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Improvement of welding heat source models for TIG-MIG hybrid welding process
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Improvement of welding heat source models for TIG-MIG hybrid welding process J. Chen ∗ , C.S. Wu, M.A. Chen MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, and Institute of Materials Joining, Shandong University, Jinan 250061, China
a r t i c l e
i n f o
Article history: Received 19 May 2014 Received in revised form 22 June 2014 Accepted 23 June 2014 Available online xxx Keywords: Adaptive heat source Numerical simulation Hybrid welding
a b s t r a c t Tungsten inert gas-metal inert gas (TIG-MIG) hybrid welding process is an effective way to improve welding productivity and quality due to advantages of the two processes. Mathematical analysis is crucial to fundamentally understand this synergetic welding process. In this study, based on experimental visualization of arc behaviors, some assumptions are proposed to deduce adaptive plane and volumetric heat source models separately for each involved welding method first. The influence of torch angles on distribution of temperature and geometry of weld bead are calculated and compared with experimental results. It shows that this developed algorithm of heat source can be employed to accurately predict welding process whether the electrode gun is slanted backward or forward to the direction of welding. Then TIG-MIG hybrid welding process is simulated and analyzed without considering the attractive or repulsive force of two arcs. The characteristic of TIG-MIG welding process is discussed compared to single MIG. It lays the foundation for the further research on the interaction of the two arcs during TIG-MIG hybrid welding. © 2014 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction With the unceasing intensification of the manufacturing competition, the traditional arc welding processes, such as tungsten inert gas welding (TIG) and metal inert gas welding (MIG), have been improved to satisfy enterprise’s requirements for welding technology with high quantity and high quality. TIG-MIG hybrid welding process is one of the effective ways to develop welding productivity and quality due to advantages of the two processes, which is similar to DE-GMAW (double-electrode gas metal arc welding) [1–4]. The major differences between TIG-MIG and DE-GMAW hybrid welding processes are as follows: (1) The mechanism of TIG-MIG is that an appropriate distribution of arc energy is simply liberated on the workpiece by a tailing TIG arc to improve traditional GMAW process directly. However, during DE-GMAW, the adding TIG arc is used as part of galvanic circle to make sure that the bypass current can flow back to the power source through the bypass TIG torch without going through the workpiece [1]. (2) The major effects of additional TIG arcs are different from each other. During TIGMIG hybrid welding, the additional TIG arc is used to reheat the
∗ Corresponding author at: MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, and Institute of Materials Joining, Shandong University, No. 17923 Jingshi Road, Jinan 250061, China. Tel.: +86 531 88395987. E-mail address: [email protected] (J. Chen).
workpiece and to improve the weld bead deformation. And during DE-GMAW, the purpose of adding tailing TIG arc is to increase the depositing rate of filler metal without imposing excessive heat on the workpiece, thus the tailing TIG arc is not directly liberated on the workpiece. And compared to tandem or T.I.M.E. welding [5–7], TIG-MIG hybrid welding is an easy way to utilize the advantages of TIG and MIG welding with low cost, since neither special shielding gas nor complex synergic powers are needed. It shows that MIG arc can be stable by simple hybridization of TIG even though pure argon shielding gas is used, which means the weld metal toughness is improved and welding quality is developed [4]. The further study indicates that it also has great potentiality to increase welding speed with high quality because of the quite stable cathode spots appearing in this hybrid welding [8]. However, it is still lack of comprehensive and profound research on physical mechanism of TIG-MIG hybrid welding, which hinders the development of this new welding method. In recent decades, many researches have been done on heat source models to reveal various welding process, such as gauss or elliptical heat source model for TIG in low welding current [9,10], double ellipsoid heat source model for MIG [11,12], double-ellipsoidal + EHGC (exponentially-tapered peak value of heat flux in Gaussian cylinder) heat source model for plasma arc welding [13], self-adaptable heat source models for laser beam welding and plasma arc welding separately by considering dynamic energy distribution during above welding processes [14]. However, all the heat
http://dx.doi.org/10.1016/j.jmapro.2014.06.002 1526-6125/© 2014 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic diagram of welding process with a slanted gun: (a) TIG and (b) MIG.
models mentioned above are focused on single welding process, which could not be used in hybrid welding directly. Though many improved heat source models have been deduced for laser + GMAW hybrid welding or laser + TIG hybrid welding, the influence of torch angles is not studied comprehensively as most of the researches are focused on the synergetic heat effects of two sources [15,16]. A new hybrid heat-source model is developed to simulate DE-GMAW process, which is similar to TIG-MIG. However, their physical mechanisms are different. For example, during DE-GMAW process, the tailing TIG arc is only the conductive path of current without directly acting on the weld pool [17]. And the parameters of all above heat or arc force models need to be verified by experiments each time if the torch angle changes. To solve this problem, Cho et al. develop a complex heat source model for submerged tandem arc welding process [18]. Two different effective radii of arc plasma are introduced to reflect the influence of torch angles on heat flux and arc pressure distribution. Considering Lorentz force due to the magnetic field induced by leading and trailing arc, the interaction of these two arcs is partially dominated by leading arc displacement. The nine different model parameters in leading and trailing arc models make it to be utilized intricately. Tanaka et al. analyze arc phenomena in TIG-MIG hybrid welding process with different torch angles using three-dimensional numerical models [19]. It is found that the convergence of heat flux will get maximum value under certain torch angles of TIG and MIG, which can be explained by the balance between the stiffness of arc and the repulsion of both arcs. However, the complex current
conservation equation and Maxwell–Ampere equation needs to be solved to study the influence of torch angles and interaction of arcs [19]. So a simple and effective way is needed to evaluate the influence of torch angles on welding process first. Based on several simple assumptions, the adaptive plane and volumetric heat source models are deduced respectively by considering the influence of torch angles and arc length in this paper. The heat transfer mechanism is investigated by solving three-dimensional numerical equations for TIG and MIG welding separately. The influence of torch angles on temperature profiles and the weld bead geometry is numerically analyzed. Good agreement is shown between the predicted and experimentally determined weld bead cross-section as well as welding thermal cycles. Then the influence of tailing TIG arc on heat transfer and formation of weld bead is calculated and analyzed compared to single MIG. It lays foundation to study the interaction of these two arcs further.
2. Formulation In arc welding process, the additional filler metal not only produce weld bead but also influences the heat conduction process. The complicated surface condition makes it difficult to solve the boundary conditions of weld bead and arc crater areas in the Cartesian coordinate system. Thus the body-fitted coordinated system is adopted in this study by the transformation of the rectangular
Fig. 2. Photo of TIG welding arc for different torch angles (90 A): (a) torch angle 90◦ and (b) torch angle 60◦ .
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Fig. 3. Photo of MIG welding arc for different torch angles (125 A): (a) torch angle 90◦ and (b) torch angle 60◦ .
coordinate system, and the corresponding governing formulations of energy and deformation have been discussed in reference [20]. To describe characteristic of welding process unambiguously, the torch angle is defined as shown in Fig. 1. Fig. 2 and Fig. 3 show that the arc is still straight even under relative low welding current during TIG and MIG processes when the angle of gun changes from 90◦ to 60◦ . Normally, the arc stiffness is improved with increasing welding current. Thus all the experimental results indicate that a particular cone composed by countless half-line with energy is an adoptable assumption of welding arc. Fig. 4(a) is the schematic diagram of welding torch working on the perpendicular position; it has been widely studied by building up serious of heat source models [9–13]. The elliptical interface of arc and workpiece is the sketch map of arc heat distribution with 95% energy. Then if the torch and workpiece are slanted backward or forward to a certain degree together, the conical arc should be the same shape as it acts on vertical position if the gravity effect on arc is ignored (as shown in Fig. 4(b)). Actually, the workpiece will not be sloped with welding torch. Hence it is clear that the heat of inclined arc on the horizontal workpiece should be distributed in the purple curve, which is the plane projection of red elliptical interface on flat as shown in Fig. 4(c). As simplification and hypothesis mentioned above, this conical arc can be divided into many triangular pieces as noted in light-blue color. And the shape of representative triangle with light-blue color is also transformed to be pink one in Fig. 4(c).
It is assumed that the heat flux distribution on workpiece has been known in Fig. 4(a), which is equal to the density of heat source on fictitious and sloped workpiece as shown in Fig. 4(b). It is significant to deduce the relationship of the heat flux distribution on real horizontal workpiece when the gun is perpendicular and the gun is slanted, as shown in Fig. 4(b) and (c). Fig. 5 is the schematic image of arbitrary cross sections for sloped arc acting on invented surface B (pink face in Fig. 4(b)) and on real horizontal surface A (blue face in Fig. 4(c)) respectively. It is clear that the relationship of heat source density on points xi and si can be written as
qxi ·
(xi+1 − xi−1 ) (s − si−1 ) = qsi · i+1 2 2
(1)
where qxi and qsi are the corresponding heat flux distribution on the intersecting lines where the arbitrary cross sections and workpiece (sloped and horizontal) are intersected as shown in Fig. 4(b), Fig. 4(c), and Fig. 5. The relationship of (xi+1 − xi−1 )/2 and (si+1 − si−1 )/2 is the key factor to calculate qxi . Usually, the uniform grids are used in the area of weld pool, and the original coordinates are x0 and s0 separately, then the relationship of arc source density on points of xi and si can be deduced by the simple trigonometric function.
Fig. 4. Schematic diagrams of welding torch and arc: (a) perpendicular position, (b) slanted position with sloped workpiece, and (c) slanted position with horizontal workpiece.
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Fig. 5. Schematic image of arbitrary cross sections for sloped arc.
On the right of x0 (xi > x0 and si > s0 ), the mathematical expressions can be presented as follows: ıi = 1 + 2 + 3 + · · · + i = arctan
x + x − x 1 i k h1
−
(2)
εi = si − s0 = h2 · tan(ıi )
(3)
k=−
(4)
h · tan() 1 DI
x1 = h1 · tan() − k · DI
(5)
i is the angle of adjacent half-line in Fig. 5, is the complementary angle of torch angle , k is the integer of Eq. (5), DI is the mesh spacing of uniform grids, and h1 and h2 are the distance from the electrode tip to the intersecting lines of L1 and L2 separately (Fig. 5). The value of these symbols can be deduced by geometrical relationship if the distance from the electrode tip to the workpiece surface of A and B is the same as h (Fig. 4(c)). And (si+1 − si−1 )/2 can be expressed as (εi+1 − εi−1 )/2. If xi is in the area of (xk , x0 ), ϕi = arctan
x + x − x 1 i k h1
−ˇ
(6)
ıi = 0 + −1 + · · · + i = − ˇ − ϕi
(7)
εi = si − s0 = h2 · tan(ıi )
(8)
Fig. 7. Flow chat of calculation process.
If xi is in the area of (x−m , xk ), ıi = k + k−1 + · · · + i = arctan
x − x − x 1 k i h1
+
(9)
εi = si − s0 = h2 · tan(ıi )
(10)
Similarly, the grid size will also be changed in the y direction if the workpiece is rotated from inclined face to horizontal face as shown in Fig. 4(c), thus the value of qxi can be modified as, q(xi,yj) = q(si,yj) · ·
(si+1 − si−1 ) (xi+1 − xi−1 ) cos(1 ) · h
cos(2 )cos(0.5 · ) ·
1 = 0.5 · − arctan 2 = arctan g
Fig. 6. The schematic figure of double ellipsoid heat source model.
h2 + (xi − xk + x1 )
1 − cos tan(0.5 · ) · cos
(11)
2
xi − xk + x1 1 − cos + arctan h tan(0.5 · ) · cos
(12)
(13)
The relationship of qxi and qsi can also be deduced in the same way if the welding torch slants backward to the welding direction. It is very easy to be calculated by computer. Eq. (13) is not only suitable for plane heat source models, such as Gauss heat model or double elliptical heat source model, but also
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Fig. 8. Comparison between theoretical and experimental thermal cycles for TIG welding (Q235, 3 mm, I = 125 A, Ua = 13.5 V, u0 = 0.3 m min−1 ): (a) torch angle: 90◦ , 3 mm to center, (b) torch angle: 75◦ , 3.2 mm to center, and (c) torch angle: 60◦ , 3.0 mm to center.
can be applied for body heat source, such as double ellipsoid heat source model, conical heat source model or even complex combination of heat source model. Here take double ellipsoid heat source model for example. Fig. 6 is the schematic figure of double ellipsoid heat source model which are widely used for MIG or MAG welding. And it can be divided into many layers along z direction. On each layer, the double ellipsoid heat source degrades into plane heat source (double elliptical). Thus if the welding torch slants forward or backward to the welding direction, the relationship of qxi and qsi can be expressed by Eq. (13) on each layer, such as layer i in Fig. 6. Here h should be replaced by , = h + zi
(14)
where zi is the distance from layer i to upper surface of workpiece. 3. Results and discussion Numerical simulations are performed for bead-on-plate welding of low carbon steel workpiece with dimension of 150 mmlength, 70 mm-length, 3 mm-thickness. The properties of low carbon steel are listed in Table 1; other parameters used in calculation are referred to Ref. [20]. Only half of the workpiece is considered since the weld is symmetrical about the weld center line, which is convenient and economical for simulation. The flow chat of calculation process is shown in Fig. 7. To validate the relationship between slant heat source distribution and vertical heat source distribution that is mentioned above, simulation and experiments are carried out to compare predicted thermal cycles and welding dimension with measured results. In TIG welding, experiment shows that when the welding current I is 125 A, arc voltage Ua is 13.5 V, and the welding speed u0 is 0.3 m min−1 , the penetration and deformation of weld bead is small, thus double elliptical heat source model can be used as shown in Eq. (15), Table 1 Properties of Q235 in calculation. Nomenclature
Symbol
Value (unit)
Thermal efficiency Density Liquidus temperature Specific heat Gravitational constant Solidus temperature Ambient temperature Thermal conductivity
Tm Cp g Tl Ta
0.66 (TIG)/0.75 (MIG) 7400 (kg m−3 ) 1770 (K) 700 (J kg−1 K−1 ) 9.8 (m s−2 ) 1758 (K) 293 (K) 33.3 (W m−1 K−1 )
Fig. 9. Heat flux distribution on the cross-section of arc center position when torch angle is 90◦ .
⎧ 3(x − u0 t − l0 )2
UI 3y2 ⎪ exp − ⎪ ⎨ 2 q2 exp − b2 a2 1 1 qa1 (x, y, t) = 2 ⎪ 2 3(x − u t − xl )
UI 3y ⎪ 0 0 ⎩ 2 exp − exp − 2 2 2 q
b
2
a
(x − u0 t − l0 )≥0
(x − u0 t − l0 ) < 0
1
(15)
where qa1 represents heat flux of arc, t is time, a1 , b1 are the parameters of heat source model when the welding torch is in perpendicular position, l0 is the position where arc ignites, q is heat distribution parameter and its influencing factors such as arc length, welding current, have been discussed in Ref. [21]. Three different torch angles are invited in calculation which are 90◦ , 75◦ , 60◦ separately, their hear flux distribution can be computed by Eqs. (13) and (15), and their arc force distribution can also be obtained similarly as mentioned above. Fig. 8 is the comparison between theoretical and experimental thermal cycles on back surface of workpiece during TIG welding. It is clear that the results of heating and cooling rate match experimental data well, which means Eq. (13) can be used for plane heat source with different torch angles. Furthermore, it also shows that the peak temperature in HAZ area decreases with lessening . The reason is that the maximum energy density decreases when the
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Fig. 10. (a) Heat flux distribution along x direction for different angles (y = 0) and (b) calculated transient variation of the temperature profiles at the top surface (0.3 m min−1 , 11.6 s).
Fig. 11. Comparison between theoretical and experimental thermal cycles for MIG welding (Q235, 3 mm, I = 150 A, Ua = 20.1 V, u0 = 0.6 m min−1 ): (a) torch angle: 90◦ , 4 mm to center, (b) torch angle: 75◦ , 4.1 mm to center, and (c) torch angle: 60◦ , 4.0 mm to center.
torch angle changes from 90◦ to 60◦ as shown in Fig. 9, which means less heat will be transferred to the boundary of weld pool, thus the diminution of peak temperature appears in Fig. 8. Fig. 10(a) also implies that more and more heat energy is deposited in the front of weld pool and its adjacent area with decreasing , which means the preheating effect of arc on the workpiece increases. Thus in Fig. 8, the cooling rate of thermal cycle (947–573 K) also decreases from 21.1 s to 24.3 s when the torch angle of reduces from 90◦ to 60◦ . Fig. 10(b) is the calculated transient variation of the temperature profiles at the top surface. Results
show that though the position of arc center is x = 108 mm constantly when the torch angle varies from 90◦ to 60◦ as shown in Fig. 10(a), the area of weld pool moves forward from x = 102.38–108.98 mm to x = 105.92–111.30 mm. It means that the preheating effect of slant arc makes the weld pool grow forward compared to vertical arc. And the length of weld pool is also lessened from 6.6 mm to 5.2 mm as the head flux distribution. To simulate MIG welding process, the double ellipsoid heat source model is applied as the arc crater and droplet impaction can make the source energy deposit along the thickness direction of workpiece.
⎧ √
2 ⎪ 6 3f1 UI 3(x − u0 t − l0 ) 3y2 3z 2 ⎪ ⎪ exp − exp − exp − (x − u0 t − l0 )≥0 √ ⎨ a bc b2 c2 a2f f qa2 (x, y, z, t) =
√ 2 ⎪ ⎪ 6 3f2 UI 3(x − u0 t − xl0 ) 3y2 3z 2 ⎪ ⎩ exp − 2 exp − 2 (x − u0 t − l0 ) < 0 √ exp − 2 ar bc
ar
b
(16)
c
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Fig. 12. Comparison between theoretical and experimental cross-section for MIG welding (Q235, 3 mm, I = 150 A, Ua = 20.1 V, u0 = 0.6 m min−1 ): (a) torch angle: 90◦ , (b) torch angle: 75◦ , and (c) torch angle: 60◦ .
f1 + f2 = 1
(17)
where ar , af , b, c are the parameters of source model and f1 , f2 are the partition coefficients of source model. The welding current is 150 A, arc voltage is 20.1 V, and welding speed is 0.6 m min−1 . Fig. 11 is the comparison between theoretical and experimental thermal cycles on back surface of workpiece during MIG welding. It shows that the results of heating rate and cooling rate also agree well with experimental data. Fig. 12 is the comparison between calculated and experimentally measured cross-section of weld. It is clear that the predicted data, such as weld width, penetration, and the shape of fusion line, match the experimental results well. All the data mentioned above also indicate that the numerical model of Eq. (13) can be used to simulate MIG welding process combined with volumetric heat source. During TIG-MIG hybrid welding process, the synergetic process includes not only the aggregate amount of energy of two arcs, but also the electromagnetic attraction or repulsion of two arcs which will change the position of the arcs. As the first step of research for hybrid welding, the leading and tailing arcs are assumed to be independent arcs without any arc interaction, the schematic figure of this welding process is shown in Fig. 13. Dt is the distance from tip of tungsten to workpiece which is 5 mm in calculation, Dl is the length of arc with value of 10 mm, L is the distance of two arc as shown in following picture, and its datum is 10 mm. 1 and 2 are the torch angles of TIG and MIG, which are 60◦ and 90◦ separately. The welding parameters are 125 A, 13.5 V for TIG and 150 A, 20.1 V for MIG, and the welding speed is 0.6 m min−1 . The corresponding heat source models can be generated from Eqs. (11)–(17) as follows:
Fig. 13. Schematic figure of TIG-MIG hybrid process.
q(xi,yj) = qTIG(si,yj) · ·
(si+1 − si−1 ) (xi+1 − xi−1 ) cos(1 ) · h
cos(2 )cos(0.5 · TIG ) ·
+qMIG(sm,yj) · z · ·
h2 + (xi − xk + xi1 )
2
(sm+1 − sm−1 ) (xm+1 − xm−1 ) cos(3 ) · h
cos(4 )cos(0.5 · MIG ) ·
qTIG(si,yj) = qa1 (x + L, y, t)
h2 + (xm − xp + xm1 )
2
(18)
(19)
Fig. 14. Calculated transient variation of the temperature profiles at the top surface (0.6 m min−1 , 9 s): (a) TIG (125 A, 13.5 V), (b) MIG (150 A, 20.1 V), and (c) TIG-MIG (125 A, 13.5 V–150 A, 20.1 V).
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Fig. 15. Heat flux distribution of TIG-MIG welding process (t = 9 s, 0.3 mm thickness layer for MIG): (a) top surface along x direction (y = 0 mm) and (b) top surface along y direction (x = 120.0 mm).
qMIG(sm,yj) = qa2 (x, y, z, t)
(20)
where xi , xm , xk , xp , si , sm are position coordinates for TIG-MIG heat source on the intersecting lines as shown in Fig. 5. The expressions of 1 , 2 , 3 , 4 , xi1 and xm1 have been shown in Eqs. (5), (12) and (13). TIG is the complementary angle of TIG torch angle ( 1 ), and MIG is the complementary angle of MIG torch angle ( 2 ). Fig. 14 is the calculated transient variation of the temperature profiles at the top surface for single TIG, MIG and TIG-MIG hybrid welding. It shows that the length of weld pool increases obviously from 11.8 mm (single MIG) to 19.59 mm (TIG-MIG). One thing should be noted that the length of weld pool for single TIG is only 4.88 mm, which means that the heating effect of tailing TIG could extent weld pool length effectively, especially for the region of high temperature (above 2440 K). Meanwhile, the width of weld pool is just changed from 5.82 mm to 5.92 mm. Fig. 15(a) shows that if the distance of heat source center for two arcs is 10 mm, the major heat of TIG arc is deposited at the tail of the welding pool. And on the cross-section, the heat flux density of TIG-MIG will be almost the same as MIG at front of weld pool, as shown in Fig. 15(b). So the width of weld pool changes little. It also indicates that the power of TIG will also influence the width of weld pool (at rear) if it is high enough or the distance of two arcs decreases to a reasonable level. 4. Conclusions Adaptive mathematical heat source models are developed for TIG and MIG welding process separately. The results show that these modifications could reflect the heat flux distribution on workpiece with varied torch angles. The influence of different slant arcs on welding process is simulated and analyzed. It shows that more and more heat energy is deposited in the front of weld pool to preheating adjacent area with decreasing , and the peak temperature of thermal cycle is reduced together. TIG-MIG hybrid welding process is calculated and discussed based on above models without considering the interaction of two arcs. And because of the tailing arc, the length of high temperature zone in the weld pool extends clearly compared to single MIG. It also shows a good potential of TIG-MIG hybrid welding in high speed welding as the force effect of tailing arc on weld pool. The next research should be focused on the influence of attractive or repulsive force between two arcs, which
will change the force and heat distribution of arcs on the workpiece. And the fluid flow in weld pool should also be considered next as it is one of the important factors that influences the heat and mass transfer mechanism.
Acknowledgements The authors are grateful to the financial support for this project from the National Natural Science Foundation of China under Grant No. 50475131, and Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20130131120013.
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[19] Mishima H, Tashiro S, Kanemaru S, Tanaka M. Numerical simulation on plasma property in TIG-MIG hybrid welding process. Q J Jpn Weld Soc 2013;31: 22s–5s. [20] Chen J, Schwenk C, Wu CS, Rethmeier M. Predicting the influence of groove angle on heat transfer and fluid flow for new gas metal arc welding processes. Int J Heat Mass Transfer 2012;55:102–11. [21] Tsai NS, Eager TW. Distribution of the heat and current fluxes in gas tungsten arcs. Metall Trans B 1985;16:841–6.
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Improvement of welding heat source models for TIG-MIG hybrid welding process J. Chen ∗ , C.S. Wu, M.A. Chen MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, and Institute of Materials Joining, Shandong University, Jinan 250061, China
a r t i c l e
i n f o
Article history: Received 19 May 2014 Received in revised form 22 June 2014 Accepted 23 June 2014 Available online xxx Keywords: Adaptive heat source Numerical simulation Hybrid welding
a b s t r a c t Tungsten inert gas-metal inert gas (TIG-MIG) hybrid welding process is an effective way to improve welding productivity and quality due to advantages of the two processes. Mathematical analysis is crucial to fundamentally understand this synergetic welding process. In this study, based on experimental visualization of arc behaviors, some assumptions are proposed to deduce adaptive plane and volumetric heat source models separately for each involved welding method first. The influence of torch angles on distribution of temperature and geometry of weld bead are calculated and compared with experimental results. It shows that this developed algorithm of heat source can be employed to accurately predict welding process whether the electrode gun is slanted backward or forward to the direction of welding. Then TIG-MIG hybrid welding process is simulated and analyzed without considering the attractive or repulsive force of two arcs. The characteristic of TIG-MIG welding process is discussed compared to single MIG. It lays the foundation for the further research on the interaction of the two arcs during TIG-MIG hybrid welding. © 2014 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction With the unceasing intensification of the manufacturing competition, the traditional arc welding processes, such as tungsten inert gas welding (TIG) and metal inert gas welding (MIG), have been improved to satisfy enterprise’s requirements for welding technology with high quantity and high quality. TIG-MIG hybrid welding process is one of the effective ways to develop welding productivity and quality due to advantages of the two processes, which is similar to DE-GMAW (double-electrode gas metal arc welding) [1–4]. The major differences between TIG-MIG and DE-GMAW hybrid welding processes are as follows: (1) The mechanism of TIG-MIG is that an appropriate distribution of arc energy is simply liberated on the workpiece by a tailing TIG arc to improve traditional GMAW process directly. However, during DE-GMAW, the adding TIG arc is used as part of galvanic circle to make sure that the bypass current can flow back to the power source through the bypass TIG torch without going through the workpiece [1]. (2) The major effects of additional TIG arcs are different from each other. During TIGMIG hybrid welding, the additional TIG arc is used to reheat the
∗ Corresponding author at: MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, and Institute of Materials Joining, Shandong University, No. 17923 Jingshi Road, Jinan 250061, China. Tel.: +86 531 88395987. E-mail address: [email protected] (J. Chen).
workpiece and to improve the weld bead deformation. And during DE-GMAW, the purpose of adding tailing TIG arc is to increase the depositing rate of filler metal without imposing excessive heat on the workpiece, thus the tailing TIG arc is not directly liberated on the workpiece. And compared to tandem or T.I.M.E. welding [5–7], TIG-MIG hybrid welding is an easy way to utilize the advantages of TIG and MIG welding with low cost, since neither special shielding gas nor complex synergic powers are needed. It shows that MIG arc can be stable by simple hybridization of TIG even though pure argon shielding gas is used, which means the weld metal toughness is improved and welding quality is developed [4]. The further study indicates that it also has great potentiality to increase welding speed with high quality because of the quite stable cathode spots appearing in this hybrid welding [8]. However, it is still lack of comprehensive and profound research on physical mechanism of TIG-MIG hybrid welding, which hinders the development of this new welding method. In recent decades, many researches have been done on heat source models to reveal various welding process, such as gauss or elliptical heat source model for TIG in low welding current [9,10], double ellipsoid heat source model for MIG [11,12], double-ellipsoidal + EHGC (exponentially-tapered peak value of heat flux in Gaussian cylinder) heat source model for plasma arc welding [13], self-adaptable heat source models for laser beam welding and plasma arc welding separately by considering dynamic energy distribution during above welding processes [14]. However, all the heat
http://dx.doi.org/10.1016/j.jmapro.2014.06.002 1526-6125/© 2014 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic diagram of welding process with a slanted gun: (a) TIG and (b) MIG.
models mentioned above are focused on single welding process, which could not be used in hybrid welding directly. Though many improved heat source models have been deduced for laser + GMAW hybrid welding or laser + TIG hybrid welding, the influence of torch angles is not studied comprehensively as most of the researches are focused on the synergetic heat effects of two sources [15,16]. A new hybrid heat-source model is developed to simulate DE-GMAW process, which is similar to TIG-MIG. However, their physical mechanisms are different. For example, during DE-GMAW process, the tailing TIG arc is only the conductive path of current without directly acting on the weld pool [17]. And the parameters of all above heat or arc force models need to be verified by experiments each time if the torch angle changes. To solve this problem, Cho et al. develop a complex heat source model for submerged tandem arc welding process [18]. Two different effective radii of arc plasma are introduced to reflect the influence of torch angles on heat flux and arc pressure distribution. Considering Lorentz force due to the magnetic field induced by leading and trailing arc, the interaction of these two arcs is partially dominated by leading arc displacement. The nine different model parameters in leading and trailing arc models make it to be utilized intricately. Tanaka et al. analyze arc phenomena in TIG-MIG hybrid welding process with different torch angles using three-dimensional numerical models [19]. It is found that the convergence of heat flux will get maximum value under certain torch angles of TIG and MIG, which can be explained by the balance between the stiffness of arc and the repulsion of both arcs. However, the complex current
conservation equation and Maxwell–Ampere equation needs to be solved to study the influence of torch angles and interaction of arcs [19]. So a simple and effective way is needed to evaluate the influence of torch angles on welding process first. Based on several simple assumptions, the adaptive plane and volumetric heat source models are deduced respectively by considering the influence of torch angles and arc length in this paper. The heat transfer mechanism is investigated by solving three-dimensional numerical equations for TIG and MIG welding separately. The influence of torch angles on temperature profiles and the weld bead geometry is numerically analyzed. Good agreement is shown between the predicted and experimentally determined weld bead cross-section as well as welding thermal cycles. Then the influence of tailing TIG arc on heat transfer and formation of weld bead is calculated and analyzed compared to single MIG. It lays foundation to study the interaction of these two arcs further.
2. Formulation In arc welding process, the additional filler metal not only produce weld bead but also influences the heat conduction process. The complicated surface condition makes it difficult to solve the boundary conditions of weld bead and arc crater areas in the Cartesian coordinate system. Thus the body-fitted coordinated system is adopted in this study by the transformation of the rectangular
Fig. 2. Photo of TIG welding arc for different torch angles (90 A): (a) torch angle 90◦ and (b) torch angle 60◦ .
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Fig. 3. Photo of MIG welding arc for different torch angles (125 A): (a) torch angle 90◦ and (b) torch angle 60◦ .
coordinate system, and the corresponding governing formulations of energy and deformation have been discussed in reference [20]. To describe characteristic of welding process unambiguously, the torch angle is defined as shown in Fig. 1. Fig. 2 and Fig. 3 show that the arc is still straight even under relative low welding current during TIG and MIG processes when the angle of gun changes from 90◦ to 60◦ . Normally, the arc stiffness is improved with increasing welding current. Thus all the experimental results indicate that a particular cone composed by countless half-line with energy is an adoptable assumption of welding arc. Fig. 4(a) is the schematic diagram of welding torch working on the perpendicular position; it has been widely studied by building up serious of heat source models [9–13]. The elliptical interface of arc and workpiece is the sketch map of arc heat distribution with 95% energy. Then if the torch and workpiece are slanted backward or forward to a certain degree together, the conical arc should be the same shape as it acts on vertical position if the gravity effect on arc is ignored (as shown in Fig. 4(b)). Actually, the workpiece will not be sloped with welding torch. Hence it is clear that the heat of inclined arc on the horizontal workpiece should be distributed in the purple curve, which is the plane projection of red elliptical interface on flat as shown in Fig. 4(c). As simplification and hypothesis mentioned above, this conical arc can be divided into many triangular pieces as noted in light-blue color. And the shape of representative triangle with light-blue color is also transformed to be pink one in Fig. 4(c).
It is assumed that the heat flux distribution on workpiece has been known in Fig. 4(a), which is equal to the density of heat source on fictitious and sloped workpiece as shown in Fig. 4(b). It is significant to deduce the relationship of the heat flux distribution on real horizontal workpiece when the gun is perpendicular and the gun is slanted, as shown in Fig. 4(b) and (c). Fig. 5 is the schematic image of arbitrary cross sections for sloped arc acting on invented surface B (pink face in Fig. 4(b)) and on real horizontal surface A (blue face in Fig. 4(c)) respectively. It is clear that the relationship of heat source density on points xi and si can be written as
qxi ·
(xi+1 − xi−1 ) (s − si−1 ) = qsi · i+1 2 2
(1)
where qxi and qsi are the corresponding heat flux distribution on the intersecting lines where the arbitrary cross sections and workpiece (sloped and horizontal) are intersected as shown in Fig. 4(b), Fig. 4(c), and Fig. 5. The relationship of (xi+1 − xi−1 )/2 and (si+1 − si−1 )/2 is the key factor to calculate qxi . Usually, the uniform grids are used in the area of weld pool, and the original coordinates are x0 and s0 separately, then the relationship of arc source density on points of xi and si can be deduced by the simple trigonometric function.
Fig. 4. Schematic diagrams of welding torch and arc: (a) perpendicular position, (b) slanted position with sloped workpiece, and (c) slanted position with horizontal workpiece.
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Fig. 5. Schematic image of arbitrary cross sections for sloped arc.
On the right of x0 (xi > x0 and si > s0 ), the mathematical expressions can be presented as follows: ıi = 1 + 2 + 3 + · · · + i = arctan
x + x − x 1 i k h1
−
(2)
εi = si − s0 = h2 · tan(ıi )
(3)
k=−
(4)
h · tan() 1 DI
x1 = h1 · tan() − k · DI
(5)
i is the angle of adjacent half-line in Fig. 5, is the complementary angle of torch angle , k is the integer of Eq. (5), DI is the mesh spacing of uniform grids, and h1 and h2 are the distance from the electrode tip to the intersecting lines of L1 and L2 separately (Fig. 5). The value of these symbols can be deduced by geometrical relationship if the distance from the electrode tip to the workpiece surface of A and B is the same as h (Fig. 4(c)). And (si+1 − si−1 )/2 can be expressed as (εi+1 − εi−1 )/2. If xi is in the area of (xk , x0 ), ϕi = arctan
x + x − x 1 i k h1
−ˇ
(6)
ıi = 0 + −1 + · · · + i = − ˇ − ϕi
(7)
εi = si − s0 = h2 · tan(ıi )
(8)
Fig. 7. Flow chat of calculation process.
If xi is in the area of (x−m , xk ), ıi = k + k−1 + · · · + i = arctan
x − x − x 1 k i h1
+
(9)
εi = si − s0 = h2 · tan(ıi )
(10)
Similarly, the grid size will also be changed in the y direction if the workpiece is rotated from inclined face to horizontal face as shown in Fig. 4(c), thus the value of qxi can be modified as, q(xi,yj) = q(si,yj) · ·
(si+1 − si−1 ) (xi+1 − xi−1 ) cos(1 ) · h
cos(2 )cos(0.5 · ) ·
1 = 0.5 · − arctan 2 = arctan g
Fig. 6. The schematic figure of double ellipsoid heat source model.
h2 + (xi − xk + x1 )
1 − cos tan(0.5 · ) · cos
(11)
2
xi − xk + x1 1 − cos + arctan h tan(0.5 · ) · cos
(12)
(13)
The relationship of qxi and qsi can also be deduced in the same way if the welding torch slants backward to the welding direction. It is very easy to be calculated by computer. Eq. (13) is not only suitable for plane heat source models, such as Gauss heat model or double elliptical heat source model, but also
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Fig. 8. Comparison between theoretical and experimental thermal cycles for TIG welding (Q235, 3 mm, I = 125 A, Ua = 13.5 V, u0 = 0.3 m min−1 ): (a) torch angle: 90◦ , 3 mm to center, (b) torch angle: 75◦ , 3.2 mm to center, and (c) torch angle: 60◦ , 3.0 mm to center.
can be applied for body heat source, such as double ellipsoid heat source model, conical heat source model or even complex combination of heat source model. Here take double ellipsoid heat source model for example. Fig. 6 is the schematic figure of double ellipsoid heat source model which are widely used for MIG or MAG welding. And it can be divided into many layers along z direction. On each layer, the double ellipsoid heat source degrades into plane heat source (double elliptical). Thus if the welding torch slants forward or backward to the welding direction, the relationship of qxi and qsi can be expressed by Eq. (13) on each layer, such as layer i in Fig. 6. Here h should be replaced by , = h + zi
(14)
where zi is the distance from layer i to upper surface of workpiece. 3. Results and discussion Numerical simulations are performed for bead-on-plate welding of low carbon steel workpiece with dimension of 150 mmlength, 70 mm-length, 3 mm-thickness. The properties of low carbon steel are listed in Table 1; other parameters used in calculation are referred to Ref. [20]. Only half of the workpiece is considered since the weld is symmetrical about the weld center line, which is convenient and economical for simulation. The flow chat of calculation process is shown in Fig. 7. To validate the relationship between slant heat source distribution and vertical heat source distribution that is mentioned above, simulation and experiments are carried out to compare predicted thermal cycles and welding dimension with measured results. In TIG welding, experiment shows that when the welding current I is 125 A, arc voltage Ua is 13.5 V, and the welding speed u0 is 0.3 m min−1 , the penetration and deformation of weld bead is small, thus double elliptical heat source model can be used as shown in Eq. (15), Table 1 Properties of Q235 in calculation. Nomenclature
Symbol
Value (unit)
Thermal efficiency Density Liquidus temperature Specific heat Gravitational constant Solidus temperature Ambient temperature Thermal conductivity
Tm Cp g Tl Ta
0.66 (TIG)/0.75 (MIG) 7400 (kg m−3 ) 1770 (K) 700 (J kg−1 K−1 ) 9.8 (m s−2 ) 1758 (K) 293 (K) 33.3 (W m−1 K−1 )
Fig. 9. Heat flux distribution on the cross-section of arc center position when torch angle is 90◦ .
⎧ 3(x − u0 t − l0 )2
UI 3y2 ⎪ exp − ⎪ ⎨ 2 q2 exp − b2 a2 1 1 qa1 (x, y, t) = 2 ⎪ 2 3(x − u t − xl )
UI 3y ⎪ 0 0 ⎩ 2 exp − exp − 2 2 2 q
b
2
a
(x − u0 t − l0 )≥0
(x − u0 t − l0 ) < 0
1
(15)
where qa1 represents heat flux of arc, t is time, a1 , b1 are the parameters of heat source model when the welding torch is in perpendicular position, l0 is the position where arc ignites, q is heat distribution parameter and its influencing factors such as arc length, welding current, have been discussed in Ref. [21]. Three different torch angles are invited in calculation which are 90◦ , 75◦ , 60◦ separately, their hear flux distribution can be computed by Eqs. (13) and (15), and their arc force distribution can also be obtained similarly as mentioned above. Fig. 8 is the comparison between theoretical and experimental thermal cycles on back surface of workpiece during TIG welding. It is clear that the results of heating and cooling rate match experimental data well, which means Eq. (13) can be used for plane heat source with different torch angles. Furthermore, it also shows that the peak temperature in HAZ area decreases with lessening . The reason is that the maximum energy density decreases when the
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Fig. 10. (a) Heat flux distribution along x direction for different angles (y = 0) and (b) calculated transient variation of the temperature profiles at the top surface (0.3 m min−1 , 11.6 s).
Fig. 11. Comparison between theoretical and experimental thermal cycles for MIG welding (Q235, 3 mm, I = 150 A, Ua = 20.1 V, u0 = 0.6 m min−1 ): (a) torch angle: 90◦ , 4 mm to center, (b) torch angle: 75◦ , 4.1 mm to center, and (c) torch angle: 60◦ , 4.0 mm to center.
torch angle changes from 90◦ to 60◦ as shown in Fig. 9, which means less heat will be transferred to the boundary of weld pool, thus the diminution of peak temperature appears in Fig. 8. Fig. 10(a) also implies that more and more heat energy is deposited in the front of weld pool and its adjacent area with decreasing , which means the preheating effect of arc on the workpiece increases. Thus in Fig. 8, the cooling rate of thermal cycle (947–573 K) also decreases from 21.1 s to 24.3 s when the torch angle of reduces from 90◦ to 60◦ . Fig. 10(b) is the calculated transient variation of the temperature profiles at the top surface. Results
show that though the position of arc center is x = 108 mm constantly when the torch angle varies from 90◦ to 60◦ as shown in Fig. 10(a), the area of weld pool moves forward from x = 102.38–108.98 mm to x = 105.92–111.30 mm. It means that the preheating effect of slant arc makes the weld pool grow forward compared to vertical arc. And the length of weld pool is also lessened from 6.6 mm to 5.2 mm as the head flux distribution. To simulate MIG welding process, the double ellipsoid heat source model is applied as the arc crater and droplet impaction can make the source energy deposit along the thickness direction of workpiece.
⎧ √
2 ⎪ 6 3f1 UI 3(x − u0 t − l0 ) 3y2 3z 2 ⎪ ⎪ exp − exp − exp − (x − u0 t − l0 )≥0 √ ⎨ a bc b2 c2 a2f f qa2 (x, y, z, t) =
√ 2 ⎪ ⎪ 6 3f2 UI 3(x − u0 t − xl0 ) 3y2 3z 2 ⎪ ⎩ exp − 2 exp − 2 (x − u0 t − l0 ) < 0 √ exp − 2 ar bc
ar
b
(16)
c
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Fig. 12. Comparison between theoretical and experimental cross-section for MIG welding (Q235, 3 mm, I = 150 A, Ua = 20.1 V, u0 = 0.6 m min−1 ): (a) torch angle: 90◦ , (b) torch angle: 75◦ , and (c) torch angle: 60◦ .
f1 + f2 = 1
(17)
where ar , af , b, c are the parameters of source model and f1 , f2 are the partition coefficients of source model. The welding current is 150 A, arc voltage is 20.1 V, and welding speed is 0.6 m min−1 . Fig. 11 is the comparison between theoretical and experimental thermal cycles on back surface of workpiece during MIG welding. It shows that the results of heating rate and cooling rate also agree well with experimental data. Fig. 12 is the comparison between calculated and experimentally measured cross-section of weld. It is clear that the predicted data, such as weld width, penetration, and the shape of fusion line, match the experimental results well. All the data mentioned above also indicate that the numerical model of Eq. (13) can be used to simulate MIG welding process combined with volumetric heat source. During TIG-MIG hybrid welding process, the synergetic process includes not only the aggregate amount of energy of two arcs, but also the electromagnetic attraction or repulsion of two arcs which will change the position of the arcs. As the first step of research for hybrid welding, the leading and tailing arcs are assumed to be independent arcs without any arc interaction, the schematic figure of this welding process is shown in Fig. 13. Dt is the distance from tip of tungsten to workpiece which is 5 mm in calculation, Dl is the length of arc with value of 10 mm, L is the distance of two arc as shown in following picture, and its datum is 10 mm. 1 and 2 are the torch angles of TIG and MIG, which are 60◦ and 90◦ separately. The welding parameters are 125 A, 13.5 V for TIG and 150 A, 20.1 V for MIG, and the welding speed is 0.6 m min−1 . The corresponding heat source models can be generated from Eqs. (11)–(17) as follows:
Fig. 13. Schematic figure of TIG-MIG hybrid process.
q(xi,yj) = qTIG(si,yj) · ·
(si+1 − si−1 ) (xi+1 − xi−1 ) cos(1 ) · h
cos(2 )cos(0.5 · TIG ) ·
+qMIG(sm,yj) · z · ·
h2 + (xi − xk + xi1 )
2
(sm+1 − sm−1 ) (xm+1 − xm−1 ) cos(3 ) · h
cos(4 )cos(0.5 · MIG ) ·
qTIG(si,yj) = qa1 (x + L, y, t)
h2 + (xm − xp + xm1 )
2
(18)
(19)
Fig. 14. Calculated transient variation of the temperature profiles at the top surface (0.6 m min−1 , 9 s): (a) TIG (125 A, 13.5 V), (b) MIG (150 A, 20.1 V), and (c) TIG-MIG (125 A, 13.5 V–150 A, 20.1 V).
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Fig. 15. Heat flux distribution of TIG-MIG welding process (t = 9 s, 0.3 mm thickness layer for MIG): (a) top surface along x direction (y = 0 mm) and (b) top surface along y direction (x = 120.0 mm).
qMIG(sm,yj) = qa2 (x, y, z, t)
(20)
where xi , xm , xk , xp , si , sm are position coordinates for TIG-MIG heat source on the intersecting lines as shown in Fig. 5. The expressions of 1 , 2 , 3 , 4 , xi1 and xm1 have been shown in Eqs. (5), (12) and (13). TIG is the complementary angle of TIG torch angle ( 1 ), and MIG is the complementary angle of MIG torch angle ( 2 ). Fig. 14 is the calculated transient variation of the temperature profiles at the top surface for single TIG, MIG and TIG-MIG hybrid welding. It shows that the length of weld pool increases obviously from 11.8 mm (single MIG) to 19.59 mm (TIG-MIG). One thing should be noted that the length of weld pool for single TIG is only 4.88 mm, which means that the heating effect of tailing TIG could extent weld pool length effectively, especially for the region of high temperature (above 2440 K). Meanwhile, the width of weld pool is just changed from 5.82 mm to 5.92 mm. Fig. 15(a) shows that if the distance of heat source center for two arcs is 10 mm, the major heat of TIG arc is deposited at the tail of the welding pool. And on the cross-section, the heat flux density of TIG-MIG will be almost the same as MIG at front of weld pool, as shown in Fig. 15(b). So the width of weld pool changes little. It also indicates that the power of TIG will also influence the width of weld pool (at rear) if it is high enough or the distance of two arcs decreases to a reasonable level. 4. Conclusions Adaptive mathematical heat source models are developed for TIG and MIG welding process separately. The results show that these modifications could reflect the heat flux distribution on workpiece with varied torch angles. The influence of different slant arcs on welding process is simulated and analyzed. It shows that more and more heat energy is deposited in the front of weld pool to preheating adjacent area with decreasing , and the peak temperature of thermal cycle is reduced together. TIG-MIG hybrid welding process is calculated and discussed based on above models without considering the interaction of two arcs. And because of the tailing arc, the length of high temperature zone in the weld pool extends clearly compared to single MIG. It also shows a good potential of TIG-MIG hybrid welding in high speed welding as the force effect of tailing arc on weld pool. The next research should be focused on the influence of attractive or repulsive force between two arcs, which
will change the force and heat distribution of arcs on the workpiece. And the fluid flow in weld pool should also be considered next as it is one of the important factors that influences the heat and mass transfer mechanism.
Acknowledgements The authors are grateful to the financial support for this project from the National Natural Science Foundation of China under Grant No. 50475131, and Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20130131120013.
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