduction and equilibrium o the weld pool surace until the stabilization the length o the solidus isotherm Formation o simulation results documents: temperature distribution geometry o the weld pool ormation area energy characteristics o the welding process Fig.4. Algorithm or numerical simulation o weld ormation in submerged arc welding (3) VIII. SIMULATION RESULTS: Figure 5 shows the result o computer simulation o the welding process under the AN-348A lux with a grain raction o mm o a double-groove preparation joint S5 o 0 mm in thickness rom 09GC steel with the Sv08GS electrode wire.

10 1846 S.S. Miller Process parameters: arc power supply voltage 30 V electric resistance o the welding circuit with electrode stick-out is 4 mω welding speed is 5 mm / s electrode diameter 4.0 mm electrode eed rate 4 mm / s stick-out is 30 mm. Fig.5. The simulation result o the weld ormation process or a welding doublegroove preparation joint rom steel 09GS 0 mm: a) cross-sectional drawing o a groove b) longitudinal section o the modeling zone c) calculated cross-section proile o the seam d) top view o the metal surace The results obtained during the simulation process: arc current is 650 A arc length is.6 mm eective anode voltage drop V cathode voltage drop V potential gradient in the arc column 5.3 V / mm arc diameter 17 mm heating the electrode to a temperature 0 C stick-out resistance mω. The total power o the process is 19 kw rom which the radiation is 8.8 kw; the arc emits 4.1 kw at the electrode and 6.1 kw at the joint surace. The heat liberation power o the electrode stick-out is 0.3 kw the temperature o its heating by the arc current is 35 C. The length o the weld pool is 30 mm or the liquidus temperature 40 mm or the solidus temperature the maximum width is 3 mm and the depth is 11 mm. The cross-sectional area o the seam is 140 mm the weld metal 50 mm the heat-aected zone is 86 mm the remolten lux area - 94 mm. The eect o the voltage o the power source and the diameter o the electrode wire was simulated when the plate o 09GS 1 mm in thickness was welded at a welding speed o 5 mm/s and an arc current was 480 A. The electrode eed rate was adjusted to obtain the speciied current value. The simulation results or dierent values o the arc voltage (4V and 40V) and or the electrode diameter 3 mm are shown in Figure 6. Modeling showed that at a voltage o 4V the length and voltage o the arc column are 1.8 mm and 8 V

11 Computer simulation o the submerged arc welding process 1847 respectively. With an increase in the source voltage to 40 V the length and voltage o the column increase to 5.4 mm and 4 V respectively. At the same time the weld pool depth has not changed much but the melting end o the electrode at high voltage is higher. The increase in the power o the arc column and the area o its contact with the lux markedly changed the amount o evaporated and remelted lux. Since most o the heat spent on evaporation and melting o the lux is transerred to the surace o the weld pool due to the low thermal conductivity o the powder lux covering the welding zone this leads to a very noticeable change in the shape o the weld. This increase in voltage led to an increase in the width o the seam rom 9 to 16.4 mm and a decrease in its convexity rom 4 mm to. mm while the bath length increased rom 18 to 5 mm. The average thickness o the layer o remelted lux increased rom 0.9 to mm. Fig.6. The results o the penetration simulation o a plate made o steel 09GS - 1 mm in thickness under a layer o lux at dierent values o the arc power source voltage (4V and 40V): a) limiting temperature distribution in the weld cross section b) temperature and lux distribution in the longitudinal plane o symmetry The simulation results or dierent values o the diameter o the electrode wire ( and 4 mm) and the voltage o the power source o the 3 V arc are shown in Figure 7. The simulation showed that to maintain the same welding current (480 A) it is necessary to change the eed rate strongly: with a mm electrode diameter the eed rate is 79 mm/s and at 4 mm - 15 mm/s. This change is more signiicant than the change in the ratio o the electrode cross section area since the temperature o heating o the electrode stick-out by the current passing through it (830 C at mm and 140 C at 4 mm) varies greatly. Thereore the amount o heat transerred by droplets o the electrode metal to the weld pool with the electrode diameter increases slightly (in this case 1.4 times) but the area o droplets expansion increases (by 4 times).

12 1848 S.S. Miller Thereore the concentration o heat input drops under the electrode increases very signiicantly which has a signiicant impact on the penetration depth. In this case with an electrode diameter o mm the penetration depth was 8.1 mm and at 4 mm mm. The pressure o the droplet low determined by the eed rate o the electrode varies very signiicantly. Thereore the depth o the crater under the arc with a small diameter electrode is much greater. Since the voltage and the length o the arc weakly depend on the diameter o the electrode the arc column with a small diameter buried in the weld pool respectively the power o heat generation in the column is spent mainly on the melting o the metal and not the lux. Accordingly the thickness o the remelted lux above the seam with a small diameter o the electrode is somewhat less than with a large (1 and 3 mm respectively). The width o the seam and the length o the bath is also slightly smaller since the diameter o the electrode at a given arc current almost does not aect the power released in the arc column. Fig.7. The results o the penetration simulation o a plate rom steel 09GS 1 mm in thickness under a layer o lux or dierent values o the electrode diameter ( and 4 mm): a) limit temperature distribution in the cross section o the weld b) temperature and lux distribution in the longitudinal plane o symmetry IX. COMPARISON WITH EXPERIMENTAL DATA The obtained simulation results explain the results o experiments (Fig.1). The dierence in the results o welding in carbon dioxide and under a lux layer with the same arc current is due to the act that when welding in shielding gases the power o the arc column is almost completely radiated into the open space and under the lux beam much o this power is transmitted by steam and melt lux rom the weld pool surace. This changes the cross-sectional proile o the seam - when welding under lux the seams have a characteristic extension at the top. The strong inluence o the power supply voltage on the penetration proile during submerged-arc welding is explained by the change in the power o the arc column which is spent mainly on the

13 Computer simulation o the submerged arc welding process 1849 evaporation o the lux and subsequent condensation on the surace o the weld pool respectively the weld width greatly increases. The depth o penetration is determined mainly by the electrodynamic pressure o the arc which is determined by the speciied arc current. The inluence o the electrode wire diameter on the depth o penetration is associated with a change in the concentration o the heat lux and the electrode drop pressure on the surace o the weld pool and the depth o the crater under the arc. CONCLUSIONS Based on the comparison o simulation results and experimental data it was established that: - A sel-consistent physico-mathematical model o the submerged-arc welding process was developed based on the system o heat and mass transer equations hydrodynamic phenomena in the weld pool and pressure equilibrium on the weld pool surace taking into account heat transer in the arc column with lux vapor and subsequent condensation on the weld pool surace the eect o the supply voltage diameter and electrode eed rate on the distribution power and pressure o the arc on the surace o the arc cavity under a layer o lux; - It is shown that the observed dierence in the results o gas-shielded welding and submerged arc welding is associated with the redistribution o the heat generation power in the arc column by the processes o evaporation and condensation o the lux in the arc cavity; - It is shown that the eect o arc voltage on the cross-sectional shape o the seam is related to the change in power redistributed by lux evaporation inside the arc cavity as well as the location o the arc in the lux layer; - It is shown that the diameter o the electrode on the cross-sectional shape o the seam is associated with changes in the power density and the low pressure o electrode metal droplets onto the weld pool surace. ACKNOWLEDGEMENTS The work was carried out with the inancial support o Ministry o Science and Higher Education o Russian Federation. The research results were obtained within the ramework o the state task o the Ministry o Science and Higher Education o Russian Federation or the project /1.; applied science. For the sponsorship and the support I wish to express my sincere gratitude. REFERENCES [1] T.Yamamoto T. Ohji F. Miyasaka Y.Tsuji. Mathematical modeling o metal active gas arc welding. Science and Technology o welding and Joining. (00). Vol. 7. No pp. [] M.A. Sholokhov V.A. Eroeev S.I. Poloskov. A method or calculating the parameters o gas-shielded twin-arc multipass consumable electrode welding Welding International. (016). V pp

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