7.5 Droplet Force Balance & Classification of Metal Transfer Regimes

7.3 Metal Transfer Physics: Short-Circuit, Globular, Spray & Pulsed-Spray

Quick Answer: Metal transfer in Gas Metal Arc Welding (GMAW) is governed by the vector sum of retaining forces—principally surface tension ($F_\gamma$)—and detaching forces—namely gravity ($F_g$), aerodynamic plasma drag ($F_d$), and the electromagnetic Lorentz pinch force ($F_{\text{em}}$). At low currents and voltages, short-circuit transfer (GMAW-S) occurs via periodic physical bridging of the weld pool ($20\text{ to }200\text{ Hz}$). At intermediate currents, globular transfer produces oversized droplets that detach irregularly; under $100\%\text{ CO}_2$, upward repulsive electromagnetic reaction forces create violent spatter. When current exceeds the critical transition current ($I_{\text{crit}}$) in an argon-rich shield ($\ge 80\%\text{ Ar}$), electromagnetic pinch forces overwhelm surface tension, establishing spatter-free axial spray transfer. Modern pulsed GMAW (GMAW-P) modulates current between a high peak ($I_p > I_{\text{crit}}$) and a low background ($I_b$), achieving precise One-Drop-Per-Pulse (ODAP) transfer with low average heat input in all welding positions.

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1. Droplet Force Mechanics & Static Force Balance Theory (SFBT)

The detachment of molten filler metal from the tip of a consumable wire electrode is modeled by the Static Force Balance Theory (SFBT), originally developed by Amson and Lancaster. A droplet detaches when the sum of detaching forces equals or exceeds the retaining surface tension force:

$$\sum F_{\text{detaching}} \ge \sum F_{\text{retaining}}$$ $$F_g + F_{\text{em}} + F_d \ge F_\gamma + F_\sigma$$

                    Solid Electrode Wire (Radius r_w)
                           |              |
                           |     ||       |  Current Flow (I)
                           |     vv       |
                           +--------------+
                            /            /   <-- Tapered Solid-Liquid Transition Zone
                           /   Liquid   /
                          |   Droplet   |    <-- Inward Radial Pinch Force: J x B
                          |  (Rad r_d)  |<===   Generates Downward Axial Vector (F_em)
                          |             |
                           /           /
                            /    +    /      <-- Retaining Surface Tension: F_gamma = 2*pi*r_w*gamma
                             +-------+           (Resists Detachment Upward)
                                 |
                                 v Detaching Forces:
                                   - Gravity: F_g = m_d * g (Downward)
                                   - Electromagnetic Pinch: F_em (Downward if necked)
                                   - Aerodynamic Drag: F_d = 1/2*C_d*rho*v_jet^2*A (Downward)

1. Retaining Surface Tension Force ($F_\gamma$)

Surface tension is the primary force preventing droplet separation. The molten droplet clings to the solid unmelted wire periphery. The maximum retaining force is formulated as:

$$F_\gamma = 2\pi \cdot r_w \cdot \gamma \cdot f_s$$

where $r_w$ is the solid wire radius, $\gamma$ is the liquid-gas surface tension ($1.0\text{ to }1.5\text{ N/m}$ for deoxidized liquid steel; $0.6\text{ to }0.9\text{ N/m}$ for aluminum), and $f_s$ is a geometric shape correction factor ($0.5\text{ to }1.0$). Surface tension decreases with increasing temperature and in the presence of active surface agents (oxygen, sulfur).

2. Gravitational Force ($F_g$)

Gravity acts on the spherical mass of the molten droplet:

$$F_g = m_d \cdot g = \left( \frac{4}{3} \pi r_d^3 \rho_m \right) g$$

where $r_d$ is droplet radius, $\rho_m$ is molten metal density ($7000\text{ kg/m}^3$ for liquid steel), and $g = 9.81\text{ m/s}^2$.

• For small spray droplets ($r_d = 0.5\text{ mm}$), $F_g \approx 3.6 \times 10^{-5}\text{ N}$ (negligible, $<1\%$ of detaching forces).
• For large globular droplets ($r_d = 2.0\text{ mm}$), $F_g \approx 2.3 \times 10^{-3}\text{ N}$, becoming the dominant detaching mechanism in flat-position globular transfer.
• Gravity is positional: in overhead welding, $F_g$ becomes a retaining force, opposing detachment.

3. Electromagnetic Lorentz Pinch Force ($F_{\text{em}}$)

Current traversing a conductor induces a concentric magnetic field ($B_\theta$). When current streamlines converge or diverge—such as where a cylindrical wire transitions into a tapered neck—the resulting Lorentz force ($\mathbf{J} \times \mathbf{B}$) develops an axial component along the wire axis ($z$).

Amson's formulation for the axial electromagnetic force acting on a necking droplet is:

$$F_{\text{em}} = \frac{\mu_0 I^2}{4\pi} \left[ \ln\left(\frac{r_d}{r_w}\right) - \frac{1}{4} + \frac{1}{1 - (r_n/r_w)^2} \ln\left(\frac{r_w}{r_n}\right) \right]$$

where $r_n$ is the instantaneous radius of the molten neck.

• When the droplet is smaller than the wire and current density is high, $F_{\text{em}}$ exerts an intense downward axial squeeze that rapidly throttles the molten neck, violently severing the droplet and accelerating it across the arc gap.
• Because $F_{\text{em}} \propto I^2$, doubling the current quadruples the electromagnetic pinch force, transforming slow globular detachment into rapid spray projection.

4. Aerodynamic Plasma Drag Force ($F_d$)

The high-speed Maecker plasma jet ($v_{\text{jet}} = 100\text{ to }300\text{ m/s}$) sweeping past the molten droplet exerts viscous and pressure drag:

$$F_d = \frac{1}{2} C_d \cdot \rho_{\text{plasma}} \cdot v_{\text{jet}}^2 \cdot (\pi r_d^2)$$

where $C_d$ is the drag coefficient ($0.4\text{ to }0.6$ for a sphere in high-temperature plasma). In axial spray transfer, aerodynamic drag accounts for $15\%\text{ to }25\%$ of the net detaching force, assisting in propelling droplets into the puddle.

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2. Classification of Metal Transfer Regimes

The American Welding Society (AWS) and the International Institute of Welding (IIW) formally categorize GMAW metal transfer into four distinct regimes based on electrical parameters, shielding gas chemistry, and droplet morphology.

   Short-Circuit (GMAW-S)         Globular Transfer            Axial Spray Transfer          Pulsed Spray (GMAW-P)
   [Low V, Low I]               [Med V, Med I, or CO2]       [High V, High I > I_crit]     [Pulsed Waveform: I_p / I_b]

         Wire                         Wire                         Wire                         Wire
          ||                           ||                           ||                           ||  Tapered tip
          ||                           ||                           || Taper                     || 
          ||                         (    ) Droplet > d_wire        o  Fine droplet               o Single droplet
   +------+------+                   (____)                         o  (d < d_wire)              (ODAP)
   |  Weld Pool  |                     ||                           v                            v
   (Bridge Contact)               +----+----+                  +----+----+                  +----+----+
   20 - 200 Hz shorts             Repelled or gravity          100 - 500 Hz axial stream    50 - 300 Hz pulses

1. Short-Circuiting Transfer (GMAW-S / Dip Transfer)

• Operating Parameters: Low voltage ($16\text{ to }21\text{ V}$) and low current ($50\text{ to }180\text{ A}$).
• Physical Mechanism: The molten droplet grows at the wire tip until it directly bridges the physical gap and contacts the weld pool ($20\text{ to }200\text{ times per second}$).
  1. Short-Circuit Phase: Contact collapses arc voltage toward zero ($<4\text{ V}$). Current surges rapidly along the circuit inductance curve ($i(t)$ ramp).
  2. Pinch & Transfer: Surface tension wicks the liquid into the puddle, aided by the escalating Lorentz pinch force ($F_{\text{em}} \propto I^2$) necking the bridge.
  3. Bridge Rupture & Re-ignition: The neck vaporizes, opening the circuit. Inductive energy produces a transient voltage spike ($L \cdot di/dt$) that instantly re-ignites the electric arc.
  4. Arc-On Phase: The arc burns, melting the advancing wire tip to form the next droplet until the cycle repeats.
• Industrial Utility: Low heat input makes GMAW-S ideal for thin sheet metal ($<3.0\text{ mm}$), root passes in pipe welding, and all-position fabrication. However, on thick plate ($>6\text{ mm}$), inadequate base metal fusion frequently causes catastrophic cold lap (lack of sidewall fusion).

2. Globular Transfer

• Operating Parameters: Intermediate current ($180\text{ to }220\text{ A}$ for $1.2\text{ mm}$ wire) and voltage ($22\text{ to }28\text{ V}$).
• Droplet Morphology: Droplets grow to diameters significantly larger than the wire ($d_{\text{drop}} = 1.5\text{ to }3.0 \times d_{\text{wire}}$) before detaching.
• Gravity vs Repelled Mode:
  • In argon-rich gas at intermediate currents, transfer occurs in a free-flight gravity mode: droplets fall irregularly into the puddle under gravity.
  • In $100\%\text{ CO}_2$ shielding, transfer occurs in the repelled globular mode across all usable currents. The physics is detailed below.

3. Axial Spray Transfer

• Operating Parameters: High current exceeding the critical transition current ($I > I_{\text{crit}}$) and high voltage ($26\text{ to }34\text{ V}$) in an argon-rich shielding gas (minimum $80\%\text{ Ar}$).
• Droplet Morphology: The wire tip melts into a sharp, pointed liquid taper. Fine, sub-millimeter droplets ($d_{\text{drop}} < d_{\text{wire}}$) detach at frequencies between $100\text{ and }500+\text{ droplets/second}$.
• Mechanics: Droplets are accelerated axially along the arc centerline by the Maecker plasma jet and Lorentz pinch forces at speeds of $10\text{ to }50\text{ m/s}$, entirely eliminating spatter.
• Industrial Utility: Produces extremely high deposition rates and deep finger-like root penetration. Restricted strictly to the flat and horizontal fillet positions due to high weld puddle fluidity.

4. Pulsed GMAW (GMAW-P)

• Operating Parameters: The power source switches electronically between a high peak current ($I_p$) and a low background current ($I_b$) at frequencies from $30\text{ to }400\text{ Hz}$.
• Waveform Dynamics:
  • Peak Current ($I_p > I_{\text{crit}}$): Held for a duration $t_p$ ($1.5\text{ to }3.5\text{ ms}$) at $350\text{ to }550\text{ A}$. The intense pinch force severs and accelerates exactly one fine spray droplet.
  • Background Current ($I_b < I_{\text{crit}}$): Drops to $30\text{ to }80\text{ A}$ for duration $t_b$. Maintains arc column ionization and thermal cathode/anode attachment without melting significant wire or overheating the puddle.
• Synergic One-Drop-Per-Pulse (ODAP): Microprocessor-controlled synergic systems adjust pulse frequency ($f = 1/T$) proportionally to wire feed speed, guaranteeing that exactly one droplet detaches per current pulse regardless of operator travel speed, providing spatter-free spray transfer across all positions.

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3. The Thermodynamics of CO2: Why Spray Transfer Is Impossible in Pure CO2

A fundamental question on the CWEng examination is why axial spray transfer cannot be achieved in $100\%\text{ CO}_2$, regardless of how high current is raised.

       Argon-Rich Shielding (>= 80% Ar)                      Pure CO2 Shielding (100% CO2)
              [Axial Spray Transfer]                             [Repelled Globular Transfer]

                   Solid Wire                                          Solid Wire
                       ||                                                  ||
                      /  |  Liquid Taper                                   ||  Blunt liquid drop
                     / Anode |                                           (    ) (d > 2*d_wire)
                    +--------+ Anode root extends                        (    )
                         o     up taper; pinch force                      /  |  Cathode spots attach
                         |     points DOWNWARD                           ^    ^ to bottom of droplet;
                         v                                               |    | Reaction force
                   Weld Puddle (Cathode)                                 +----+ points UPWARD!
                   Smooth Axial Stream                                     Weld Puddle

Thermodynamic & Electrodynamic Mechanism

1. Thermal Dissociation: In the high-temperature plasma ($>6000\text{ K}$), carbon dioxide undergoes intense endothermic molecular dissociation: $$\text{CO}_2 \longleftrightarrow \text{CO} + \frac{1}{2} \text{O}_2 \quad (\Delta H = +283\text{ kJ/mol})$$ This dissociation absorbs massive amounts of thermal energy from the plasma periphery, constricting the conductive column into a narrow, concentrated central core.
2. Cathode Attachment Shift: Under DCEP, the base plate is the cathode. In $100\%\text{ CO}_2$, the extreme column constriction and rapid cooling prevent anode attachment roots from spreading up the wire taper. Instead, anode current enters only the very tip of the molten wire droplet.
3. Upward Repulsive Lorentz Pinch Force: Because the current must flare outward as it enters the larger droplet from the narrow wire, current streamlines diverge near the droplet base. The resulting Lorentz body force ($\mathbf{J} \times \mathbf{B}$) develops an upward axial component that acts against gravity and surface tension.
4. Droplet Levitation & Violent Ejection: This upward electromagnetic reaction force physically supports the liquid droplet, preventing detachment. The droplet grows to $2\text{ to }4$ times the wire diameter, wobbling erratically at the wire tip until it either touches the puddle (explosive short) or is blown violently sideways as coarse, adherent spatter.
5. The Buried Arc Solution: To utilize inexpensive $100\%\text{ CO}_2$ at high currents ($>300\text{ A}$) without catastrophic spatter, fabricators utilize a buried arc. Voltage is reduced ($22\text{ to }26\text{ V}$), forcing the wire tip beneath the workpiece plate surface into a localized cavity; spatter generated by droplet explosion is trapped entirely within the molten crater walls.

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