Estimating Weld Metal Deposition Rate for Dual-Wire Submerged Arc Welding: A Precision Engineering Guide

What Is This Calculation and Why It Matters

The weld metal deposition rate (WMDR) is a foundational productivity metric in industrial welding—particularly in high-volume, automated processes like Submerged Arc Welding (SAW). For dual-wire SAW configurations—where two consumable electrodes are fed simultaneously into a shared molten pool—the deposition rate is not merely additive; it is governed by complex interdependencies among electrical parameters, wire geometry, feed dynamics, thermal efficiency, and metallurgical behavior. Accurately estimating WMDR is critical for:

• Production planning: Matching deposition capacity to joint geometry (e.g., groove depth, root face) and required pass count.
• Heat input control: Excessive deposition without proportional travel speed increases heat per unit length—risking distortion, residual stress, and HAZ embrittlement per AWS D1.1 Clause 3.2.
• Cost optimization: Over-specifying wire feed or current wastes energy and consumables; underestimating leads to rework or multi-pass inefficiencies.
• Quality assurance: Deposition efficiency directly correlates with spatter loss, slag entrapment, and porosity risk—factors explicitly addressed in AWS D1.1 Table 3.1 for SAW process qualification limits.

Unlike single-wire SAW, dual-wire systems introduce asymmetry: the leading wire (typically higher current, lower voltage) dominates penetration, while the trailing wire (lower current, higher voltage) enhances fill and surface contour. Their combined effect on melt-off rate, arc stability, and droplet transfer efficiency necessitates a physics-based, empirically calibrated estimation—not simple summation.

Theory and Formula Walkthrough

The dual-wire SAW deposition rate is derived from mass conservation principles applied to each electrode, adjusted for process-specific efficiency losses. The core formula is:

$$ \text{Deposition Rate } (\dot{m}) = \frac{\pi}{4} \cdot \left( d_1^2 \cdot \rho \cdot v_{f1} + d_2^2 \cdot \rho \cdot v_{f2} \right) \cdot \eta_d \cdot 60 $$

Where:

• $d_1$, $d_2$: Wire diameters (mm) — must be converted to cm for consistency with density units (g/cm³).
• $\rho$: Density of welding wire (g/cm³) — typically 7.8 g/cm³ for carbon steel; varies slightly with alloy content (e.g., 8.0 for stainless, 7.6 for low-alloy).
• $v_{f1}, v_{f2}$: Wire feed rates (m/min) — converted to cm/min (×100) for dimensional consistency.
• $\eta_d$: Deposition efficiency (%) — expressed as decimal (e.g., 95% → 0.95).
• Factor 60: Converts g/min → g/h, then divided by 1000 for kg/h.

Key Variables Explained

Wire Diameter ($d$): Not just geometric—it governs current density, resistive heating, and melt-off kinetics. A 1.6 mm wire at 600 A carries ~300 A/mm²; exceeding 350 A/mm² risks excessive stubbing or burnback. Dual-wire systems often use matched diameters (e.g., both 1.6 mm), but mismatched configurations (e.g., 1.2 mm + 2.4 mm) require recalibration of $\eta_d$ due to differing arc stiffness and droplet size distributions.

Wire Feed Rate ($v_f$): Directly sets theoretical wire consumption. However, actual melt-off depends on net power input. If $v_f$ exceeds what the arc can melt, “bird-nesting” occurs; if too low, arc instability degrades $\eta_d$. In dual-wire setups, $v_f$ must be balanced so that the leading wire’s melt-off matches its current share, while the trailing wire compensates for voltage drop across the shared slag pool.

Density ($\rho$): Though often assumed constant, variations matter: flux-coated wires may have effective density reduced by 5–8% due to coating mass (not included in this estimator—assumes bare wire density). For precision work, consult wire manufacturer data sheets (e.g., ESAB EM12K: ρ = 7.82 g/cm³).

Deposition Efficiency ($\eta_d$): The most nuanced parameter. For dual-wire SAW, $\eta_d$ is not the arithmetic mean of individual wire efficiencies. Empirical studies (e.g., IIW Recommended Practice WRC 2022) show it follows:

$$ \eta_d = 0.92 + 0.00015 \cdot (I_1 + I_2) - 0.00002 \cdot (V_1 + V_2) - 0.00008 \cdot \left| I_1 - I_2 \right| $$

Where $I_1$, $I_2$ are currents (A), $V_1$, $V_2$ voltages (V). This accounts for: increased efficiency with total current (enhanced arc force), reduced efficiency with higher voltage (greater arc blow, spatter), and penalty for current imbalance (uneven pool agitation). Typical $\eta_d$ ranges: 92–97% for well-tuned dual-wire SAW—significantly higher than single-wire (88–94%) due to slag coverage and arc coupling.

Travel Speed ($v_t$): While not in the deposition mass formula, it critically constrains practical deposition rate. Per AWS D1.1 Clause 3.2, heat input $Q = \frac{VI}{v_t} \cdot \frac{60}{1000}$ (kJ/mm) must stay within qualified limits. If $\dot{m}$ implies $v_t$ < minimum stable speed (e.g., <250 mm/min), burn-through or poor fusion results—even if mass balance checks out.

Standard Requirements

AWS D1.1 Structural Welding Code – Steel governs deposition rate estimation implicitly through process control requirements:

• Table 3.1 (Welding Process Parameters): Specifies maximum allowable heat input for base metals ≥ 19 mm thick (e.g., 45 kJ/mm for ASTM A572 Gr. 50). Since $Q \propto VI / v_t$, any deposition rate estimate must verify resulting $v_t$ yields $Q ≤ Q_{\text{max}}$. For dual-wire, $I$ and $V$ are total values—but note: voltage is not additive; $V_{\text{total}} ≈ V_1 + V_2 - \Delta V_{\text{slag}}$ (typically 2–4 V drop across slag layer).

• Clause 3.2 (Heat Input Control): Mandates documented procedure qualification (PQR) for heat input ranges. Dual-wire SAW procedures must demonstrate that the estimated $\dot{m}$, when paired with qualified $v_t$, produces sound welds per AWS D1.1 Section 4 (Qualification). Crucially, Clause 3.2 prohibits extrapolation: a PQR qualified at 500 A/28 V/350 mm/min does not validate 700 A/32 V/450 mm/min—even if $\dot{m}$ scales linearly.

• Annex D (SAW-Specific Guidance): Recommends monitoring wire feed rate per electrode (not total) and verifying current split (e.g., 60/40 ratio) via shunt measurements—directly impacting $\eta_d$ accuracy.

Common Mistakes and How to Avoid Them

1. Assuming Additive Deposition Efficiencies
   Mistake: Using $\eta_d = (\eta_{d1} + \eta_{d2})/2 = 93%$ based on single-wire data.
   Consequence: Overestimates $\dot{m}$ by 2–4%, risking undersized passes or excessive interpass temperature.
   Fix: Apply the empirical $\eta_d$ formula above—or better, calibrate $\eta_d$ using coupon weigh-loss tests: deposit known length, clean, weigh deposited metal vs. wire consumed.

2. Ignoring Voltage Interaction in Dual-Wire Systems
   Mistake: Setting $V_1 = 28$ V, $V_2 = 32$ V, then using $V = 60$ V in heat input calculations.
   Consequence: Overestimates $Q$ by ~15%, triggering unnecessary preheat or violating Clause 3.2.
   Fix: Measure actual arc voltage at each electrode tip (not power source output); subtract 3 V for slag resistance. Use $V_{\text{eff}} = V_1 + V_2 - 3$ for $Q$.

3. Using Nominal Wire Diameter Without Verification
   Mistake: Assuming $d = 1.6$ mm when actual diameter is 1.58 mm (common tolerance: ±0.03 mm).
   Consequence: $d^2$ error → 2.5% $\dot{m}$ error (since area ∝ $d^2$).
   Fix: Calibrate wire diameter with micrometer at three points per spool; use mean value.

4. Neglecting Travel Speed Constraints in Estimation
   Mistake: Computing $\dot{m} = 22.5$ kg/h, then assuming $v_t = 400$ mm/min is always viable.
   Consequence: For a 12-mm deep U-groove, required $v_t$ may be only 320 mm/min to avoid excessive reinforcement—forcing $\dot{m}$ reduction.
   Fix: Always cross-check $\dot{m}$ against joint geometry: $v_t^{\text{min}} = \frac{\dot{m} \cdot 1000}{\rho \cdot A_{\text{bead}} \cdot \eta_d}$, where $A_{\text{bead}}$ is target cross-sectional area (cm²).

5. Applying Single-Wire Density to Flux-Cored Wires
   Mistake: Using $\rho = 7.8$ g/cm³ for self-shielded dual-wire SAW (rare, but emerging).
   Consequence: Underestimates $\dot{m}$ by up to 10% due to lower effective density.
   Fix: Obtain manufacturer’s effective density or measure via Archimedes’ principle on 1-m sample.

Worked Example with Realistic Numbers

Scenario: Dual-wire SAW on ASTM A572 Gr. 50 plate (25 mm thick), double-U groove (10 mm depth per side). Qualified procedure: $I_1 = 580$ A, $I_2 = 620$ A, $V_1 = 29$ V, $V_2 = 31$ V, $v_{f1} = v_{f2} = 10.2$ m/min, $d_1 = d_2 = 1.6$ mm, $\rho = 7.8$ g/cm³.

Step 1: Compute Deposition Efficiency
$$ \eta_d = 0.92 + 0.00015 \cdot (580 + 620) - 0.00002 \cdot (29 + 31) - 0.00008 \cdot |580 - 620| $$ $$ = 0.92 + 0.18 - 0.0012 - 0.0032 = 0.92 + 0.1756 = 0.9256 \approx 92.56% $$

Step 2: Convert Units
$d = 1.6 , \text{mm} = 0.16 , \text{cm}$
$v_f = 10.2 , \text{m/min} = 1020 , \text{cm/min}$

Step 3: Calculate Mass Flow per Wire
Area per wire = $\frac{\pi}{4} \cdot (0.16)^2 = 0.0201 , \text{cm}^2$
Mass flow (one wire) = $0.0201 \cdot 7.8 \cdot 1020 = 159.9 , \text{g/min}$
Total theoretical = $2 \cdot 159.9 = 319.8 , \text{g/min} = 19.19 , \text{kg/h}$

Step 4: Apply Efficiency
$\dot{m} = 19.19 \cdot 0.9256 = 17.76 , \text{kg/h}$

Step 5: Validate Against Heat Input & Travel Speed
Effective voltage: $V_{\text{eff}} = 29 + 31 - 3 = 57$ V
Total current: $I = 580 + 620 = 1200$ A
Heat input: $Q = \frac{57 \cdot 1200}{v_t} \cdot 0.06 = \frac{4104}{v_t}$ kJ/mm
For $Q ≤ 45$ kJ/mm (AWS D1.1 Table 3.1), $v_t ≥ 4104 / 45 = 91.2$ mm/min — well below typical 400 mm/min. But joint geometry demands: Target bead area = 10 mm × 10 mm = 100 mm² = 1.0 cm². Required $v_t = \frac{17.76 \cdot 1000}{7.8 \cdot 1.0 \cdot 0.9256} = \frac{17760}{7.22} ≈ 2460$ mm/min? Wait—this is impossible. Error identified: Bead area is per pass, not per side. For double-U, first pass needs ~1.5 cm² (15 mm width × 10 mm depth). Recompute: $v_t = 17760 / (7.8 \cdot 1.5 \cdot 0.9256) ≈ 1640$ mm/min — still unrealistic. Thus, $\dot{m}$ must be reduced: target $v_t = 400$ mm/min → max $\dot{m} = \frac{7.8 \cdot 1.5 \cdot 0.9256 \cdot 400}{1000} = 4.33$ kg/h per pass. Therefore, dual-wire must run at lower $v_f$ or $I$ to match joint geometry—not full capacity. Final adjusted $\dot{m} = 4.3$ kg/h (with $\eta_d$ recalculated at lower currents). This illustrates why estimation must precede, not follow, joint design.

In conclusion, dual-wire SAW deposition estimation is a systems engineering task—integrating metallurgy, electrodynamics, and geometry. Rigorous application of the formulas herein, grounded in AWS D1.1 compliance and empirical validation, transforms estimation from guesswork into a predictable, auditable, and scalable engineering discipline.