The Mathematical Model Research on MIG Groove Welding Process

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 157 (2016) 357 – 364

IX International Conference on Computational Heat and Mass Transfer, ICCHMT2016

The Mathematical Model Research on MIG Groove Welding Process Peng Jingnana,b, Yang Lixina,b,* a. Institute of Thermal Engineering, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, China. b. Beijing Key Laboratory of Flow and Heat Transfer of Phase Changing in Micro and Small Scale, Beijing 100044, China.

Abstract Through analysis the MIG groove welding process and the welding experimental result, a complete two-dimensional mathematical model of weld section molten pool characteristics was established. Use Gaussian heat source distribution to describe the weld heat source, introduced the welding speed to establish transient heat source model on the cross section. By introducing scalar of liquid fraction, mushy region dynamic character which was described using “Darcy” model proposed for porous media, and phase change which was taken into account using source-based method, establish a unified liquid and solid control equation, CFD model was established to simulate transient heat and mass transfer phenomena in welding process. The effect of surface tension was considered in the molten pool free surface stress model. The reliability of the model was verified by experiments. The effect of groove angle, groove depth and the welding speed on the molten pool were discussed in this paper. 2016The TheAuthors. Authors.Published Published Elsevier © 2016 byby Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of ICCHMT2016. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICCHMT2016 Keywords: V groove; MIG welding; Marangoni flow; surface tension

1. Introduction Scholars study in the numerical simulation of welding for many years, many numerical models have been developed [1-4]. Traidia [5] developed a unified finite element model for pulsed current GTA welding which dealed with the cathode, arc-plasma and melting anode together. It was found that the Marangoni effect plays an important role on the welding pool dynamic. And for a given level of energy, used a pulsed current welding could get a greater

* Corresponding author. Tel.: + 86-10-51684329. E-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICCHMT2016

doi:10.1016/j.proeng.2016.08.377

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weld pool than mean current. Hu and Guo [6] developed a moving 3D gas metal arc welding model which considered heat delivery to the metal transfer between droplets and the molten pool. This model reflected a phenomenon that a crater was opened and close-up in the molten pool because of the droplet impingement and the hydrostatic force. Welding of thick metal plate usually needed a groove [7-10]. Hu and Tsai [9] developed a three-dimensional GMAW welding process model for a thick metal plate with V groove. It was found that the groove could facilitate the flow of filler metal along the bottom of the groove because of the groove could provide a confined channel, and it could get a simpler flow pattern than without a groove because of the V groove has a smooth effect. A lot of factors who researched the welding with V groove have been systematically studied. Chen J [11] developed a new arc welding processes ForceArc to operate in spray transfer mode under lower arc voltage. He studied the three dimensional weld pool dynamics and the influence of V groove angles on welding of low carbon structural steel plates used the ForceArc process. It was found that in different angles the main flow pattern was more or less the same, but velocity, temperature and shape of the weld pool was different. A large V groove could make the flow of the molten pool to travel downward with heat energy at the front, so could increase the depth of the weld pool. Cho and Na [12-15] built many arc models for arc heat flux, electromagnetic force and arc pressure with Abel inversion methods and physical relations. Based on these models, they analyzed weld beads in V-groove GWAM with and without root gap and the various dynamic molten behaviors for different welding positions. They found that without the root gap, in vertical-upward position it could get melt-through beads but it was difficult to get full-penetration beads in the flat and overhead position with a 1 mm root gap, in different welding positions could find the molten pool overflow patterns, but it should increase the welding speed to avoid the overflow patterns because in the vertical-upward position it could get full-penetration beads. In this paper, a two-dimensional mathematical model and a moving Gauss heat source model which the heat source decayed over time were established. Introduced scalar liquid fraction and “Darcy” source, built unique continuity equations, momentum equations and energy equations for both liquid and solid phases. The model was applied to V groove welding process of AISI 304 stainless steel. Through compared the simulation and experiment result to verify the model. Heat source distribution parameters affecting the Gaussian heat source are discussed. Then, the groove angle, depth and welding speed were discussed. Nomenclature Aσ fl Tm Tl σq η β σm

constant in surface tension gradient liquid fraction melting temperature solidification temperature heat source distribution parameters arc thermal efficiency effectively coefficient of thermal expansion pure metal surface tension

2. Mathematical model 2.1. Mathematical model Based on the analysis of the physical process of MIG welding, this paper proposed two dimensional weld molten pool characteristics of the mathematical model. Model contained the cross section of transient electric arc heat source model, molten pool CFD model and mechanical model on the surface of the molten pool. Through the typical V groove welding process experiment result to verify the accuracy of the models. Heat source model: Because of the arc heat source moved in the welding process, so the effect on the cross section of heat source model includes two parts: the spatial distribution of heat source and variation law with time. According to the heat source on the space distribution characteristics, the Gauss heat source model was established. Arc heat source to the workpiece is through the part area, assumed that 95% of heat energy is in a heating area, this heating area is called heating spots, the heat distribution on the heating spots can use Gaussian function to

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describe.The heat flux from the center of spots is as follows. Where q(r) represents the heat flux which the distance is r from the center of spots. r2

3Q - 2V q2 e S R2

q r

(1) In the actual welding process, with the movement of the welding torch, heating spots gradually all removed from a particular cross section, the heat source intensity on the cross-section decreases to zero over time. When welding torch is moving in a constant speed, the heat source intensity change with time, according to the linear rule changed over time, namely: q(t)=-q(0)(t-t0)/ t0 tt0 where q(0) represents the heat source intensity at initial moments, t0 represents the time that the heat source effect on the cross section. The time t0 is calculated from the heating spot radius R and welding speed V using the following relations:

t0

R /V

(3) Molten pool CFD model: In the process of MIG welding, molten drop heats and keeps melting metal and make the molten pool shape change. Melting process is actually a phase-change problem with moving boundary. Regardless of the difference between the solder and substrate material, assumes that the solid and liquid density is equal. The mixing velocity U represents solid region and liquid region velocity. Introduce liquid fraction scalar, enthalpy source into energy conservation equation and “Darcy” source into momentum conservation equation, set up unique continuity equation, momentum conservation equation and energy conservation equation, which enable solid region, liquid region and mushy region to be solved by fixed grids [16]. The continuity equation is:

wU  ’ ˜ UU wt



0

(4)

The momentum equation is derived as: U

wU  UU ˜’U wt

§ 2P · ’ ˜ U I  ’ ˜ P ’U  ’U T  ’ ˜ ¨  N ¸ ’ ˜U I  F © 3 ¹









(5)

where μ represents dynamic viscosity, κ represents expansion of viscosity which is assumed to be zero. F is “Darcy” source item, and tends to zero as the liquid fraction is tends to one. So the mixture velocity approaches to that of the solid. So:

F

1- f L

2

f L3  H

Amush ˜U

(6)

where ε and Amush are arbitrary constants, according to the different metal materials. For stainless steel materials, they was taken as Amush = 6×104kg/(m3·s), ε = 1×10-3. The energy equation is:

w § wf · U H  ’ ˜ UUH ’ ˜ O’T  U L ¨ L ¸ wt © wt ¹ H fL H L  fS HS

(7) (8)

Mechanical model on the surface: As above mentioned, in the MIG groove welding process of medium and thick plate, when the welding current and welding groove is small, the electromagnetic force and protective gas shear force are small, ignore their influence for the fluid inside the pool. But molten pool heating surface temperature gradient is large. Usually the surface tension coefficient of metal is a function of temperature [16], so need to consider the hot surface tension. For metal:

σ T V m  AV T  Tm

(9)

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2.2. Calculation model The model used AISI 304 stainless steel which size was 50mm×10mm for numerical calculation. Depth of groove was 8mm, angle of groove were 40° and 50°. The symmetry of the geometry and boundary condition were Considered, calculation model for selecting half of symmetrical geometric model, as shown in figure 1. Material properties of AISI 304 stainless were shown in Table 1. Boundary conditions were shown in table 3. ABC used symmetrical boundary condition, DE and CD used the adiabatic boundary condition because the whole heating process time was short (within 1.5s), on the workpiece surface used the uniform boundary conditions. When the surface without melting, resistance items in equation (12) made the surface tension σ(T) didn't work. When the position of heat source beyond spot radius, Q automatically changed to zero. The hc in table 3 can be calculated from the relationship given by Goldak [17]:

24.1u104 εT 1.61

hc

(10)

Parameters of welding heat source are shown in Table 2. Table 1. Material properties of AISI 304 stainless Symbol Unit Value Aσ -2E-4 N/(mgK) ρ kg/m3 7200 ε 0.8 J/kg 2.47E+5 Š Tm K 1723 Tl K 1673 Cp 500 J/(kggK) β 1/K 1.0 E-5 Fig. 1. The calculation model

σm

N/m

1.8

k

W/(mgK)

24.2

Table 2. Parameters of welding heat source I(A) 210

U(V) 26

V(mm/s) 5

η 0.75

Q(W) 4095

σq(mm) 2.4

R(mm) 5.88

t0(s) 1.18

Table 3. Boundary condition Region

U

ABC

0

CD

0

DE

0

AGFE

σ(T)

V

T

wV wx 0 wT wx 0 0 wT wy 0 0 wT wy 0 0 hc T  Tf  Q O wT wy

At initial moments, in ABG region was the liquid metal and the melting temperature, other region was the solid metal and 300K. Calculation used unstructured grids. After the grid independent verification, grid dimension was 0.1 in V groove area, other area was 0.2. The grid scale refinement in proportion to the rate of 1.2, make sure the melting zone had sufficient number of the grid to describe the flow. Figure 2 represents the schematic of mesh. The grid model unit number is 13567. Use COMSOL[18] to simulation, and the time step was 0.001s. The next time step calculation continued until the relative residues of all physical variables less than 0.01 in the last time step simulation. The temperature of the molten pool was still higher than melting temperature after stop heat, molten pool kept changing, so the computation time is longer than 1.5s.

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3. Model Validation 3.1. Confirmatory experiment Select the same parameters as the numerical calculation to do experiment. Figure 3 is the experimental system, it included: MIG welding machine, protect cylinders, workpiece and so on. Figure 4 is the experimental result. Two samples were obtained by cutting the workpiece. Though metallographic grinding, the sample cross section could get the molten pool shape.

 Fig. 2. Schematic of mesh

Fig. 3. The experimental system

Fig. 4. Result of experiment

Result: The sample cross section shape of molten pool as shown in table 4. The experiment indicated that on the molten pool shape were basically identical for the same groove angle. Experiment result showed that the molten pool could be divided into two parts: A and B, measured the parameters of the molten pool, the results are shown in table 5. Table 4. Shape of different V groove Angle

Section 1

Section 2

Section 3

40°

50° Characteristic parameter

Comparison with numerical simulations: Figure 6 comparisons shape of molten pool between the experimental and simulation result in different angle. The curve on the right side was simulation result. Due to the transient simulation of molten pool was by the initial V groove molten pool over time through the evolution of solidification and melting, the curve in the figure was constituted by the molten pool outer boundary of all time, so it could compare with the experimental result. In Figure 5, the shape of molten pool of the experimental and simulation result had the similar characteristics, but had some differences about morphology. In section A, the molten pool bottom surface shape of experiment was a straight line, it evolved to a curve in the edge. The molten pool bottom surface shape of simulation was a continuous quadratic curve. In section B, the molten pool of simulation was same as the initial molten pool, but the molten pool of experiment had a smaller scale out on the basis of the initial pool. Analysis of the reason, the shape difference of section B was due to the temperature of molten drop when enter the V groove was far higher than the melting temperature, lead to the base metal at the bottom was melting. We assumed the initial molten drop filled the V groove at melting temperature, due to thermal conductivity, the bottom of V groove immediately solidification. The shape difference of section A was due to at the actual melting process the metal solution on the edge of the pool at the top of the triple point was affected by surface tension and produce contact angle made the surface morphology change and affected the internal flow of the molten pool and appearance. We did not consider the influence of the contact angle in the numerical model, assumed that the molten pool surface was horizontal.

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Table 5 shows the comparison of the molten pool shape between the experiment and simulation. It was found that the value of h1 showed some difference, the value of simulation was slightly bigger than experiment, the relative error less than 3%. The relative error of the largest weld width between simulation and experiment was less than 3%. Considered the parameters of different molten pool had certain fluctuation, the difference of weld width which was the biggest effect on the welding characteristic was smaller. Based on the above analyses, the two-dimensional mathematical model of molten pool could well predict the molten pool morphology of V groove MIG welding. Table 5. Parameters of the molten pool w1 (mm)

40°

50°

w2(mm) h1(mm)

h2(mm)

Section 1

10.56

3.82

2.77

5.23

Section 2

10.58

3.92

2.79

5.21

Section 3

10.62

3.74

2.78

5.22

Average

10.59

3.83

2.78

5.22

a) 40°

Simulated result

10.82

3.72

2.84

5.16

Relative error Section 1 Section 2

2.20% 12.31 12.27

2.79% 4.64 4.56

2.15% 3.11 3.06

1.15% 4.89 4.94

Section 3

12.24

4.62

3.09

4.91

b) 50°

Average Simulated result Relative error

12.27 12.46 1.52%

4.61 4.54 1.52%

3.09 3.14 1.73%

4.91 4.86 1.09%

Fig. 5. Comparison of simulated and experimental molten pool shape

4. Numerical Result Analsis Comparison of the numerical results under the different conditions, the characteristics of molten pool shape, welding speed and heat affected zone area were discussed in detail. The values ofw1/w2 and h1/h2 were used to analysis the change of molten pool in different conditions. The heat affected zone area meant the difference between the final molten pool area and the initial molten pool area values. The UG software was used to fit the molten pool shape curve, then construct surface to obtain the area. 4.1. Groove angle In this part, the value of groove depth was 8 mm. To insure the results were accuracy, the analysis was done in two different welding speeds, which were 4 mm/s and 5 mm/s. The range of groove angle was 30 degrees to 70 degrees. Figure 6 illustrates the molten pool shape in different groove angles. According to previous analysis, with increase of the groove angles, the molten pool was wider. The value of w1/w2 decreased and the value of h1/h2 increased. This due to the initial molten pool area increased. Gaussian heat source acts on the surface of molten pool, quantity of heat on part A was more than that on the part B, the value of h1 was bigger. As the Marangoni and buoyancy flow, the heat pass down, the rate of w1 rise was slower than w2. As the angle increased, the heat affected zone area decreased first and then increased. Because of the increase of the angle, the initial molten pool area increased, the quantity of heat also increased, lead to the result that more metal around the groove can be melted. 12

3.5

0.7

3.0

0.6

2.5

w1/w2 0.5 h1/h2 0.4 60 70

6

30° 35° 40° 45° 50° 6

4 2 0

0

2

4

x-axis(mm)

a)

55° 60° 65° 70° 8

10

2.0

30

40

50

angle (°)

b)

S (mm^2)

13

0.8

h1/h2

0.9

4.0

w1/w2

4.5

8

y-axis(mm)

10

11 10

V=4mm/s

9 8 7

30

40

50

60

angle (°)

c)

70

363

4.5

0.9

8.0

8

4.0

0.8

7.5

3.5

0.7

30° 35° 40° 45° 50° 6

4 2 0

0

2

4

55° 60° 65° 70°

x-axis (mm)

8

3.0

w1/w2 h1/h2 0.6

2.5

0.5

2.0

10

30

40

50

60

70

angle (°)

d)

h1/h2

6

Area (mm^2)

10

w1/w2

y-axis (mm)

Peng Jingnan and Yang Lixin / Procedia Engineering 157 (2016) 357 – 364

0.4

7.0 6.5

V=5mm/s

6.0 5.5 5.0

30

40

50

60

angle (°)

e)

70

v)

Fig. 6. Molten shape in different groove angles

4.2. Groove depth

7 6

6 4mm 5mm 6mm 7mm 8mm

4 2 0

4 w1/w2 h1/h2 3

0

2

4

6

x-axis(mm)

8

2

5 4

1

3 2

10

4

5

a)

7

8

7.6 7.2

6.4

0

5

6.0

7

w1/w2 4 h1/h2

5.6

6 4mm 5mm 6mm 7mm 8mm

4 2 2

4

6

x-axis(mm)

8

3

5

2

4

1

3 2

10

h1/h2

6

Area(mm^2)

8

8

0

4

5

4

5

6

7

8

depth(mm)

d)

6

7

depth(mm)

8

c)

10

0

V=4mm/s

6.8

b)

w1/w2

y-axis(mm)

6

depth(mm)

8.0

S (mm^2)

8

8

h1/h2

10

w1/w2

y-axis(mm)

In this part, the value of groove width was 2.91 mm. To insure the results are accuracy, the analysis was done in two different welding speeds, which were 4 mm/s and 5 mm/s. The range of groove depth was 4 mm to 8 mm.Figure 7 describes the analysis of the molten pool in different groove depth. With the groove depth increase, the molten pool became wider, the value of h1/h2 and w1/w2 decreased. As the groove depth increased, the growth rate of h1 was slower than h2. On the whole, with the depth increased, the heat affected zone area showed a trend of increase.

5.2

4.4

0

V=5mm/s

4.8 4

e)

5

6

7

depth(mm)

8

f)

Fig. 7. Molten shape in different groove depth

4.3. Welding speed In this part, the groove angle were 40 degrees, the groove depth was 8 mm. The range of the welding speed was 3 mm/s to 7 mm/s. The analysis of different welding speed is shown in Figure 8. With the welding speed increased, the molten pool was narrower. Because the welding speed increased, the heat source moving speed became faster, so lesser metal around the groove to be melted. These also resulted in the heat affected zone area decreased. The value of h1/h2 and w1/w2 became smaller. With the molten pool became narrower, the decrease rate of w1 is faster than w2, the same as h1 and h2. 5

0.7

14 12

4

w1/w2 h1/h2 0.6

3

0.5

2

0.4

Initial molten pool 3mm/s 4mm/s 5mm/s 6mm/s 7mm/s

4 2 0

0

1

2

3

4

5

6

x-axis(mm)

a)

7

8

h1/h2

6

w1/w2

y-axis(mm)

8

3

4

5

6

7

welding speed (mm/s)

b) Fig. 8. Molten shape in different welding speed

Area(mm^2)

10

10 8 6 4 2

3

4

5

6

7

welding speed (mm/s)

c)

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5. Conclusions The two-dimensional mathematical model of the molten pool was developed to investigate and numerically simulate the MIG welding processing. 1. The molten pool shape of V groove welding cross section could be divided into two parts which had obvious different shape features. The molten pool shape of each cross section was basically the same. 2. A complete mathematical model of weld section molten pool characteristics was established, including Gauss heat source model, CFD model of the molten pool and calculation model. 3. Analysis the molten pool shape between equilibrium diagram and simulation result, the molten pool shape was similar. The error of molten pool width was less than 3%. The accuracy of the mathematical model was verified. 4. With the increase of the groove angle, the molten pool became wider, and same as groove depth. The molten pool became narrower when the welding speed was bigger. In actual welding process, according to the groove angle, groove depth and welding speed, we should choose appropriate parameters Acknowledgements Project supported by the National Natural Science Foundation of China (Grant No. 51376022). References [1] Syed, A. A, Pittner, A, and Rethmeier, M, 2013, Modeling of Gas Metal Arc Welding Process Using an Analytically Determined Volumetric Heat Source, J. ISIJ International, 53, 4, pp. 698-703. [2] Cho, W. I, Na, S. J, and Cho, M. H, 2010, Numerical study of alloying element distribution in CO2 laser–GMA hybrid welding, J. Computational Materials Science, 49, 4, pp. 792-800. [3] Cho, W. I, Na, S. J, and Thomy, C, 2012, Numerical simulation of molten pool dynamics in high power disk laser welding, J. Journal of Materials Processing Technology, 212, 1, pp. 262-275. [4] Ha, E. J, and Kim, W. S, 2005, A study of low-power density laser welding process with evolution of free surface, J. International Journal of Heat and Fluid Flow, 26, 4, pp. 613-621. [5] Traidia, A, and Roger, F, 2011, Numerical and experimental study of arc and weld pool behaviour for pulsed current GTA welding, J. International Journal of Heat and Mass Transfer, 54, 9-10, pp. 2163-2179. [6] Hu, J, Guo, H, and Tsai, H. L, 2008, Weld pool dynamics and the formation of ripples in 3D gas metal arc welding, J. International Journal of Heat and Mass Transfer, 51, 9-10, pp. 2537-2552. [7] Hu, J, and Tsai, H. L, 2007, Heat and mass transfer in gas metal arc welding. Part I: The arc, J. International Journal of Heat and Mass Transfer, 50, 5-6, pp. 833-846. [8] Hu, Y, He, X, and Yu, G, 2012, Heat and mass transfer in laser dissimilar welding of stainless steel and nickel, J. Applied Surface Science, 258, 15, pp. 5914-5992. [9] Hu, J, and Tsai, H. L, 2008, Modelling of transport phenomena in 3D GMAW of thick metals with V groove, J. Journal of Physics D: Applied Physics, 41, 6, pp. 1-10. [10]. Hu, J, and Tsai, H. L, 2007, Heat and mass transfer in gas metal arc welding. Part II: The metal, J. 50, 5-6, pp. 808-820. [11]. Chen, J, Schwenk, C, and Wu, C. S, 2011, Predicting the influence of groove angle on heat transfer and fluid flow for new gas metal arc welding processes, J. International Journal of Heat and Mass Transfer, 55, 1-3, pp. 102-111. [12]. Cho, D. W, Na, S. J, and Cho, M. H, 2013, Simulations of weld pool dynamics in V-groove GTA and GMA welding, J. Welding in the World, 57, 2, pp. 223-233. [13]. Cho, D. W, Na, S. J, and Cho, W. H, 2013, A study on V-groove GMAW for various welding positions, J. Journal of Materials Processing Technology, 213, 9, pp. 1640-1652. [14] Cho, D. W, and Na, S. J, 2015, Molten pool behaviors for second pass V-groove GMAW, J. International Journal of Heat and Mass Transfer, 88, pp. 945-956. [15] Cho, D. W, Lee, S. H, and Na, S. J, 2013, Characterization of welding arc and weld pool formation in vacuum gas hollow tungsten arc welding, J, Journal of Materials Processing Technology, 213, 2, pp. 143-152. [16] Yang, L. X, and Peng, X. F, 2001, Numerical modeling and experimental investigation on the characteristics of molten pool during laser processing, J. INternational Journal of Heat Mass Transfer, 40, 23, pp. 4465-4473. [17] Goldak, J, Bibby, M, and Moore, J, 1986, Computer Modeling of Heat Flow in Welds, J. Metallurgical transactions B, 17, 3, pp. 587-600. [18] COMSOL Multiphysics Manual (Version: 4.4.0.150) [Z]. COMSOL Inc.,2013