# Complex Behavior of Droplet Transfer and Spreading in Cold Metal Transfer

Authors: Shuai Yang; Yanfeng Xing; Fuyong Yang; Juyong Cao
Journal: Shock and Vibration
 (2020)

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## Abstract

In intelligent manufacturing, an intelligent control method of welding process is an important process of intelligent welding manufacturing technology (IWMT). Metal transfer is a key factor to control the welding process. Metal transfer and droplet spreading are of vital importance for welding formation. A new theoretical model of cold metal transfer (CMT) in short-circuit transfer mode is proposed in this paper. In this model, the CMT welding process is regarded as a continuous process of arc heating, mass transfer, short-circuit, and spreading, and the relations between these processes are analyzed. The calculation equations used by the model can analyze the welding formation clearly and simplify the complex welding process into continuous physical behavior. The predicted welding width shows good agreement with the measurement results. The mechanism of increased welding width is also comprehensively analyzed. Results have a certain guiding effect on aluminum alloy welding process control.


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## Body

## 1. Introduction

In intelligent manufacturing, a weld controller is a typical system of the intelligent welding manufacturing system [1]. Intelligent control of welding dynamic process is one of main problems of intelligent welding technology. One of problems in intelligent control of welding dynamic process is welding pool dynamic process [2]. The short-circuit transfer in the metal transition is controlled through traditional MIG (metal inert gas)/MAG (metal active gas) welding to control the heat input and reduce the welding defects. Cold metal transfer (CMT) is an improvement of short-circuit transfer in GMAW (gas-metal arc welding) process, which has the characteristics of low splash and low-heat input. CMT allows a better microstructure to be obtained than MIG. Feng et al. [3] carried out experiments through CMT technology to weld a 1 mm thick pure aluminum alloy with minimal deflection. Lei et al. [4] welded a 1 mm thick AA6061-T6 by using three welding arc modes of standard, pulsed, and CMT. They found that CMT arc mode produced the fewest welding defects. Cao et al. [5, 6] joined 1.0 mm thick AA6061-T6 to 1.0 mm thick galvanized mild steel using the cold metal transfer method, and the welded joint strength can meet the requirements. These studies confirm that CMT is superior to MIG/MAG in thin-plate welding and dissimilar metal welding. CMT can effectively control the heat affected zone (HAZ) and enhance the weldability of thin metal plates and dissimilar metals.To ensure the formation of welding, scholars have focused on optimization of CMT welding parameters. Wang et al. [7] studied the influences of parameters such as boost current, arcing current, breaking current, boosting voltage, and wire moving speed in CMT welding on the CMT boosting phase, arcing phase, and short-circuit phase. Chen et al. [8] analyzed the effects of CMT current waveform on welding formation. Kumar [9] investigated the effect of welding current and welding speed on welding formation, dilution, and contact angle during cold metal transfer (CMT) process These studies investigated the control of the welding formation through experiments, but the reasons for the changes in the welding formation were not explained theoretically.Metal droplet behavior has been a largely underexplored domain. Few theoretical models can describe the relationship between metal droplet behavior and welding formation in the CMT process. Most studies on welding formation model are based on traditional welding methods, such as GMAW. Murphy et al. [10] modeled the arc plasma and weld pool of MIG welding, and predicted the weld depth and shape. Komen et al. [11] simulated the weld pool and the bead formation of GMAW. The simulation realized the droplet transfer into the molten pool, but the model is only used for the prediction of free-flight transfer. The metal droplet detachment from the wire electrode is affected by various forces. Wu et al. [12] developed a metal transfer model of GMAW, which considered droplet oscillation and detachment. Doodman Tipi et al. [13] studied the detachment of GMAW welding and proposed a method for control of the detachment frequency in automatic GMAW process. Chapuis et al. [14] investigated the metal deposition of GMAW and found the law of the metal spreading. Che et al. [15] simulated the evolution of metal spreading. The model assumes that droplets drip freely from a certain height. These studies use simulation to analyze the effect of droplet transfer on the formation of welding, which is a lot of work, and it is difficult to analyze the relationship between physical behaviors.Wire melting, droplet oscillation, droplet transfer, molten pool cooling, and droplet solidification are important factors that influence the welding process. Droplet transfer is a significant part of welding formation. Some researchers have studied the metal transfer behavior of welding. Bless [16] performed a physical analysis of the short-circuit transition behavior during the welding process. Ersoy et al. [17] studied the drop oscillation and detachment of droplets on GMA by using a mass spring damping system. Kang et al. [18] proposed a dynamic model that describes the growth and separation of droplets for GMAW, considering the effect of electrode melting to form a tapered electrode. These methods enable us to consider all physical phenomena.Sufficient attention to current and weld metal surface tension can lead to reduced spatter and improved process control. Scotti et al. [19] studied metal transfer in solid wire GMAW welding and classified metal transfer modes. Huang et al. [20] studied the influence of bypass current on metal transfer. Planckaert et al. [21] proposed a hybrid model to investigate MIG/MAG welding process in short-circuit transfer. The three classes of metal transfer modes are nature metal transfer, controlled metal transfer, and interchangeable metal transfer. These studies have investigated the effect of droplet transfer on weld formation during the GMAW process but did not consider the effect of wire feeding on droplet transition, so they cannot explain welding formation of CMT.In this study, a new CMT droplet model considering the wire electrode movement of short-circuit mode is proposed. This model combines two continuously physical phenomena, namely, metal transfer and metal spreading. In this model, the relations between each stage are analyzed, including droplet growth and short-circuit. The model predicts the formation of droplets at the wire electrode and their transfer into the molten pool in CMT process. The model is validated using experimental measured metal transfer as well as metal spreading. This model allows us to better understand the relationship between welding parameters and weld formation. Results provide a theoretical basis for the control of metal transfer, and solve the main problem of intelligent welding technology. The work helps to control the welding dynamic process in intelligent welding manufacturing.


## 2. Experimental Procedure

To study the behavior of the droplet and verify the consistency of the theory, we carried out a series of experiments.From the aspect of droplet transfer, the theory analyzes the change in the wire feed speed of a single cycle CMT that affects the droplet transfer and the weld width. Based on the model of the welding geometry, the CMT welding experiments were carried out, and results were recorded by a high-speed camera. The diagram of experimental equipment is shown in Figure1. The experimental data were compared with the model to analyze the effect of droplet transfer on the increase in the melt width.Figure 1
Welding schematic.The experimental setup is shown in Figure2. The experimental materials were AA6061-T6 aluminum. The size of the test pieces was 150 mm 150 mm 2 mm, and the butt joints were used in experiments.Figure 2
The size of workpiece.In the experiment, the high-speed camera was Optronis’ CP80-3-M, and the recorded videos were used to accurately observe the dynamic droplet transfer behavior during welding. The frame capture rate of the high-speed camera was 4000 frames per second. The images in the high-speed camera were image-extracted and collected, and a total of 10000 images were obtained. The camera also recorded the welding of CMT in different parameters.The welding equipment used in the study includes Fronius’ TPS4000CMT. The welding wire was made of 1.2 mm ER4043 as the filling material, and the shielding gas was argon with a purity of 99.995%. The welding schematic is shown in Figure1. During the welding process, the welding torch was always perpendicular to the aluminum plate. To reduce the influence of other factors, the test piece was precleaned before welding. More details of the welding parameters are listed in Table 1.Table 1
Experimental parameters used in CMT welding.
Test codeWire feed speed (m/min)Welding speed (m/min)Shielding gas (vol.% Ar)13.00.4899.99523.50.4899.99534.00.4899.99544.50.4899.99555.00.4899.995The welding speed of all experiments was set as 0.48 m/min, and the arc correction was −10%. It is to ensure that the droplet deposition is not affected by welding speed and arc correction. In this study, when the wire feed speed is 5.0 m/min, the welding current used in the experiment obtained through the monitoring board is 118 A.


## 3. Analytical Modeling of Metal Transfer in CMT

### 3.1. Controlled Short-Circuit Transfer

Arc welding can be seen as a cycle of arc stage and metal transfer stage. In arc stage, with the ignition of the arc, the temperature rises rapidly, which causes the wire melting to form a liquid droplet on the electrode. As the wire gradually melts, metal transfer occurs and thus the mass flows into droplet. When the droplet does not attach on the electrode, it begins to separate from the electrode, then drip into the molten pool, and finally solidify to form a weld to join the metals together.In the GAMW process, different metal transfer modes can be controlled by current and are affected by wire materials, shielding gas, and process parameters. In the natural state, metal transfer modes can be classified into contact transfer and free-flight transfer. In the free-flight transfer, the droplet is affected by external force and naturally separated from the wire electrode. In this case, arc welding can be divided into the following stages according to the metal transfer behavior: droplet growth stage, droplet separation stage, and droplet spreading stage. In short-circuit transfer, the metal droplet is expanded to the molten pool before separation, and the metal droplet comes in contact with the liquid molten pool. The metal behavior is mainly in the following four stages: droplet growth stage, short-circuit stage, droplet separation stage, and droplet spreading stage.For some special welding requirements, droplet transfer can be controlled. For example, thin-plate welding and dissimilar metal welding need low-heat input. During the short-circuit transfer mode, droplet slash and heat input become easier to control due to physical contact between the metal droplet and the molten pool. Therefore, some controlled short-circuit transfer technologies have been developed based on short-circuit transfer technology, as reported by Norrish et al. [22].CMT is related to controlled metal transfer. CMT is based on short-circuit transfer and controls the movement of the wire electrode. The CMT droplet transfer is shown in Figure3. The transfer of droplet occurs during the short-circuit stage of the welding process cycle, and the movement of the wire helps the droplet transfer into the molten pool. In the necking stage, the movement of the wire is used to assist the separation of the droplet from the wire electrode. In CMT, the controlled short-circuit transfer can reduce the current heat input and the droplet shock, as reported by Pang et al. [23].Figure 3
Short-circuit transfer in CMT.
(a)(b)(c)(d)(e)(f)


### 3.2. The Growth of Droplet

Welding parameters on CMT mainly affect welding wire melting and droplet transfer. The adjustment of parameters will affect the growth and separation of droplets. In the CMT welding process, the behavior of the metal transfer is influenced by current. In the droplet growth phase, the arc ignites the wire electrode, which is affected by arc heat and Joule heat. The welding wire melts to form droplets at the electrode.Joule heat can be calculated by(1)QJ=∫VρTI2dV=ρ¯ALI2,where ρ¯ is the average electrical resistivity, L is the electrode extension, and A is the cross sectional area of the electrode. Arc heat can be obtained by(2)QA=32kTae+Va+ΦI,where k is the Boltzmann constant, e is the elementary charge, Va is the voltage value that characterizes the wire heating by the arc, Ta is the average arc temperature, and Φ is the work function of the electrode material.Assuming that all heat input is used to melt the wire, the melting rate is the total heat input by the system divided by the heat required to melt the unit mass of the materials, as reported by Planckaert et al. [21]:(3)dmRdt=ρ¯ALI2+3/2kT/e+Va+ΦI∫T1T2CpdT+ΔHT+ΔHM,where ΔHT is the heat of crystalline transition and ΔHM is the heat of fusion. TW is the wire temperature. The melting rate can be further simplified as a function of welding current, as reported by Modenesi et al. [24]:(4)dmRdt=m˙R=MR=αI+βlsI2,mR=43πR3ρ,where MR is the wire melting rate, α is the arc heat coefficient, β is the Joule heat coefficient, mR is the droplet mass, R is the droplet radius, and ρ is the mass density of metal droplet. These values of physical parameters are listed in Table 2.Table 2
Physical parameter values used for calculations.
Properties (units)ValuesρDensity (kg·m−3)2700AArea of the electrode (mm2)1.44VaArc voltage (V)18αArc heating parameter (kg/As)7.992 × 10−11βJoule heating parameter (kg/mA2s)1.252 × 10−11γSurface tension (N/m)1.2The wire feed speed is not completely equal to the melting caused by the welding current. The wire feed system controls the wire feed speed. When the wire feed speed increases, it feeds downward, and when it decreases, it draws back:(5)dlsdt=vwfd−dmπρr2dt,where r is the electrode radius, and vwfd is the wire feed speed. When the electrode wire feeding is higher than the wire melting rate, the droplet grows and the wire electrode feed motion helps droplets contact the weld pool.The growth and separation of droplets can be described by establishing a dynamic model of CMT. The state of the droplets during the transition can be studied using a dynamic model to investigate analyze the influence of the movement of droplet transfer on the melting width of the molten pool.Assuming that the droplets formed by the welding are spherical droplets, the molten material from the electrodes enters the droplets at a velocity. During the growth phase of the droplet, according to the conservation of momentum, the mass of the droplet changes fromm1 to m1+dm, and the speed of the droplet relative to the system changes from v1 to v1+dv, as shown in Figure 4, where u1 is the speed of the fluid mass change relative to the droplet, that is, the speed at which the molten wire flows into the droplet.Figure 4
Variable mass system of droplet growth.The growth stage of the droplet can be regarded as a variable mass system. The system meets the momentum theorem. According to the momentum theorem, the liquid metal melted flows into the droplet, and the mass of the droplet increases. The droplet is affected to an external force, and the system momentum changes:(6)dp=p2−p1.The impulse of the combined external force on an object is equal to the increase in its momentum, and the equation can be written as(7)Fedt=m1+dmv1+dv−m1v1+u1dm,Fedt=m1v1+v1dm+m1dv+dmdv−v1dm−u1dm−m1v1,Fedt=m1dv+dmdv−u1dm,Fedt+u1dm=m1+dmdv.The conservation of momentum for the metal droplet can be written as(8)mtdvdt=Fe+u1dmdt,where mt=mR=∫MRdt, Fe is the external forces, and u1=MR/4πρr2.The external forces that affect droplets are Lorentz force, surface tension, and gravitational force, as reported by Ersoy et al. [17]. In the CMT process, the electrode feed force also needs to be considered, as shown in Figure 5. In the short-circuit stage, the wire feeding system controls the wire drawing to assist the liquid bridge break and metal transfer to the molten pool:(9)Fem=μ04πI2P,Fs=2πRγ,Fg=43πR3ρg,P=lnRsinθzr−14−11−cosθz+21−cosθz2ln21+cosθz,where γ is the surface tension coefficient, Fem is the Lorentz force, Fs is the surface tension, Fg is the gravitational force, Ff is the electrode feed force, μ0 is the permeability of free space, R is the droplet radius, r is the electrode radius, and θz is the conduction zone radius.Figure 5
Short-circuit transfer model in cold metal transfer.
(a)(b)(c)(d)(e)(f)In this model, the droplet displacement caused by the increase in the droplet mass is small, so the liquid bridge shrinkage is ignored in the growth stage. In this case, the liquid bridge radius is equal to the wire radius. In the droplet growth stage, the wire feed force is 0; when the current level is high, external forces will change the droplet transfer mode, which becomes a combination of short-circuit transitions and other transitional forms.When droplet transfer occurs, the droplet transfer is mainly realized by electrode feeding, as shown in Figure6. In thin-plate welding, less current is required, the external forces are smaller, the droplets are always attached to the wire electrode, and the transition of the droplet to the molten pool requires electrode movement.Figure 6
Electrode movement in CMT process.Short-circuit transfer is affected by wire feed and droplet size. As shown in Figure7, d is the initial distance between the welding wire and the molten pool, the wire electrode length is lw, Δlw is the amount of change in wire length, the arc length is la, the distance between the droplet and the wire electrode is dw, and the displacement of the droplet is Dt:(10)Dt=Rt+dw+Δlw.Figure 7
Distance of droplet and workpiece.When the value ofDt increases to be equal to the value of d, a short-circuit transfer occurs, and the condition of short-circuit is(11)Dt=d.In the short-circuit stage, the wire feeds and contacts the molten pool, and the arc length is 0. The radius of the droplet when a short-circuit transition occurs is recorded asRi, which is used for subsequent calculations.Equations (8) and (10) can be combined to obtain the radius of droplet and the displacement of electrode. The calculation results are shown in Figure 8, from which the motion of the droplet can be analyzed.Figure 8
Motion of metal droplet in CMT (wire feed speed is 5.0 m/min).


### 3.3. Separation of Electrode and Metal Droplet

When the wire is pumped back, the CMT process enters into the necking stage. As shown in Figure9, when the droplet starts to contact the surface of the base material, the meniscus liquid surface is formed. In this stage, the electrode and the molten pool are connected by a metal liquid bridge.Figure 9
Molten metal bridge.As the wire is pumped back, the liquid bridge begins to shrink. According to the research of Planckaert, the pressure of the liquid bridge is calculated by(12)PB=μ0I28π2R12+γ1R1+1R2.When the value ofPB is greater than 0, the liquid bridge is broken, where γ is the surface tension of the liquid bridge. According to the momentum theorem of the variable mass system, the residual mass remaining on the wire electrode can be obtained, which will not be further discussed in this paper.The flow velocity of the metal bridge flowing into the molten pool surface is calculated by(13)υ=2ρPB+ρgh,where h is the distance from the center of liquid bridge to the surface of molten pool, which is affected by the wire extension.


### 3.4. The Spreading of Metal Droplet on the Surface of the Workpiece

The droplet that transitions into the molten pool will deform quickly, and in this stage, the motion of the droplet can be simplified as droplet spreading, as reported by Sivakumar et al. [25].The droplet has an initial velocity that strikes the workpiece. In the CMT process, the droplet is always attached to the wire electrode when impacting the workpiece. Due to the influence of short-circuit transfer, the droplet is not affected by the acceleration of gravity before contacting the workpiece surface. The initial velocity of the droplet is equal to the wire feed speed.In CMT, the free surface deformation of molten pool is small, the contact interface between droplet and base metal is assumed to be liquid-solid. The metal droplet is difficult to infiltrate the surface of the workpiece, the droplet cannot spread completely over the workpiece and will gradually spread to equilibrium, and the contact angle gradually changes fromθi to θe, as shown in Figure 10.Figure 10
Metal droplet deformation.
(a)(b)(c)According to the research by Suli et al. [26], when the droplet impacts with velocity V, the radius of the droplet can be written as(14)RBRi2=We+1231−cosθ+4We/Ry,where We=ρRV2/γ, Ry=ρRV/μ, V is the initial velocity of the droplet when it contacts the surface of the molten pool, Ri is the initial radius of the droplet when it comes into contact with the surface of the base material, RB is the base radius of droplet in spreading process, γ is the surface tension coefficient, and μ is the viscosity coefficient.Contact angle is expressed as a function of the cosine of the contact angle and time, and is used to describe spreading in reaction-limited wetting:(15)cosθe−cosθ=cosθe−cosθiexp−λt,where θi is the initial contact angle, θe is the contact angle in equilibrium, and λ is the kinetic constant, assuming that the kinetic constant does not change with temperature. These values are shown in Table 3.Table 3
Physical parameter values used for calculations.
Properties (units)ValuesθiInitial contact angle (°)40θeContact angle in equilibrium (°)160λKinetic constant20Equations (14) and (15) lead to the following expression:(16)RB=R0We+1231+cosθe−cosθiexp−λt−cosθe+4We/Ry.When the droplet spreads to the equilibrium state, the radius after solidification is the weld width because the droplet solidification time is longer than the spread time.


## 3.1. Controlled Short-Circuit Transfer

Arc welding can be seen as a cycle of arc stage and metal transfer stage. In arc stage, with the ignition of the arc, the temperature rises rapidly, which causes the wire melting to form a liquid droplet on the electrode. As the wire gradually melts, metal transfer occurs and thus the mass flows into droplet. When the droplet does not attach on the electrode, it begins to separate from the electrode, then drip into the molten pool, and finally solidify to form a weld to join the metals together.In the GAMW process, different metal transfer modes can be controlled by current and are affected by wire materials, shielding gas, and process parameters. In the natural state, metal transfer modes can be classified into contact transfer and free-flight transfer. In the free-flight transfer, the droplet is affected by external force and naturally separated from the wire electrode. In this case, arc welding can be divided into the following stages according to the metal transfer behavior: droplet growth stage, droplet separation stage, and droplet spreading stage. In short-circuit transfer, the metal droplet is expanded to the molten pool before separation, and the metal droplet comes in contact with the liquid molten pool. The metal behavior is mainly in the following four stages: droplet growth stage, short-circuit stage, droplet separation stage, and droplet spreading stage.For some special welding requirements, droplet transfer can be controlled. For example, thin-plate welding and dissimilar metal welding need low-heat input. During the short-circuit transfer mode, droplet slash and heat input become easier to control due to physical contact between the metal droplet and the molten pool. Therefore, some controlled short-circuit transfer technologies have been developed based on short-circuit transfer technology, as reported by Norrish et al. [22].CMT is related to controlled metal transfer. CMT is based on short-circuit transfer and controls the movement of the wire electrode. The CMT droplet transfer is shown in Figure3. The transfer of droplet occurs during the short-circuit stage of the welding process cycle, and the movement of the wire helps the droplet transfer into the molten pool. In the necking stage, the movement of the wire is used to assist the separation of the droplet from the wire electrode. In CMT, the controlled short-circuit transfer can reduce the current heat input and the droplet shock, as reported by Pang et al. [23].Figure 3
Short-circuit transfer in CMT.
(a)(b)(c)(d)(e)(f)


## 3.2. The Growth of Droplet

Welding parameters on CMT mainly affect welding wire melting and droplet transfer. The adjustment of parameters will affect the growth and separation of droplets. In the CMT welding process, the behavior of the metal transfer is influenced by current. In the droplet growth phase, the arc ignites the wire electrode, which is affected by arc heat and Joule heat. The welding wire melts to form droplets at the electrode.Joule heat can be calculated by(1)QJ=∫VρTI2dV=ρ¯ALI2,where ρ¯ is the average electrical resistivity, L is the electrode extension, and A is the cross sectional area of the electrode. Arc heat can be obtained by(2)QA=32kTae+Va+ΦI,where k is the Boltzmann constant, e is the elementary charge, Va is the voltage value that characterizes the wire heating by the arc, Ta is the average arc temperature, and Φ is the work function of the electrode material.Assuming that all heat input is used to melt the wire, the melting rate is the total heat input by the system divided by the heat required to melt the unit mass of the materials, as reported by Planckaert et al. [21]:(3)dmRdt=ρ¯ALI2+3/2kT/e+Va+ΦI∫T1T2CpdT+ΔHT+ΔHM,where ΔHT is the heat of crystalline transition and ΔHM is the heat of fusion. TW is the wire temperature. The melting rate can be further simplified as a function of welding current, as reported by Modenesi et al. [24]:(4)dmRdt=m˙R=MR=αI+βlsI2,mR=43πR3ρ,where MR is the wire melting rate, α is the arc heat coefficient, β is the Joule heat coefficient, mR is the droplet mass, R is the droplet radius, and ρ is the mass density of metal droplet. These values of physical parameters are listed in Table 2.Table 2
Physical parameter values used for calculations.
Properties (units)ValuesρDensity (kg·m−3)2700AArea of the electrode (mm2)1.44VaArc voltage (V)18αArc heating parameter (kg/As)7.992 × 10−11βJoule heating parameter (kg/mA2s)1.252 × 10−11γSurface tension (N/m)1.2The wire feed speed is not completely equal to the melting caused by the welding current. The wire feed system controls the wire feed speed. When the wire feed speed increases, it feeds downward, and when it decreases, it draws back:(5)dlsdt=vwfd−dmπρr2dt,where r is the electrode radius, and vwfd is the wire feed speed. When the electrode wire feeding is higher than the wire melting rate, the droplet grows and the wire electrode feed motion helps droplets contact the weld pool.The growth and separation of droplets can be described by establishing a dynamic model of CMT. The state of the droplets during the transition can be studied using a dynamic model to investigate analyze the influence of the movement of droplet transfer on the melting width of the molten pool.Assuming that the droplets formed by the welding are spherical droplets, the molten material from the electrodes enters the droplets at a velocity. During the growth phase of the droplet, according to the conservation of momentum, the mass of the droplet changes fromm1 to m1+dm, and the speed of the droplet relative to the system changes from v1 to v1+dv, as shown in Figure 4, where u1 is the speed of the fluid mass change relative to the droplet, that is, the speed at which the molten wire flows into the droplet.Figure 4
Variable mass system of droplet growth.The growth stage of the droplet can be regarded as a variable mass system. The system meets the momentum theorem. According to the momentum theorem, the liquid metal melted flows into the droplet, and the mass of the droplet increases. The droplet is affected to an external force, and the system momentum changes:(6)dp=p2−p1.The impulse of the combined external force on an object is equal to the increase in its momentum, and the equation can be written as(7)Fedt=m1+dmv1+dv−m1v1+u1dm,Fedt=m1v1+v1dm+m1dv+dmdv−v1dm−u1dm−m1v1,Fedt=m1dv+dmdv−u1dm,Fedt+u1dm=m1+dmdv.The conservation of momentum for the metal droplet can be written as(8)mtdvdt=Fe+u1dmdt,where mt=mR=∫MRdt, Fe is the external forces, and u1=MR/4πρr2.The external forces that affect droplets are Lorentz force, surface tension, and gravitational force, as reported by Ersoy et al. [17]. In the CMT process, the electrode feed force also needs to be considered, as shown in Figure 5. In the short-circuit stage, the wire feeding system controls the wire drawing to assist the liquid bridge break and metal transfer to the molten pool:(9)Fem=μ04πI2P,Fs=2πRγ,Fg=43πR3ρg,P=lnRsinθzr−14−11−cosθz+21−cosθz2ln21+cosθz,where γ is the surface tension coefficient, Fem is the Lorentz force, Fs is the surface tension, Fg is the gravitational force, Ff is the electrode feed force, μ0 is the permeability of free space, R is the droplet radius, r is the electrode radius, and θz is the conduction zone radius.Figure 5
Short-circuit transfer model in cold metal transfer.
(a)(b)(c)(d)(e)(f)In this model, the droplet displacement caused by the increase in the droplet mass is small, so the liquid bridge shrinkage is ignored in the growth stage. In this case, the liquid bridge radius is equal to the wire radius. In the droplet growth stage, the wire feed force is 0; when the current level is high, external forces will change the droplet transfer mode, which becomes a combination of short-circuit transitions and other transitional forms.When droplet transfer occurs, the droplet transfer is mainly realized by electrode feeding, as shown in Figure6. In thin-plate welding, less current is required, the external forces are smaller, the droplets are always attached to the wire electrode, and the transition of the droplet to the molten pool requires electrode movement.Figure 6
Electrode movement in CMT process.Short-circuit transfer is affected by wire feed and droplet size. As shown in Figure7, d is the initial distance between the welding wire and the molten pool, the wire electrode length is lw, Δlw is the amount of change in wire length, the arc length is la, the distance between the droplet and the wire electrode is dw, and the displacement of the droplet is Dt:(10)Dt=Rt+dw+Δlw.Figure 7
Distance of droplet and workpiece.When the value ofDt increases to be equal to the value of d, a short-circuit transfer occurs, and the condition of short-circuit is(11)Dt=d.In the short-circuit stage, the wire feeds and contacts the molten pool, and the arc length is 0. The radius of the droplet when a short-circuit transition occurs is recorded asRi, which is used for subsequent calculations.Equations (8) and (10) can be combined to obtain the radius of droplet and the displacement of electrode. The calculation results are shown in Figure 8, from which the motion of the droplet can be analyzed.Figure 8
Motion of metal droplet in CMT (wire feed speed is 5.0 m/min).


## 3.3. Separation of Electrode and Metal Droplet

When the wire is pumped back, the CMT process enters into the necking stage. As shown in Figure9, when the droplet starts to contact the surface of the base material, the meniscus liquid surface is formed. In this stage, the electrode and the molten pool are connected by a metal liquid bridge.Figure 9
Molten metal bridge.As the wire is pumped back, the liquid bridge begins to shrink. According to the research of Planckaert, the pressure of the liquid bridge is calculated by(12)PB=μ0I28π2R12+γ1R1+1R2.When the value ofPB is greater than 0, the liquid bridge is broken, where γ is the surface tension of the liquid bridge. According to the momentum theorem of the variable mass system, the residual mass remaining on the wire electrode can be obtained, which will not be further discussed in this paper.The flow velocity of the metal bridge flowing into the molten pool surface is calculated by(13)υ=2ρPB+ρgh,where h is the distance from the center of liquid bridge to the surface of molten pool, which is affected by the wire extension.


## 3.4. The Spreading of Metal Droplet on the Surface of the Workpiece

The droplet that transitions into the molten pool will deform quickly, and in this stage, the motion of the droplet can be simplified as droplet spreading, as reported by Sivakumar et al. [25].The droplet has an initial velocity that strikes the workpiece. In the CMT process, the droplet is always attached to the wire electrode when impacting the workpiece. Due to the influence of short-circuit transfer, the droplet is not affected by the acceleration of gravity before contacting the workpiece surface. The initial velocity of the droplet is equal to the wire feed speed.In CMT, the free surface deformation of molten pool is small, the contact interface between droplet and base metal is assumed to be liquid-solid. The metal droplet is difficult to infiltrate the surface of the workpiece, the droplet cannot spread completely over the workpiece and will gradually spread to equilibrium, and the contact angle gradually changes fromθi to θe, as shown in Figure 10.Figure 10
Metal droplet deformation.
(a)(b)(c)According to the research by Suli et al. [26], when the droplet impacts with velocity V, the radius of the droplet can be written as(14)RBRi2=We+1231−cosθ+4We/Ry,where We=ρRV2/γ, Ry=ρRV/μ, V is the initial velocity of the droplet when it contacts the surface of the molten pool, Ri is the initial radius of the droplet when it comes into contact with the surface of the base material, RB is the base radius of droplet in spreading process, γ is the surface tension coefficient, and μ is the viscosity coefficient.Contact angle is expressed as a function of the cosine of the contact angle and time, and is used to describe spreading in reaction-limited wetting:(15)cosθe−cosθ=cosθe−cosθiexp−λt,where θi is the initial contact angle, θe is the contact angle in equilibrium, and λ is the kinetic constant, assuming that the kinetic constant does not change with temperature. These values are shown in Table 3.Table 3
Physical parameter values used for calculations.
Properties (units)ValuesθiInitial contact angle (°)40θeContact angle in equilibrium (°)160λKinetic constant20Equations (14) and (15) lead to the following expression:(16)RB=R0We+1231+cosθe−cosθiexp−λt−cosθe+4We/Ry.When the droplet spreads to the equilibrium state, the radius after solidification is the weld width because the droplet solidification time is longer than the spread time.


## 4. Results and Discussion

During the entire CMT welding cycle, the droplet is formed during the arcing phase, the ends of the wire are melted to form droplets, and the droplet forms a small bridge when in contact with the molten pool. At the same time, the CMT welding obtains a short-circuit signal, then cuts off the current, and the wire is pumped back to help the droplet separate from the electrode.As shown in Figure11, the generation of the arc and the growth of the droplet correspond to the arcing phase of the CMT, and the droplet radius increases rapidly. This stage is defined as diffusion. The initial rapid diffusion of droplet is affected by the initial velocity of droplet and the direct heating of arc. This kind of direct arc heating contributes to the rapid diffusion of droplet. At the beginning of the short-circuit transition, the formed droplets are in contact with the electrodes to the surface of the base metal, and are forced to diffuse under the action of inertial forces. This diffusion is affected by surface tension and viscous resistance, and finally reaches equilibrium. When the wire feed speed increases, the welding wire will start to move from a higher distance to the metal surface, the duration of the droplet growth process increases slightly, and the amount of wire metal melted at the end of the wire increases.Figure 11
Arc shape and droplet transfer at different process levels: (a) wire feed speed is 3.0 m/min; (b) wire feed speed is 5.0 m/min.
(a)(b)The droplet motion is recorded by a high-speed camera, and the contour of the droplet is extracted. The metal transfer and spreading of droplets recorded by the high-speed camera are shown in Figure12.Figure 12
Droplet spreading process (wire feed speed is 5.0 m/min).Measurements of droplet dimensions are conducted using MATLAB (up to 10,000 frames a test). The program extracts the values of several geometrical characteristics by turning the original image into a binary image. The program is also used to find the edge and calculate the base droplet radius, as shown in Figure13.Figure 13
Binary image of the droplet radius (wire feed speed is 5.0 m/min).The comparison of the droplet spreading motion with the model calculations shows a better agreement, as shown in Figure14. The base radius changes very rapidly at the beginning of the spreading. The initial velocity of the droplet transfer to the surface of the sheet is affected by the feed of the wire. After this rapid change, the spreading of the large droplets becomes smoother, and the welding heat is not directly heated by the arc but is conducted through the heat affect zone. According to the spreading dynamics theory, the average expansion speed of metal droplets is lower than the initial phase.Figure 14
Variation of droplet base radius in spreading stage (wire feed speed is 5.0 m/min).The changes in the base radius at different wire feeding speeds are shown in Figure15. For thin-plate welding, the change in parameters causes the external force of the droplet to change. At the same time, the increase in the current level will change the melting rate of the wire, ensuring that the short-circuit transfer occurs smoothly at a large wire feed speed.Figure 15
Predictions of the droplet spreading in different wire feed speeds.
(a)(b)When the wire feeding speed is increased, the molten pool will be affected by the wire movement, thereby increasing the penetration depth and the welding width. Therefore, in the CMT process, the welding formation is mainly controlled by the movement of the electrode. The droplet transfer is mainly achieved in the form of a short-circuit transition.The experiment also studied the movement of the droplet under different parameters to verify the versatility and guidance of the theoretical model.The model is used to calculate the welding width after droplet spreading and solidification. Figure16 shows the welding formations in different wire feed speeds. The welding width increases with increasing wire feed speed, and the theoretical calculations show good agreement with the experimental results. In this study, the droplet spreading is considered for the base material with smooth surface, so errors between theoretical calculations and experimental results may exist.Figure 16
Welding formation in different wire feed speeds.


## 5. Conclusions

A theoretical model of CMT is developed and used to study geometry formation of a droplet during its transfer.According to the working mechanism of CMT, the influence of CMT pumping motion on wire feeding speed control is analyzed, and the influence of the balance between wire feeding speed and wire melting speed on wire drawing is investigated. Based on wire melting, droplet transfer, and droplet spreading, the droplet movement in CMT welding is analyzed.Based on the analysis of CMT working mechanism and droplet transfer, the relationship between CMT pumping motion and wire melting rate is considered, the droplet growth and transition model in the CMT working environment is established. Considering the influence of the contact angle on the spreading has been considered, a spreading model of the droplet is established.The proposed model can effectively predict the motion of droplet in CMT welding and calculate the melting width of the droplet solidified on the base metal.The theoretical model and the experimental results show a high degree of consistency and can predict the geometry of the weld. This theory allows us to study the motion of this macroscopic droplet in the CMT process.



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*Source: 6650155-2020-11-18.xml*