**NUMERICAL SIMULATION SYSTEM OF DEVELOPMENT OF**

**ULTRA-NARROW GAP GMAW PROCESS**

**T.Nakamura^\*^ , K.Hiraoka^\*^**

**ABSTRACT**

An Ultra Narrow Gap GMA welding (UNGW) process with less than 5mm gap
width has been developed in which the arc occurring at wire tip is
forcibly oscillated over the groove wall in the thickness direction. To
control the wire tip position, the low-frequency pulse current is used.

An UNGW process simulation system which is based on analysis of
non-steady state wire melting under low-frequency pulse arc welding
conditions has been proposed to obtain defect free joints and find out
adaptive welding conditions. In this simulation system, the equivalent
electric circuit of arc welding and many factors on welding phenomena
are conceded such as the digging action by arc force, motion of molten
pool, equivalent heat input in wire tip, super heat of droplets, arc
current-voltage characteristics and so on.

This simulation system makes it possible to find out appropriate welding
conditions for UNGW which is characterized by many pulse parameters that
correlate in a complex manner.

**KEYWORDS**

GMA welding, Ultra-narrow gap, Numerical simulation, Non-steady state,
and adaptive welding condition

**INTRODUCTION**

New type steel with various properties have recently been developed, and
using these materials, high quality and efficient welding methods that
maintain the properties of the materials is expected (Ref.　1). To
reduce deterioration of joint properties by welding heat　and welding
deformation, small heat input welding method is effective, however
high　efficient welding　is difficult for this welding process.

Narrow gap welding has been developed as a highly efficient and small
heat input welding method (Ref.　2). The smaller groove width is more
effective　to small heat input　welding and higher efficiency　welding,
however good welding is impossible with a groove width less than 5 mm.
Because the arc is so unstable that the arc pole irregularly traverses
up and down the groove wall, and welding defects such as lack of fusion
are formed. To obtain good joint by prevention of unstable arc,
mechanical weaving method　in the direction of the groove width is used
(Ref.　2). However, since the welding speed is limited if mechanical
weaving is used, the high welding efficiency, which is the advantage of
narrow gap welding, cannot be sufficiently obtained.

We developed ultra-narrow gap welding (UNGW), in which stable and high
efficiency welding is possible in the groove with a width narrowed until
mechanical weaving in the direction of the groove width becomes
unnecessary(Ref.　3,4).The welding of the I-type joint with a groove
width less than 5 mm is achieved by oscillating the arc pole over the
groove wall in the thickness direction using low frequency pulse current
less than 10 Hz.

To obtain both　melting of the root area and concave surface beads, the
choice of the amplitude and position of oscillation over the groove wall
in the thickness direction is important. To obtain the appropriate
conditions for oscillation in UNGW, it is necessary to determine many
control parameters such as the pulse peak current, pulse base current,
pulse peak duration, pulse base duration, frequency of pulse current and
wire feed rate. Furthermore, arc behavior in the groove strongly affect
the molten pool behavior rand　the oscillation of the wire tip over the
groove wall in the thickness direction. However, it will be impractical
to determine appropriate parameters by experiments, because a
tremendously large number of experiments are necessary. Therefore, GMA
welding process simulation is useful to investigate optimum welding
conditions and numerical models for GMA welding has been studied
(Ref.　5-8).

In this study, we propose a numerical simulation system using a model of
ultra-narrow gap GMA welding. In the model of ultra-narrow gap GMA
welding, non-steady wire melting behavior, molten pool and arc behavior
in the groove and GMA welding electric circuit were considered. The
appropriate conditions of UNGW with many parameters were studied using
the numerical simulation system. 5678

**NUMERICAL SIMULATION MODEL FOR UNGW**

![](media/image1.wmf){width="3.1875in" height="2.23125in"}

As the arc generating point (wire tip) is oscillated over the groove
wall in the thickness direction by using low frequency pulse current
less than 10 Hz, the wire melting behavior is in　non-steady state (Ref.
9,10). Numerical simulation of non-steady state　of　wire melting
behavior is performed in the equivalent electric circuit of GMA welding
shown in Fig. 1.

![](media/image2.wmf){width="2.5779527559055118in"
height="0.45984251968503936in"}The temperature　distribution of wire is
expressed　the following one-dimensional heat conduction equation on the
fixed coordinate system.

where *U*(*X*, *t*) is the temperature(K) at time *t*(s) and position
*X* (mm), and λ, γ, *C*, *ρ~s~* and *S* are the thermal conductivity of
the wire (J/mm⋅s⋅K), density(g/mm3), specific heat (J/g⋅K), electrical
resistivity(Ω⋅mm),and cross-sectional area of wire(mm2), respectively.
![](media/image3.wmf){width="1.7673228346456693in"
height="0.4326771653543307in"}The extended wire is divided shown in Fig.
2. The equation (1) is converted into the moving coordinate system
expressed as *Z*=*X*-*v~f\ ~*×*t* ,following　equation　is　obtained.

where *T*(*Z*, *t*)　is temperature(K) at time *t* (s) and position *Z*
(mm). The temperature-dependence is considered in λ, γ and *C*.

A new element is added in front of the contact tip every *∆t*(s), and
the origin of the moving coordinate system is set in front of a new
element. The relationship between *∆t　*and　*∆Z* is expressed as
*∆Z*=*v~f~* ×*∆t*.

The increment time of heat conduction is defined as*  δt*(s), and the
calculation is performed *K~n~* =*∆t* /*δt* times during *∆t* until a
new element is added. To obtain a stable convergent solution, it is
necessary that *δt*(s) and *∆Z* satisfy the following equation (Ref.
11).

![](media/image4.wmf){width="1.4590551181102362in" height="0.4in"}The
experimental ranges of this study are as follows :*v~f\ ~*= 100 -250
mm/s;　*∆t* =10-3 -10-4 s; *∆Z* = 0.01-0.25 mm ; *δt* =10-7-

10-8 s　(Ref. 9,10).

![](media/image5.wmf) input *q~a~*=*I*×*Φ * (Ref. 12) is provided to the
wire tip element, where *I* * *is current (A) and　*Φ * * *is equivalent
anode melting potential (V). Correlations between *Φ* and superheat
temperature　of droplets *∆T* (K)　expressed as function of
*I　*are　applied (Ref. 9,10). Assuming that　*∆T* is 500K in CO~2~
welding　of 1.2mm　wire, *Φ  *is expressed as the following equation .

![](media/image6.wmf){width="1.455511811023622in"
height="0.19921259842519684in"}

Elements which become *T~M~* +*∆T* are immediately removed from the wire
tip as a droplet ,where *T~M　~*is melting temperature (K).

**[Arc length in groove]{.underline}**

It is assumed that the arc occurs at the minimal geometric distance
between the wire tip and groove wall, which is *W~G~*/2 (mm), or the
minimal geometric distance between the wire tip and the surface of the
molten pool just under the wire, which is *L~bottom~* (mm). The arc
length *L~a~* (mm) is *W~G~*/2 at *W~G~*/2 ≤ *L~bottom~* , and *L~a~* =
*L~bottom~* at *W~G~*/2 \> *L~bottom~* .

**[Molten metal behavior in groove]{.underline}**

![](media/image7.wmf){width="2.144488188976378in"
height="0.25905511811023624in"}The molten pool depression by arc force
is discussed. We assumed that　the surface of molten pool just under the
wire tip is depressed to the position of
hydrostatic　potential　of　molten　metal *H~g~* (mm) which is
balanced　with arc force *F*. In this study, arc force is related to
hydrostatic　potential　of　molten　metal (HPMM), and the following
experimental equation is used (Ref. 13).

The molten　metal can not response because　of the viscosity and surface
tension of molten metal, when the　arc force changed by the low
frequency pulse current. Therefore, transient responses
of　molten　metal are discussed. The depression depth *Y* (mm) is
defined as the distance between the surface of weld metal in the groove
and the surface of the molten pool just under the wire. The temporal
changes of *Y* is expressed by a dashpot　with the viscous damping
coefficient *c*, spring force with the spring constant *k*　and external
force *F* shown in Fig. 3 (Ref. 　14). As the viscosity of molten metal
suppresses its movement as the resistance, the viscosity works as same
as the dashpot when external force is added. Since the HPMM increases
corresponding to the concavity of molten metal, the force balancing with
the HPMM is assumed to be in proportion to the concavity (displacement),
and replaced by spring force with the spring constant *k*. The
relation　of　displacement *Y　*of (A) shown in Fig. 3　　is
expressed　following equation.

![](media/image8.wmf) the arc occurs between the wire tip and the
surface of the molten pool, we　assumed　that　arc force *f* acts on the
surface of the molten pool just under the wire tip independent of wire
tip position, and this arc force is *F*, and the HPMM is *H~g~*. In
equation (6), the time constant *c*/*k* is regarded as *τ *(s), The arc
force is replaced by the HPMM, the following equation is obtained.
　　　　　　　　　　　　　　

![](media/image11.wmf){width="0.9716535433070866in"
height="0.41023622047244096in"}s between the wire tip and the groove
wall, we　assumed　that　the arc force acting on the molten pool is
regarded as *f* =α*F*, and the HPMM is α*H~g\ ~*(α, constant).The
following equation is obtained.
![](media/image12.wmf){width="4.269444444444445in"
height="1.9145833333333333in"}

![](media/image13.wmf){width="1.051968503937008in"
height="0.41023622047244096in"} *τ  *and *α*, the behavior of the molten
pool just under the wire in the narrow groove is observed by a
high-speed video camera (Fig. 4). The time *t~sp~*≥0(s) of swelling of
the surface of the molten pool from the groove bottom is 0.17-0.19s
(Fig. 4　(c)～(f)), and the maximal swelling of the surface of the
molten pool {*S~p~*}*~max~* (mm) was 1.7-2.1 mm.

Combinations of *α* and *τ* are determined so that {*S~p~*}*~max~* is
included in the hatched area　in Fig. 5(a). For example, combinations of
*τ*\<0.05 at *α*=0.8, 0.08\<*τ*\<0.14 at *α*=0.6 and 0.28\<*τ* at
*α*=0.4 are agreed with measurements. The combination of *α* and *τ*
determined from Fig. 5(b) in the same manner is *τ*\<0.16 at
0.8\>*α*\>0.4. To satisfy the measurement of both {*S~p~*}*~max~* and
*t~sp~*≥ 0 simultaneously,*α* is about 0.6, and the *τ* is about 0.1.

**SIMULATION SYSTEM FOR UNGW**

**[Procedure of numerical simulation　system]{.underline}**

Figure shows flowchart of numerical simulation on the behavior of the
melting wire tip and molten
pool.![](media/image14.wmf){width="2.754861111111111in"
height="8.630555555555556in"} In part A, input of welding conditions,
welding speed *v*(mm/s),wire diameter *d*(mm), wire feed rate *v~f~*
(mm/s), distance between contact tip and groove bottom *L~T~(*mm),
groove gap width *W~G~*(mm) and setting of the pulse conditions are
performed. Initial conditions, current *I~0~*(A), extension *L~0~*(mm)
and wire temperature *T~0\ ~*(K) are inputted.

In part B, the one-dimensional non-steady heat conduction FDM analysis
of wire extension is performed. *∆Z*, *∆t*, *δ t* and *K~n\ ~*are set.
The *Φ *is determined from equation (4). The arc heat *I*×*Φ* is　added
at the　tip　element. The calculations of the heat conduction are
performed *K~n~* times during *∆t*. Wire tip elements with temperature
higher than *T~M~* + *∆T*(K)　are deleted as droplet. The extension
*L~t+∆t~*(mm), temperature $T_{i}^{t + \delta t}$, melting rate
*v~m~*(mm/s) and voltage drop of extension *V~L~* (V) are determined at
the time *t*+*∆t*.

In part C, the molten pool position just under wire tip is determined.
The position of the molten pool surface just under wire tip is
determined from the hydrostatic　potential　of　molten　metal *H~g~* and
depression depth *Y*.

In part D, the arc length and arc voltage *V~a~*(V) are determined. The
distance between the molten pool surface just under wire tip and the
wire tip and the minimal distance between the wire tip and groove wall
are compared, and the shorter one is regarded as the arc length *L~a~*.
The arc voltage is determined from the following properties of CO~2~
arc(Ref. 15).

![](media/image15.wmf){width="2.8854330708661418in"
height="0.2437007874015748in"}where wire diameter is 1.2mm .

In part E, current *I~t+∆t~* at *t+∆t* (s) is determined by following
equation.　

![](media/image16.wmf){width="3.1188976377952757in"
height="0.4755905511811024in"}

where *E~0~* and *K~s~* are the non-load voltage (V) of the constant
voltage power source and the slope of the external characteristics
(V/A), respectively. The inductance and resistance of the circuit are
0.3 mH and 0.025 Ω, respectively.

![](media/image17.wmf)

**[Numerical simulation and the experimental results in
UNGW]{.underline}**

Simulation results of I-type joints with a groove width of 5 mm are
compared with experimental results. The position of the wire tip in the
groove are examined by　a high speed video camera system (2250
flames/s). The current and voltage at moments corresponding to the
images obtained by this camera system are indicated in Fig. 7 using thin
lines. Numerical simulations are performed under the same welding
conditions. Current, voltage, wire tip position and pool surface
position are indicated in Fig. 7 using thick lines.

Qualitatively, simulation results of current wave patterns, voltage wave
patterns and the wire tip position are agreed with the experimental
results. The lowest position of the molten pool surface by the
simulation was 2.1 mm, and the penetration depth at root was 3.0 mm.
These simulated values agreed with the results of experiments. These
results indicate that the wire tip position in the ultra-narrow groove,
current, voltage and the molten pool position can be simulated.

**SEARCH FOR APPROPRIATE PULSE CONDITONS OF UNGW**

Oscillation ranges and position of the wire tip are simulated to obtain
appropriate welding conditions. Criterions　to melt root area and to
form　the concave bead surface in the ultra-narrow gap　are　determined
as follows：

\(1\) To melt the root area, the lower limit *Z~min~* of the wire tip
oscillation should be set below the root surface (*Z~min~* ≤ 0). 　

\(2\) To obtain the concave bead surface, the upper limit *Z~max~* of
the wire tip oscillation should be set　at top of the weld metal (throat
thickness) *H~T　\ ~*(*Z~max~* =*H~T~*).

The no load voltage *V~P~* during the peak period is searched under the
following pulse condition；

　　no loaf voltage of during the base period *V~b~* = 37 V, the pulse
frequency is 2.8 Hz,

pulse peak duration *t~P~* : pulse base duration *t~b~* = 1 : 4.

The simulation results of　 *Z~min~* , *Z~ma~*~x~ and *H~T\ ~* are shown
in Fig. 8. Criterions ,which is *Z~min~* ≤ 0*,　Z~max~* =*H~T~* are
satisfied　in the hatched area.

![](media/image19.wmf){width="3.1069444444444443in"
height="2.0972222222222223in"}ltra-narrow gap GMA welding with a groove
width of 5 mm is performed at *V~P~* = 44 V and *V~P\ ~*= 41V. Figure 9
shows the simulated results of *Z~min~* and *Z~ma~*~x~ and cross section
of experimental joins. As the penetration shape is thin and long at
*V~P~* = 44V, the arc heat is distributed effectively in the upper and
lower groove areas. *Z~min~* locates near the root face and *Z~ma~*~x~
locates near the bead surface, these results indicate that criterions
are satisfied by this appropriate pulse condition. The position of the
maximal penetration width is center of penetration shape at *V~P~*= 41V.
As *Z~max~* locates lower that in Fig. 9(b), it is considered that wire
tip is oscillated around the groove bottom.

These results obtained in the above simulation are the example of the
appropriate conditions. There are many appropriate conditions among
combinations of other pulse conditions.

The GMA welding process numerical simulation is useful because
quantitative evaluation is possible　to examine the range of appropriate
conditions for UNGW, in which many welding condition parameters and
factors are related. Appropriate welding conditions can be efficiently
obtained　 according to changes in the pulse frequency, the relative
ratio of the peak to base periods　and wire feed rat　by　 this
simulation system.

**CONCLUSION**

(1)We developed a GMA welding process numerical simulation system
considered　non-steady　wire melting behavior, the　temporal changes of
molten pool depression by arc force, characteristics of the arc
current-voltage, equivalent arc heat input at the wire tip and the
welding electric source circuit.

\(2\) In ultra-narrow gap GMA welding with a groove width of 5 mm, the
oscillation behavior of the wire tip induced by low frequency pulse
current was measured, and it was indicated from the measured results
that numerical simulation was possible.

\(3\) It was indicated that welding conditions to obtain melting in the
ultra-narrow groove bottom and formation of the concave bead surface
could be searched using this numerical simulation system, and the
usefulness of this　system was demonstrated by ultra-narrow gap GMA
welding.

This simulation system makes it possible to find out adaptive welding
conditions for UNGW which is characterized by many pulse parameters that
correlate in a complex manner.

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