Modeling and simulation of arc dynamic behavior in Tri-Arc twin wire GMAW

The triple-arc (Tri-Arc) twin wire gas metal arc welding (GMAW) is an innovative approach to twin-wire welding. It establishes two arcs between the welding wires and the workpiece and introduces a third arc, called the “M arc” between the two wires. To theoretically analyze how various welding parameters affect this process, an equivalent circuit method is employed to establish a dynamic mathematical model for Tri-Arc twin wire gas metal arc welding. The welding process is characterized and simulated using MATLAB simulations to analyze variations in current signals and the wire stick-out. The results indicate that the main arc burns in a dynamic equilibrium state with periodic fluctuations, the current gradually decreases over time, and the arc is elongated. These simulation outcomes closely mirror real welding processes.


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In the context of rapidly evolving modern manufacturing, the demands on welding technology have intensified.Amid this context, the Tri-Arc twin wire Gas Metal Arc Welding (GMAW) technique emerged as a highly efficient method, originally proposed by Geng et al. [1].The Tri-Arc twin wire GMAW distinguishes itself from conventional twin wire welding by introducing an additional "M arc" between the two welding wires.This innovative approach allows for generating multiple arcs beyond the number of welding wires, thereby fundamentally transforming the welding dynamics.The M arc exerts a regulatory influence on the welding process.Consequently, this method enhances the cladding rate while reducing the heat input directed at the base metal.
Currently, there is a lack of research on the Tri-Arc twin wire Gas Metal Arc Welding (GMAW) technique.The existing body of research mainly focuses on conventional welding methodologies and process parameters.For example, using plate surfacing techniques, Zheng et al. [2] investigated the effect of different process parameters on arc geometry, droplet transfer dynamics, and weld structure.Remarkably, it was found that welding spatter incidence experiences a substantial increase with heightened M arc current.Furthermore, increasing the main arc switching frequency leads to a corresponding escalation, which warrants a preliminary analysis of the underlying influencing mechanisms.
Compared to conventional twin wire welding techniques, the Tri-Arc twin wire GMAW method alternates between arcs from left to right, creating a complex interaction between the welding M arc and the principal arc [3].This coordination highlights the inherent instabilities in the Tri-Arc twin wire welding process.Therefore, developing a comprehensive mathematical model for the Tri-Arc twin wire GMAW approach is essential, supported by simulation and thorough analysis.is to accurately predict and effectively manage the complexities of the actual welding procedure.

Tri-arc twin wire GMAW principle
The working principle of this simplified welding power source is shown in Figure 1(b).It consists of two power sources: U 1 , a constant voltage source providing power for the main arc, and U 2 , a constant current source providing power for the M arc.The four IGBT switches are divided into K1 and K4 and K2 and K3.Each group of switches turns on and off synchronously, with the two groups complementing each other.The duty cycle can express the ratio of their turn-on and turn-off.These two groups of switches form a Tri-Arc twin wire GMAW power supply welding system.This system has three arcs: two main arcs and one M arc.The main arcs alternate between burning and extinguishing, while the direction of the current flowing through the M arc changes with the switching of the main arcs.

Tri-arc twin wire GMAW electrical system model
The Tri-Arc twin wire GMAW process can be equivalent to an electrical circuit.The arc voltage is the most significant voltage drop in the circuit.For weak current, the control voltage U is almost equal to the arc voltage.However, for a stronger current, the control voltage must be slightly larger due to the resistance of the wire and electrode and the inductance of the varying current [4].The model of the circuit can be derived as shown in Figure 2. When the constant voltage source U 1 is loaded on the left arc, the voltage division of the circuit wire cannot be ignored.U 2 is a constant current source, and the wire voltage division is ignored, as shown in Figure 2

Tri-arc twin wire GMAW arc model
To investigate the dynamic arc system of the Tri-Arc twin wire GMAW, we simplify and represent the actual welding process's arc shape using an equivalent circuit diagram, as illustrated in Figure 3. (1) U 1 is an ideal constant voltage source, and U 2 is an ideal constant current source.L, M, and R arcs burn stably to form a well-established plasma channel.
(2) The L, M, and R arcs are planarized, and the coupling point between the main arc and the M arc is simplified to the end of the wire.
(3) Arc follows the minimum energy principle, regardless of arc volume changes.Based on the above assumptions, there is a modeling analysis of Tri-Arc twin wire GMAW.
When the left arc burns, the welding current relationship is shown in Equation (3).
When the right arc burns, the welding current relationship is shown in Equation ( 4). .
where M I represents the current of the M arc and W I represents the current flowing through the base material.The arc voltage is mainly affected by the arc current and arc length in twin-wire three-arc welding.
The mathematical model of the GMAW arc is generally based on the Ayrton equation [5], such as Equation (5).where a U represents the arc voltage; 0 U represents the sum of anode voltage drop and anode voltage drop; a R represents the arc resistance constant; a E represents the arc length factor; a K represents the length and current factor; a l represents the arc length.When the left arc burns, the voltages of the L, M, and R arcs are shown in Equation (6).
When the right arc burns, the voltages of the L, M, and R arcs are shown in Equation (7).

Melting equilibrium model of Tri-arc twin wire GMAW welding wire
The melting of wire is comprised of the combined effects of arc heat and resistance heat generated within the wire.The equation proposed by Lesnewich A [6] represents the rate at which the wire undergoes melting as Equation ( 8).Tri-Arc twin wire GMAW can work stably, and its optimal droplet transfer mode is one droplet per pulse.The melting of the left and right welding wires has periodicity and symmetry (with a duty cycle of 50%).Therefore, this study utilizes the left-welding wire as a case study to conduct an in-depth analysis of the melting equilibrium of the welding wire.
The melting rate formula of the left wire when the left arc burns can be expressed as: The melting rate formula of the left wire when the right arc burns can be expressed as: , Tri-Arc twin wire GMAW is a constant speed wire feeding arc control system.The equilibrium model of wire melting can be expressed as Equation (13). .

Dynamic simulation and analysis
The dynamic system of Tri-Arc twin wire GMAW is simulated using MATLAB based on a mathematical model.The calculation is performed using the fourth order Runge-Kutta method.The simulation results are shown in Figure 4.The current flowing through the main arc exhibits a downward trend in each cycle.The current decreases from 155 A to 145 A during stable welding.In this phase, the stick-out initially decreases and then increases in each cycle, as depicted in Figure 5, which corresponds to the dynamic balance mode.This phenomenon occurs because the melting speed of the welding wire is faster than its feeding speed when the left arc burns, resulting in an elongated arc length.However, when switching to right arc burning, only the M arc acts on the wire end at that moment.Generally, the M arc's current is set below the critical value for wire melting.Consequently, the wire feeding speed exceeds its melting speed, leading to increased stick-out and a shorter arc length.It can be observed that maintaining a stable arc length in Tri-Arc twin-wire GMAW involves a dynamic equilibrium process.

Test materials and methods
The test setup for Tri-arc twin wire welding consists of two main sections: the welding system and the synchronized image signal acquisition system, as illustrated in Figure 1(a).In testing, a flat plate stack was utilized.The chosen parameters were a test welding voltage of U 1 =32 V, the M-arc current of I M = 95 A, the wire feed speed of v f =6 m/min, the distance from the conductive nozzle to the weld metal surface (H) of 22 mm, an arc switching frequency (f) of 50 Hz, and a 50% duty cycle for the left-and right-wire combustion (n).Further welding parameters can be found in Table 2.

Discussion
The test results are presented in Figure 6, and the measured values demonstrate excellent agreement with the simulation results.The primary arc current is 125 A to 175 A, and there is only a 13% discrepancy between the simulated and actual values.In every cycle, the left arc initiates burning, as shown in Figure 6  The simulation results exhibit remarkable consistency with the actual measurements.The current coursing through the main arc displays a diminishing pattern within each cycle.The pinnacle of the current exhibits remarkable stability during welding intervals characterized by stability.The stick-out during these stable welding phases also follows a cyclic pattern of decrease and subsequent increase, indicative of a dynamic equilibrium mode.This phenomenon can be attributed to the interplay between wire combustion and melting speed.Specifically, during periods of left arc combustion, the wire's melting speed exceeds its feeding rate, leading to an elongation of the arc length.Conversely, the M arc takes precedence at the wire end upon transitioning to right arc combustion.The magnitude of the M arc current is typically preconfigured below the critical current threshold required for wire melting.Consequently, the wire's melting speed falls short of the feeding rate, resulting in increased stick-out and a subsequent reduction in arc length.Maintaining a stable arc length within the context of dual-wire triple-arc welding aligns with the dynamic equilibrium paradigm, where intricate interplays of melting speeds, wire feeding rates, and arc dynamics manifest.

Conclusion
In this paper, a numerical model of the dynamic arc system of the Tri-Arc twin wire GMAW system is established.The simulation results exhibit excellent concordance with the actual measurement outcomes, substantiating the model's precision in predicting the welding process.The current flowing through the main arc decreases continuously during each welding cycle.In the stable welding stage, there is a cyclic change in the stick-out, which decreases first and then increases, showing a dynamic equilibrium mode.This phenomenon is due to the imbalance between the wire melting and feeding speeds.

3
(a).When the constant voltage source voltage U 1 is loaded on the right arc, as shown in Figure 2(b).When the left arc burns, the voltage relationship is shown in Equation (1).When the right arc burns, the voltage relationship is shown in Equation (2). of the left wire.CD I represents the current of the right wire.L I represents the current of the left arc.R I represents the current of the right arc.L U and R U represent the voltage of the left and right arc, respectively; r  is the density of wire; SL l and SR l represent the stick-out of left and right wires, respectively.W L and W R represent the equivalent inductance and resistance of the wire.

Figure 3 (Figure 3 .
Figure 3. Simplified diagram of double wire three arcs.In this paper, the following assumptions are established for the model of the Tri-Arc twin wire system:(1) U 1 is an ideal constant voltage source, and U 2 is an ideal constant current source.L, M, and R arcs burn stably to form a well-established plasma channel.(2)The L, M, and R arcs are planarized, and the coupling point between the main arc and the M arc is simplified to the end of the wire.(3)Arc follows the minimum energy principle, regardless of arc volume changes.Based on the above assumptions, there is a modeling analysis of Tri-Arc twin wire GMAW.When the left arc burns, the welding current relationship is shown in Equation (3).

v
represents the melting speed. 1 K represents the arc thermal constant related to the chemical composition of arc electrode and welding wire and shielding gas.

2 K
represents the resistance thermal constant related to welding wire resistance.S l represents the wire elongation.
The relationship between stick-out and arc length is shown in Equation (11).The dynamic change equation of wire elongation is Equation (12), where H represents the distance from the base metal to the conductive nozzle and f v represents the wire feeding speed.,

Figure 4 .
Figure 4. Left arc current simulation waveform.Figure 5. Simulation waveforms of L a , L S , and H.

Figure 5 .
Figure 4. Left arc current simulation waveform.Figure 5. Simulation waveforms of L a , L S , and H.

Figure 6 .
Figure 6.The actual measured currents in the left, right and M arcs.

Figure 7 .
Figure 7. Localized magnification of the currents in the left, right and M arcs.
The ultimate goal

Table 1
f v , the distance between the conductive nozzle and the surface of the base material is =22mm H , the left and right arc switching