Heat Transfer to Anode of Pulsed Arc as Function of Duty Ratio
Masakazu Kojima*, Toru Iwao*, Shinichi Tashiro**, Manabu Tanaka**, Motoshige Yumoto*
* Tokyo City University
** Osaka University
Abstract: The pulsed arc welding is regulated by the current parameters that consist of base
and peak current, current frequency and duty ratio for current waveform. It controls the heat
flux to the anode and welding speed with them. Moreover, the high frequency pulsed current
in pulsed GTAW is used in order to control the weld pool. However, the heat transfer to the
anode of pulsed arc as function of current parameters has not been elucidated. The heat
transfer to the anode of pulsed arc as function of duty ratio was elucidated by using the MHD
simulation. The heat flux of pulsed arc becomes high at the center area on the anode. It is
considered that it depends on the constriction of anode root and current path on the anode
based on the peak and base period of current waveform.
Keywords: GTAW, pulsed welding, transient arc, numerical simulation, heat transfer
1. Introduction
The plasma arc has a lot of characteristics such as
the ultra high temperature, the high intense
radiation and the high energy density. The arc
welding is one of the joining technologies using
these characteristics. In arc welding, a pulsed
current is used to improve welding speed and
quality. And, the pulsed arc welding has been
developed rapidly [1]. Pulsed arc welding has been
used widely in conjunction with the improvement
of power supply performance. For consumable
electrodes such as those used in MIG and MAG
welding, it is mainly used to control a droplet
transfer. For GTAW (Gas Tungsten Arc Welding), it
is used to control the heat transfer, with improved
stability and high-speed welding with small current.
In pulsed arc welding, the frequency is changed
normally. However, welding parameters such as
frequency, current waveform, and welding speed
are determined empirically. For GTAW, arc
property and energy balance changes are more
important than those of MIG and MAG welding,
because GTAW has no droplet. Especially, when the
frequency increases, the discussion of the steady
state is insufficient for pulsed arc welding because
the transitional time is long.
In pulsed arc welding, the parameters are
frequency, duty ratio in the waveform of current.
Therefore, the pulsed arc welding has many factors
for control. However, it is difficult to elucidate the
heat transfer of pulsed arc with the experiment.
In this paper, the heat transfer to anode of pulsed
arc as a function of duty ratio was elucidated by
MHD simulation in order to know the heat transfer
affected by the current waveform.
2. Calculation methods
The calculation condition of the pulsed arc is
affected by (1) the local thermal equilibrium (LTE),
(2) chemical equilibrium, (3) optically thin plasma,
(4) absence of turbulence, and (5) the cylinder axis
object of the arc. The calculation model,
simultaneous equations of MHD, thermal and
transport properties, and the pulsed current
waveform were used for this simulation. Pressure
and velocity were calculated using SIMPLER
method[2].
2.1 Calculation model
Figure 1 depicts the calculation model. The GTAW
was simulated; the droplet transfer was not
considered. The cathode was tungsten; the anode
was SUS304. The electrode gap was 5 mm. Gas is
Ar and flow rate was 10 slm at B–C. Table 1
presents the boundary conditions. The calculation
area circumference was 300 K.
2.2 Pulsed current waveform
Figure 2 shows the pulsed current waveform used
for this calculation: it had 150 A peak current and
50 A base current and 250 Hz frequency. Transition
duration of current is 0.5 ms. The three calculation
conditions of duty ratio 0.3, 0.5 and 0.7 are used.
The initial current and values of velocity,
temperature, and pressure are the same in this
calculation.
2.3 MHD equations
The MHD equations used in this calculation are
shown below.
Fig. 1 Calculation model.
Table. 1 Boundary conditions.
Mass conservation equation
 1 
rvr    vz   0

t r r
z
(1)
Momentum conservation equation (radial direction)



vr   1  rvr2   vr v z 
t
r r
z
P
1   vr  2    vr 1 ( rv r )  
 

 j z B 

 2


r
r r 
r  3 r   z r r  

  vr
v 
v
  z   2 r2

r  z
r 
r
(2)
Momentum conservation equation (axial direction)


 

vz   1  rvr vz   vz2
t
r r
z
P
1   vz
v

 jr B 
 r r
 r
z
r r 
z
r
 2    vr 1 ( rvr )  
 


   g
 3 z   z r r  
(3)
Energy conservation equation

h   1  rv r h   v z h 
t
r r
z



1   r h     h 


 j r E r  j z E z  Prad
r r  C p r  z  C p z 
(4)
Current continuity equation
1 
rjr     j z   0
r r
z
(5)
Ohm’s law
jr  

r
j z  

z
(6)
Fig. 2 Pulsed current waveform.
Maxwell’s equation
1 
rB   0 jz
r r
(7)
In those equations, the following variables are
used: r and z (m) , respectively, signify the position
coordinates of the radial direction and axial
direction; v (m/s) is the velocity; P (Pa) is the
pressure; ρ (kg/m3) is the mass density; h (J/Kg)
represents the enthalpy; Cp (J/(kg K)) is the specific
heat; κ (W/(m K)) is the coefficient of thermal
conductivity; σ (A/(Vm)) is the electrical
Fig. 3 Heat transfer energy to all anode area.
Fig. 5 Radius of current path as function of time.
the surface emissivity of material; α (W/(m2K4)) is
the Stefan Boltzmann constant (=5.67×10-8); and k
(J/K) is the Boltzmann constant (=1.38 × 10-23). In
this calculation, SUS304 is a = 4.65 eV.
Fig.4 Heat transfer energy to position at1mm of anode area.
conductivity; η (Pa s) is the viscosity; Φ(V) stands
for the electrical potential; E (V/m) is the electric
field; j (A/m2) is the current density; Bθ (T) is the
flux of azimuthal component; μ0 (H/m) is the
magnetic permeability in vacuum; Prad (W/m3) is the
radiation power, and T (K) is the arc temperature.
2.4 Heat transfer to Anode
In the calculation model, the electrode and the arc
are combined into one system and simultaneously
analysed[3][4]. The transfer of energy between the
arc and the electrode is obtained from the equation
below and added as a localized source term in the
equation for conservation of energy. The heat flux
to electrodes is calculated using the unified model
(cathode – arc – anode). The formula used for
calculation is shown below.
Thermal flux from the arc to the anode
 T 
4
qa   
  jza   aTa
 z 
(8)
Therein, Ta (K) is the anode temperature; a, a (eV)
is the work function; εa and respectively represent
3. Results and discussion
3.1 Heat transfer affected by anode root
and current path
Figure 3 shows the heat transfer energy to all
anode area in pulsed arc and steady arc at 100 A.
They does not change so much, and are to be 1760 J
at 2 s.
Figure 4 shows the heat transfer energy to position
at 1 mm of anode area. It increases to be 430 J in
the case of pulsed arc and 360 J in the case of stable
arc 100 A at 2s. The current path of anode root leads
to the differences in heat transfer energy to position
at 1mm of anode area because of the constricted
anode root. The heat transfer to anode is calculated
by equation (8) in this research. Therefore, it
considered that the heat transfer to anode increases
because of the constriction of anode root and
current path at the center area of high current
density. The current path is defined by 99% of total
current density to radial direction. Figure 5 shows
the radius of current path as function of time. The
current path was constricted in the case of pulsed
arc. Therefore, the heat transfer to position at 1mm
of anode area was increased as shown in figure 4.
Fig. 6 Heat transfer energy to all anode area with duty ratio.
Fig. 8 Heat transfer energy to position at 1mm of anode area
with duty ratio.
most difference was about 20 J by time of 2s.
Therefore, the heat transfer of low duty ratio is
higher than that of high duty ratio under saving the
input power.
4. Summary
Fig. 7 Heat transfer as a function current to all anode area
with duty ratio.
3.2 Heat transfer affected by duty ratio
The anode root and current path are important for
heat transfer as mentioned in section 3.1. In
addition, they depend on the duty ratio, because the
peak and base current time are controlled. Figure 6
shows the heat transfer to all anode area as function
of time with duty ratio. The heat transfer to all
anode area at duty ratio 0.3 is larger than it at duty
ratio 0.5 at 1.3s. In addition, the input power at 1.3s
becomes to be 1010 J at duty ratio 0.3 and 1310 J at
duty ratio 0.5. Therefore, the heat transfer to all
anode area becomes high although the input power
is low in the case of duty ratio 0.3.
Figure 7 shows the heat transfer as a function
current to all anode area with duty ratio. It doesn’t
change so much at duty ratio 0.5 and 0.7. However,
in the case of duty ratio 0.3, it is higher than other
duty ratio.
Figure 8 shows the heat transfer energy to position
at 1mm of anode area with duty ratio. This
difference was not so much in the heat transfer
energy to position at 1mm of anode area and the
The heat transfer to anode of pulsed arc as
function of duty ratio was elucidated in order to
know the heat transfer affected by the current
waveform. The main results are shown below.
(1) The heat transfer energy to position at 1mm of
anode are at pulsed arc was higher than it at
stable arc 100A.
(2) The heat transfer to anode increases because of
the constriction of anode root and current path at
the center area of high current density. Therefore,
the heat transfer is affected by anode root and
current path.
(3) The heat transfer of low duty ratio is higher
than that of high duty ratio under saving the
input power. Therefore, the heat transfer is
affected by duty ratio.
References
[1] Yoshinori Hirata, Journal of the Japan Welding
Society, 71(5), pp.389-404 (2002).
[2] S. V. Patanker: Numerical Heat Transfer and Fluid
Flow, Hemisphere Publishing Corp., pp.116-139
(1980).
[3] M.Tanaka，H.Terasaki，M.Ushio, J.J.Lowke：，
Metallurgical and Materials ， 33A ， pp.2043-2051
(2002).
[4] M.Tanaka, H.Terasaki, R.Narita, K.Kobayashi,
H.Fujii, M.Ushio: Quarterly Journal of the Japan
Welding Society, 23(3), pp.398-404 (2005).