Vacuum 177 (2020) 109391
Contents lists available at ScienceDirect
Vacuum
journal homepage: http://www.elsevier.com/locate/vacuum
Numerical investigation on the effect of process parameters on arc and
metal transfer in magnetically controlled gas metal arc welding
Lin Wang, Ji Chen *, ChuanSong Wu
MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, Institute of Materials Joining, Shandong University, Jinan, China
A R T I C L E I N F O
A B S T R A C T
Keywords:
Gas metal arc welding
Arc behavior
Metal transfer
Excitation current
Numerical simulation
Gas metal arc welding assisted by an external compound magnetic field was proved to effectively suppress the
weld bead defects in high speed welding. A three dimensional numerical model including the interactions among
the arc plasma, filler metal and the external magnetic field was developed. The distributions of some physical
quantities including temperature, velocity, current density, arc plasma force and electromagnetic force were
calculated. Then the influence of the process parameters on the arc and droplet behaviors was investigated. With
the increase of the excitation current, the inclination angles of the arc and droplet along both x-axis and y-axis
were increased and the metal transfer frequency was increased. The excitation frequency had little influence on
the arc inclination, and metal transfer frequency but affected the droplet inclination angle along y-axis. The
action mechanism of the external magnetic field parameters on the arc and droplet behaviors were analyzed.
1. Introduction
External magnetic field assisted arc welding process is an advanced
welding technology by introducing an external magnetic field to control
and improve the welding process [1,2]. The external magnetic field can
improve weld bead quality and stabilize the welding process by regu­
lating the arc, droplet and weld pool behaviors [3–6]. For example,
Nomura et al. [7] applied a cusp-type magnetic field to change the
cross-section of the arc from a circular to an elliptical shape in tungsten
inert gas (TIG) welding. The results showed that the welding speed can
be increased without welding bead defects. Chang et al. [8] introduced a
synchronous magnetic field including a low-frequency magnetic field in
the arc-burning phase and a high-frequency magnetic field in the
short-circuit phase to improve the frequency of metal transfer and
diminish the spatter for short-circuit gas metal arc welding (GMAW).
Wang et al. [9] found that the distribution of arc pressure and arc energy
was reasonably allocated by the synergistic effect of an alternating
magnetic field and low frequency pulsed welding current during narrow
gap TIG welding, which protected sidewalls from lack-of-fusion defect.
Chen et al. [10] proposed the steady magnetic field assisted laser-MIG
hybrid welding method. The external steady magnetic field was bene­
ficial to the low-temperature impact toughness of weld metal as its
microstructural refinement, ferrite reduction and randomness was
improved. Curiel et al. [11] found that the low-intensity axial magnetic
field increased the resistance to pitting and intergranular corrosion for
cold deformed AISI 304 stainless steel during GMAW. Sharma et al. [12]
used the transverse magnetic field to improve the mechanical properties
of weld (magnesium alloy-AZ31B) by decreasing the weld cracks and
porosities. Sun et al. [13] achieved the effective joining of Al/Ti dis­
similar metals by coupling CMT welding process and external magnetic
field. The flowability and wettability of the Al/Ti dissimilar metal joint
was improved, and the microhardness of HAZ zone was increased as well
as the lap tensile shear strength. Chen et al. [14] developed the com­
pound external magnetic field (EMF) assisted GMAW process to suppress
the undercutting defects in high speed GMAW. A compound magnetic
field comprised by a steady transverse magnetic field and an alternating
parallel magnetic field was generated to control the arc and droplet
behaviors. It was observed that the arc and droplet not only inclined
forward along the welding direction but also swung perpendicular to the
welding direction under the action of the compound magnetic field by
experiments. However, the influence of the EMF on the thermodynamic
characteristics of the arc and droplet needs to be further explored.
During the GMAW process, a thermal plasma arc is generated be­
tween the wire and workpiece. Under the action of thermal plasma, the
wire is melted and a droplet transfers into the weld pool periodically. It
is a very complicated physical phenomenon and there are very complex
* Corresponding author. Key Laboratory for Liquid-Solid Structural Evolution & Processing of Materials, Ministry of Education, Institute of Materials Joining,
Shandong University, 17923# Jingshi Road, Jinan, 250061, PR China.
E-mail address: chenji@sdu.edu.cn (J. Chen).
https://doi.org/10.1016/j.vacuum.2020.109391
Received 20 January 2020; Received in revised form 9 April 2020; Accepted 10 April 2020
Available online 18 April 2020
0042-207X/© 2020 Elsevier Ltd. All rights reserved.
L. Wang et al.
Vacuum 177 (2020) 109391
pool which pushed the molten metal to move to the edge of the pool, so
the uniformity and smoothness of the overlapping beads were opti­
mized. The effect of the external magnetic field on the arc and droplet
behaviors was not considered in this model. Xiao et al. [18] proposed a
two-dimensional model for axial magnetic field controlled GMAW pro­
cess to study the interactions among arc plasma, droplet and the metal
vapor. Compared to the traditional GMAW, the axial magnetic field
decreased metal transfer frequency and increased droplet volume.
However, the arc and droplet were assumed to be always axisymmetric
to the wire axis though they should rotate around the wire axis under the
action of the axial magnetic field.
In this study, a comprehensive three-dimensional numerical model
was proposed to investigate the arc and droplet behaviors coupling with
compound EMF during GMAW process. Compared to traditional GMAW,
the self-induced and additional electromagnetic forces acted on the arc
and droplet were analyzed and the effect of EMF parameters (including
the excitation current level and frequency) on arc behavior and metal
transfer was revealed. The varied welding currents were utilized to
explore the relationships among current density, arc deflection and arc
stiffness. The simulation results lay a foundation for the further welding
process optimization.
2. Numerical model
2.1. Generator of compound EMF
Fig. 1 shows the self-designed magnetic field generator and the
waveforms of the excitation current. The magnetic generator is
composed of an irregular iron core with three poles and two coils. The
two coils are energized periodically based on the waveforms of the
excitation current, as shown in Fig. 1b. During Δt1, the coli 1 is energized
so the direction of the magnetic field directs from pole 1 to pole 2 and
pole 3. During Δt2, the coli 2 is energized so the direction of the mag­
netic field is from pole 1 to pole 2 and from pole3 to pole 2. As indicated
in Fig. 1a, the direction of the magnetic field along the welding direction
is alternative in each cycle of the excitation current while the direction
of the magnetic field is constantly perpendicular to the welding direc­
tion. The more detailed information about the experiment setup was
discussed in the reference [14].
Fig. 1. Schematic diagram of compound EMF.
interactions among the arc, droplet, weld pool and the EMF especially
when the magnetic field is introduced into the welding process. It is very
necessary to reveal the physical mechanism of external magnetic field
assisted GAMW process for deeply understanding the effect of the
magnetic field on the welding process. But it is difficult to quantitatively
analyze the distributions of physical quantity including pressure, tem­
perature, velocity and forces etc. only by experiments. Therefore, the
numerical simulation assisted with little experimental study becomes
preferable to study the arc and droplet behaviors under the action of the
EMF. Recently, the researchers developed the numerical simulation
models to investigate the influence of external magnetic field on the arc,
droplet and the weld pool behaviors. Yin et al. [15] established a
three-dimensional model of arc and weld pool for TIG welding with
uniform axial magnetic field. The results showed that the arc was radi­
ally spread and the temperature, current density and the arc pressure on
the workpiece became double-peaked. Chen et al. [16] numerically
investigated the arc behavior under an axial magnetic field during TIG
welding. The rotating arc and Magneto-Hydro Dynamics pumping effect
for arc pressure were induced by the above magnetic field, which was
responsible for the shrinkage of cathode arc attachment. However, the
magnetic flux density was assumed to be uniform without the calcula­
tion and the filler metal was not included in this study. Zhou et al. [17]
studied the effect of external longitudinal static magnetic field on the
molten pool behavior for the arc based additive manufacturing process.
They found that the tangential stirring force was produced in the molten
2.2. Physical considerations
The model in this study focused on the investigation of the arc and
the droplet behavior in GMAW process. Therefore, the description of the
workpiece and weld pool was omitted. The interactions between the
liquid metal and the arc plasma were described by a multiphase
formulation. The filler metal and shielding gas were treated as incom­
pressible and immiscible phases. And the fluid flow of the gaseous and
liquid phase were assumed to be laminar flow. The energy exchange
between arc and droplet was considered but the melting process of the
wire was not considered. The temperature of filler metal flowing into the
computational domain was assumed to be melting point of the wire
(1800K [19]), and then it was heated and driven by the arc plasma. The
metal vapor can cause the temperature reduction at the edges of the
plasma column [20]. This study mainly aims to investigate the effect of
the EMF on the arc and droplet behaviors, so the metal vapor and the
weld pool was not considered [21,22].
2.3. Governing equations and source terms
The mass continuity equation, momentum conservation equation,
energy conservation equation, potential continuity equation and other
equations were used as follows.
Mass continuity:
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Vacuum 177 (2020) 109391
!
electric potential, A is the magnetic vector potential and μ0 represents
the magnetic permeability.
The continuum surface force (CSF) [23] model was used to calculate
the surface tension force by transferring the surface tension force into a
volume force in the surface region:
�
�
⇀
rFm
rFm
FST ¼ γr⋅
(8)
jrFm j jrFm j
where γ is the surface tension coefficient of the molten metal, Fm is the
volume fraction of the metal phase.
In addition to thermal conduction, convective flow and Ohmic
heating, the heat transfer associated with the thermionic heating by the
electrons and the radiation loss was considered in the arc region, so the
third term S of Eq. (3) was calculated as follows:
S¼
Table 1
Thermo-physical properties of the wire.
Symbol
Value (Unit)
Density
Melting temperature
Electrical conductivity
Thermal conductivity
Dynamic viscosity
Specific heat
ρ
7860 (kg m 3) [32]
1800 (K)
7.7 � 105 (Ω 1 m 1) [33]
26-52 (W m 1 K 1) [33]
0.006 (Pa s) [32]
695-800 (J kg 1 K 1) [33]
Tm
σ
k
ε
Cp
∂ρ
ν Þ¼0
þ r ⋅ ðρ!
∂t
!
S ¼ j j⋅ rFm j ⋅ ϕAnode
∂t
ν ⋅!
ν Þ¼
þ r ⋅ ðρ!
!
! !
!
g þ j A � ð B S þ B E Þ þ F ST
rp þ rτ þ ρ!
(2)
dF ∂F
¼ þ ð!
v ⋅ rFÞ ¼ 0
dt ∂t
Energy conservation:
!
∂ρh
jj j2
ν ⋅ hÞ ¼ r ⋅ ðkrTÞ þ A þ S
þ r ⋅ ðρ!
∂t
σ
(4)
!
μ0 j
A
(5)
Ohm’s law:
!
j A¼
σ ⋅rφ
(6)
Magnetic field:
!
!
BS ¼r� A
(11)
Fig. 2 shows the calculation domain and boundary conditions of the
numerical model. Area 1 was defined as the inlet of the shielding gas and
Area 2 was defined as an inlet of the filler metal. Area 3, ADHE, DCGH,
CGFB and BAFE were the gas outlet boundaries and their temperature
was set to 1000K [20,27]. For the inflow of the shielding gas from the
nozzle, the horizontal velocity component (vx and vy) was not considered
and the vertical velocity component (vz) was calculated from the for­
mula of pipe flow as following [28]:
(
pffiffiffiffiffiffiffiffi � �)
� ln x2 þy2 Rn
R2n ðx2 þ y2 Þ þ R2n R2w
lnðRn =RW Þ
ln pffiRffi2ffinffiffiffiffi2ffi
2Q
x þy
(
)
vz ðx; yÞ ¼
þ vw
Rn
π
ln
2 R2 2
R
ð
Þ
Rw
R4n R4W þ lnðRn n =RwW Þ
Magnetic vector potential:
!
r2 A ¼
(10)
2.4. Computational domain and boundary conditions
(3)
Electric potential:
r ⋅ ðσrφÞ ¼ 0
εαT 4 jrFm j
!
where j j⋅ rFm j is the current density normal to the electrode surface,
ϕAnode is the work function of the electrode wire, ε is the emissivity of the
wire surface and α is the Stefan-Boltzmann constant.
The filler metal transfer involves the deformation of a free surface,
which was tracked in this model by the volume-of-fluid method [19,23].
(1)
Momentum:
∂ρ!
ν
(9)
SR
where KB is the Boltzmann constant, e is electron charge, SR is the ra­
diation loss.
In the molten metal region, only the thermal conduction, convective
flow and Ohmic heating was considered, so the third term S of Eq. (3)
was regarded as zero.
At the plasma-electrode interface, there exists a sheath layer, which
departs from the thermo-dynamic equilibrium state. Since the thickness
of the sheath layer is less than 2 μm, it is not physically constructed in
the model. In this study, the ’LTE-diffusion approximation’ method
[24–26] was used and the heating effect at the sheath region was taken
into consideration by adding energy fluxes at the sheath region near the
anode. The energy flux is given by the following equation:
Fig. 2. Computational domain of arc and droplet for GMAW.
Nomenclature
5KB
j⋅rT
2e
(7)
In Eqs. (1)–(7), ρ represents the density, t is the time, !
v is the ve­
locity vector, p represents the pressure, τ represents the stress tensor, !
g
!
is the acceleration due to gravity, j A is the current density in the
!
!
welding arc column, B S is self-induced magnetic field and B E is the
!
external magnetic field, F ST is the momentum source terms of the sur­
face tension force, σ represents the electrical conductivity, h represents
the enthalpy, k represents the thermal conductivity, T represents the
temperature, S represents the energy source term, φ represents the
(12)
where Q is the inflow rate of the shielding gas, Rw is the radius of the
wire, Rn is the radius of the gas nozzle and vw is the wire feeding rate.
The metal phase flowed into the computational domain through
boundary Area 2 at the wire melting rate, which was estimated by the
empirical equation [29]:
vwire ¼ aI þ bEx I 2
3
(13)
L. Wang et al.
Vacuum 177 (2020) 109391
Table 2
Welding parameters and magnetic field parameters.
Process parameters
Value (Unit)
Welding current I
Flow rate of shielding gas
Diameter of wire
Diameter of the gas nozzle
Excitation current Ie
Excitation frequency f
200 -250 (A)
20 (L/min) (Pure Ar)
1.2 (mm)
15 (mm)
0-6 (A)
15-30 (Hz)
where a and b are constants depended on the radius and properties of the
wire, Ex is the wire extension. Uniform current density was applied to
Area 2. The voltage of EFGH was set to zero.
2.5. Material properties
The welding wire was assumed to be mild steel and a detailed
thermo-physical properties of the wire are listed in Table 1. In this study,
pure argon was used as the shielding gas and temperature-dependent
physical properties of the gas were used according to the datasets of
Fig. 3. Simulated arc temperature and flow velocity at different times without EMF (I ¼ 250A).
Fig. 4. Simulated arc and droplet with EMF at xoz plane (I ¼ 250 A, Ie ¼ 4A, f ¼ 15Hz).
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Vacuum 177 (2020) 109391
Fig. 5. Simulated arc and droplet with EMF at yoz plane (I ¼ 250 A, Ie ¼ 4A, f ¼ 15Hz).
Fig. 7. Change of temperature with time under different excitation currents.
Fig. 6. The inclination angles of droplet at different times (Ie ¼ 4A, f ¼ 15 Hz).
2.7. Numerical solution method and procedure
Boulos et al. [30] and Murphy et al. [31].
Firstly, the calculation of external magnetic field distribution was
carried out using ANSYS electromagnetic module [34]. The steady
magnetic fields (BE1) excited by coil 1 and the steady magnetic fields
(BE2) excited by coil 2 were calculated, respectively. Then, the arc and
droplet behaviors were calculated using the commercial software of
ANSYS Fluent 14.5. User defined scalars (UDSs) equations were used to
solve Maxwell’s equations, and user defined functions (UDFs) were
applied to add the energy and momentum term sources or boundary
2.6. Process parameters
In order to investigate the effect of the magnetic field parameters on
the arc and droplet behaviors, the numerical simulation cases with
different magnetic field parameters and welding parameters were car­
ried out, respectively. The main welding parameters in this study are
listed in Table 2.
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Vacuum 177 (2020) 109391
Fig. 8. Effect of excitation current on arc and droplet inclination.
Fig. 9. Effect of excitation current on frequency and volume of droplet.
conditions. In this study, the time step size was set as 2✕10 6 s. A
pressure-based solver and PISO algorithm were used for the
pressure-velocity coupling. Meanwhile, the calculated data of the
external magnetic field was imported by the User-defined function
(UDF). As shown in Fig. 1, the excitation current cycle can be divided
into Δt1 and Δt2. If the calculation time belongs to Δt1, BE1 was imported
into the model. Otherwise, BE2 was imported into the model. Therefore,
an external alternating magnetic field was applied to the model to
calculate the effect of the external magnetic field on the arc and droplet.
Fig. 10. Additional electromagnetic force of the arc under different excita­
tion currents.
limited in the area between the wire tip and the detached droplet, and
the maximum velocity was about 200 m/s. Near the workpiece, the arc
plasma flow became outward and upward.
Fig. 4 and Fig. 5 display the arc profile and flow velocity when the
EMF was applied (welding current 250 A, excitation current 4A, exci­
tation frequency 15Hz). The arc and droplet was inclined invariably
along the x-axis (welding direction) within a cycle under the effect of
magnetic field, as shown in Fig. 4. The maximum temperature was still
about 21000K and distributed around the filler metal. The arc and
droplet was also be inclined along the positive y-axis (perpendicular to
the welding direction) at the first half cycle (Δt1 ¼ 0.0333 s) and then
inclined along the negative y-axis at the rear half cycle (Δt2 ¼ 0.0333 s),
as shown in Fig. 5. Meanwhile, the region of the arc plasma with high
3. Result and discussion
3.1. Effect of excitation current level
Fig. 3 shows the temperature profile and velocity distribution of the
simulated arc plasma when no EMF was applied (welding current 250A).
The maximum temperature was about 21000K and distributed around
the filler metal. The filler metal was transferred into the weld pool
vertically and the trajectory of the filler metal was along the wire axis.
The velocity distribution of the arc plasma was symmetrical along the
welding wire. The arc plasma flowed downward and inward toward the
workpiece with very high velocities. The high velocity arc plasma was
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Vacuum 177 (2020) 109391
Fig. 11. Distributions of forces acted on the filler metal when EMF is applied.
velocity (more than 200 m/s) was increased compared with that in
normal case without EMF (Fig. 3).
In order to investigate the effect of the EMF on arc and droplet
inclination, the inclination angle of the arc was defined as the angle
between the wire axis and centerline of arc temperature isotherm with
14000K, as shown in Fig. 4a. The inclination angle of droplet was
schematically shown in Fig. 4c. Fig. 6 shows the inclination angles of the
arc and all droplets within three cycles based on the simulation results.
Both the inclination angles of the arc and droplet along x-axis kept
stable. The average inclination angles of the arc and droplet along x-axis
were 21.6� and 13.7� , respectively. However, the inclination angles of
the arc and droplet along y-axis fluctuated periodically due to the swing
of the arc and droplet. The positive value of angle represented that the
arc and droplet inclined along positive y-axis and the negative value
meant they inclined along negative y-axis. The maximum inclination
angles of the arc and droplet along y-axis are 11.9 � and 6.0� , respec­
tively. The density of the arc plasma is extremely small so it is very prone
to interference of the additional forces. The density of the filler metal is
much larger than the arc plasma, the droplet is not so sensitive to the
additional forces. Therefore, the inclination angle of the arc is larger
than the droplet when the additional electromagnetic force is applied on
the arc and droplet. The detailed reason for the inclination of the arc and
droplet will be analyzed in the latter part.
The periodic swing of the arc influenced the temperature distribution
of the workpiece. Fig. 7 shows the temperature of point P (0, 4, 0.5) near
the workpiece (0.5 mm above, as shown in Fig. 2) at different levels of
excitation current within two cycles of the excitation current. Because of
the swing of the arc, the temperature of point P was very high when the
arc was inclined to the side of the point during Δt1 in each cycle (such as
Fig. 5a and b). And then the temperature decreased lower than 8000K
when the arc was inclined to other side (Fig. 5c and d) during Δt2.
Besdies, the temperature of point P fluctuated periodically during Δt1 or
Δt2. This is because the periodical growth, detachment and flight of the
droplet also infulenced the temperature distribution of the arc and
workpiece. With the increase of the excitation current, the temperature
of the point was increased during Δt1 but decreased during Δt2. It
demonstrated that the incliantion angle of the arc was increased with the
increase of the excitation current. Therefore, when the arc was inclined
to the side of the point P (Δt1), the high temperature was closer to the
point due to the increase of the inclination angle. On the contrary, when
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L. Wang et al.
Vacuum 177 (2020) 109391
Fig. 10 shows the distribution of the additional electromagnetic force
in the arc region at xoz plane under different excitation current. The arc
inclination is related to both the self-induced and additional electro­
magnetic forces. The self-induced electromagnetic force can make the
arc constricted and protect the arc from inclination. The additional
electromagnetic force is the drivinhg force for the arc inclination. When
the welding current was constant, the current density and the selfinduced magnetic field were unchanged. With the increase of the exci­
tation current, the external magnetic field was increased. The selfinduced electromagnetic force was unchanged while the additional
electromagnetic force was increased so the inclination angle of the arc
was increased. For the droplet incliantion, not only an additional elec­
tromagnetic force was extered on the droplet but also the inclination of
the arc changed the level and direction of the arc plasma force of the
droplet. Consequently, both the additional electromagnetic force and
arc plsma force should be responsible for the inclination of the droplet.
According to Xu et al. [35], the magnitude of the arc plasma force can be
estimated by the empirical formula as follows:
� 2�
1
πDd
(14)
Fpla ¼ Cds ρg v2g
2
4
Fig. 12. Effect of excitation current on average arc plasma force on the
filler metal.
where Cds is the drag coefficient for a sphere; ρg is the plasma gas den­
sity; vg is the plasma gas velocity; and Dd is the diameter of droplet.
Fig. 11 shows the distribution of the additional electromagnetic force
and arc plasma force of the droplet. Because the arc plasma force acts on
the droplet surface and it is a surface force, the arc plasma force was
transferred into the volume force in Fig. 11. It shows that the magnitude
of the additional electromagnetic force was much smaller than the arc
plasma force. So the change of the arc plasma force had greater effect on
the droplet inclination and its transfer. Fig. 12 shows the mean arc
plasma force at different level of the excitation current along three di­
rection (x, y and z). With the increase of the excitation current, both the
components of arc plasma force along x-axis and y-axis were increased.
So both the inclination angles along x-axis and y-axis were increased.
Meanwhile, the average arc plasma force along x-axis was higher than
that along y-axis, so the inclination angle of the droplet along x-axis
(welding direction) was higher than that along y-axis (perpendicular to
the welding direction). In addition, the components of arc plasma force
along z-axis was also increased with the increasing excitation current,
which was helpful to promote the metal transfer. Consequently, the
metal transfer frequency was increased when the excitation current was
the arc was inclined to the opposite side of the point P (Δt2), the high
temperature of arc is far away from this point, so its temperature was
decreasd when the excitation current is increased. It can be inferred that
the external magnetic field increased the heating area along y-axis,
which can lead to the increase of the width of the weld pool. The effect of
the inclined arc on the weld pool behavior will be numerically investi­
gated in our future work.
In order to investigate the effect of the EMF on arc and droplet be­
haviors, the inclination angles of the arc and droplet, the droplet transfer
frequency and droplet volume under different excitation current were
calculated. Fig. 8 shows the inclination angles of the arc and detached
droplets at different levels of excitation current. With the increase of the
excitation current from 0 to 6A, both the forward inclination angle
(along x-axis) and the left-to-right swinging angle (along y-axis) of the
arc and droplet were increased, respectively. Fig. 9 shows the effect of
excitation current on frequency and volume of droplet. With the increase
of the excitation current from 0 to 6A, the metal transfer frequency was
increased from 140 Hz to 160 Hz and the volume of the droplet was
decreased from 0.975 mm3 to 0.794 mm3.
Fig. 13. Effect of excitation frequency on arc shape.
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Vacuum 177 (2020) 109391
Fig. 16. Effect of excitation frequency on arc and droplet inclination.
Fig. 14. Arc profiles and velocity distributions of arc plasma with 30 Hz
excitation current.
Fig. 17. Effect of excitation frequency on frequency and volume of droplet.
compound magnetic field to swing the arc and droplet to the edge of the
weld pool, so it is difficult to suppress the undercutting defect. So the
used excitation current frequency in this study is 15–30 Hz. Fig. 13
displays the projections of the arc temperature isothermal with 10000K
on the xoz and yoz sections at different levels of excitation frequency.
The arc shape barely changed although the frequency of the excitation
current was increased from 15 Hz to 30Hz. Fig. 14 displays the arc
plasma velocity distribution when the excitation frequency was 30 Hz.
The simulated results were much similar to the data that was calculated
when the excitation current was 15 Hz (Figs. 4d and 5d). It indicates that
the frequency of the excitation current has little effect on the arc shape.
Fig. 15 shows the temperature of the point P at different levels of
excitation frequency. Although the frequency of the temperature fluc­
tuation was increased with the increase of the excitation frequency, the
maximum and minimum temperature within each cycle was kept con­
stant. In this study, the difference between the used maximum and
minimum excitation frequency was only 15Hz, so the excitation fre­
quency had little effect on the arc shape and temperature. The effect of
higher excitation frequency on arc behaviors should be investigated in
the future work.
Fig. 16 shows the inclination angles at different levels of excitation
frequency. With the increase of the excitation frequency from 15 Hz to
Fig. 15. Change of temperature with time under different excitation
frequencies.
increased.
3.2. Effect of excitation frequency
For the designated experiments in this study, the experiment shows
that optimal excitation current frequency is less than 30Hz [14]. When
the excitation current was very higher, there was no enough time for the
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Vacuum 177 (2020) 109391
would be redirected due to the change of direction in the force com­
ponents along y-axis. So the inclination angle along y-axis was reduced
when the excitation frequency was increased.
Fig. 17 shows the effect of excitation frequency on metal transfer
frequency and volume of droplet. With the increase of the excitation
frequency, both the metal transfer frequency and the volume of the
droplet changed little. The difference of the volume and transfer fre­
quency were only 0.014 mm3 and 3.2 Hz. On one hand, the constant
excitation current produced unchanged value of additional electro­
magnetic force. On other hand, the arc shape was almost the same at
different excitation frequency (as shown in Fig. 13), so the arc plasma
force was unchanged. As a consequence, the metal transfer frequency
was almost constant with different excitation frequency.
3.3. Effect of welding current
Fig. 18 displays the projections of the arc temperature isothermal
with 10000K on the xoz section at different levels of welding current
when the excitation current level and frequency were constant (Ie ¼ 2 A,
f ¼ 15 Hz). Fig. 19 shows the inclination angles of the ac and droplet at
different levels of welding current. When the welding current increased
from 200A to 250A, the inclination angles of the arc and droplet was
decreased. With the increase of welding current, the self-induced elec­
tromagnetic force was increased due to the increase of the current
density. Meanwhile, the increase of self-induced electromagnetic force
also increased the stiffness of the arc so it was more difficult for the arc to
be inclined by the additional force. As a result, though the additional
electromagnetic force was increased with increasing welding current,
the inclination amplitude of the arc might be decreased. However, when
the welding current increased from 250A to 300A, the inclination angle
of the arc and droplet along x-axis were increased but the inclination
angles along y-axis were decreased. The increase of the welding current
will cause the increase of both self-induced electromagnetic force and
additional electromagnetic force. The additional electromagnetic force
can cause the inclination but the self-induced electromagnetic force can
prevent the arc and droplet from inclination. Which one has more effect
on the arc and droplet inclination is closely related to the level of the
welding current. The underlying relationship among the welding cur­
rent, excitation current and arc and droplet inclination needs to be
further explored.
Fig. 18. Effect of welding current on arc shape.
3.4. Effect on weld pool behavior
As mentioned above, the arc and droplet was inclined along the
welding direction continuously and swung along the direction perpen­
dicular to the welding direction periodically. Within each cycle of
excitation current, the arc and droplet was inclined to the left front along
the welding direction during Δt1, as indicated in Fig. 20a. So the molten
metal in the weld pool was pushed to flow to the left boundary and the
fore part of the weld pool, which was beneficial to fill the left weld toe
and increase the thickness of the molten metal layer in the front of the
weld pool. Similarly, during Δt2, the arc and droplet was inclined to the
right front along the welding direction, as indicated in Fig. 20b. The
molten metal in the weld pool was pushed to flow to the right boundary
and the fore part of the weld pool. As a result, the right weld toe could be
filled by the molten metal, and the thickness of the molten metal layer in
the front of the weld pool can also be increased. Such arc and droplet
behaviors were changed periodically by the EMF, which improved the
weld pool behaviors to suppress the weld bead defects. It should be
noted that the droplet inclination can change the velocity of the droplet
including the magnitude and direction, which will also affect the weld
pool behavior. However, the quantitative analysis on the influence of
droplet on the weld pool cannot be conducted in the present model.
Besides, the calculated temperature of the droplet by the present model
is higher than the experiment due to the ignorance of the metal vapor. It
is necessary to establish a more comprehensive and accurate model
Fig. 19. Effect of welding current on arc and droplet inclination.
30 Hz, both the forward inclination angles (along x-axis) of arc and
droplet under different excitation frequency were almost constant.
Along y-axis, inclination angle of the droplet was decreased from 7.0� to
5.0� while the inclination angle of the arc kept constant. Although the
excitation frequency was changed, the additional electromagnetic force
was always along the forward welding direction. So the forward incli­
nation angles at different levels of excitation frequency were almost
unchanged. Due to the periodic change of the direction for the addi­
tional electromagnetic force component along y-axis, the increase of the
excitation current reduced the action time of the additional electro­
magnetic force component on the droplet along y-axis. The inclined
droplet could not reach its maximum inclination angle, and then it
10
L. Wang et al.
Vacuum 177 (2020) 109391
Fig. 20. Schematic of the arc, droplet and weld pool with EMF.
Fig. 21. Comparison between the experiment measurement and simulated result for temperature distribution.
containing the arc, droplet and weld pool for GMAW to investigate the
influence of the EMF on the weld pool behavior in the future work.
3.5. Experiment validation
To examine the validity of the model, the temperature contours for a
free burning argon arc was calculated and compared with the mea­
surement results by Hsu et al. [36] (welding current 300 A, arc length
10 mm). Fig. 21 shows that the calculated temperature contours and the
measured results are in good agreements.
The welding experiment with the EMF was conducted (welding
current 250A, excitation current 4A, excitation frequency 15 Hz). Fig. 22
displays the weld bead appearance and cross sections with and without
EMF in high-speed GMAW (welding speed 1.7 m/min). It indicates that
the EMF can suppress the undercutting defect by choosing appropriate
excitation current and frequency.
The droplet images were captured by high-speed cameras during the
welding process. Fig. 23 shows the captured images and calculated re­
sults of the metal transfer process during one excitation current cycle.
The simulated droplet size basically exhibited good agreements with the
Fig. 22. Suppression of undercutting in high-speed GMAW with EMF.
11
L. Wang et al.
Vacuum 177 (2020) 109391
Fig. 23. Comparison of the calculated and measured metal transfer process.
Fig. 24. Comparison of the inclination angles between captured and calculated droplets.
experimental data.
Fig. 24 shows the comparison of the inclination angles between the
observed images and calculated results. Along x-axis, the measured
inclination angle of the droplet was 13.4� and the simulated result was
14.6� . Along y-axis, the measured inclination angle of the droplet was
7.4� and the simulated result was 6.8� . The simulated inclination angles
of the droplet were also in good agreements with the experiment results.
high-velocity region of the arc plasma flow (more than 200 m/s)
was increased.
(2) For every 1A increase in excitation current, the arc inclination
angles along x-axis and y-axis would increase by about 1.20� and
0.85� , respectively. The droplet inclination angles along x-axis
and y-axis would increase by 0.75� and 0.51� , respectively. The
component of arc plasma force along z-axis was increased with
the increase of the excitation current, which caused the increase
of metal transfer frequency.
(3) With the increase of the excitation frequency, there was no
obvious change for arc shape and arc temperature. The left-toright inclination angle (along y-axis) was decreased and the for­
ward inclination angles of arc and droplet (along x-axis) were
almost the same. Both the metal transfer frequency and the vol­
ume of the droplet also had little change.
4. Conclusions
(1) A comprehensive 3D model including the interactions among the
arc plasma, droplet and the external magnetic field was estab­
lished. When the compound external magnetic field was applied,
the maximum temperature of the arc was still constant but the
12
L. Wang et al.
Vacuum 177 (2020) 109391
(4) The forward inclination of the arc and droplet could pushed more
molten metal to flow towards the fore part of the weld pool and
the swing of the arc and droplet could push molten metal to flow
towards the two sides of the weld pool. Consequently, the un­
dercutting defect in high-speed GAMW can be suppressed.
[14]
[15]
[16]
Declaration of competing interest
[17]
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
[18]
Acknowledgements
[19]
This work was supported by the National Natural Science Foundation
of China (No. 51775313), Major Program of Shandong Province Natural
Science Foundation (No. ZR2018ZC1760), Young Scholars Program of
Shandong University (No. 2017WLJH24) and China Postdoctoral Sci­
ence Foundation (No. 2019M662351).
[20]
[21]
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